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(),
830 getEffectiveSCEVType(Ty))));
832 // trunc(trunc(x)) --> trunc(x)
833 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
834 return getTruncateExpr(ST->getOperand(), Ty);
836 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
837 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
838 return getTruncateOrSignExtend(SS->getOperand(), Ty);
840 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
841 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
842 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
844 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
845 // eliminate all the truncates.
846 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
847 SmallVector<const SCEV *, 4> Operands;
848 bool hasTrunc = false;
849 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
850 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
851 hasTrunc = isa<SCEVTruncateExpr>(S);
852 Operands.push_back(S);
855 return getAddExpr(Operands);
856 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
859 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
860 // eliminate all the truncates.
861 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
862 SmallVector<const SCEV *, 4> Operands;
863 bool hasTrunc = false;
864 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
865 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
866 hasTrunc = isa<SCEVTruncateExpr>(S);
867 Operands.push_back(S);
870 return getMulExpr(Operands);
871 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
874 // If the input value is a chrec scev, truncate the chrec's operands.
875 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
876 SmallVector<const SCEV *, 4> Operands;
877 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
878 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
879 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
882 // As a special case, fold trunc(undef) to undef. We don't want to
883 // know too much about SCEVUnknowns, but this special case is handy
885 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
886 if (isa<UndefValue>(U->getValue()))
887 return getSCEV(UndefValue::get(Ty));
889 // The cast wasn't folded; create an explicit cast node. We can reuse
890 // the existing insert position since if we get here, we won't have
891 // made any changes which would invalidate it.
892 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
894 UniqueSCEVs.InsertNode(S, IP);
898 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
900 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
901 "This is not an extending conversion!");
902 assert(isSCEVable(Ty) &&
903 "This is not a conversion to a SCEVable type!");
904 Ty = getEffectiveSCEVType(Ty);
906 // Fold if the operand is constant.
907 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
909 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
910 getEffectiveSCEVType(Ty))));
912 // zext(zext(x)) --> zext(x)
913 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
914 return getZeroExtendExpr(SZ->getOperand(), Ty);
916 // Before doing any expensive analysis, check to see if we've already
917 // computed a SCEV for this Op and Ty.
919 ID.AddInteger(scZeroExtend);
923 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
925 // zext(trunc(x)) --> zext(x) or x or trunc(x)
926 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
927 // It's possible the bits taken off by the truncate were all zero bits. If
928 // so, we should be able to simplify this further.
929 const SCEV *X = ST->getOperand();
930 ConstantRange CR = getUnsignedRange(X);
931 unsigned TruncBits = getTypeSizeInBits(ST->getType());
932 unsigned NewBits = getTypeSizeInBits(Ty);
933 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
934 CR.zextOrTrunc(NewBits)))
935 return getTruncateOrZeroExtend(X, Ty);
938 // If the input value is a chrec scev, and we can prove that the value
939 // did not overflow the old, smaller, value, we can zero extend all of the
940 // operands (often constants). This allows analysis of something like
941 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
942 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
943 if (AR->isAffine()) {
944 const SCEV *Start = AR->getStart();
945 const SCEV *Step = AR->getStepRecurrence(*this);
946 unsigned BitWidth = getTypeSizeInBits(AR->getType());
947 const Loop *L = AR->getLoop();
949 // If we have special knowledge that this addrec won't overflow,
950 // we don't need to do any further analysis.
951 if (AR->getNoWrapFlags(SCEV::FlagNUW))
952 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
953 getZeroExtendExpr(Step, Ty),
954 L, AR->getNoWrapFlags());
956 // Check whether the backedge-taken count is SCEVCouldNotCompute.
957 // Note that this serves two purposes: It filters out loops that are
958 // simply not analyzable, and it covers the case where this code is
959 // being called from within backedge-taken count analysis, such that
960 // attempting to ask for the backedge-taken count would likely result
961 // in infinite recursion. In the later case, the analysis code will
962 // cope with a conservative value, and it will take care to purge
963 // that value once it has finished.
964 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
965 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
966 // Manually compute the final value for AR, checking for
969 // Check whether the backedge-taken count can be losslessly casted to
970 // the addrec's type. The count is always unsigned.
971 const SCEV *CastedMaxBECount =
972 getTruncateOrZeroExtend(MaxBECount, Start->getType());
973 const SCEV *RecastedMaxBECount =
974 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
975 if (MaxBECount == RecastedMaxBECount) {
976 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
977 // Check whether Start+Step*MaxBECount has no unsigned overflow.
978 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
979 const SCEV *Add = getAddExpr(Start, ZMul);
980 const SCEV *OperandExtendedAdd =
981 getAddExpr(getZeroExtendExpr(Start, WideTy),
982 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
983 getZeroExtendExpr(Step, WideTy)));
984 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
985 // Cache knowledge of AR NUW, which is propagated to this AddRec.
986 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
987 // Return the expression with the addrec on the outside.
988 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
989 getZeroExtendExpr(Step, Ty),
990 L, AR->getNoWrapFlags());
992 // Similar to above, only this time treat the step value as signed.
993 // This covers loops that count down.
994 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
995 Add = getAddExpr(Start, SMul);
997 getAddExpr(getZeroExtendExpr(Start, WideTy),
998 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
999 getSignExtendExpr(Step, WideTy)));
1000 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1001 // Cache knowledge of AR NW, which is propagated to this AddRec.
1002 // Negative step causes unsigned wrap, but it still can't self-wrap.
1003 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1004 // Return the expression with the addrec on the outside.
1005 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1006 getSignExtendExpr(Step, Ty),
1007 L, AR->getNoWrapFlags());
1011 // If the backedge is guarded by a comparison with the pre-inc value
1012 // the addrec is safe. Also, if the entry is guarded by a comparison
1013 // with the start value and the backedge is guarded by a comparison
1014 // with the post-inc value, the addrec is safe.
1015 if (isKnownPositive(Step)) {
1016 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1017 getUnsignedRange(Step).getUnsignedMax());
1018 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1019 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1020 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1021 AR->getPostIncExpr(*this), N))) {
1022 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1023 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1024 // Return the expression with the addrec on the outside.
1025 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1026 getZeroExtendExpr(Step, Ty),
1027 L, AR->getNoWrapFlags());
1029 } else if (isKnownNegative(Step)) {
1030 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1031 getSignedRange(Step).getSignedMin());
1032 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1033 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1034 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1035 AR->getPostIncExpr(*this), N))) {
1036 // Cache knowledge of AR NW, which is propagated to this AddRec.
1037 // Negative step causes unsigned wrap, but it still can't self-wrap.
1038 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1039 // Return the expression with the addrec on the outside.
1040 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1041 getSignExtendExpr(Step, Ty),
1042 L, AR->getNoWrapFlags());
1048 // The cast wasn't folded; create an explicit cast node.
1049 // Recompute the insert position, as it may have been invalidated.
1050 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1051 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1053 UniqueSCEVs.InsertNode(S, IP);
1057 // Get the limit of a recurrence such that incrementing by Step cannot cause
1058 // signed overflow as long as the value of the recurrence within the loop does
1059 // not exceed this limit before incrementing.
1060 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1061 ICmpInst::Predicate *Pred,
1062 ScalarEvolution *SE) {
1063 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1064 if (SE->isKnownPositive(Step)) {
1065 *Pred = ICmpInst::ICMP_SLT;
1066 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1067 SE->getSignedRange(Step).getSignedMax());
1069 if (SE->isKnownNegative(Step)) {
1070 *Pred = ICmpInst::ICMP_SGT;
1071 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1072 SE->getSignedRange(Step).getSignedMin());
1077 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1078 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1079 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1080 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1081 // result, the expression "Step + sext(PreIncAR)" is congruent with
1082 // "sext(PostIncAR)"
1083 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1085 ScalarEvolution *SE) {
1086 const Loop *L = AR->getLoop();
1087 const SCEV *Start = AR->getStart();
1088 const SCEV *Step = AR->getStepRecurrence(*SE);
1090 // Check for a simple looking step prior to loop entry.
1091 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1095 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1096 // subtraction is expensive. For this purpose, perform a quick and dirty
1097 // difference, by checking for Step in the operand list.
1098 SmallVector<const SCEV *, 4> DiffOps;
1099 for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end();
1102 DiffOps.push_back(*I);
1104 if (DiffOps.size() == SA->getNumOperands())
1107 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1108 // same three conditions that getSignExtendedExpr checks.
1110 // 1. NSW flags on the step increment.
1111 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1112 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1113 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1115 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1118 // 2. Direct overflow check on the step operation's expression.
1119 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1120 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1121 const SCEV *OperandExtendedStart =
1122 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1123 SE->getSignExtendExpr(Step, WideTy));
1124 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1125 // Cache knowledge of PreAR NSW.
1127 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1128 // FIXME: this optimization needs a unit test
1129 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1133 // 3. Loop precondition.
1134 ICmpInst::Predicate Pred;
1135 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1137 if (OverflowLimit &&
1138 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1144 // Get the normalized sign-extended expression for this AddRec's Start.
1145 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1147 ScalarEvolution *SE) {
1148 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1150 return SE->getSignExtendExpr(AR->getStart(), Ty);
1152 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1153 SE->getSignExtendExpr(PreStart, Ty));
1156 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1158 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1159 "This is not an extending conversion!");
1160 assert(isSCEVable(Ty) &&
1161 "This is not a conversion to a SCEVable type!");
1162 Ty = getEffectiveSCEVType(Ty);
1164 // Fold if the operand is constant.
1165 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1167 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1168 getEffectiveSCEVType(Ty))));
1170 // sext(sext(x)) --> sext(x)
1171 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1172 return getSignExtendExpr(SS->getOperand(), Ty);
1174 // sext(zext(x)) --> zext(x)
1175 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1176 return getZeroExtendExpr(SZ->getOperand(), Ty);
1178 // Before doing any expensive analysis, check to see if we've already
1179 // computed a SCEV for this Op and Ty.
1180 FoldingSetNodeID ID;
1181 ID.AddInteger(scSignExtend);
1185 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1187 // If the input value is provably positive, build a zext instead.
1188 if (isKnownNonNegative(Op))
1189 return getZeroExtendExpr(Op, Ty);
1191 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1192 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1193 // It's possible the bits taken off by the truncate were all sign bits. If
1194 // so, we should be able to simplify this further.
1195 const SCEV *X = ST->getOperand();
1196 ConstantRange CR = getSignedRange(X);
1197 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1198 unsigned NewBits = getTypeSizeInBits(Ty);
1199 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1200 CR.sextOrTrunc(NewBits)))
1201 return getTruncateOrSignExtend(X, Ty);
1204 // If the input value is a chrec scev, and we can prove that the value
1205 // did not overflow the old, smaller, value, we can sign extend all of the
1206 // operands (often constants). This allows analysis of something like
1207 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1208 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1209 if (AR->isAffine()) {
1210 const SCEV *Start = AR->getStart();
1211 const SCEV *Step = AR->getStepRecurrence(*this);
1212 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1213 const Loop *L = AR->getLoop();
1215 // If we have special knowledge that this addrec won't overflow,
1216 // we don't need to do any further analysis.
1217 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1218 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1219 getSignExtendExpr(Step, Ty),
1222 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1223 // Note that this serves two purposes: It filters out loops that are
1224 // simply not analyzable, and it covers the case where this code is
1225 // being called from within backedge-taken count analysis, such that
1226 // attempting to ask for the backedge-taken count would likely result
1227 // in infinite recursion. In the later case, the analysis code will
1228 // cope with a conservative value, and it will take care to purge
1229 // that value once it has finished.
1230 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1231 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1232 // Manually compute the final value for AR, checking for
1235 // Check whether the backedge-taken count can be losslessly casted to
1236 // the addrec's type. The count is always unsigned.
1237 const SCEV *CastedMaxBECount =
1238 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1239 const SCEV *RecastedMaxBECount =
1240 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1241 if (MaxBECount == RecastedMaxBECount) {
1242 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1243 // Check whether Start+Step*MaxBECount has no signed overflow.
1244 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1245 const SCEV *Add = getAddExpr(Start, SMul);
1246 const SCEV *OperandExtendedAdd =
1247 getAddExpr(getSignExtendExpr(Start, WideTy),
1248 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1249 getSignExtendExpr(Step, WideTy)));
1250 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1251 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1252 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1253 // Return the expression with the addrec on the outside.
1254 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1255 getSignExtendExpr(Step, Ty),
1256 L, AR->getNoWrapFlags());
1258 // Similar to above, only this time treat the step value as unsigned.
1259 // This covers loops that count up with an unsigned step.
1260 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1261 Add = getAddExpr(Start, UMul);
1262 OperandExtendedAdd =
1263 getAddExpr(getSignExtendExpr(Start, WideTy),
1264 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1265 getZeroExtendExpr(Step, WideTy)));
1266 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1267 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1268 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1269 // Return the expression with the addrec on the outside.
1270 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1271 getZeroExtendExpr(Step, Ty),
1272 L, AR->getNoWrapFlags());
1276 // If the backedge is guarded by a comparison with the pre-inc value
1277 // the addrec is safe. Also, if the entry is guarded by a comparison
1278 // with the start value and the backedge is guarded by a comparison
1279 // with the post-inc value, the addrec is safe.
1280 ICmpInst::Predicate Pred;
1281 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1282 if (OverflowLimit &&
1283 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1284 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1285 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1287 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1288 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1289 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1290 getSignExtendExpr(Step, Ty),
1291 L, AR->getNoWrapFlags());
1296 // The cast wasn't folded; create an explicit cast node.
1297 // Recompute the insert position, as it may have been invalidated.
1298 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1299 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1301 UniqueSCEVs.InsertNode(S, IP);
1305 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1306 /// unspecified bits out to the given type.
1308 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1310 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1311 "This is not an extending conversion!");
1312 assert(isSCEVable(Ty) &&
1313 "This is not a conversion to a SCEVable type!");
1314 Ty = getEffectiveSCEVType(Ty);
1316 // Sign-extend negative constants.
1317 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1318 if (SC->getValue()->getValue().isNegative())
1319 return getSignExtendExpr(Op, Ty);
1321 // Peel off a truncate cast.
1322 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1323 const SCEV *NewOp = T->getOperand();
1324 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1325 return getAnyExtendExpr(NewOp, Ty);
1326 return getTruncateOrNoop(NewOp, Ty);
1329 // Next try a zext cast. If the cast is folded, use it.
1330 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1331 if (!isa<SCEVZeroExtendExpr>(ZExt))
1334 // Next try a sext cast. If the cast is folded, use it.
1335 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1336 if (!isa<SCEVSignExtendExpr>(SExt))
1339 // Force the cast to be folded into the operands of an addrec.
1340 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1341 SmallVector<const SCEV *, 4> Ops;
1342 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1344 Ops.push_back(getAnyExtendExpr(*I, Ty));
1345 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1348 // As a special case, fold anyext(undef) to undef. We don't want to
1349 // know too much about SCEVUnknowns, but this special case is handy
1351 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1352 if (isa<UndefValue>(U->getValue()))
1353 return getSCEV(UndefValue::get(Ty));
1355 // If the expression is obviously signed, use the sext cast value.
1356 if (isa<SCEVSMaxExpr>(Op))
1359 // Absent any other information, use the zext cast value.
1363 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1364 /// a list of operands to be added under the given scale, update the given
1365 /// map. This is a helper function for getAddRecExpr. As an example of
1366 /// what it does, given a sequence of operands that would form an add
1367 /// expression like this:
1369 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1371 /// where A and B are constants, update the map with these values:
1373 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1375 /// and add 13 + A*B*29 to AccumulatedConstant.
1376 /// This will allow getAddRecExpr to produce this:
1378 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1380 /// This form often exposes folding opportunities that are hidden in
1381 /// the original operand list.
1383 /// Return true iff it appears that any interesting folding opportunities
1384 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1385 /// the common case where no interesting opportunities are present, and
1386 /// is also used as a check to avoid infinite recursion.
1389 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1390 SmallVector<const SCEV *, 8> &NewOps,
1391 APInt &AccumulatedConstant,
1392 const SCEV *const *Ops, size_t NumOperands,
1394 ScalarEvolution &SE) {
1395 bool Interesting = false;
1397 // Iterate over the add operands. They are sorted, with constants first.
1399 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1401 // Pull a buried constant out to the outside.
1402 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1404 AccumulatedConstant += Scale * C->getValue()->getValue();
1407 // Next comes everything else. We're especially interested in multiplies
1408 // here, but they're in the middle, so just visit the rest with one loop.
1409 for (; i != NumOperands; ++i) {
1410 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1411 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1413 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1414 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1415 // A multiplication of a constant with another add; recurse.
1416 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1418 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1419 Add->op_begin(), Add->getNumOperands(),
1422 // A multiplication of a constant with some other value. Update
1424 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1425 const SCEV *Key = SE.getMulExpr(MulOps);
1426 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1427 M.insert(std::make_pair(Key, NewScale));
1429 NewOps.push_back(Pair.first->first);
1431 Pair.first->second += NewScale;
1432 // The map already had an entry for this value, which may indicate
1433 // a folding opportunity.
1438 // An ordinary operand. Update the map.
1439 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1440 M.insert(std::make_pair(Ops[i], Scale));
1442 NewOps.push_back(Pair.first->first);
1444 Pair.first->second += Scale;
1445 // The map already had an entry for this value, which may indicate
1446 // a folding opportunity.
1456 struct APIntCompare {
1457 bool operator()(const APInt &LHS, const APInt &RHS) const {
1458 return LHS.ult(RHS);
1463 /// getAddExpr - Get a canonical add expression, or something simpler if
1465 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1466 SCEV::NoWrapFlags Flags) {
1467 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1468 "only nuw or nsw allowed");
1469 assert(!Ops.empty() && "Cannot get empty add!");
1470 if (Ops.size() == 1) return Ops[0];
1472 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1473 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1474 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1475 "SCEVAddExpr operand types don't match!");
1478 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1480 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1481 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1482 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1484 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1485 E = Ops.end(); I != E; ++I)
1486 if (!isKnownNonNegative(*I)) {
1490 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1493 // Sort by complexity, this groups all similar expression types together.
1494 GroupByComplexity(Ops, LI);
1496 // If there are any constants, fold them together.
1498 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1500 assert(Idx < Ops.size());
1501 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1502 // We found two constants, fold them together!
1503 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1504 RHSC->getValue()->getValue());
1505 if (Ops.size() == 2) return Ops[0];
1506 Ops.erase(Ops.begin()+1); // Erase the folded element
1507 LHSC = cast<SCEVConstant>(Ops[0]);
1510 // If we are left with a constant zero being added, strip it off.
1511 if (LHSC->getValue()->isZero()) {
1512 Ops.erase(Ops.begin());
1516 if (Ops.size() == 1) return Ops[0];
1519 // Okay, check to see if the same value occurs in the operand list more than
1520 // once. If so, merge them together into an multiply expression. Since we
1521 // sorted the list, these values are required to be adjacent.
1522 Type *Ty = Ops[0]->getType();
1523 bool FoundMatch = false;
1524 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1525 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1526 // Scan ahead to count how many equal operands there are.
1528 while (i+Count != e && Ops[i+Count] == Ops[i])
1530 // Merge the values into a multiply.
1531 const SCEV *Scale = getConstant(Ty, Count);
1532 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1533 if (Ops.size() == Count)
1536 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1537 --i; e -= Count - 1;
1541 return getAddExpr(Ops, Flags);
1543 // Check for truncates. If all the operands are truncated from the same
1544 // type, see if factoring out the truncate would permit the result to be
1545 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1546 // if the contents of the resulting outer trunc fold to something simple.
1547 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1548 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1549 Type *DstType = Trunc->getType();
1550 Type *SrcType = Trunc->getOperand()->getType();
1551 SmallVector<const SCEV *, 8> LargeOps;
1553 // Check all the operands to see if they can be represented in the
1554 // source type of the truncate.
1555 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1556 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1557 if (T->getOperand()->getType() != SrcType) {
1561 LargeOps.push_back(T->getOperand());
1562 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1563 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1564 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1565 SmallVector<const SCEV *, 8> LargeMulOps;
1566 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1567 if (const SCEVTruncateExpr *T =
1568 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1569 if (T->getOperand()->getType() != SrcType) {
1573 LargeMulOps.push_back(T->getOperand());
1574 } else if (const SCEVConstant *C =
1575 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1576 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1583 LargeOps.push_back(getMulExpr(LargeMulOps));
1590 // Evaluate the expression in the larger type.
1591 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1592 // If it folds to something simple, use it. Otherwise, don't.
1593 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1594 return getTruncateExpr(Fold, DstType);
1598 // Skip past any other cast SCEVs.
1599 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1602 // If there are add operands they would be next.
1603 if (Idx < Ops.size()) {
1604 bool DeletedAdd = false;
1605 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1606 // If we have an add, expand the add operands onto the end of the operands
1608 Ops.erase(Ops.begin()+Idx);
1609 Ops.append(Add->op_begin(), Add->op_end());
1613 // If we deleted at least one add, we added operands to the end of the list,
1614 // and they are not necessarily sorted. Recurse to resort and resimplify
1615 // any operands we just acquired.
1617 return getAddExpr(Ops);
1620 // Skip over the add expression until we get to a multiply.
1621 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1624 // Check to see if there are any folding opportunities present with
1625 // operands multiplied by constant values.
1626 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1627 uint64_t BitWidth = getTypeSizeInBits(Ty);
1628 DenseMap<const SCEV *, APInt> M;
1629 SmallVector<const SCEV *, 8> NewOps;
1630 APInt AccumulatedConstant(BitWidth, 0);
1631 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1632 Ops.data(), Ops.size(),
1633 APInt(BitWidth, 1), *this)) {
1634 // Some interesting folding opportunity is present, so its worthwhile to
1635 // re-generate the operands list. Group the operands by constant scale,
1636 // to avoid multiplying by the same constant scale multiple times.
1637 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1638 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1639 E = NewOps.end(); I != E; ++I)
1640 MulOpLists[M.find(*I)->second].push_back(*I);
1641 // Re-generate the operands list.
1643 if (AccumulatedConstant != 0)
1644 Ops.push_back(getConstant(AccumulatedConstant));
1645 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1646 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1648 Ops.push_back(getMulExpr(getConstant(I->first),
1649 getAddExpr(I->second)));
1651 return getConstant(Ty, 0);
1652 if (Ops.size() == 1)
1654 return getAddExpr(Ops);
1658 // If we are adding something to a multiply expression, make sure the
1659 // something is not already an operand of the multiply. If so, merge it into
1661 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1662 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1663 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1664 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1665 if (isa<SCEVConstant>(MulOpSCEV))
1667 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1668 if (MulOpSCEV == Ops[AddOp]) {
1669 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1670 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1671 if (Mul->getNumOperands() != 2) {
1672 // If the multiply has more than two operands, we must get the
1674 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1675 Mul->op_begin()+MulOp);
1676 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1677 InnerMul = getMulExpr(MulOps);
1679 const SCEV *One = getConstant(Ty, 1);
1680 const SCEV *AddOne = getAddExpr(One, InnerMul);
1681 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1682 if (Ops.size() == 2) return OuterMul;
1684 Ops.erase(Ops.begin()+AddOp);
1685 Ops.erase(Ops.begin()+Idx-1);
1687 Ops.erase(Ops.begin()+Idx);
1688 Ops.erase(Ops.begin()+AddOp-1);
1690 Ops.push_back(OuterMul);
1691 return getAddExpr(Ops);
1694 // Check this multiply against other multiplies being added together.
1695 for (unsigned OtherMulIdx = Idx+1;
1696 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1698 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1699 // If MulOp occurs in OtherMul, we can fold the two multiplies
1701 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1702 OMulOp != e; ++OMulOp)
1703 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1704 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1705 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1706 if (Mul->getNumOperands() != 2) {
1707 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1708 Mul->op_begin()+MulOp);
1709 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1710 InnerMul1 = getMulExpr(MulOps);
1712 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1713 if (OtherMul->getNumOperands() != 2) {
1714 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1715 OtherMul->op_begin()+OMulOp);
1716 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1717 InnerMul2 = getMulExpr(MulOps);
1719 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1720 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1721 if (Ops.size() == 2) return OuterMul;
1722 Ops.erase(Ops.begin()+Idx);
1723 Ops.erase(Ops.begin()+OtherMulIdx-1);
1724 Ops.push_back(OuterMul);
1725 return getAddExpr(Ops);
1731 // If there are any add recurrences in the operands list, see if any other
1732 // added values are loop invariant. If so, we can fold them into the
1734 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1737 // Scan over all recurrences, trying to fold loop invariants into them.
1738 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1739 // Scan all of the other operands to this add and add them to the vector if
1740 // they are loop invariant w.r.t. the recurrence.
1741 SmallVector<const SCEV *, 8> LIOps;
1742 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1743 const Loop *AddRecLoop = AddRec->getLoop();
1744 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1745 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1746 LIOps.push_back(Ops[i]);
1747 Ops.erase(Ops.begin()+i);
1751 // If we found some loop invariants, fold them into the recurrence.
1752 if (!LIOps.empty()) {
1753 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1754 LIOps.push_back(AddRec->getStart());
1756 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1758 AddRecOps[0] = getAddExpr(LIOps);
1760 // Build the new addrec. Propagate the NUW and NSW flags if both the
1761 // outer add and the inner addrec are guaranteed to have no overflow.
1762 // Always propagate NW.
1763 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1764 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1766 // If all of the other operands were loop invariant, we are done.
1767 if (Ops.size() == 1) return NewRec;
1769 // Otherwise, add the folded AddRec by the non-invariant parts.
1770 for (unsigned i = 0;; ++i)
1771 if (Ops[i] == AddRec) {
1775 return getAddExpr(Ops);
1778 // Okay, if there weren't any loop invariants to be folded, check to see if
1779 // there are multiple AddRec's with the same loop induction variable being
1780 // added together. If so, we can fold them.
1781 for (unsigned OtherIdx = Idx+1;
1782 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1784 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1785 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1786 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1788 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1790 if (const SCEVAddRecExpr *OtherAddRec =
1791 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1792 if (OtherAddRec->getLoop() == AddRecLoop) {
1793 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1795 if (i >= AddRecOps.size()) {
1796 AddRecOps.append(OtherAddRec->op_begin()+i,
1797 OtherAddRec->op_end());
1800 AddRecOps[i] = getAddExpr(AddRecOps[i],
1801 OtherAddRec->getOperand(i));
1803 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1805 // Step size has changed, so we cannot guarantee no self-wraparound.
1806 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1807 return getAddExpr(Ops);
1810 // Otherwise couldn't fold anything into this recurrence. Move onto the
1814 // Okay, it looks like we really DO need an add expr. Check to see if we
1815 // already have one, otherwise create a new one.
1816 FoldingSetNodeID ID;
1817 ID.AddInteger(scAddExpr);
1818 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1819 ID.AddPointer(Ops[i]);
1822 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1824 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1825 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1826 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1828 UniqueSCEVs.InsertNode(S, IP);
1830 S->setNoWrapFlags(Flags);
1834 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1836 if (j > 1 && k / j != i) Overflow = true;
1840 /// Compute the result of "n choose k", the binomial coefficient. If an
1841 /// intermediate computation overflows, Overflow will be set and the return will
1842 /// be garbage. Overflow is not cleared on absense of overflow.
1843 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1844 // We use the multiplicative formula:
1845 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1846 // At each iteration, we take the n-th term of the numeral and divide by the
1847 // (k-n)th term of the denominator. This division will always produce an
1848 // integral result, and helps reduce the chance of overflow in the
1849 // intermediate computations. However, we can still overflow even when the
1850 // final result would fit.
1852 if (n == 0 || n == k) return 1;
1853 if (k > n) return 0;
1859 for (uint64_t i = 1; i <= k; ++i) {
1860 r = umul_ov(r, n-(i-1), Overflow);
1866 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1868 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1869 SCEV::NoWrapFlags Flags) {
1870 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1871 "only nuw or nsw allowed");
1872 assert(!Ops.empty() && "Cannot get empty mul!");
1873 if (Ops.size() == 1) return Ops[0];
1875 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1876 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1877 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1878 "SCEVMulExpr operand types don't match!");
1881 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1883 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1884 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1885 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1887 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1888 E = Ops.end(); I != E; ++I)
1889 if (!isKnownNonNegative(*I)) {
1893 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1896 // Sort by complexity, this groups all similar expression types together.
1897 GroupByComplexity(Ops, LI);
1899 // If there are any constants, fold them together.
1901 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1903 // C1*(C2+V) -> C1*C2 + C1*V
1904 if (Ops.size() == 2)
1905 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1906 if (Add->getNumOperands() == 2 &&
1907 isa<SCEVConstant>(Add->getOperand(0)))
1908 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1909 getMulExpr(LHSC, Add->getOperand(1)));
1912 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1913 // We found two constants, fold them together!
1914 ConstantInt *Fold = ConstantInt::get(getContext(),
1915 LHSC->getValue()->getValue() *
1916 RHSC->getValue()->getValue());
1917 Ops[0] = getConstant(Fold);
1918 Ops.erase(Ops.begin()+1); // Erase the folded element
1919 if (Ops.size() == 1) return Ops[0];
1920 LHSC = cast<SCEVConstant>(Ops[0]);
1923 // If we are left with a constant one being multiplied, strip it off.
1924 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1925 Ops.erase(Ops.begin());
1927 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1928 // If we have a multiply of zero, it will always be zero.
1930 } else if (Ops[0]->isAllOnesValue()) {
1931 // If we have a mul by -1 of an add, try distributing the -1 among the
1933 if (Ops.size() == 2) {
1934 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1935 SmallVector<const SCEV *, 4> NewOps;
1936 bool AnyFolded = false;
1937 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1938 E = Add->op_end(); I != E; ++I) {
1939 const SCEV *Mul = getMulExpr(Ops[0], *I);
1940 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1941 NewOps.push_back(Mul);
1944 return getAddExpr(NewOps);
1946 else if (const SCEVAddRecExpr *
1947 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1948 // Negation preserves a recurrence's no self-wrap property.
1949 SmallVector<const SCEV *, 4> Operands;
1950 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1951 E = AddRec->op_end(); I != E; ++I) {
1952 Operands.push_back(getMulExpr(Ops[0], *I));
1954 return getAddRecExpr(Operands, AddRec->getLoop(),
1955 AddRec->getNoWrapFlags(SCEV::FlagNW));
1960 if (Ops.size() == 1)
1964 // Skip over the add expression until we get to a multiply.
1965 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1968 // If there are mul operands inline them all into this expression.
1969 if (Idx < Ops.size()) {
1970 bool DeletedMul = false;
1971 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1972 // If we have an mul, expand the mul operands onto the end of the operands
1974 Ops.erase(Ops.begin()+Idx);
1975 Ops.append(Mul->op_begin(), Mul->op_end());
1979 // If we deleted at least one mul, we added operands to the end of the list,
1980 // and they are not necessarily sorted. Recurse to resort and resimplify
1981 // any operands we just acquired.
1983 return getMulExpr(Ops);
1986 // If there are any add recurrences in the operands list, see if any other
1987 // added values are loop invariant. If so, we can fold them into the
1989 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1992 // Scan over all recurrences, trying to fold loop invariants into them.
1993 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1994 // Scan all of the other operands to this mul and add them to the vector if
1995 // they are loop invariant w.r.t. the recurrence.
1996 SmallVector<const SCEV *, 8> LIOps;
1997 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1998 const Loop *AddRecLoop = AddRec->getLoop();
1999 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2000 if (isLoopInvariant(Ops[i], AddRecLoop)) {
2001 LIOps.push_back(Ops[i]);
2002 Ops.erase(Ops.begin()+i);
2006 // If we found some loop invariants, fold them into the recurrence.
2007 if (!LIOps.empty()) {
2008 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2009 SmallVector<const SCEV *, 4> NewOps;
2010 NewOps.reserve(AddRec->getNumOperands());
2011 const SCEV *Scale = getMulExpr(LIOps);
2012 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2013 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2015 // Build the new addrec. Propagate the NUW and NSW flags if both the
2016 // outer mul and the inner addrec are guaranteed to have no overflow.
2018 // No self-wrap cannot be guaranteed after changing the step size, but
2019 // will be inferred if either NUW or NSW is true.
2020 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2021 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2023 // If all of the other operands were loop invariant, we are done.
2024 if (Ops.size() == 1) return NewRec;
2026 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2027 for (unsigned i = 0;; ++i)
2028 if (Ops[i] == AddRec) {
2032 return getMulExpr(Ops);
2035 // Okay, if there weren't any loop invariants to be folded, check to see if
2036 // there are multiple AddRec's with the same loop induction variable being
2037 // multiplied together. If so, we can fold them.
2038 for (unsigned OtherIdx = Idx+1;
2039 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2041 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
2042 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2043 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2044 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2045 // ]]],+,...up to x=2n}.
2046 // Note that the arguments to choose() are always integers with values
2047 // known at compile time, never SCEV objects.
2049 // The implementation avoids pointless extra computations when the two
2050 // addrec's are of different length (mathematically, it's equivalent to
2051 // an infinite stream of zeros on the right).
2052 bool OpsModified = false;
2053 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2055 if (const SCEVAddRecExpr *OtherAddRec =
2056 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
2057 if (OtherAddRec->getLoop() == AddRecLoop) {
2058 bool Overflow = false;
2059 Type *Ty = AddRec->getType();
2060 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2061 SmallVector<const SCEV*, 7> AddRecOps;
2062 for (int x = 0, xe = AddRec->getNumOperands() +
2063 OtherAddRec->getNumOperands() - 1;
2064 x != xe && !Overflow; ++x) {
2065 const SCEV *Term = getConstant(Ty, 0);
2066 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2067 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2068 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2069 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2070 z < ze && !Overflow; ++z) {
2071 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2073 if (LargerThan64Bits)
2074 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2076 Coeff = Coeff1*Coeff2;
2077 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2078 const SCEV *Term1 = AddRec->getOperand(y-z);
2079 const SCEV *Term2 = OtherAddRec->getOperand(z);
2080 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2083 AddRecOps.push_back(Term);
2086 const SCEV *NewAddRec = getAddRecExpr(AddRecOps,
2089 if (Ops.size() == 2) return NewAddRec;
2090 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
2091 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2096 return getMulExpr(Ops);
2100 // Otherwise couldn't fold anything into this recurrence. Move onto the
2104 // Okay, it looks like we really DO need an mul expr. Check to see if we
2105 // already have one, otherwise create a new one.
2106 FoldingSetNodeID ID;
2107 ID.AddInteger(scMulExpr);
2108 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2109 ID.AddPointer(Ops[i]);
2112 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2114 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2115 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2116 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2118 UniqueSCEVs.InsertNode(S, IP);
2120 S->setNoWrapFlags(Flags);
2124 /// getUDivExpr - Get a canonical unsigned division expression, or something
2125 /// simpler if possible.
2126 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2128 assert(getEffectiveSCEVType(LHS->getType()) ==
2129 getEffectiveSCEVType(RHS->getType()) &&
2130 "SCEVUDivExpr operand types don't match!");
2132 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2133 if (RHSC->getValue()->equalsInt(1))
2134 return LHS; // X udiv 1 --> x
2135 // If the denominator is zero, the result of the udiv is undefined. Don't
2136 // try to analyze it, because the resolution chosen here may differ from
2137 // the resolution chosen in other parts of the compiler.
2138 if (!RHSC->getValue()->isZero()) {
2139 // Determine if the division can be folded into the operands of
2141 // TODO: Generalize this to non-constants by using known-bits information.
2142 Type *Ty = LHS->getType();
2143 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2144 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2145 // For non-power-of-two values, effectively round the value up to the
2146 // nearest power of two.
2147 if (!RHSC->getValue()->getValue().isPowerOf2())
2149 IntegerType *ExtTy =
2150 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2151 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2152 if (const SCEVConstant *Step =
2153 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2154 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2155 const APInt &StepInt = Step->getValue()->getValue();
2156 const APInt &DivInt = RHSC->getValue()->getValue();
2157 if (!StepInt.urem(DivInt) &&
2158 getZeroExtendExpr(AR, ExtTy) ==
2159 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2160 getZeroExtendExpr(Step, ExtTy),
2161 AR->getLoop(), SCEV::FlagAnyWrap)) {
2162 SmallVector<const SCEV *, 4> Operands;
2163 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2164 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2165 return getAddRecExpr(Operands, AR->getLoop(),
2168 /// Get a canonical UDivExpr for a recurrence.
2169 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2170 // We can currently only fold X%N if X is constant.
2171 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2172 if (StartC && !DivInt.urem(StepInt) &&
2173 getZeroExtendExpr(AR, ExtTy) ==
2174 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2175 getZeroExtendExpr(Step, ExtTy),
2176 AR->getLoop(), SCEV::FlagAnyWrap)) {
2177 const APInt &StartInt = StartC->getValue()->getValue();
2178 const APInt &StartRem = StartInt.urem(StepInt);
2180 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2181 AR->getLoop(), SCEV::FlagNW);
2184 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2185 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2186 SmallVector<const SCEV *, 4> Operands;
2187 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2188 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2189 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2190 // Find an operand that's safely divisible.
2191 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2192 const SCEV *Op = M->getOperand(i);
2193 const SCEV *Div = getUDivExpr(Op, RHSC);
2194 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2195 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2198 return getMulExpr(Operands);
2202 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2203 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2204 SmallVector<const SCEV *, 4> Operands;
2205 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2206 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2207 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2209 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2210 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2211 if (isa<SCEVUDivExpr>(Op) ||
2212 getMulExpr(Op, RHS) != A->getOperand(i))
2214 Operands.push_back(Op);
2216 if (Operands.size() == A->getNumOperands())
2217 return getAddExpr(Operands);
2221 // Fold if both operands are constant.
2222 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2223 Constant *LHSCV = LHSC->getValue();
2224 Constant *RHSCV = RHSC->getValue();
2225 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2231 FoldingSetNodeID ID;
2232 ID.AddInteger(scUDivExpr);
2236 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2237 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2239 UniqueSCEVs.InsertNode(S, IP);
2244 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2245 /// Simplify the expression as much as possible.
2246 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2248 SCEV::NoWrapFlags Flags) {
2249 SmallVector<const SCEV *, 4> Operands;
2250 Operands.push_back(Start);
2251 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2252 if (StepChrec->getLoop() == L) {
2253 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2254 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2257 Operands.push_back(Step);
2258 return getAddRecExpr(Operands, L, Flags);
2261 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2262 /// Simplify the expression as much as possible.
2264 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2265 const Loop *L, SCEV::NoWrapFlags Flags) {
2266 if (Operands.size() == 1) return Operands[0];
2268 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2269 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2270 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2271 "SCEVAddRecExpr operand types don't match!");
2272 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2273 assert(isLoopInvariant(Operands[i], L) &&
2274 "SCEVAddRecExpr operand is not loop-invariant!");
2277 if (Operands.back()->isZero()) {
2278 Operands.pop_back();
2279 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2282 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2283 // use that information to infer NUW and NSW flags. However, computing a
2284 // BE count requires calling getAddRecExpr, so we may not yet have a
2285 // meaningful BE count at this point (and if we don't, we'd be stuck
2286 // with a SCEVCouldNotCompute as the cached BE count).
2288 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2290 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2291 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2292 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2294 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2295 E = Operands.end(); I != E; ++I)
2296 if (!isKnownNonNegative(*I)) {
2300 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2303 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2304 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2305 const Loop *NestedLoop = NestedAR->getLoop();
2306 if (L->contains(NestedLoop) ?
2307 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2308 (!NestedLoop->contains(L) &&
2309 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2310 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2311 NestedAR->op_end());
2312 Operands[0] = NestedAR->getStart();
2313 // AddRecs require their operands be loop-invariant with respect to their
2314 // loops. Don't perform this transformation if it would break this
2316 bool AllInvariant = true;
2317 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2318 if (!isLoopInvariant(Operands[i], L)) {
2319 AllInvariant = false;
2323 // Create a recurrence for the outer loop with the same step size.
2325 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2326 // inner recurrence has the same property.
2327 SCEV::NoWrapFlags OuterFlags =
2328 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2330 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2331 AllInvariant = true;
2332 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2333 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2334 AllInvariant = false;
2338 // Ok, both add recurrences are valid after the transformation.
2340 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2341 // the outer recurrence has the same property.
2342 SCEV::NoWrapFlags InnerFlags =
2343 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2344 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2347 // Reset Operands to its original state.
2348 Operands[0] = NestedAR;
2352 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2353 // already have one, otherwise create a new one.
2354 FoldingSetNodeID ID;
2355 ID.AddInteger(scAddRecExpr);
2356 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2357 ID.AddPointer(Operands[i]);
2361 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2363 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2364 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2365 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2366 O, Operands.size(), L);
2367 UniqueSCEVs.InsertNode(S, IP);
2369 S->setNoWrapFlags(Flags);
2373 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2375 SmallVector<const SCEV *, 2> Ops;
2378 return getSMaxExpr(Ops);
2382 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2383 assert(!Ops.empty() && "Cannot get empty smax!");
2384 if (Ops.size() == 1) return Ops[0];
2386 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2387 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2388 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2389 "SCEVSMaxExpr operand types don't match!");
2392 // Sort by complexity, this groups all similar expression types together.
2393 GroupByComplexity(Ops, LI);
2395 // If there are any constants, fold them together.
2397 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2399 assert(Idx < Ops.size());
2400 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2401 // We found two constants, fold them together!
2402 ConstantInt *Fold = ConstantInt::get(getContext(),
2403 APIntOps::smax(LHSC->getValue()->getValue(),
2404 RHSC->getValue()->getValue()));
2405 Ops[0] = getConstant(Fold);
2406 Ops.erase(Ops.begin()+1); // Erase the folded element
2407 if (Ops.size() == 1) return Ops[0];
2408 LHSC = cast<SCEVConstant>(Ops[0]);
2411 // If we are left with a constant minimum-int, strip it off.
2412 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2413 Ops.erase(Ops.begin());
2415 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2416 // If we have an smax with a constant maximum-int, it will always be
2421 if (Ops.size() == 1) return Ops[0];
2424 // Find the first SMax
2425 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2428 // Check to see if one of the operands is an SMax. If so, expand its operands
2429 // onto our operand list, and recurse to simplify.
2430 if (Idx < Ops.size()) {
2431 bool DeletedSMax = false;
2432 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2433 Ops.erase(Ops.begin()+Idx);
2434 Ops.append(SMax->op_begin(), SMax->op_end());
2439 return getSMaxExpr(Ops);
2442 // Okay, check to see if the same value occurs in the operand list twice. If
2443 // so, delete one. Since we sorted the list, these values are required to
2445 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2446 // X smax Y smax Y --> X smax Y
2447 // X smax Y --> X, if X is always greater than Y
2448 if (Ops[i] == Ops[i+1] ||
2449 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2450 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2452 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2453 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2457 if (Ops.size() == 1) return Ops[0];
2459 assert(!Ops.empty() && "Reduced smax down to nothing!");
2461 // Okay, it looks like we really DO need an smax expr. Check to see if we
2462 // already have one, otherwise create a new one.
2463 FoldingSetNodeID ID;
2464 ID.AddInteger(scSMaxExpr);
2465 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2466 ID.AddPointer(Ops[i]);
2468 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2469 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2470 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2471 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2473 UniqueSCEVs.InsertNode(S, IP);
2477 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2479 SmallVector<const SCEV *, 2> Ops;
2482 return getUMaxExpr(Ops);
2486 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2487 assert(!Ops.empty() && "Cannot get empty umax!");
2488 if (Ops.size() == 1) return Ops[0];
2490 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2491 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2492 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2493 "SCEVUMaxExpr operand types don't match!");
2496 // Sort by complexity, this groups all similar expression types together.
2497 GroupByComplexity(Ops, LI);
2499 // If there are any constants, fold them together.
2501 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2503 assert(Idx < Ops.size());
2504 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2505 // We found two constants, fold them together!
2506 ConstantInt *Fold = ConstantInt::get(getContext(),
2507 APIntOps::umax(LHSC->getValue()->getValue(),
2508 RHSC->getValue()->getValue()));
2509 Ops[0] = getConstant(Fold);
2510 Ops.erase(Ops.begin()+1); // Erase the folded element
2511 if (Ops.size() == 1) return Ops[0];
2512 LHSC = cast<SCEVConstant>(Ops[0]);
2515 // If we are left with a constant minimum-int, strip it off.
2516 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2517 Ops.erase(Ops.begin());
2519 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2520 // If we have an umax with a constant maximum-int, it will always be
2525 if (Ops.size() == 1) return Ops[0];
2528 // Find the first UMax
2529 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2532 // Check to see if one of the operands is a UMax. If so, expand its operands
2533 // onto our operand list, and recurse to simplify.
2534 if (Idx < Ops.size()) {
2535 bool DeletedUMax = false;
2536 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2537 Ops.erase(Ops.begin()+Idx);
2538 Ops.append(UMax->op_begin(), UMax->op_end());
2543 return getUMaxExpr(Ops);
2546 // Okay, check to see if the same value occurs in the operand list twice. If
2547 // so, delete one. Since we sorted the list, these values are required to
2549 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2550 // X umax Y umax Y --> X umax Y
2551 // X umax Y --> X, if X is always greater than Y
2552 if (Ops[i] == Ops[i+1] ||
2553 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2554 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2556 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2557 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2561 if (Ops.size() == 1) return Ops[0];
2563 assert(!Ops.empty() && "Reduced umax down to nothing!");
2565 // Okay, it looks like we really DO need a umax expr. Check to see if we
2566 // already have one, otherwise create a new one.
2567 FoldingSetNodeID ID;
2568 ID.AddInteger(scUMaxExpr);
2569 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2570 ID.AddPointer(Ops[i]);
2572 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2573 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2574 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2575 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2577 UniqueSCEVs.InsertNode(S, IP);
2581 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2583 // ~smax(~x, ~y) == smin(x, y).
2584 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2587 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2589 // ~umax(~x, ~y) == umin(x, y)
2590 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2593 const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) {
2594 // If we have TargetData, we can bypass creating a target-independent
2595 // constant expression and then folding it back into a ConstantInt.
2596 // This is just a compile-time optimization.
2598 return getConstant(TD->getIntPtrType(getContext()),
2599 TD->getTypeAllocSize(AllocTy));
2601 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2602 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2603 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2605 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2606 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2609 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2610 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2611 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2612 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2614 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2615 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2618 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy,
2620 // If we have TargetData, we can bypass creating a target-independent
2621 // constant expression and then folding it back into a ConstantInt.
2622 // This is just a compile-time optimization.
2624 return getConstant(TD->getIntPtrType(getContext()),
2625 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2627 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2628 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2629 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2631 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2632 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2635 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2636 Constant *FieldNo) {
2637 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2638 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2639 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2641 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2642 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2645 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2646 // Don't attempt to do anything other than create a SCEVUnknown object
2647 // here. createSCEV only calls getUnknown after checking for all other
2648 // interesting possibilities, and any other code that calls getUnknown
2649 // is doing so in order to hide a value from SCEV canonicalization.
2651 FoldingSetNodeID ID;
2652 ID.AddInteger(scUnknown);
2655 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2656 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2657 "Stale SCEVUnknown in uniquing map!");
2660 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2662 FirstUnknown = cast<SCEVUnknown>(S);
2663 UniqueSCEVs.InsertNode(S, IP);
2667 //===----------------------------------------------------------------------===//
2668 // Basic SCEV Analysis and PHI Idiom Recognition Code
2671 /// isSCEVable - Test if values of the given type are analyzable within
2672 /// the SCEV framework. This primarily includes integer types, and it
2673 /// can optionally include pointer types if the ScalarEvolution class
2674 /// has access to target-specific information.
2675 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2676 // Integers and pointers are always SCEVable.
2677 return Ty->isIntegerTy() || Ty->isPointerTy();
2680 /// getTypeSizeInBits - Return the size in bits of the specified type,
2681 /// for which isSCEVable must return true.
2682 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2683 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2685 // If we have a TargetData, use it!
2687 return TD->getTypeSizeInBits(Ty);
2689 // Integer types have fixed sizes.
2690 if (Ty->isIntegerTy())
2691 return Ty->getPrimitiveSizeInBits();
2693 // The only other support type is pointer. Without TargetData, conservatively
2694 // assume pointers are 64-bit.
2695 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2699 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2700 /// the given type and which represents how SCEV will treat the given
2701 /// type, for which isSCEVable must return true. For pointer types,
2702 /// this is the pointer-sized integer type.
2703 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2704 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2706 if (Ty->isIntegerTy())
2709 // The only other support type is pointer.
2710 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2711 if (TD) return TD->getIntPtrType(getContext());
2713 // Without TargetData, conservatively assume pointers are 64-bit.
2714 return Type::getInt64Ty(getContext());
2717 const SCEV *ScalarEvolution::getCouldNotCompute() {
2718 return &CouldNotCompute;
2721 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2722 /// expression and create a new one.
2723 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2724 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2726 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2727 if (I != ValueExprMap.end()) return I->second;
2728 const SCEV *S = createSCEV(V);
2730 // The process of creating a SCEV for V may have caused other SCEVs
2731 // to have been created, so it's necessary to insert the new entry
2732 // from scratch, rather than trying to remember the insert position
2734 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2738 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2740 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2741 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2743 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2745 Type *Ty = V->getType();
2746 Ty = getEffectiveSCEVType(Ty);
2747 return getMulExpr(V,
2748 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2751 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2752 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2753 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2755 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2757 Type *Ty = V->getType();
2758 Ty = getEffectiveSCEVType(Ty);
2759 const SCEV *AllOnes =
2760 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2761 return getMinusSCEV(AllOnes, V);
2764 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2765 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2766 SCEV::NoWrapFlags Flags) {
2767 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2769 // Fast path: X - X --> 0.
2771 return getConstant(LHS->getType(), 0);
2774 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2777 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2778 /// input value to the specified type. If the type must be extended, it is zero
2781 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2782 Type *SrcTy = V->getType();
2783 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2784 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2785 "Cannot truncate or zero extend with non-integer arguments!");
2786 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2787 return V; // No conversion
2788 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2789 return getTruncateExpr(V, Ty);
2790 return getZeroExtendExpr(V, Ty);
2793 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2794 /// input value to the specified type. If the type must be extended, it is sign
2797 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2799 Type *SrcTy = V->getType();
2800 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2801 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2802 "Cannot truncate or zero extend with non-integer arguments!");
2803 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2804 return V; // No conversion
2805 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2806 return getTruncateExpr(V, Ty);
2807 return getSignExtendExpr(V, Ty);
2810 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2811 /// input value to the specified type. If the type must be extended, it is zero
2812 /// extended. The conversion must not be narrowing.
2814 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2815 Type *SrcTy = V->getType();
2816 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2817 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2818 "Cannot noop or zero extend with non-integer arguments!");
2819 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2820 "getNoopOrZeroExtend cannot truncate!");
2821 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2822 return V; // No conversion
2823 return getZeroExtendExpr(V, Ty);
2826 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2827 /// input value to the specified type. If the type must be extended, it is sign
2828 /// extended. The conversion must not be narrowing.
2830 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2831 Type *SrcTy = V->getType();
2832 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2833 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2834 "Cannot noop or sign extend with non-integer arguments!");
2835 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2836 "getNoopOrSignExtend cannot truncate!");
2837 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2838 return V; // No conversion
2839 return getSignExtendExpr(V, Ty);
2842 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2843 /// the input value to the specified type. If the type must be extended,
2844 /// it is extended with unspecified bits. The conversion must not be
2847 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2848 Type *SrcTy = V->getType();
2849 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2850 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2851 "Cannot noop or any extend with non-integer arguments!");
2852 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2853 "getNoopOrAnyExtend cannot truncate!");
2854 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2855 return V; // No conversion
2856 return getAnyExtendExpr(V, Ty);
2859 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2860 /// input value to the specified type. The conversion must not be widening.
2862 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2863 Type *SrcTy = V->getType();
2864 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2865 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2866 "Cannot truncate or noop with non-integer arguments!");
2867 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2868 "getTruncateOrNoop cannot extend!");
2869 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2870 return V; // No conversion
2871 return getTruncateExpr(V, Ty);
2874 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2875 /// the types using zero-extension, and then perform a umax operation
2877 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2879 const SCEV *PromotedLHS = LHS;
2880 const SCEV *PromotedRHS = RHS;
2882 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2883 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2885 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2887 return getUMaxExpr(PromotedLHS, PromotedRHS);
2890 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2891 /// the types using zero-extension, and then perform a umin operation
2893 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2895 const SCEV *PromotedLHS = LHS;
2896 const SCEV *PromotedRHS = RHS;
2898 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2899 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2901 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2903 return getUMinExpr(PromotedLHS, PromotedRHS);
2906 /// getPointerBase - Transitively follow the chain of pointer-type operands
2907 /// until reaching a SCEV that does not have a single pointer operand. This
2908 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2909 /// but corner cases do exist.
2910 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2911 // A pointer operand may evaluate to a nonpointer expression, such as null.
2912 if (!V->getType()->isPointerTy())
2915 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2916 return getPointerBase(Cast->getOperand());
2918 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2919 const SCEV *PtrOp = 0;
2920 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2922 if ((*I)->getType()->isPointerTy()) {
2923 // Cannot find the base of an expression with multiple pointer operands.
2931 return getPointerBase(PtrOp);
2936 /// PushDefUseChildren - Push users of the given Instruction
2937 /// onto the given Worklist.
2939 PushDefUseChildren(Instruction *I,
2940 SmallVectorImpl<Instruction *> &Worklist) {
2941 // Push the def-use children onto the Worklist stack.
2942 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2944 Worklist.push_back(cast<Instruction>(*UI));
2947 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2948 /// instructions that depend on the given instruction and removes them from
2949 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2952 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2953 SmallVector<Instruction *, 16> Worklist;
2954 PushDefUseChildren(PN, Worklist);
2956 SmallPtrSet<Instruction *, 8> Visited;
2958 while (!Worklist.empty()) {
2959 Instruction *I = Worklist.pop_back_val();
2960 if (!Visited.insert(I)) continue;
2962 ValueExprMapType::iterator It =
2963 ValueExprMap.find(static_cast<Value *>(I));
2964 if (It != ValueExprMap.end()) {
2965 const SCEV *Old = It->second;
2967 // Short-circuit the def-use traversal if the symbolic name
2968 // ceases to appear in expressions.
2969 if (Old != SymName && !hasOperand(Old, SymName))
2972 // SCEVUnknown for a PHI either means that it has an unrecognized
2973 // structure, it's a PHI that's in the progress of being computed
2974 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2975 // additional loop trip count information isn't going to change anything.
2976 // In the second case, createNodeForPHI will perform the necessary
2977 // updates on its own when it gets to that point. In the third, we do
2978 // want to forget the SCEVUnknown.
2979 if (!isa<PHINode>(I) ||
2980 !isa<SCEVUnknown>(Old) ||
2981 (I != PN && Old == SymName)) {
2982 forgetMemoizedResults(Old);
2983 ValueExprMap.erase(It);
2987 PushDefUseChildren(I, Worklist);
2991 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2992 /// a loop header, making it a potential recurrence, or it doesn't.
2994 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2995 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2996 if (L->getHeader() == PN->getParent()) {
2997 // The loop may have multiple entrances or multiple exits; we can analyze
2998 // this phi as an addrec if it has a unique entry value and a unique
3000 Value *BEValueV = 0, *StartValueV = 0;
3001 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3002 Value *V = PN->getIncomingValue(i);
3003 if (L->contains(PN->getIncomingBlock(i))) {
3006 } else if (BEValueV != V) {
3010 } else if (!StartValueV) {
3012 } else if (StartValueV != V) {
3017 if (BEValueV && StartValueV) {
3018 // While we are analyzing this PHI node, handle its value symbolically.
3019 const SCEV *SymbolicName = getUnknown(PN);
3020 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
3021 "PHI node already processed?");
3022 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3024 // Using this symbolic name for the PHI, analyze the value coming around
3026 const SCEV *BEValue = getSCEV(BEValueV);
3028 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3029 // has a special value for the first iteration of the loop.
3031 // If the value coming around the backedge is an add with the symbolic
3032 // value we just inserted, then we found a simple induction variable!
3033 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3034 // If there is a single occurrence of the symbolic value, replace it
3035 // with a recurrence.
3036 unsigned FoundIndex = Add->getNumOperands();
3037 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3038 if (Add->getOperand(i) == SymbolicName)
3039 if (FoundIndex == e) {
3044 if (FoundIndex != Add->getNumOperands()) {
3045 // Create an add with everything but the specified operand.
3046 SmallVector<const SCEV *, 8> Ops;
3047 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3048 if (i != FoundIndex)
3049 Ops.push_back(Add->getOperand(i));
3050 const SCEV *Accum = getAddExpr(Ops);
3052 // This is not a valid addrec if the step amount is varying each
3053 // loop iteration, but is not itself an addrec in this loop.
3054 if (isLoopInvariant(Accum, L) ||
3055 (isa<SCEVAddRecExpr>(Accum) &&
3056 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3057 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3059 // If the increment doesn't overflow, then neither the addrec nor
3060 // the post-increment will overflow.
3061 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3062 if (OBO->hasNoUnsignedWrap())
3063 Flags = setFlags(Flags, SCEV::FlagNUW);
3064 if (OBO->hasNoSignedWrap())
3065 Flags = setFlags(Flags, SCEV::FlagNSW);
3066 } else if (const GEPOperator *GEP =
3067 dyn_cast<GEPOperator>(BEValueV)) {
3068 // If the increment is an inbounds GEP, then we know the address
3069 // space cannot be wrapped around. We cannot make any guarantee
3070 // about signed or unsigned overflow because pointers are
3071 // unsigned but we may have a negative index from the base
3073 if (GEP->isInBounds())
3074 Flags = setFlags(Flags, SCEV::FlagNW);
3077 const SCEV *StartVal = getSCEV(StartValueV);
3078 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3080 // Since the no-wrap flags are on the increment, they apply to the
3081 // post-incremented value as well.
3082 if (isLoopInvariant(Accum, L))
3083 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3086 // Okay, for the entire analysis of this edge we assumed the PHI
3087 // to be symbolic. We now need to go back and purge all of the
3088 // entries for the scalars that use the symbolic expression.
3089 ForgetSymbolicName(PN, SymbolicName);
3090 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3094 } else if (const SCEVAddRecExpr *AddRec =
3095 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3096 // Otherwise, this could be a loop like this:
3097 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3098 // In this case, j = {1,+,1} and BEValue is j.
3099 // Because the other in-value of i (0) fits the evolution of BEValue
3100 // i really is an addrec evolution.
3101 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3102 const SCEV *StartVal = getSCEV(StartValueV);
3104 // If StartVal = j.start - j.stride, we can use StartVal as the
3105 // initial step of the addrec evolution.
3106 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3107 AddRec->getOperand(1))) {
3108 // FIXME: For constant StartVal, we should be able to infer
3110 const SCEV *PHISCEV =
3111 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3114 // Okay, for the entire analysis of this edge we assumed the PHI
3115 // to be symbolic. We now need to go back and purge all of the
3116 // entries for the scalars that use the symbolic expression.
3117 ForgetSymbolicName(PN, SymbolicName);
3118 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3126 // If the PHI has a single incoming value, follow that value, unless the
3127 // PHI's incoming blocks are in a different loop, in which case doing so
3128 // risks breaking LCSSA form. Instcombine would normally zap these, but
3129 // it doesn't have DominatorTree information, so it may miss cases.
3130 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
3131 if (LI->replacementPreservesLCSSAForm(PN, V))
3134 // If it's not a loop phi, we can't handle it yet.
3135 return getUnknown(PN);
3138 /// createNodeForGEP - Expand GEP instructions into add and multiply
3139 /// operations. This allows them to be analyzed by regular SCEV code.
3141 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3143 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3144 // Add expression, because the Instruction may be guarded by control flow
3145 // and the no-overflow bits may not be valid for the expression in any
3147 bool isInBounds = GEP->isInBounds();
3149 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3150 Value *Base = GEP->getOperand(0);
3151 // Don't attempt to analyze GEPs over unsized objects.
3152 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3153 return getUnknown(GEP);
3154 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3155 gep_type_iterator GTI = gep_type_begin(GEP);
3156 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3160 // Compute the (potentially symbolic) offset in bytes for this index.
3161 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3162 // For a struct, add the member offset.
3163 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3164 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
3166 // Add the field offset to the running total offset.
3167 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3169 // For an array, add the element offset, explicitly scaled.
3170 const SCEV *ElementSize = getSizeOfExpr(*GTI);
3171 const SCEV *IndexS = getSCEV(Index);
3172 // Getelementptr indices are signed.
3173 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3175 // Multiply the index by the element size to compute the element offset.
3176 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3177 isInBounds ? SCEV::FlagNSW :
3180 // Add the element offset to the running total offset.
3181 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3185 // Get the SCEV for the GEP base.
3186 const SCEV *BaseS = getSCEV(Base);
3188 // Add the total offset from all the GEP indices to the base.
3189 return getAddExpr(BaseS, TotalOffset,
3190 isInBounds ? SCEV::FlagNUW : SCEV::FlagAnyWrap);
3193 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3194 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3195 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3196 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3198 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3199 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3200 return C->getValue()->getValue().countTrailingZeros();
3202 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3203 return std::min(GetMinTrailingZeros(T->getOperand()),
3204 (uint32_t)getTypeSizeInBits(T->getType()));
3206 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3207 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3208 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3209 getTypeSizeInBits(E->getType()) : OpRes;
3212 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3213 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3214 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3215 getTypeSizeInBits(E->getType()) : OpRes;
3218 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3219 // The result is the min of all operands results.
3220 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3221 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3222 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3226 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3227 // The result is the sum of all operands results.
3228 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3229 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3230 for (unsigned i = 1, e = M->getNumOperands();
3231 SumOpRes != BitWidth && i != e; ++i)
3232 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3237 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3238 // The result is the min of all operands results.
3239 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3240 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3241 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3245 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3246 // The result is the min of all operands results.
3247 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3248 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3249 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3253 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3254 // The result is the min of all operands results.
3255 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3256 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3257 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3261 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3262 // For a SCEVUnknown, ask ValueTracking.
3263 unsigned BitWidth = getTypeSizeInBits(U->getType());
3264 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3265 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3266 return Zeros.countTrailingOnes();
3273 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3276 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3277 // See if we've computed this range already.
3278 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3279 if (I != UnsignedRanges.end())
3282 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3283 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3285 unsigned BitWidth = getTypeSizeInBits(S->getType());
3286 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3288 // If the value has known zeros, the maximum unsigned value will have those
3289 // known zeros as well.
3290 uint32_t TZ = GetMinTrailingZeros(S);
3292 ConservativeResult =
3293 ConstantRange(APInt::getMinValue(BitWidth),
3294 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3296 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3297 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3298 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3299 X = X.add(getUnsignedRange(Add->getOperand(i)));
3300 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3303 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3304 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3305 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3306 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3307 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3310 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3311 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3312 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3313 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3314 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3317 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3318 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3319 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3320 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3321 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3324 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3325 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3326 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3327 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3330 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3331 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3332 return setUnsignedRange(ZExt,
3333 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3336 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3337 ConstantRange X = getUnsignedRange(SExt->getOperand());
3338 return setUnsignedRange(SExt,
3339 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3342 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3343 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3344 return setUnsignedRange(Trunc,
3345 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3348 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3349 // If there's no unsigned wrap, the value will never be less than its
3351 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3352 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3353 if (!C->getValue()->isZero())
3354 ConservativeResult =
3355 ConservativeResult.intersectWith(
3356 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3358 // TODO: non-affine addrec
3359 if (AddRec->isAffine()) {
3360 Type *Ty = AddRec->getType();
3361 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3362 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3363 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3364 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3366 const SCEV *Start = AddRec->getStart();
3367 const SCEV *Step = AddRec->getStepRecurrence(*this);
3369 ConstantRange StartRange = getUnsignedRange(Start);
3370 ConstantRange StepRange = getSignedRange(Step);
3371 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3372 ConstantRange EndRange =
3373 StartRange.add(MaxBECountRange.multiply(StepRange));
3375 // Check for overflow. This must be done with ConstantRange arithmetic
3376 // because we could be called from within the ScalarEvolution overflow
3378 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3379 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3380 ConstantRange ExtMaxBECountRange =
3381 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3382 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3383 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3385 return setUnsignedRange(AddRec, ConservativeResult);
3387 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3388 EndRange.getUnsignedMin());
3389 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3390 EndRange.getUnsignedMax());
3391 if (Min.isMinValue() && Max.isMaxValue())
3392 return setUnsignedRange(AddRec, ConservativeResult);
3393 return setUnsignedRange(AddRec,
3394 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3398 return setUnsignedRange(AddRec, ConservativeResult);
3401 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3402 // For a SCEVUnknown, ask ValueTracking.
3403 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3404 ComputeMaskedBits(U->getValue(), Zeros, Ones, TD);
3405 if (Ones == ~Zeros + 1)
3406 return setUnsignedRange(U, ConservativeResult);
3407 return setUnsignedRange(U,
3408 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3411 return setUnsignedRange(S, ConservativeResult);
3414 /// getSignedRange - Determine the signed range for a particular SCEV.
3417 ScalarEvolution::getSignedRange(const SCEV *S) {
3418 // See if we've computed this range already.
3419 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3420 if (I != SignedRanges.end())
3423 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3424 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3426 unsigned BitWidth = getTypeSizeInBits(S->getType());
3427 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3429 // If the value has known zeros, the maximum signed value will have those
3430 // known zeros as well.
3431 uint32_t TZ = GetMinTrailingZeros(S);
3433 ConservativeResult =
3434 ConstantRange(APInt::getSignedMinValue(BitWidth),
3435 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3437 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3438 ConstantRange X = getSignedRange(Add->getOperand(0));
3439 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3440 X = X.add(getSignedRange(Add->getOperand(i)));
3441 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3444 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3445 ConstantRange X = getSignedRange(Mul->getOperand(0));
3446 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3447 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3448 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3451 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3452 ConstantRange X = getSignedRange(SMax->getOperand(0));
3453 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3454 X = X.smax(getSignedRange(SMax->getOperand(i)));
3455 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3458 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3459 ConstantRange X = getSignedRange(UMax->getOperand(0));
3460 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3461 X = X.umax(getSignedRange(UMax->getOperand(i)));
3462 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3465 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3466 ConstantRange X = getSignedRange(UDiv->getLHS());
3467 ConstantRange Y = getSignedRange(UDiv->getRHS());
3468 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3471 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3472 ConstantRange X = getSignedRange(ZExt->getOperand());
3473 return setSignedRange(ZExt,
3474 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3477 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3478 ConstantRange X = getSignedRange(SExt->getOperand());
3479 return setSignedRange(SExt,
3480 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3483 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3484 ConstantRange X = getSignedRange(Trunc->getOperand());
3485 return setSignedRange(Trunc,
3486 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3489 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3490 // If there's no signed wrap, and all the operands have the same sign or
3491 // zero, the value won't ever change sign.
3492 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3493 bool AllNonNeg = true;
3494 bool AllNonPos = true;
3495 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3496 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3497 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3500 ConservativeResult = ConservativeResult.intersectWith(
3501 ConstantRange(APInt(BitWidth, 0),
3502 APInt::getSignedMinValue(BitWidth)));
3504 ConservativeResult = ConservativeResult.intersectWith(
3505 ConstantRange(APInt::getSignedMinValue(BitWidth),
3506 APInt(BitWidth, 1)));
3509 // TODO: non-affine addrec
3510 if (AddRec->isAffine()) {
3511 Type *Ty = AddRec->getType();
3512 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3513 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3514 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3515 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3517 const SCEV *Start = AddRec->getStart();
3518 const SCEV *Step = AddRec->getStepRecurrence(*this);
3520 ConstantRange StartRange = getSignedRange(Start);
3521 ConstantRange StepRange = getSignedRange(Step);
3522 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3523 ConstantRange EndRange =
3524 StartRange.add(MaxBECountRange.multiply(StepRange));
3526 // Check for overflow. This must be done with ConstantRange arithmetic
3527 // because we could be called from within the ScalarEvolution overflow
3529 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3530 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3531 ConstantRange ExtMaxBECountRange =
3532 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3533 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3534 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3536 return setSignedRange(AddRec, ConservativeResult);
3538 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3539 EndRange.getSignedMin());
3540 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3541 EndRange.getSignedMax());
3542 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3543 return setSignedRange(AddRec, ConservativeResult);
3544 return setSignedRange(AddRec,
3545 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3549 return setSignedRange(AddRec, ConservativeResult);
3552 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3553 // For a SCEVUnknown, ask ValueTracking.
3554 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3555 return setSignedRange(U, ConservativeResult);
3556 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3558 return setSignedRange(U, ConservativeResult);
3559 return setSignedRange(U, ConservativeResult.intersectWith(
3560 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3561 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3564 return setSignedRange(S, ConservativeResult);
3567 /// createSCEV - We know that there is no SCEV for the specified value.
3568 /// Analyze the expression.
3570 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3571 if (!isSCEVable(V->getType()))
3572 return getUnknown(V);
3574 unsigned Opcode = Instruction::UserOp1;
3575 if (Instruction *I = dyn_cast<Instruction>(V)) {
3576 Opcode = I->getOpcode();
3578 // Don't attempt to analyze instructions in blocks that aren't
3579 // reachable. Such instructions don't matter, and they aren't required
3580 // to obey basic rules for definitions dominating uses which this
3581 // analysis depends on.
3582 if (!DT->isReachableFromEntry(I->getParent()))
3583 return getUnknown(V);
3584 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3585 Opcode = CE->getOpcode();
3586 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3587 return getConstant(CI);
3588 else if (isa<ConstantPointerNull>(V))
3589 return getConstant(V->getType(), 0);
3590 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3591 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3593 return getUnknown(V);
3595 Operator *U = cast<Operator>(V);
3597 case Instruction::Add: {
3598 // The simple thing to do would be to just call getSCEV on both operands
3599 // and call getAddExpr with the result. However if we're looking at a
3600 // bunch of things all added together, this can be quite inefficient,
3601 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3602 // Instead, gather up all the operands and make a single getAddExpr call.
3603 // LLVM IR canonical form means we need only traverse the left operands.
3605 // Don't apply this instruction's NSW or NUW flags to the new
3606 // expression. The instruction may be guarded by control flow that the
3607 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3608 // mapped to the same SCEV expression, and it would be incorrect to transfer
3609 // NSW/NUW semantics to those operations.
3610 SmallVector<const SCEV *, 4> AddOps;
3611 AddOps.push_back(getSCEV(U->getOperand(1)));
3612 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3613 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3614 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3616 U = cast<Operator>(Op);
3617 const SCEV *Op1 = getSCEV(U->getOperand(1));
3618 if (Opcode == Instruction::Sub)
3619 AddOps.push_back(getNegativeSCEV(Op1));
3621 AddOps.push_back(Op1);
3623 AddOps.push_back(getSCEV(U->getOperand(0)));
3624 return getAddExpr(AddOps);
3626 case Instruction::Mul: {
3627 // Don't transfer NSW/NUW for the same reason as AddExpr.
3628 SmallVector<const SCEV *, 4> MulOps;
3629 MulOps.push_back(getSCEV(U->getOperand(1)));
3630 for (Value *Op = U->getOperand(0);
3631 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3632 Op = U->getOperand(0)) {
3633 U = cast<Operator>(Op);
3634 MulOps.push_back(getSCEV(U->getOperand(1)));
3636 MulOps.push_back(getSCEV(U->getOperand(0)));
3637 return getMulExpr(MulOps);
3639 case Instruction::UDiv:
3640 return getUDivExpr(getSCEV(U->getOperand(0)),
3641 getSCEV(U->getOperand(1)));
3642 case Instruction::Sub:
3643 return getMinusSCEV(getSCEV(U->getOperand(0)),
3644 getSCEV(U->getOperand(1)));
3645 case Instruction::And:
3646 // For an expression like x&255 that merely masks off the high bits,
3647 // use zext(trunc(x)) as the SCEV expression.
3648 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3649 if (CI->isNullValue())
3650 return getSCEV(U->getOperand(1));
3651 if (CI->isAllOnesValue())
3652 return getSCEV(U->getOperand(0));
3653 const APInt &A = CI->getValue();
3655 // Instcombine's ShrinkDemandedConstant may strip bits out of
3656 // constants, obscuring what would otherwise be a low-bits mask.
3657 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3658 // knew about to reconstruct a low-bits mask value.
3659 unsigned LZ = A.countLeadingZeros();
3660 unsigned BitWidth = A.getBitWidth();
3661 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3662 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD);
3664 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3666 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3668 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3669 IntegerType::get(getContext(), BitWidth - LZ)),
3674 case Instruction::Or:
3675 // If the RHS of the Or is a constant, we may have something like:
3676 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3677 // optimizations will transparently handle this case.
3679 // In order for this transformation to be safe, the LHS must be of the
3680 // form X*(2^n) and the Or constant must be less than 2^n.
3681 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3682 const SCEV *LHS = getSCEV(U->getOperand(0));
3683 const APInt &CIVal = CI->getValue();
3684 if (GetMinTrailingZeros(LHS) >=
3685 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3686 // Build a plain add SCEV.
3687 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3688 // If the LHS of the add was an addrec and it has no-wrap flags,
3689 // transfer the no-wrap flags, since an or won't introduce a wrap.
3690 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3691 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3692 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3693 OldAR->getNoWrapFlags());
3699 case Instruction::Xor:
3700 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3701 // If the RHS of the xor is a signbit, then this is just an add.
3702 // Instcombine turns add of signbit into xor as a strength reduction step.
3703 if (CI->getValue().isSignBit())
3704 return getAddExpr(getSCEV(U->getOperand(0)),
3705 getSCEV(U->getOperand(1)));
3707 // If the RHS of xor is -1, then this is a not operation.
3708 if (CI->isAllOnesValue())
3709 return getNotSCEV(getSCEV(U->getOperand(0)));
3711 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3712 // This is a variant of the check for xor with -1, and it handles
3713 // the case where instcombine has trimmed non-demanded bits out
3714 // of an xor with -1.
3715 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3716 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3717 if (BO->getOpcode() == Instruction::And &&
3718 LCI->getValue() == CI->getValue())
3719 if (const SCEVZeroExtendExpr *Z =
3720 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3721 Type *UTy = U->getType();
3722 const SCEV *Z0 = Z->getOperand();
3723 Type *Z0Ty = Z0->getType();
3724 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3726 // If C is a low-bits mask, the zero extend is serving to
3727 // mask off the high bits. Complement the operand and
3728 // re-apply the zext.
3729 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3730 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3732 // If C is a single bit, it may be in the sign-bit position
3733 // before the zero-extend. In this case, represent the xor
3734 // using an add, which is equivalent, and re-apply the zext.
3735 APInt Trunc = CI->getValue().trunc(Z0TySize);
3736 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3738 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3744 case Instruction::Shl:
3745 // Turn shift left of a constant amount into a multiply.
3746 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3747 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3749 // If the shift count is not less than the bitwidth, the result of
3750 // the shift is undefined. Don't try to analyze it, because the
3751 // resolution chosen here may differ from the resolution chosen in
3752 // other parts of the compiler.
3753 if (SA->getValue().uge(BitWidth))
3756 Constant *X = ConstantInt::get(getContext(),
3757 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3758 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3762 case Instruction::LShr:
3763 // Turn logical shift right of a constant into a unsigned divide.
3764 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3765 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3767 // If the shift count is not less than the bitwidth, the result of
3768 // the shift is undefined. Don't try to analyze it, because the
3769 // resolution chosen here may differ from the resolution chosen in
3770 // other parts of the compiler.
3771 if (SA->getValue().uge(BitWidth))
3774 Constant *X = ConstantInt::get(getContext(),
3775 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3776 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3780 case Instruction::AShr:
3781 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3782 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3783 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3784 if (L->getOpcode() == Instruction::Shl &&
3785 L->getOperand(1) == U->getOperand(1)) {
3786 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3788 // If the shift count is not less than the bitwidth, the result of
3789 // the shift is undefined. Don't try to analyze it, because the
3790 // resolution chosen here may differ from the resolution chosen in
3791 // other parts of the compiler.
3792 if (CI->getValue().uge(BitWidth))
3795 uint64_t Amt = BitWidth - CI->getZExtValue();
3796 if (Amt == BitWidth)
3797 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3799 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3800 IntegerType::get(getContext(),
3806 case Instruction::Trunc:
3807 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3809 case Instruction::ZExt:
3810 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3812 case Instruction::SExt:
3813 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3815 case Instruction::BitCast:
3816 // BitCasts are no-op casts so we just eliminate the cast.
3817 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3818 return getSCEV(U->getOperand(0));
3821 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3822 // lead to pointer expressions which cannot safely be expanded to GEPs,
3823 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3824 // simplifying integer expressions.
3826 case Instruction::GetElementPtr:
3827 return createNodeForGEP(cast<GEPOperator>(U));
3829 case Instruction::PHI:
3830 return createNodeForPHI(cast<PHINode>(U));
3832 case Instruction::Select:
3833 // This could be a smax or umax that was lowered earlier.
3834 // Try to recover it.
3835 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3836 Value *LHS = ICI->getOperand(0);
3837 Value *RHS = ICI->getOperand(1);
3838 switch (ICI->getPredicate()) {
3839 case ICmpInst::ICMP_SLT:
3840 case ICmpInst::ICMP_SLE:
3841 std::swap(LHS, RHS);
3843 case ICmpInst::ICMP_SGT:
3844 case ICmpInst::ICMP_SGE:
3845 // a >s b ? a+x : b+x -> smax(a, b)+x
3846 // a >s b ? b+x : a+x -> smin(a, b)+x
3847 if (LHS->getType() == U->getType()) {
3848 const SCEV *LS = getSCEV(LHS);
3849 const SCEV *RS = getSCEV(RHS);
3850 const SCEV *LA = getSCEV(U->getOperand(1));
3851 const SCEV *RA = getSCEV(U->getOperand(2));
3852 const SCEV *LDiff = getMinusSCEV(LA, LS);
3853 const SCEV *RDiff = getMinusSCEV(RA, RS);
3855 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3856 LDiff = getMinusSCEV(LA, RS);
3857 RDiff = getMinusSCEV(RA, LS);
3859 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3862 case ICmpInst::ICMP_ULT:
3863 case ICmpInst::ICMP_ULE:
3864 std::swap(LHS, RHS);
3866 case ICmpInst::ICMP_UGT:
3867 case ICmpInst::ICMP_UGE:
3868 // a >u b ? a+x : b+x -> umax(a, b)+x
3869 // a >u b ? b+x : a+x -> umin(a, b)+x
3870 if (LHS->getType() == U->getType()) {
3871 const SCEV *LS = getSCEV(LHS);
3872 const SCEV *RS = getSCEV(RHS);
3873 const SCEV *LA = getSCEV(U->getOperand(1));
3874 const SCEV *RA = getSCEV(U->getOperand(2));
3875 const SCEV *LDiff = getMinusSCEV(LA, LS);
3876 const SCEV *RDiff = getMinusSCEV(RA, RS);
3878 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3879 LDiff = getMinusSCEV(LA, RS);
3880 RDiff = getMinusSCEV(RA, LS);
3882 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3885 case ICmpInst::ICMP_NE:
3886 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3887 if (LHS->getType() == U->getType() &&
3888 isa<ConstantInt>(RHS) &&
3889 cast<ConstantInt>(RHS)->isZero()) {
3890 const SCEV *One = getConstant(LHS->getType(), 1);
3891 const SCEV *LS = getSCEV(LHS);
3892 const SCEV *LA = getSCEV(U->getOperand(1));
3893 const SCEV *RA = getSCEV(U->getOperand(2));
3894 const SCEV *LDiff = getMinusSCEV(LA, LS);
3895 const SCEV *RDiff = getMinusSCEV(RA, One);
3897 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3900 case ICmpInst::ICMP_EQ:
3901 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3902 if (LHS->getType() == U->getType() &&
3903 isa<ConstantInt>(RHS) &&
3904 cast<ConstantInt>(RHS)->isZero()) {
3905 const SCEV *One = getConstant(LHS->getType(), 1);
3906 const SCEV *LS = getSCEV(LHS);
3907 const SCEV *LA = getSCEV(U->getOperand(1));
3908 const SCEV *RA = getSCEV(U->getOperand(2));
3909 const SCEV *LDiff = getMinusSCEV(LA, One);
3910 const SCEV *RDiff = getMinusSCEV(RA, LS);
3912 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3920 default: // We cannot analyze this expression.
3924 return getUnknown(V);
3929 //===----------------------------------------------------------------------===//
3930 // Iteration Count Computation Code
3933 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3934 /// normal unsigned value. Returns 0 if the trip count is unknown or not
3935 /// constant. Will also return 0 if the maximum trip count is very large (>=
3938 /// This "trip count" assumes that control exits via ExitingBlock. More
3939 /// precisely, it is the number of times that control may reach ExitingBlock
3940 /// before taking the branch. For loops with multiple exits, it may not be the
3941 /// number times that the loop header executes because the loop may exit
3942 /// prematurely via another branch.
3943 unsigned ScalarEvolution::
3944 getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock) {
3945 const SCEVConstant *ExitCount =
3946 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
3950 ConstantInt *ExitConst = ExitCount->getValue();
3952 // Guard against huge trip counts.
3953 if (ExitConst->getValue().getActiveBits() > 32)
3956 // In case of integer overflow, this returns 0, which is correct.
3957 return ((unsigned)ExitConst->getZExtValue()) + 1;
3960 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3961 /// trip count of this loop as a normal unsigned value, if possible. This
3962 /// means that the actual trip count is always a multiple of the returned
3963 /// value (don't forget the trip count could very well be zero as well!).
3965 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3966 /// multiple of a constant (which is also the case if the trip count is simply
3967 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3968 /// if the trip count is very large (>= 2^32).
3970 /// As explained in the comments for getSmallConstantTripCount, this assumes
3971 /// that control exits the loop via ExitingBlock.
3972 unsigned ScalarEvolution::
3973 getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock) {
3974 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
3975 if (ExitCount == getCouldNotCompute())
3978 // Get the trip count from the BE count by adding 1.
3979 const SCEV *TCMul = getAddExpr(ExitCount,
3980 getConstant(ExitCount->getType(), 1));
3981 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
3982 // to factor simple cases.
3983 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
3984 TCMul = Mul->getOperand(0);
3986 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
3990 ConstantInt *Result = MulC->getValue();
3992 // Guard against huge trip counts.
3993 if (!Result || Result->getValue().getActiveBits() > 32)
3996 return (unsigned)Result->getZExtValue();
3999 // getExitCount - Get the expression for the number of loop iterations for which
4000 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return
4001 // SCEVCouldNotCompute.
4002 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4003 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4006 /// getBackedgeTakenCount - If the specified loop has a predictable
4007 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4008 /// object. The backedge-taken count is the number of times the loop header
4009 /// will be branched to from within the loop. This is one less than the
4010 /// trip count of the loop, since it doesn't count the first iteration,
4011 /// when the header is branched to from outside the loop.
4013 /// Note that it is not valid to call this method on a loop without a
4014 /// loop-invariant backedge-taken count (see
4015 /// hasLoopInvariantBackedgeTakenCount).
4017 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4018 return getBackedgeTakenInfo(L).getExact(this);
4021 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4022 /// return the least SCEV value that is known never to be less than the
4023 /// actual backedge taken count.
4024 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4025 return getBackedgeTakenInfo(L).getMax(this);
4028 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4029 /// onto the given Worklist.
4031 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4032 BasicBlock *Header = L->getHeader();
4034 // Push all Loop-header PHIs onto the Worklist stack.
4035 for (BasicBlock::iterator I = Header->begin();
4036 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4037 Worklist.push_back(PN);
4040 const ScalarEvolution::BackedgeTakenInfo &
4041 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4042 // Initially insert an invalid entry for this loop. If the insertion
4043 // succeeds, proceed to actually compute a backedge-taken count and
4044 // update the value. The temporary CouldNotCompute value tells SCEV
4045 // code elsewhere that it shouldn't attempt to request a new
4046 // backedge-taken count, which could result in infinite recursion.
4047 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4048 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4050 return Pair.first->second;
4052 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4053 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4054 // must be cleared in this scope.
4055 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4057 if (Result.getExact(this) != getCouldNotCompute()) {
4058 assert(isLoopInvariant(Result.getExact(this), L) &&
4059 isLoopInvariant(Result.getMax(this), L) &&
4060 "Computed backedge-taken count isn't loop invariant for loop!");
4061 ++NumTripCountsComputed;
4063 else if (Result.getMax(this) == getCouldNotCompute() &&
4064 isa<PHINode>(L->getHeader()->begin())) {
4065 // Only count loops that have phi nodes as not being computable.
4066 ++NumTripCountsNotComputed;
4069 // Now that we know more about the trip count for this loop, forget any
4070 // existing SCEV values for PHI nodes in this loop since they are only
4071 // conservative estimates made without the benefit of trip count
4072 // information. This is similar to the code in forgetLoop, except that
4073 // it handles SCEVUnknown PHI nodes specially.
4074 if (Result.hasAnyInfo()) {
4075 SmallVector<Instruction *, 16> Worklist;
4076 PushLoopPHIs(L, Worklist);
4078 SmallPtrSet<Instruction *, 8> Visited;
4079 while (!Worklist.empty()) {
4080 Instruction *I = Worklist.pop_back_val();
4081 if (!Visited.insert(I)) continue;
4083 ValueExprMapType::iterator It =
4084 ValueExprMap.find(static_cast<Value *>(I));
4085 if (It != ValueExprMap.end()) {
4086 const SCEV *Old = It->second;
4088 // SCEVUnknown for a PHI either means that it has an unrecognized
4089 // structure, or it's a PHI that's in the progress of being computed
4090 // by createNodeForPHI. In the former case, additional loop trip
4091 // count information isn't going to change anything. In the later
4092 // case, createNodeForPHI will perform the necessary updates on its
4093 // own when it gets to that point.
4094 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4095 forgetMemoizedResults(Old);
4096 ValueExprMap.erase(It);
4098 if (PHINode *PN = dyn_cast<PHINode>(I))
4099 ConstantEvolutionLoopExitValue.erase(PN);
4102 PushDefUseChildren(I, Worklist);
4106 // Re-lookup the insert position, since the call to
4107 // ComputeBackedgeTakenCount above could result in a
4108 // recusive call to getBackedgeTakenInfo (on a different
4109 // loop), which would invalidate the iterator computed
4111 return BackedgeTakenCounts.find(L)->second = Result;
4114 /// forgetLoop - This method should be called by the client when it has
4115 /// changed a loop in a way that may effect ScalarEvolution's ability to
4116 /// compute a trip count, or if the loop is deleted.
4117 void ScalarEvolution::forgetLoop(const Loop *L) {
4118 // Drop any stored trip count value.
4119 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4120 BackedgeTakenCounts.find(L);
4121 if (BTCPos != BackedgeTakenCounts.end()) {
4122 BTCPos->second.clear();
4123 BackedgeTakenCounts.erase(BTCPos);
4126 // Drop information about expressions based on loop-header PHIs.
4127 SmallVector<Instruction *, 16> Worklist;
4128 PushLoopPHIs(L, Worklist);
4130 SmallPtrSet<Instruction *, 8> Visited;
4131 while (!Worklist.empty()) {
4132 Instruction *I = Worklist.pop_back_val();
4133 if (!Visited.insert(I)) continue;
4135 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4136 if (It != ValueExprMap.end()) {
4137 forgetMemoizedResults(It->second);
4138 ValueExprMap.erase(It);
4139 if (PHINode *PN = dyn_cast<PHINode>(I))
4140 ConstantEvolutionLoopExitValue.erase(PN);
4143 PushDefUseChildren(I, Worklist);
4146 // Forget all contained loops too, to avoid dangling entries in the
4147 // ValuesAtScopes map.
4148 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4152 /// forgetValue - This method should be called by the client when it has
4153 /// changed a value in a way that may effect its value, or which may
4154 /// disconnect it from a def-use chain linking it to a loop.
4155 void ScalarEvolution::forgetValue(Value *V) {
4156 Instruction *I = dyn_cast<Instruction>(V);
4159 // Drop information about expressions based on loop-header PHIs.
4160 SmallVector<Instruction *, 16> Worklist;
4161 Worklist.push_back(I);
4163 SmallPtrSet<Instruction *, 8> Visited;
4164 while (!Worklist.empty()) {
4165 I = Worklist.pop_back_val();
4166 if (!Visited.insert(I)) continue;
4168 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4169 if (It != ValueExprMap.end()) {
4170 forgetMemoizedResults(It->second);
4171 ValueExprMap.erase(It);
4172 if (PHINode *PN = dyn_cast<PHINode>(I))
4173 ConstantEvolutionLoopExitValue.erase(PN);
4176 PushDefUseChildren(I, Worklist);
4180 /// getExact - Get the exact loop backedge taken count considering all loop
4181 /// exits. A computable result can only be return for loops with a single exit.
4182 /// Returning the minimum taken count among all exits is incorrect because one
4183 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4184 /// the limit of each loop test is never skipped. This is a valid assumption as
4185 /// long as the loop exits via that test. For precise results, it is the
4186 /// caller's responsibility to specify the relevant loop exit using
4187 /// getExact(ExitingBlock, SE).
4189 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4190 // If any exits were not computable, the loop is not computable.
4191 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4193 // We need exactly one computable exit.
4194 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4195 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4197 const SCEV *BECount = 0;
4198 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4199 ENT != 0; ENT = ENT->getNextExit()) {
4201 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4204 BECount = ENT->ExactNotTaken;
4205 else if (BECount != ENT->ExactNotTaken)
4206 return SE->getCouldNotCompute();
4208 assert(BECount && "Invalid not taken count for loop exit");
4212 /// getExact - Get the exact not taken count for this loop exit.
4214 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4215 ScalarEvolution *SE) const {
4216 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4217 ENT != 0; ENT = ENT->getNextExit()) {
4219 if (ENT->ExitingBlock == ExitingBlock)
4220 return ENT->ExactNotTaken;
4222 return SE->getCouldNotCompute();
4225 /// getMax - Get the max backedge taken count for the loop.
4227 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4228 return Max ? Max : SE->getCouldNotCompute();
4231 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4232 /// computable exit into a persistent ExitNotTakenInfo array.
4233 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4234 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4235 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4238 ExitNotTaken.setIncomplete();
4240 unsigned NumExits = ExitCounts.size();
4241 if (NumExits == 0) return;
4243 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4244 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4245 if (NumExits == 1) return;
4247 // Handle the rare case of multiple computable exits.
4248 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4250 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4251 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4252 PrevENT->setNextExit(ENT);
4253 ENT->ExitingBlock = ExitCounts[i].first;
4254 ENT->ExactNotTaken = ExitCounts[i].second;
4258 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4259 void ScalarEvolution::BackedgeTakenInfo::clear() {
4260 ExitNotTaken.ExitingBlock = 0;
4261 ExitNotTaken.ExactNotTaken = 0;
4262 delete[] ExitNotTaken.getNextExit();
4265 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4266 /// of the specified loop will execute.
4267 ScalarEvolution::BackedgeTakenInfo
4268 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4269 SmallVector<BasicBlock *, 8> ExitingBlocks;
4270 L->getExitingBlocks(ExitingBlocks);
4272 // Examine all exits and pick the most conservative values.
4273 const SCEV *MaxBECount = getCouldNotCompute();
4274 bool CouldComputeBECount = true;
4275 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4276 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4277 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4278 if (EL.Exact == getCouldNotCompute())
4279 // We couldn't compute an exact value for this exit, so
4280 // we won't be able to compute an exact value for the loop.
4281 CouldComputeBECount = false;
4283 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4285 if (MaxBECount == getCouldNotCompute())
4286 MaxBECount = EL.Max;
4287 else if (EL.Max != getCouldNotCompute()) {
4288 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4289 // skip some loop tests. Taking the max over the exits is sufficiently
4290 // conservative. TODO: We could do better taking into consideration
4291 // that (1) the loop has unit stride (2) the last loop test is
4292 // less-than/greater-than (3) any loop test is less-than/greater-than AND
4293 // falls-through some constant times less then the other tests.
4294 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4298 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4301 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4302 /// loop will execute if it exits via the specified block.
4303 ScalarEvolution::ExitLimit
4304 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4306 // Okay, we've chosen an exiting block. See what condition causes us to
4307 // exit at this block.
4309 // FIXME: we should be able to handle switch instructions (with a single exit)
4310 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4311 if (ExitBr == 0) return getCouldNotCompute();
4312 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4314 // At this point, we know we have a conditional branch that determines whether
4315 // the loop is exited. However, we don't know if the branch is executed each
4316 // time through the loop. If not, then the execution count of the branch will
4317 // not be equal to the trip count of the loop.
4319 // Currently we check for this by checking to see if the Exit branch goes to
4320 // the loop header. If so, we know it will always execute the same number of
4321 // times as the loop. We also handle the case where the exit block *is* the
4322 // loop header. This is common for un-rotated loops.
4324 // If both of those tests fail, walk up the unique predecessor chain to the
4325 // header, stopping if there is an edge that doesn't exit the loop. If the
4326 // header is reached, the execution count of the branch will be equal to the
4327 // trip count of the loop.
4329 // More extensive analysis could be done to handle more cases here.
4331 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4332 ExitBr->getSuccessor(1) != L->getHeader() &&
4333 ExitBr->getParent() != L->getHeader()) {
4334 // The simple checks failed, try climbing the unique predecessor chain
4335 // up to the header.
4337 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4338 BasicBlock *Pred = BB->getUniquePredecessor();
4340 return getCouldNotCompute();
4341 TerminatorInst *PredTerm = Pred->getTerminator();
4342 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4343 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4346 // If the predecessor has a successor that isn't BB and isn't
4347 // outside the loop, assume the worst.
4348 if (L->contains(PredSucc))
4349 return getCouldNotCompute();
4351 if (Pred == L->getHeader()) {
4358 return getCouldNotCompute();
4361 // Proceed to the next level to examine the exit condition expression.
4362 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4363 ExitBr->getSuccessor(0),
4364 ExitBr->getSuccessor(1));
4367 /// ComputeExitLimitFromCond - Compute the number of times the
4368 /// backedge of the specified loop will execute if its exit condition
4369 /// were a conditional branch of ExitCond, TBB, and FBB.
4370 ScalarEvolution::ExitLimit
4371 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4375 // Check if the controlling expression for this loop is an And or Or.
4376 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4377 if (BO->getOpcode() == Instruction::And) {
4378 // Recurse on the operands of the and.
4379 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4380 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4381 const SCEV *BECount = getCouldNotCompute();
4382 const SCEV *MaxBECount = getCouldNotCompute();
4383 if (L->contains(TBB)) {
4384 // Both conditions must be true for the loop to continue executing.
4385 // Choose the less conservative count.
4386 if (EL0.Exact == getCouldNotCompute() ||
4387 EL1.Exact == getCouldNotCompute())
4388 BECount = getCouldNotCompute();
4390 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4391 if (EL0.Max == getCouldNotCompute())
4392 MaxBECount = EL1.Max;
4393 else if (EL1.Max == getCouldNotCompute())
4394 MaxBECount = EL0.Max;
4396 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4398 // Both conditions must be true at the same time for the loop to exit.
4399 // For now, be conservative.
4400 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4401 if (EL0.Max == EL1.Max)
4402 MaxBECount = EL0.Max;
4403 if (EL0.Exact == EL1.Exact)
4404 BECount = EL0.Exact;
4407 return ExitLimit(BECount, MaxBECount);
4409 if (BO->getOpcode() == Instruction::Or) {
4410 // Recurse on the operands of the or.
4411 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4412 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4413 const SCEV *BECount = getCouldNotCompute();
4414 const SCEV *MaxBECount = getCouldNotCompute();
4415 if (L->contains(FBB)) {
4416 // Both conditions must be false for the loop to continue executing.
4417 // Choose the less conservative count.
4418 if (EL0.Exact == getCouldNotCompute() ||
4419 EL1.Exact == getCouldNotCompute())
4420 BECount = getCouldNotCompute();
4422 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4423 if (EL0.Max == getCouldNotCompute())
4424 MaxBECount = EL1.Max;
4425 else if (EL1.Max == getCouldNotCompute())
4426 MaxBECount = EL0.Max;
4428 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4430 // Both conditions must be false at the same time for the loop to exit.
4431 // For now, be conservative.
4432 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4433 if (EL0.Max == EL1.Max)
4434 MaxBECount = EL0.Max;
4435 if (EL0.Exact == EL1.Exact)
4436 BECount = EL0.Exact;
4439 return ExitLimit(BECount, MaxBECount);
4443 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4444 // Proceed to the next level to examine the icmp.
4445 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4446 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB);
4448 // Check for a constant condition. These are normally stripped out by
4449 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4450 // preserve the CFG and is temporarily leaving constant conditions
4452 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4453 if (L->contains(FBB) == !CI->getZExtValue())
4454 // The backedge is always taken.
4455 return getCouldNotCompute();
4457 // The backedge is never taken.
4458 return getConstant(CI->getType(), 0);
4461 // If it's not an integer or pointer comparison then compute it the hard way.
4462 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4465 /// ComputeExitLimitFromICmp - Compute the number of times the
4466 /// backedge of the specified loop will execute if its exit condition
4467 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4468 ScalarEvolution::ExitLimit
4469 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4474 // If the condition was exit on true, convert the condition to exit on false
4475 ICmpInst::Predicate Cond;
4476 if (!L->contains(FBB))
4477 Cond = ExitCond->getPredicate();
4479 Cond = ExitCond->getInversePredicate();
4481 // Handle common loops like: for (X = "string"; *X; ++X)
4482 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4483 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4485 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4486 if (ItCnt.hasAnyInfo())
4490 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4491 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4493 // Try to evaluate any dependencies out of the loop.
4494 LHS = getSCEVAtScope(LHS, L);
4495 RHS = getSCEVAtScope(RHS, L);
4497 // At this point, we would like to compute how many iterations of the
4498 // loop the predicate will return true for these inputs.
4499 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4500 // If there is a loop-invariant, force it into the RHS.
4501 std::swap(LHS, RHS);
4502 Cond = ICmpInst::getSwappedPredicate(Cond);
4505 // Simplify the operands before analyzing them.
4506 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4508 // If we have a comparison of a chrec against a constant, try to use value
4509 // ranges to answer this query.
4510 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4511 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4512 if (AddRec->getLoop() == L) {
4513 // Form the constant range.
4514 ConstantRange CompRange(
4515 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4517 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4518 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4522 case ICmpInst::ICMP_NE: { // while (X != Y)
4523 // Convert to: while (X-Y != 0)
4524 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4525 if (EL.hasAnyInfo()) return EL;
4528 case ICmpInst::ICMP_EQ: { // while (X == Y)
4529 // Convert to: while (X-Y == 0)
4530 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4531 if (EL.hasAnyInfo()) return EL;
4534 case ICmpInst::ICMP_SLT: {
4535 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true);
4536 if (EL.hasAnyInfo()) return EL;
4539 case ICmpInst::ICMP_SGT: {
4540 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4541 getNotSCEV(RHS), L, true);
4542 if (EL.hasAnyInfo()) return EL;
4545 case ICmpInst::ICMP_ULT: {
4546 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false);
4547 if (EL.hasAnyInfo()) return EL;
4550 case ICmpInst::ICMP_UGT: {
4551 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4552 getNotSCEV(RHS), L, false);
4553 if (EL.hasAnyInfo()) return EL;
4558 dbgs() << "ComputeBackedgeTakenCount ";
4559 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4560 dbgs() << "[unsigned] ";
4561 dbgs() << *LHS << " "
4562 << Instruction::getOpcodeName(Instruction::ICmp)
4563 << " " << *RHS << "\n";
4567 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4570 static ConstantInt *
4571 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4572 ScalarEvolution &SE) {
4573 const SCEV *InVal = SE.getConstant(C);
4574 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4575 assert(isa<SCEVConstant>(Val) &&
4576 "Evaluation of SCEV at constant didn't fold correctly?");
4577 return cast<SCEVConstant>(Val)->getValue();
4580 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4581 /// 'icmp op load X, cst', try to see if we can compute the backedge
4582 /// execution count.
4583 ScalarEvolution::ExitLimit
4584 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4588 ICmpInst::Predicate predicate) {
4590 if (LI->isVolatile()) return getCouldNotCompute();
4592 // Check to see if the loaded pointer is a getelementptr of a global.
4593 // TODO: Use SCEV instead of manually grubbing with GEPs.
4594 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4595 if (!GEP) return getCouldNotCompute();
4597 // Make sure that it is really a constant global we are gepping, with an
4598 // initializer, and make sure the first IDX is really 0.
4599 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4600 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4601 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4602 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4603 return getCouldNotCompute();
4605 // Okay, we allow one non-constant index into the GEP instruction.
4607 std::vector<Constant*> Indexes;
4608 unsigned VarIdxNum = 0;
4609 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4610 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4611 Indexes.push_back(CI);
4612 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4613 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4614 VarIdx = GEP->getOperand(i);
4616 Indexes.push_back(0);
4619 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4621 return getCouldNotCompute();
4623 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4624 // Check to see if X is a loop variant variable value now.
4625 const SCEV *Idx = getSCEV(VarIdx);
4626 Idx = getSCEVAtScope(Idx, L);
4628 // We can only recognize very limited forms of loop index expressions, in
4629 // particular, only affine AddRec's like {C1,+,C2}.
4630 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4631 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4632 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4633 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4634 return getCouldNotCompute();
4636 unsigned MaxSteps = MaxBruteForceIterations;
4637 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4638 ConstantInt *ItCst = ConstantInt::get(
4639 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4640 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4642 // Form the GEP offset.
4643 Indexes[VarIdxNum] = Val;
4645 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4647 if (Result == 0) break; // Cannot compute!
4649 // Evaluate the condition for this iteration.
4650 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4651 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4652 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4654 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4655 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4658 ++NumArrayLenItCounts;
4659 return getConstant(ItCst); // Found terminating iteration!
4662 return getCouldNotCompute();
4666 /// CanConstantFold - Return true if we can constant fold an instruction of the
4667 /// specified type, assuming that all operands were constants.
4668 static bool CanConstantFold(const Instruction *I) {
4669 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4670 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4674 if (const CallInst *CI = dyn_cast<CallInst>(I))
4675 if (const Function *F = CI->getCalledFunction())
4676 return canConstantFoldCallTo(F);
4680 /// Determine whether this instruction can constant evolve within this loop
4681 /// assuming its operands can all constant evolve.
4682 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4683 // An instruction outside of the loop can't be derived from a loop PHI.
4684 if (!L->contains(I)) return false;
4686 if (isa<PHINode>(I)) {
4687 if (L->getHeader() == I->getParent())
4690 // We don't currently keep track of the control flow needed to evaluate
4691 // PHIs, so we cannot handle PHIs inside of loops.
4695 // If we won't be able to constant fold this expression even if the operands
4696 // are constants, bail early.
4697 return CanConstantFold(I);
4700 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4701 /// recursing through each instruction operand until reaching a loop header phi.
4703 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4704 DenseMap<Instruction *, PHINode *> &PHIMap) {
4706 // Otherwise, we can evaluate this instruction if all of its operands are
4707 // constant or derived from a PHI node themselves.
4709 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4710 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4712 if (isa<Constant>(*OpI)) continue;
4714 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4715 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4717 PHINode *P = dyn_cast<PHINode>(OpInst);
4719 // If this operand is already visited, reuse the prior result.
4720 // We may have P != PHI if this is the deepest point at which the
4721 // inconsistent paths meet.
4722 P = PHIMap.lookup(OpInst);
4724 // Recurse and memoize the results, whether a phi is found or not.
4725 // This recursive call invalidates pointers into PHIMap.
4726 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4729 if (P == 0) return 0; // Not evolving from PHI
4730 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4733 // This is a expression evolving from a constant PHI!
4737 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4738 /// in the loop that V is derived from. We allow arbitrary operations along the
4739 /// way, but the operands of an operation must either be constants or a value
4740 /// derived from a constant PHI. If this expression does not fit with these
4741 /// constraints, return null.
4742 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4743 Instruction *I = dyn_cast<Instruction>(V);
4744 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4746 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4750 // Record non-constant instructions contained by the loop.
4751 DenseMap<Instruction *, PHINode *> PHIMap;
4752 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4755 /// EvaluateExpression - Given an expression that passes the
4756 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4757 /// in the loop has the value PHIVal. If we can't fold this expression for some
4758 /// reason, return null.
4759 static Constant *EvaluateExpression(Value *V, const Loop *L,
4760 DenseMap<Instruction *, Constant *> &Vals,
4761 const TargetData *TD,
4762 const TargetLibraryInfo *TLI) {
4763 // Convenient constant check, but redundant for recursive calls.
4764 if (Constant *C = dyn_cast<Constant>(V)) return C;
4765 Instruction *I = dyn_cast<Instruction>(V);
4768 if (Constant *C = Vals.lookup(I)) return C;
4770 // An instruction inside the loop depends on a value outside the loop that we
4771 // weren't given a mapping for, or a value such as a call inside the loop.
4772 if (!canConstantEvolve(I, L)) return 0;
4774 // An unmapped PHI can be due to a branch or another loop inside this loop,
4775 // or due to this not being the initial iteration through a loop where we
4776 // couldn't compute the evolution of this particular PHI last time.
4777 if (isa<PHINode>(I)) return 0;
4779 std::vector<Constant*> Operands(I->getNumOperands());
4781 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4782 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4784 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4785 if (!Operands[i]) return 0;
4788 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
4794 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4795 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4796 Operands[1], TD, TLI);
4797 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4798 if (!LI->isVolatile())
4799 return ConstantFoldLoadFromConstPtr(Operands[0], TD);
4801 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
4805 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4806 /// in the header of its containing loop, we know the loop executes a
4807 /// constant number of times, and the PHI node is just a recurrence
4808 /// involving constants, fold it.
4810 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4813 DenseMap<PHINode*, Constant*>::const_iterator I =
4814 ConstantEvolutionLoopExitValue.find(PN);
4815 if (I != ConstantEvolutionLoopExitValue.end())
4818 if (BEs.ugt(MaxBruteForceIterations))
4819 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4821 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4823 DenseMap<Instruction *, Constant *> CurrentIterVals;
4824 BasicBlock *Header = L->getHeader();
4825 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4827 // Since the loop is canonicalized, the PHI node must have two entries. One
4828 // entry must be a constant (coming in from outside of the loop), and the
4829 // second must be derived from the same PHI.
4830 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4832 for (BasicBlock::iterator I = Header->begin();
4833 (PHI = dyn_cast<PHINode>(I)); ++I) {
4834 Constant *StartCST =
4835 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4836 if (StartCST == 0) continue;
4837 CurrentIterVals[PHI] = StartCST;
4839 if (!CurrentIterVals.count(PN))
4842 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4844 // Execute the loop symbolically to determine the exit value.
4845 if (BEs.getActiveBits() >= 32)
4846 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4848 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4849 unsigned IterationNum = 0;
4850 for (; ; ++IterationNum) {
4851 if (IterationNum == NumIterations)
4852 return RetVal = CurrentIterVals[PN]; // Got exit value!
4854 // Compute the value of the PHIs for the next iteration.
4855 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
4856 DenseMap<Instruction *, Constant *> NextIterVals;
4857 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
4860 return 0; // Couldn't evaluate!
4861 NextIterVals[PN] = NextPHI;
4863 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
4865 // Also evaluate the other PHI nodes. However, we don't get to stop if we
4866 // cease to be able to evaluate one of them or if they stop evolving,
4867 // because that doesn't necessarily prevent us from computing PN.
4868 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
4869 for (DenseMap<Instruction *, Constant *>::const_iterator
4870 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4871 PHINode *PHI = dyn_cast<PHINode>(I->first);
4872 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
4873 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
4875 // We use two distinct loops because EvaluateExpression may invalidate any
4876 // iterators into CurrentIterVals.
4877 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
4878 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
4879 PHINode *PHI = I->first;
4880 Constant *&NextPHI = NextIterVals[PHI];
4881 if (!NextPHI) { // Not already computed.
4882 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4883 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4885 if (NextPHI != I->second)
4886 StoppedEvolving = false;
4889 // If all entries in CurrentIterVals == NextIterVals then we can stop
4890 // iterating, the loop can't continue to change.
4891 if (StoppedEvolving)
4892 return RetVal = CurrentIterVals[PN];
4894 CurrentIterVals.swap(NextIterVals);
4898 /// ComputeExitCountExhaustively - If the loop is known to execute a
4899 /// constant number of times (the condition evolves only from constants),
4900 /// try to evaluate a few iterations of the loop until we get the exit
4901 /// condition gets a value of ExitWhen (true or false). If we cannot
4902 /// evaluate the trip count of the loop, return getCouldNotCompute().
4903 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4906 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4907 if (PN == 0) return getCouldNotCompute();
4909 // If the loop is canonicalized, the PHI will have exactly two entries.
4910 // That's the only form we support here.
4911 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4913 DenseMap<Instruction *, Constant *> CurrentIterVals;
4914 BasicBlock *Header = L->getHeader();
4915 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4917 // One entry must be a constant (coming in from outside of the loop), and the
4918 // second must be derived from the same PHI.
4919 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4921 for (BasicBlock::iterator I = Header->begin();
4922 (PHI = dyn_cast<PHINode>(I)); ++I) {
4923 Constant *StartCST =
4924 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4925 if (StartCST == 0) continue;
4926 CurrentIterVals[PHI] = StartCST;
4928 if (!CurrentIterVals.count(PN))
4929 return getCouldNotCompute();
4931 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4932 // the loop symbolically to determine when the condition gets a value of
4935 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4936 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
4937 ConstantInt *CondVal =
4938 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
4941 // Couldn't symbolically evaluate.
4942 if (!CondVal) return getCouldNotCompute();
4944 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4945 ++NumBruteForceTripCountsComputed;
4946 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4949 // Update all the PHI nodes for the next iteration.
4950 DenseMap<Instruction *, Constant *> NextIterVals;
4952 // Create a list of which PHIs we need to compute. We want to do this before
4953 // calling EvaluateExpression on them because that may invalidate iterators
4954 // into CurrentIterVals.
4955 SmallVector<PHINode *, 8> PHIsToCompute;
4956 for (DenseMap<Instruction *, Constant *>::const_iterator
4957 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4958 PHINode *PHI = dyn_cast<PHINode>(I->first);
4959 if (!PHI || PHI->getParent() != Header) continue;
4960 PHIsToCompute.push_back(PHI);
4962 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
4963 E = PHIsToCompute.end(); I != E; ++I) {
4965 Constant *&NextPHI = NextIterVals[PHI];
4966 if (NextPHI) continue; // Already computed!
4968 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4969 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4971 CurrentIterVals.swap(NextIterVals);
4974 // Too many iterations were needed to evaluate.
4975 return getCouldNotCompute();
4978 /// getSCEVAtScope - Return a SCEV expression for the specified value
4979 /// at the specified scope in the program. The L value specifies a loop
4980 /// nest to evaluate the expression at, where null is the top-level or a
4981 /// specified loop is immediately inside of the loop.
4983 /// This method can be used to compute the exit value for a variable defined
4984 /// in a loop by querying what the value will hold in the parent loop.
4986 /// In the case that a relevant loop exit value cannot be computed, the
4987 /// original value V is returned.
4988 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4989 // Check to see if we've folded this expression at this loop before.
4990 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4991 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4992 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4994 return Pair.first->second ? Pair.first->second : V;
4996 // Otherwise compute it.
4997 const SCEV *C = computeSCEVAtScope(V, L);
4998 ValuesAtScopes[V][L] = C;
5002 /// This builds up a Constant using the ConstantExpr interface. That way, we
5003 /// will return Constants for objects which aren't represented by a
5004 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5005 /// Returns NULL if the SCEV isn't representable as a Constant.
5006 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5007 switch (V->getSCEVType()) {
5008 default: // TODO: smax, umax.
5009 case scCouldNotCompute:
5013 return cast<SCEVConstant>(V)->getValue();
5015 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5016 case scSignExtend: {
5017 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5018 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5019 return ConstantExpr::getSExt(CastOp, SS->getType());
5022 case scZeroExtend: {
5023 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5024 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5025 return ConstantExpr::getZExt(CastOp, SZ->getType());
5029 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5030 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5031 return ConstantExpr::getTrunc(CastOp, ST->getType());
5035 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5036 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5037 if (C->getType()->isPointerTy())
5038 C = ConstantExpr::getBitCast(C, Type::getInt8PtrTy(C->getContext()));
5039 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5040 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5044 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5046 // The offsets have been converted to bytes. We can add bytes to an
5047 // i8* by GEP with the byte count in the first index.
5048 C = ConstantExpr::getBitCast(C,Type::getInt8PtrTy(C->getContext()));
5051 // Don't bother trying to sum two pointers. We probably can't
5052 // statically compute a load that results from it anyway.
5053 if (C2->getType()->isPointerTy())
5056 if (C->getType()->isPointerTy()) {
5057 if (cast<PointerType>(C->getType())->getElementType()->isStructTy())
5058 C2 = ConstantExpr::getIntegerCast(
5059 C2, Type::getInt32Ty(C->getContext()), true);
5060 C = ConstantExpr::getGetElementPtr(C, C2);
5062 C = ConstantExpr::getAdd(C, C2);
5069 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5070 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5071 // Don't bother with pointers at all.
5072 if (C->getType()->isPointerTy()) return 0;
5073 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5074 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5075 if (!C2 || C2->getType()->isPointerTy()) return 0;
5076 C = ConstantExpr::getMul(C, C2);
5083 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5084 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5085 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5086 if (LHS->getType() == RHS->getType())
5087 return ConstantExpr::getUDiv(LHS, RHS);
5094 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5095 if (isa<SCEVConstant>(V)) return V;
5097 // If this instruction is evolved from a constant-evolving PHI, compute the
5098 // exit value from the loop without using SCEVs.
5099 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5100 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5101 const Loop *LI = (*this->LI)[I->getParent()];
5102 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5103 if (PHINode *PN = dyn_cast<PHINode>(I))
5104 if (PN->getParent() == LI->getHeader()) {
5105 // Okay, there is no closed form solution for the PHI node. Check
5106 // to see if the loop that contains it has a known backedge-taken
5107 // count. If so, we may be able to force computation of the exit
5109 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5110 if (const SCEVConstant *BTCC =
5111 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5112 // Okay, we know how many times the containing loop executes. If
5113 // this is a constant evolving PHI node, get the final value at
5114 // the specified iteration number.
5115 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5116 BTCC->getValue()->getValue(),
5118 if (RV) return getSCEV(RV);
5122 // Okay, this is an expression that we cannot symbolically evaluate
5123 // into a SCEV. Check to see if it's possible to symbolically evaluate
5124 // the arguments into constants, and if so, try to constant propagate the
5125 // result. This is particularly useful for computing loop exit values.
5126 if (CanConstantFold(I)) {
5127 SmallVector<Constant *, 4> Operands;
5128 bool MadeImprovement = false;
5129 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5130 Value *Op = I->getOperand(i);
5131 if (Constant *C = dyn_cast<Constant>(Op)) {
5132 Operands.push_back(C);
5136 // If any of the operands is non-constant and if they are
5137 // non-integer and non-pointer, don't even try to analyze them
5138 // with scev techniques.
5139 if (!isSCEVable(Op->getType()))
5142 const SCEV *OrigV = getSCEV(Op);
5143 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5144 MadeImprovement |= OrigV != OpV;
5146 Constant *C = BuildConstantFromSCEV(OpV);
5148 if (C->getType() != Op->getType())
5149 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5153 Operands.push_back(C);
5156 // Check to see if getSCEVAtScope actually made an improvement.
5157 if (MadeImprovement) {
5159 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5160 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5161 Operands[0], Operands[1], TD,
5163 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5164 if (!LI->isVolatile())
5165 C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
5167 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5175 // This is some other type of SCEVUnknown, just return it.
5179 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5180 // Avoid performing the look-up in the common case where the specified
5181 // expression has no loop-variant portions.
5182 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5183 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5184 if (OpAtScope != Comm->getOperand(i)) {
5185 // Okay, at least one of these operands is loop variant but might be
5186 // foldable. Build a new instance of the folded commutative expression.
5187 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5188 Comm->op_begin()+i);
5189 NewOps.push_back(OpAtScope);
5191 for (++i; i != e; ++i) {
5192 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5193 NewOps.push_back(OpAtScope);
5195 if (isa<SCEVAddExpr>(Comm))
5196 return getAddExpr(NewOps);
5197 if (isa<SCEVMulExpr>(Comm))
5198 return getMulExpr(NewOps);
5199 if (isa<SCEVSMaxExpr>(Comm))
5200 return getSMaxExpr(NewOps);
5201 if (isa<SCEVUMaxExpr>(Comm))
5202 return getUMaxExpr(NewOps);
5203 llvm_unreachable("Unknown commutative SCEV type!");
5206 // If we got here, all operands are loop invariant.
5210 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5211 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5212 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5213 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5214 return Div; // must be loop invariant
5215 return getUDivExpr(LHS, RHS);
5218 // If this is a loop recurrence for a loop that does not contain L, then we
5219 // are dealing with the final value computed by the loop.
5220 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5221 // First, attempt to evaluate each operand.
5222 // Avoid performing the look-up in the common case where the specified
5223 // expression has no loop-variant portions.
5224 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5225 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5226 if (OpAtScope == AddRec->getOperand(i))
5229 // Okay, at least one of these operands is loop variant but might be
5230 // foldable. Build a new instance of the folded commutative expression.
5231 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5232 AddRec->op_begin()+i);
5233 NewOps.push_back(OpAtScope);
5234 for (++i; i != e; ++i)
5235 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5237 const SCEV *FoldedRec =
5238 getAddRecExpr(NewOps, AddRec->getLoop(),
5239 AddRec->getNoWrapFlags(SCEV::FlagNW));
5240 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5241 // The addrec may be folded to a nonrecurrence, for example, if the
5242 // induction variable is multiplied by zero after constant folding. Go
5243 // ahead and return the folded value.
5249 // If the scope is outside the addrec's loop, evaluate it by using the
5250 // loop exit value of the addrec.
5251 if (!AddRec->getLoop()->contains(L)) {
5252 // To evaluate this recurrence, we need to know how many times the AddRec
5253 // loop iterates. Compute this now.
5254 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5255 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5257 // Then, evaluate the AddRec.
5258 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5264 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5265 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5266 if (Op == Cast->getOperand())
5267 return Cast; // must be loop invariant
5268 return getZeroExtendExpr(Op, Cast->getType());
5271 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5272 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5273 if (Op == Cast->getOperand())
5274 return Cast; // must be loop invariant
5275 return getSignExtendExpr(Op, Cast->getType());
5278 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5279 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5280 if (Op == Cast->getOperand())
5281 return Cast; // must be loop invariant
5282 return getTruncateExpr(Op, Cast->getType());
5285 llvm_unreachable("Unknown SCEV type!");
5288 /// getSCEVAtScope - This is a convenience function which does
5289 /// getSCEVAtScope(getSCEV(V), L).
5290 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5291 return getSCEVAtScope(getSCEV(V), L);
5294 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5295 /// following equation:
5297 /// A * X = B (mod N)
5299 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5300 /// A and B isn't important.
5302 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5303 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5304 ScalarEvolution &SE) {
5305 uint32_t BW = A.getBitWidth();
5306 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5307 assert(A != 0 && "A must be non-zero.");
5311 // The gcd of A and N may have only one prime factor: 2. The number of
5312 // trailing zeros in A is its multiplicity
5313 uint32_t Mult2 = A.countTrailingZeros();
5316 // 2. Check if B is divisible by D.
5318 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5319 // is not less than multiplicity of this prime factor for D.
5320 if (B.countTrailingZeros() < Mult2)
5321 return SE.getCouldNotCompute();
5323 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5326 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5327 // bit width during computations.
5328 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5329 APInt Mod(BW + 1, 0);
5330 Mod.setBit(BW - Mult2); // Mod = N / D
5331 APInt I = AD.multiplicativeInverse(Mod);
5333 // 4. Compute the minimum unsigned root of the equation:
5334 // I * (B / D) mod (N / D)
5335 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5337 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5339 return SE.getConstant(Result.trunc(BW));
5342 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5343 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5344 /// might be the same) or two SCEVCouldNotCompute objects.
5346 static std::pair<const SCEV *,const SCEV *>
5347 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5348 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5349 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5350 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5351 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5353 // We currently can only solve this if the coefficients are constants.
5354 if (!LC || !MC || !NC) {
5355 const SCEV *CNC = SE.getCouldNotCompute();
5356 return std::make_pair(CNC, CNC);
5359 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5360 const APInt &L = LC->getValue()->getValue();
5361 const APInt &M = MC->getValue()->getValue();
5362 const APInt &N = NC->getValue()->getValue();
5363 APInt Two(BitWidth, 2);
5364 APInt Four(BitWidth, 4);
5367 using namespace APIntOps;
5369 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5370 // The B coefficient is M-N/2
5374 // The A coefficient is N/2
5375 APInt A(N.sdiv(Two));
5377 // Compute the B^2-4ac term.
5380 SqrtTerm -= Four * (A * C);
5382 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5383 // integer value or else APInt::sqrt() will assert.
5384 APInt SqrtVal(SqrtTerm.sqrt());
5386 // Compute the two solutions for the quadratic formula.
5387 // The divisions must be performed as signed divisions.
5390 if (TwoA.isMinValue()) {
5391 const SCEV *CNC = SE.getCouldNotCompute();
5392 return std::make_pair(CNC, CNC);
5395 LLVMContext &Context = SE.getContext();
5397 ConstantInt *Solution1 =
5398 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5399 ConstantInt *Solution2 =
5400 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5402 return std::make_pair(SE.getConstant(Solution1),
5403 SE.getConstant(Solution2));
5404 } // end APIntOps namespace
5407 /// HowFarToZero - Return the number of times a backedge comparing the specified
5408 /// value to zero will execute. If not computable, return CouldNotCompute.
5410 /// This is only used for loops with a "x != y" exit test. The exit condition is
5411 /// now expressed as a single expression, V = x-y. So the exit test is
5412 /// effectively V != 0. We know and take advantage of the fact that this
5413 /// expression only being used in a comparison by zero context.
5414 ScalarEvolution::ExitLimit
5415 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
5416 // If the value is a constant
5417 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5418 // If the value is already zero, the branch will execute zero times.
5419 if (C->getValue()->isZero()) return C;
5420 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5423 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5424 if (!AddRec || AddRec->getLoop() != L)
5425 return getCouldNotCompute();
5427 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5428 // the quadratic equation to solve it.
5429 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5430 std::pair<const SCEV *,const SCEV *> Roots =
5431 SolveQuadraticEquation(AddRec, *this);
5432 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5433 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5436 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5437 << " sol#2: " << *R2 << "\n";
5439 // Pick the smallest positive root value.
5440 if (ConstantInt *CB =
5441 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5444 if (CB->getZExtValue() == false)
5445 std::swap(R1, R2); // R1 is the minimum root now.
5447 // We can only use this value if the chrec ends up with an exact zero
5448 // value at this index. When solving for "X*X != 5", for example, we
5449 // should not accept a root of 2.
5450 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5452 return R1; // We found a quadratic root!
5455 return getCouldNotCompute();
5458 // Otherwise we can only handle this if it is affine.
5459 if (!AddRec->isAffine())
5460 return getCouldNotCompute();
5462 // If this is an affine expression, the execution count of this branch is
5463 // the minimum unsigned root of the following equation:
5465 // Start + Step*N = 0 (mod 2^BW)
5469 // Step*N = -Start (mod 2^BW)
5471 // where BW is the common bit width of Start and Step.
5473 // Get the initial value for the loop.
5474 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5475 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5477 // For now we handle only constant steps.
5479 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5480 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5481 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5482 // We have not yet seen any such cases.
5483 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5485 return getCouldNotCompute();
5487 // For positive steps (counting up until unsigned overflow):
5488 // N = -Start/Step (as unsigned)
5489 // For negative steps (counting down to zero):
5491 // First compute the unsigned distance from zero in the direction of Step.
5492 bool CountDown = StepC->getValue()->getValue().isNegative();
5493 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5495 // Handle unitary steps, which cannot wraparound.
5496 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5497 // N = Distance (as unsigned)
5498 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5499 ConstantRange CR = getUnsignedRange(Start);
5500 const SCEV *MaxBECount;
5501 if (!CountDown && CR.getUnsignedMin().isMinValue())
5502 // When counting up, the worst starting value is 1, not 0.
5503 MaxBECount = CR.getUnsignedMax().isMinValue()
5504 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5505 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5507 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5508 : -CR.getUnsignedMin());
5509 return ExitLimit(Distance, MaxBECount);
5512 // If the recurrence is known not to wraparound, unsigned divide computes the
5513 // back edge count. We know that the value will either become zero (and thus
5514 // the loop terminates), that the loop will terminate through some other exit
5515 // condition first, or that the loop has undefined behavior. This means
5516 // we can't "miss" the exit value, even with nonunit stride.
5518 // FIXME: Prove that loops always exhibits *acceptable* undefined
5519 // behavior. Loops must exhibit defined behavior until a wrapped value is
5520 // actually used. So the trip count computed by udiv could be smaller than the
5521 // number of well-defined iterations.
5522 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5523 // FIXME: We really want an "isexact" bit for udiv.
5524 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5526 // Then, try to solve the above equation provided that Start is constant.
5527 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5528 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5529 -StartC->getValue()->getValue(),
5531 return getCouldNotCompute();
5534 /// HowFarToNonZero - Return the number of times a backedge checking the
5535 /// specified value for nonzero will execute. If not computable, return
5537 ScalarEvolution::ExitLimit
5538 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5539 // Loops that look like: while (X == 0) are very strange indeed. We don't
5540 // handle them yet except for the trivial case. This could be expanded in the
5541 // future as needed.
5543 // If the value is a constant, check to see if it is known to be non-zero
5544 // already. If so, the backedge will execute zero times.
5545 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5546 if (!C->getValue()->isNullValue())
5547 return getConstant(C->getType(), 0);
5548 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5551 // We could implement others, but I really doubt anyone writes loops like
5552 // this, and if they did, they would already be constant folded.
5553 return getCouldNotCompute();
5556 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5557 /// (which may not be an immediate predecessor) which has exactly one
5558 /// successor from which BB is reachable, or null if no such block is
5561 std::pair<BasicBlock *, BasicBlock *>
5562 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5563 // If the block has a unique predecessor, then there is no path from the
5564 // predecessor to the block that does not go through the direct edge
5565 // from the predecessor to the block.
5566 if (BasicBlock *Pred = BB->getSinglePredecessor())
5567 return std::make_pair(Pred, BB);
5569 // A loop's header is defined to be a block that dominates the loop.
5570 // If the header has a unique predecessor outside the loop, it must be
5571 // a block that has exactly one successor that can reach the loop.
5572 if (Loop *L = LI->getLoopFor(BB))
5573 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5575 return std::pair<BasicBlock *, BasicBlock *>();
5578 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5579 /// testing whether two expressions are equal, however for the purposes of
5580 /// looking for a condition guarding a loop, it can be useful to be a little
5581 /// more general, since a front-end may have replicated the controlling
5584 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5585 // Quick check to see if they are the same SCEV.
5586 if (A == B) return true;
5588 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5589 // two different instructions with the same value. Check for this case.
5590 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5591 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5592 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5593 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5594 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5597 // Otherwise assume they may have a different value.
5601 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5602 /// predicate Pred. Return true iff any changes were made.
5604 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5605 const SCEV *&LHS, const SCEV *&RHS) {
5606 bool Changed = false;
5608 // Canonicalize a constant to the right side.
5609 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5610 // Check for both operands constant.
5611 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5612 if (ConstantExpr::getICmp(Pred,
5614 RHSC->getValue())->isNullValue())
5615 goto trivially_false;
5617 goto trivially_true;
5619 // Otherwise swap the operands to put the constant on the right.
5620 std::swap(LHS, RHS);
5621 Pred = ICmpInst::getSwappedPredicate(Pred);
5625 // If we're comparing an addrec with a value which is loop-invariant in the
5626 // addrec's loop, put the addrec on the left. Also make a dominance check,
5627 // as both operands could be addrecs loop-invariant in each other's loop.
5628 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5629 const Loop *L = AR->getLoop();
5630 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5631 std::swap(LHS, RHS);
5632 Pred = ICmpInst::getSwappedPredicate(Pred);
5637 // If there's a constant operand, canonicalize comparisons with boundary
5638 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5639 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5640 const APInt &RA = RC->getValue()->getValue();
5642 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5643 case ICmpInst::ICMP_EQ:
5644 case ICmpInst::ICMP_NE:
5646 case ICmpInst::ICMP_UGE:
5647 if ((RA - 1).isMinValue()) {
5648 Pred = ICmpInst::ICMP_NE;
5649 RHS = getConstant(RA - 1);
5653 if (RA.isMaxValue()) {
5654 Pred = ICmpInst::ICMP_EQ;
5658 if (RA.isMinValue()) goto trivially_true;
5660 Pred = ICmpInst::ICMP_UGT;
5661 RHS = getConstant(RA - 1);
5664 case ICmpInst::ICMP_ULE:
5665 if ((RA + 1).isMaxValue()) {
5666 Pred = ICmpInst::ICMP_NE;
5667 RHS = getConstant(RA + 1);
5671 if (RA.isMinValue()) {
5672 Pred = ICmpInst::ICMP_EQ;
5676 if (RA.isMaxValue()) goto trivially_true;
5678 Pred = ICmpInst::ICMP_ULT;
5679 RHS = getConstant(RA + 1);
5682 case ICmpInst::ICMP_SGE:
5683 if ((RA - 1).isMinSignedValue()) {
5684 Pred = ICmpInst::ICMP_NE;
5685 RHS = getConstant(RA - 1);
5689 if (RA.isMaxSignedValue()) {
5690 Pred = ICmpInst::ICMP_EQ;
5694 if (RA.isMinSignedValue()) goto trivially_true;
5696 Pred = ICmpInst::ICMP_SGT;
5697 RHS = getConstant(RA - 1);
5700 case ICmpInst::ICMP_SLE:
5701 if ((RA + 1).isMaxSignedValue()) {
5702 Pred = ICmpInst::ICMP_NE;
5703 RHS = getConstant(RA + 1);
5707 if (RA.isMinSignedValue()) {
5708 Pred = ICmpInst::ICMP_EQ;
5712 if (RA.isMaxSignedValue()) goto trivially_true;
5714 Pred = ICmpInst::ICMP_SLT;
5715 RHS = getConstant(RA + 1);
5718 case ICmpInst::ICMP_UGT:
5719 if (RA.isMinValue()) {
5720 Pred = ICmpInst::ICMP_NE;
5724 if ((RA + 1).isMaxValue()) {
5725 Pred = ICmpInst::ICMP_EQ;
5726 RHS = getConstant(RA + 1);
5730 if (RA.isMaxValue()) goto trivially_false;
5732 case ICmpInst::ICMP_ULT:
5733 if (RA.isMaxValue()) {
5734 Pred = ICmpInst::ICMP_NE;
5738 if ((RA - 1).isMinValue()) {
5739 Pred = ICmpInst::ICMP_EQ;
5740 RHS = getConstant(RA - 1);
5744 if (RA.isMinValue()) goto trivially_false;
5746 case ICmpInst::ICMP_SGT:
5747 if (RA.isMinSignedValue()) {
5748 Pred = ICmpInst::ICMP_NE;
5752 if ((RA + 1).isMaxSignedValue()) {
5753 Pred = ICmpInst::ICMP_EQ;
5754 RHS = getConstant(RA + 1);
5758 if (RA.isMaxSignedValue()) goto trivially_false;
5760 case ICmpInst::ICMP_SLT:
5761 if (RA.isMaxSignedValue()) {
5762 Pred = ICmpInst::ICMP_NE;
5766 if ((RA - 1).isMinSignedValue()) {
5767 Pred = ICmpInst::ICMP_EQ;
5768 RHS = getConstant(RA - 1);
5772 if (RA.isMinSignedValue()) goto trivially_false;
5777 // Check for obvious equality.
5778 if (HasSameValue(LHS, RHS)) {
5779 if (ICmpInst::isTrueWhenEqual(Pred))
5780 goto trivially_true;
5781 if (ICmpInst::isFalseWhenEqual(Pred))
5782 goto trivially_false;
5785 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5786 // adding or subtracting 1 from one of the operands.
5788 case ICmpInst::ICMP_SLE:
5789 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5790 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5792 Pred = ICmpInst::ICMP_SLT;
5794 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5795 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5797 Pred = ICmpInst::ICMP_SLT;
5801 case ICmpInst::ICMP_SGE:
5802 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5803 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5805 Pred = ICmpInst::ICMP_SGT;
5807 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5808 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5810 Pred = ICmpInst::ICMP_SGT;
5814 case ICmpInst::ICMP_ULE:
5815 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5816 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5818 Pred = ICmpInst::ICMP_ULT;
5820 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5821 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5823 Pred = ICmpInst::ICMP_ULT;
5827 case ICmpInst::ICMP_UGE:
5828 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5829 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5831 Pred = ICmpInst::ICMP_UGT;
5833 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5834 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5836 Pred = ICmpInst::ICMP_UGT;
5844 // TODO: More simplifications are possible here.
5850 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5851 Pred = ICmpInst::ICMP_EQ;
5856 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5857 Pred = ICmpInst::ICMP_NE;
5861 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5862 return getSignedRange(S).getSignedMax().isNegative();
5865 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5866 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5869 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5870 return !getSignedRange(S).getSignedMin().isNegative();
5873 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5874 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5877 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5878 return isKnownNegative(S) || isKnownPositive(S);
5881 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5882 const SCEV *LHS, const SCEV *RHS) {
5883 // Canonicalize the inputs first.
5884 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5886 // If LHS or RHS is an addrec, check to see if the condition is true in
5887 // every iteration of the loop.
5888 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5889 if (isLoopEntryGuardedByCond(
5890 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5891 isLoopBackedgeGuardedByCond(
5892 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5894 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5895 if (isLoopEntryGuardedByCond(
5896 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5897 isLoopBackedgeGuardedByCond(
5898 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5901 // Otherwise see what can be done with known constant ranges.
5902 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5906 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5907 const SCEV *LHS, const SCEV *RHS) {
5908 if (HasSameValue(LHS, RHS))
5909 return ICmpInst::isTrueWhenEqual(Pred);
5911 // This code is split out from isKnownPredicate because it is called from
5912 // within isLoopEntryGuardedByCond.
5915 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5916 case ICmpInst::ICMP_SGT:
5917 Pred = ICmpInst::ICMP_SLT;
5918 std::swap(LHS, RHS);
5919 case ICmpInst::ICMP_SLT: {
5920 ConstantRange LHSRange = getSignedRange(LHS);
5921 ConstantRange RHSRange = getSignedRange(RHS);
5922 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5924 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5928 case ICmpInst::ICMP_SGE:
5929 Pred = ICmpInst::ICMP_SLE;
5930 std::swap(LHS, RHS);
5931 case ICmpInst::ICMP_SLE: {
5932 ConstantRange LHSRange = getSignedRange(LHS);
5933 ConstantRange RHSRange = getSignedRange(RHS);
5934 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5936 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5940 case ICmpInst::ICMP_UGT:
5941 Pred = ICmpInst::ICMP_ULT;
5942 std::swap(LHS, RHS);
5943 case ICmpInst::ICMP_ULT: {
5944 ConstantRange LHSRange = getUnsignedRange(LHS);
5945 ConstantRange RHSRange = getUnsignedRange(RHS);
5946 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5948 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5952 case ICmpInst::ICMP_UGE:
5953 Pred = ICmpInst::ICMP_ULE;
5954 std::swap(LHS, RHS);
5955 case ICmpInst::ICMP_ULE: {
5956 ConstantRange LHSRange = getUnsignedRange(LHS);
5957 ConstantRange RHSRange = getUnsignedRange(RHS);
5958 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5960 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5964 case ICmpInst::ICMP_NE: {
5965 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5967 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5970 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5971 if (isKnownNonZero(Diff))
5975 case ICmpInst::ICMP_EQ:
5976 // The check at the top of the function catches the case where
5977 // the values are known to be equal.
5983 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5984 /// protected by a conditional between LHS and RHS. This is used to
5985 /// to eliminate casts.
5987 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5988 ICmpInst::Predicate Pred,
5989 const SCEV *LHS, const SCEV *RHS) {
5990 // Interpret a null as meaning no loop, where there is obviously no guard
5991 // (interprocedural conditions notwithstanding).
5992 if (!L) return true;
5994 BasicBlock *Latch = L->getLoopLatch();
5998 BranchInst *LoopContinuePredicate =
5999 dyn_cast<BranchInst>(Latch->getTerminator());
6000 if (!LoopContinuePredicate ||
6001 LoopContinuePredicate->isUnconditional())
6004 return isImpliedCond(Pred, LHS, RHS,
6005 LoopContinuePredicate->getCondition(),
6006 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6009 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6010 /// by a conditional between LHS and RHS. This is used to help avoid max
6011 /// expressions in loop trip counts, and to eliminate casts.
6013 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6014 ICmpInst::Predicate Pred,
6015 const SCEV *LHS, const SCEV *RHS) {
6016 // Interpret a null as meaning no loop, where there is obviously no guard
6017 // (interprocedural conditions notwithstanding).
6018 if (!L) return false;
6020 // Starting at the loop predecessor, climb up the predecessor chain, as long
6021 // as there are predecessors that can be found that have unique successors
6022 // leading to the original header.
6023 for (std::pair<BasicBlock *, BasicBlock *>
6024 Pair(L->getLoopPredecessor(), L->getHeader());
6026 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6028 BranchInst *LoopEntryPredicate =
6029 dyn_cast<BranchInst>(Pair.first->getTerminator());
6030 if (!LoopEntryPredicate ||
6031 LoopEntryPredicate->isUnconditional())
6034 if (isImpliedCond(Pred, LHS, RHS,
6035 LoopEntryPredicate->getCondition(),
6036 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6043 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6044 /// and RHS is true whenever the given Cond value evaluates to true.
6045 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6046 const SCEV *LHS, const SCEV *RHS,
6047 Value *FoundCondValue,
6049 // Recursively handle And and Or conditions.
6050 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6051 if (BO->getOpcode() == Instruction::And) {
6053 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6054 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6055 } else if (BO->getOpcode() == Instruction::Or) {
6057 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6058 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6062 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6063 if (!ICI) return false;
6065 // Bail if the ICmp's operands' types are wider than the needed type
6066 // before attempting to call getSCEV on them. This avoids infinite
6067 // recursion, since the analysis of widening casts can require loop
6068 // exit condition information for overflow checking, which would
6070 if (getTypeSizeInBits(LHS->getType()) <
6071 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6074 // Now that we found a conditional branch that dominates the loop, check to
6075 // see if it is the comparison we are looking for.
6076 ICmpInst::Predicate FoundPred;
6078 FoundPred = ICI->getInversePredicate();
6080 FoundPred = ICI->getPredicate();
6082 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6083 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6085 // Balance the types. The case where FoundLHS' type is wider than
6086 // LHS' type is checked for above.
6087 if (getTypeSizeInBits(LHS->getType()) >
6088 getTypeSizeInBits(FoundLHS->getType())) {
6089 if (CmpInst::isSigned(Pred)) {
6090 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6091 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6093 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6094 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6098 // Canonicalize the query to match the way instcombine will have
6099 // canonicalized the comparison.
6100 if (SimplifyICmpOperands(Pred, LHS, RHS))
6102 return CmpInst::isTrueWhenEqual(Pred);
6103 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6104 if (FoundLHS == FoundRHS)
6105 return CmpInst::isFalseWhenEqual(Pred);
6107 // Check to see if we can make the LHS or RHS match.
6108 if (LHS == FoundRHS || RHS == FoundLHS) {
6109 if (isa<SCEVConstant>(RHS)) {
6110 std::swap(FoundLHS, FoundRHS);
6111 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6113 std::swap(LHS, RHS);
6114 Pred = ICmpInst::getSwappedPredicate(Pred);
6118 // Check whether the found predicate is the same as the desired predicate.
6119 if (FoundPred == Pred)
6120 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6122 // Check whether swapping the found predicate makes it the same as the
6123 // desired predicate.
6124 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6125 if (isa<SCEVConstant>(RHS))
6126 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6128 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6129 RHS, LHS, FoundLHS, FoundRHS);
6132 // Check whether the actual condition is beyond sufficient.
6133 if (FoundPred == ICmpInst::ICMP_EQ)
6134 if (ICmpInst::isTrueWhenEqual(Pred))
6135 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6137 if (Pred == ICmpInst::ICMP_NE)
6138 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6139 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6142 // Otherwise assume the worst.
6146 /// isImpliedCondOperands - Test whether the condition described by Pred,
6147 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6148 /// and FoundRHS is true.
6149 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6150 const SCEV *LHS, const SCEV *RHS,
6151 const SCEV *FoundLHS,
6152 const SCEV *FoundRHS) {
6153 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6154 FoundLHS, FoundRHS) ||
6155 // ~x < ~y --> x > y
6156 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6157 getNotSCEV(FoundRHS),
6158 getNotSCEV(FoundLHS));
6161 /// isImpliedCondOperandsHelper - Test whether the condition described by
6162 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6163 /// FoundLHS, and FoundRHS is true.
6165 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6166 const SCEV *LHS, const SCEV *RHS,
6167 const SCEV *FoundLHS,
6168 const SCEV *FoundRHS) {
6170 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6171 case ICmpInst::ICMP_EQ:
6172 case ICmpInst::ICMP_NE:
6173 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6176 case ICmpInst::ICMP_SLT:
6177 case ICmpInst::ICMP_SLE:
6178 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6179 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6182 case ICmpInst::ICMP_SGT:
6183 case ICmpInst::ICMP_SGE:
6184 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6185 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6188 case ICmpInst::ICMP_ULT:
6189 case ICmpInst::ICMP_ULE:
6190 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6191 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6194 case ICmpInst::ICMP_UGT:
6195 case ICmpInst::ICMP_UGE:
6196 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6197 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6205 /// getBECount - Subtract the end and start values and divide by the step,
6206 /// rounding up, to get the number of times the backedge is executed. Return
6207 /// CouldNotCompute if an intermediate computation overflows.
6208 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
6212 assert(!isKnownNegative(Step) &&
6213 "This code doesn't handle negative strides yet!");
6215 Type *Ty = Start->getType();
6217 // When Start == End, we have an exact BECount == 0. Short-circuit this case
6218 // here because SCEV may not be able to determine that the unsigned division
6219 // after rounding is zero.
6221 return getConstant(Ty, 0);
6223 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
6224 const SCEV *Diff = getMinusSCEV(End, Start);
6225 const SCEV *RoundUp = getAddExpr(Step, NegOne);
6227 // Add an adjustment to the difference between End and Start so that
6228 // the division will effectively round up.
6229 const SCEV *Add = getAddExpr(Diff, RoundUp);
6232 // Check Add for unsigned overflow.
6233 // TODO: More sophisticated things could be done here.
6234 Type *WideTy = IntegerType::get(getContext(),
6235 getTypeSizeInBits(Ty) + 1);
6236 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
6237 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
6238 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
6239 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
6240 return getCouldNotCompute();
6243 return getUDivExpr(Add, Step);
6246 /// HowManyLessThans - Return the number of times a backedge containing the
6247 /// specified less-than comparison will execute. If not computable, return
6248 /// CouldNotCompute.
6249 ScalarEvolution::ExitLimit
6250 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6251 const Loop *L, bool isSigned) {
6252 // Only handle: "ADDREC < LoopInvariant".
6253 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
6255 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
6256 if (!AddRec || AddRec->getLoop() != L)
6257 return getCouldNotCompute();
6259 // Check to see if we have a flag which makes analysis easy.
6260 bool NoWrap = isSigned ?
6261 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNW)) :
6262 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNW));
6264 if (AddRec->isAffine()) {
6265 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
6266 const SCEV *Step = AddRec->getStepRecurrence(*this);
6269 return getCouldNotCompute();
6270 if (Step->isOne()) {
6271 // With unit stride, the iteration never steps past the limit value.
6272 } else if (isKnownPositive(Step)) {
6273 // Test whether a positive iteration can step past the limit
6274 // value and past the maximum value for its type in a single step.
6275 // Note that it's not sufficient to check NoWrap here, because even
6276 // though the value after a wrap is undefined, it's not undefined
6277 // behavior, so if wrap does occur, the loop could either terminate or
6278 // loop infinitely, but in either case, the loop is guaranteed to
6279 // iterate at least until the iteration where the wrapping occurs.
6280 const SCEV *One = getConstant(Step->getType(), 1);
6282 APInt Max = APInt::getSignedMaxValue(BitWidth);
6283 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
6284 .slt(getSignedRange(RHS).getSignedMax()))
6285 return getCouldNotCompute();
6287 APInt Max = APInt::getMaxValue(BitWidth);
6288 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
6289 .ult(getUnsignedRange(RHS).getUnsignedMax()))
6290 return getCouldNotCompute();
6293 // TODO: Handle negative strides here and below.
6294 return getCouldNotCompute();
6296 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6297 // m. So, we count the number of iterations in which {n,+,s} < m is true.
6298 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6299 // treat m-n as signed nor unsigned due to overflow possibility.
6301 // First, we get the value of the LHS in the first iteration: n
6302 const SCEV *Start = AddRec->getOperand(0);
6304 // Determine the minimum constant start value.
6305 const SCEV *MinStart = getConstant(isSigned ?
6306 getSignedRange(Start).getSignedMin() :
6307 getUnsignedRange(Start).getUnsignedMin());
6309 // If we know that the condition is true in order to enter the loop,
6310 // then we know that it will run exactly (m-n)/s times. Otherwise, we
6311 // only know that it will execute (max(m,n)-n)/s times. In both cases,
6312 // the division must round up.
6313 const SCEV *End = RHS;
6314 if (!isLoopEntryGuardedByCond(L,
6315 isSigned ? ICmpInst::ICMP_SLT :
6317 getMinusSCEV(Start, Step), RHS))
6318 End = isSigned ? getSMaxExpr(RHS, Start)
6319 : getUMaxExpr(RHS, Start);
6321 // Determine the maximum constant end value.
6322 const SCEV *MaxEnd = getConstant(isSigned ?
6323 getSignedRange(End).getSignedMax() :
6324 getUnsignedRange(End).getUnsignedMax());
6326 // If MaxEnd is within a step of the maximum integer value in its type,
6327 // adjust it down to the minimum value which would produce the same effect.
6328 // This allows the subsequent ceiling division of (N+(step-1))/step to
6329 // compute the correct value.
6330 const SCEV *StepMinusOne = getMinusSCEV(Step,
6331 getConstant(Step->getType(), 1));
6334 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6337 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6340 // Finally, we subtract these two values and divide, rounding up, to get
6341 // the number of times the backedge is executed.
6342 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6344 // The maximum backedge count is similar, except using the minimum start
6345 // value and the maximum end value.
6346 // If we already have an exact constant BECount, use it instead.
6347 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6348 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6350 // If the stride is nonconstant, and NoWrap == true, then
6351 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6352 // exact BECount and invalid MaxBECount, which should be avoided to catch
6353 // more optimization opportunities.
6354 if (isa<SCEVCouldNotCompute>(MaxBECount))
6355 MaxBECount = BECount;
6357 return ExitLimit(BECount, MaxBECount);
6360 return getCouldNotCompute();
6363 /// getNumIterationsInRange - Return the number of iterations of this loop that
6364 /// produce values in the specified constant range. Another way of looking at
6365 /// this is that it returns the first iteration number where the value is not in
6366 /// the condition, thus computing the exit count. If the iteration count can't
6367 /// be computed, an instance of SCEVCouldNotCompute is returned.
6368 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6369 ScalarEvolution &SE) const {
6370 if (Range.isFullSet()) // Infinite loop.
6371 return SE.getCouldNotCompute();
6373 // If the start is a non-zero constant, shift the range to simplify things.
6374 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6375 if (!SC->getValue()->isZero()) {
6376 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6377 Operands[0] = SE.getConstant(SC->getType(), 0);
6378 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6379 getNoWrapFlags(FlagNW));
6380 if (const SCEVAddRecExpr *ShiftedAddRec =
6381 dyn_cast<SCEVAddRecExpr>(Shifted))
6382 return ShiftedAddRec->getNumIterationsInRange(
6383 Range.subtract(SC->getValue()->getValue()), SE);
6384 // This is strange and shouldn't happen.
6385 return SE.getCouldNotCompute();
6388 // The only time we can solve this is when we have all constant indices.
6389 // Otherwise, we cannot determine the overflow conditions.
6390 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6391 if (!isa<SCEVConstant>(getOperand(i)))
6392 return SE.getCouldNotCompute();
6395 // Okay at this point we know that all elements of the chrec are constants and
6396 // that the start element is zero.
6398 // First check to see if the range contains zero. If not, the first
6400 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6401 if (!Range.contains(APInt(BitWidth, 0)))
6402 return SE.getConstant(getType(), 0);
6405 // If this is an affine expression then we have this situation:
6406 // Solve {0,+,A} in Range === Ax in Range
6408 // We know that zero is in the range. If A is positive then we know that
6409 // the upper value of the range must be the first possible exit value.
6410 // If A is negative then the lower of the range is the last possible loop
6411 // value. Also note that we already checked for a full range.
6412 APInt One(BitWidth,1);
6413 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6414 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6416 // The exit value should be (End+A)/A.
6417 APInt ExitVal = (End + A).udiv(A);
6418 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6420 // Evaluate at the exit value. If we really did fall out of the valid
6421 // range, then we computed our trip count, otherwise wrap around or other
6422 // things must have happened.
6423 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6424 if (Range.contains(Val->getValue()))
6425 return SE.getCouldNotCompute(); // Something strange happened
6427 // Ensure that the previous value is in the range. This is a sanity check.
6428 assert(Range.contains(
6429 EvaluateConstantChrecAtConstant(this,
6430 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6431 "Linear scev computation is off in a bad way!");
6432 return SE.getConstant(ExitValue);
6433 } else if (isQuadratic()) {
6434 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6435 // quadratic equation to solve it. To do this, we must frame our problem in
6436 // terms of figuring out when zero is crossed, instead of when
6437 // Range.getUpper() is crossed.
6438 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6439 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6440 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6441 // getNoWrapFlags(FlagNW)
6444 // Next, solve the constructed addrec
6445 std::pair<const SCEV *,const SCEV *> Roots =
6446 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6447 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6448 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6450 // Pick the smallest positive root value.
6451 if (ConstantInt *CB =
6452 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6453 R1->getValue(), R2->getValue()))) {
6454 if (CB->getZExtValue() == false)
6455 std::swap(R1, R2); // R1 is the minimum root now.
6457 // Make sure the root is not off by one. The returned iteration should
6458 // not be in the range, but the previous one should be. When solving
6459 // for "X*X < 5", for example, we should not return a root of 2.
6460 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6463 if (Range.contains(R1Val->getValue())) {
6464 // The next iteration must be out of the range...
6465 ConstantInt *NextVal =
6466 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6468 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6469 if (!Range.contains(R1Val->getValue()))
6470 return SE.getConstant(NextVal);
6471 return SE.getCouldNotCompute(); // Something strange happened
6474 // If R1 was not in the range, then it is a good return value. Make
6475 // sure that R1-1 WAS in the range though, just in case.
6476 ConstantInt *NextVal =
6477 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6478 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6479 if (Range.contains(R1Val->getValue()))
6481 return SE.getCouldNotCompute(); // Something strange happened
6486 return SE.getCouldNotCompute();
6491 //===----------------------------------------------------------------------===//
6492 // SCEVCallbackVH Class Implementation
6493 //===----------------------------------------------------------------------===//
6495 void ScalarEvolution::SCEVCallbackVH::deleted() {
6496 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6497 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6498 SE->ConstantEvolutionLoopExitValue.erase(PN);
6499 SE->ValueExprMap.erase(getValPtr());
6500 // this now dangles!
6503 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6504 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6506 // Forget all the expressions associated with users of the old value,
6507 // so that future queries will recompute the expressions using the new
6509 Value *Old = getValPtr();
6510 SmallVector<User *, 16> Worklist;
6511 SmallPtrSet<User *, 8> Visited;
6512 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6514 Worklist.push_back(*UI);
6515 while (!Worklist.empty()) {
6516 User *U = Worklist.pop_back_val();
6517 // Deleting the Old value will cause this to dangle. Postpone
6518 // that until everything else is done.
6521 if (!Visited.insert(U))
6523 if (PHINode *PN = dyn_cast<PHINode>(U))
6524 SE->ConstantEvolutionLoopExitValue.erase(PN);
6525 SE->ValueExprMap.erase(U);
6526 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6528 Worklist.push_back(*UI);
6530 // Delete the Old value.
6531 if (PHINode *PN = dyn_cast<PHINode>(Old))
6532 SE->ConstantEvolutionLoopExitValue.erase(PN);
6533 SE->ValueExprMap.erase(Old);
6534 // this now dangles!
6537 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6538 : CallbackVH(V), SE(se) {}
6540 //===----------------------------------------------------------------------===//
6541 // ScalarEvolution Class Implementation
6542 //===----------------------------------------------------------------------===//
6544 ScalarEvolution::ScalarEvolution()
6545 : FunctionPass(ID), FirstUnknown(0) {
6546 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6549 bool ScalarEvolution::runOnFunction(Function &F) {
6551 LI = &getAnalysis<LoopInfo>();
6552 TD = getAnalysisIfAvailable<TargetData>();
6553 TLI = &getAnalysis<TargetLibraryInfo>();
6554 DT = &getAnalysis<DominatorTree>();
6558 void ScalarEvolution::releaseMemory() {
6559 // Iterate through all the SCEVUnknown instances and call their
6560 // destructors, so that they release their references to their values.
6561 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6565 ValueExprMap.clear();
6567 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6568 // that a loop had multiple computable exits.
6569 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6570 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6575 BackedgeTakenCounts.clear();
6576 ConstantEvolutionLoopExitValue.clear();
6577 ValuesAtScopes.clear();
6578 LoopDispositions.clear();
6579 BlockDispositions.clear();
6580 UnsignedRanges.clear();
6581 SignedRanges.clear();
6582 UniqueSCEVs.clear();
6583 SCEVAllocator.Reset();
6586 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6587 AU.setPreservesAll();
6588 AU.addRequiredTransitive<LoopInfo>();
6589 AU.addRequiredTransitive<DominatorTree>();
6590 AU.addRequired<TargetLibraryInfo>();
6593 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6594 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6597 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6599 // Print all inner loops first
6600 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6601 PrintLoopInfo(OS, SE, *I);
6604 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6607 SmallVector<BasicBlock *, 8> ExitBlocks;
6608 L->getExitBlocks(ExitBlocks);
6609 if (ExitBlocks.size() != 1)
6610 OS << "<multiple exits> ";
6612 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6613 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6615 OS << "Unpredictable backedge-taken count. ";
6620 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6623 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6624 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6626 OS << "Unpredictable max backedge-taken count. ";
6632 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6633 // ScalarEvolution's implementation of the print method is to print
6634 // out SCEV values of all instructions that are interesting. Doing
6635 // this potentially causes it to create new SCEV objects though,
6636 // which technically conflicts with the const qualifier. This isn't
6637 // observable from outside the class though, so casting away the
6638 // const isn't dangerous.
6639 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6641 OS << "Classifying expressions for: ";
6642 WriteAsOperand(OS, F, /*PrintType=*/false);
6644 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6645 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6648 const SCEV *SV = SE.getSCEV(&*I);
6651 const Loop *L = LI->getLoopFor((*I).getParent());
6653 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6660 OS << "\t\t" "Exits: ";
6661 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6662 if (!SE.isLoopInvariant(ExitValue, L)) {
6663 OS << "<<Unknown>>";
6672 OS << "Determining loop execution counts for: ";
6673 WriteAsOperand(OS, F, /*PrintType=*/false);
6675 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6676 PrintLoopInfo(OS, &SE, *I);
6679 ScalarEvolution::LoopDisposition
6680 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6681 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6682 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6683 Values.insert(std::make_pair(L, LoopVariant));
6685 return Pair.first->second;
6687 LoopDisposition D = computeLoopDisposition(S, L);
6688 return LoopDispositions[S][L] = D;
6691 ScalarEvolution::LoopDisposition
6692 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6693 switch (S->getSCEVType()) {
6695 return LoopInvariant;
6699 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6700 case scAddRecExpr: {
6701 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6703 // If L is the addrec's loop, it's computable.
6704 if (AR->getLoop() == L)
6705 return LoopComputable;
6707 // Add recurrences are never invariant in the function-body (null loop).
6711 // This recurrence is variant w.r.t. L if L contains AR's loop.
6712 if (L->contains(AR->getLoop()))
6715 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6716 if (AR->getLoop()->contains(L))
6717 return LoopInvariant;
6719 // This recurrence is variant w.r.t. L if any of its operands
6721 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6723 if (!isLoopInvariant(*I, L))
6726 // Otherwise it's loop-invariant.
6727 return LoopInvariant;
6733 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6734 bool HasVarying = false;
6735 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6737 LoopDisposition D = getLoopDisposition(*I, L);
6738 if (D == LoopVariant)
6740 if (D == LoopComputable)
6743 return HasVarying ? LoopComputable : LoopInvariant;
6746 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6747 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6748 if (LD == LoopVariant)
6750 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6751 if (RD == LoopVariant)
6753 return (LD == LoopInvariant && RD == LoopInvariant) ?
6754 LoopInvariant : LoopComputable;
6757 // All non-instruction values are loop invariant. All instructions are loop
6758 // invariant if they are not contained in the specified loop.
6759 // Instructions are never considered invariant in the function body
6760 // (null loop) because they are defined within the "loop".
6761 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6762 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6763 return LoopInvariant;
6764 case scCouldNotCompute:
6765 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6766 default: llvm_unreachable("Unknown SCEV kind!");
6770 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6771 return getLoopDisposition(S, L) == LoopInvariant;
6774 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6775 return getLoopDisposition(S, L) == LoopComputable;
6778 ScalarEvolution::BlockDisposition
6779 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6780 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6781 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6782 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6784 return Pair.first->second;
6786 BlockDisposition D = computeBlockDisposition(S, BB);
6787 return BlockDispositions[S][BB] = D;
6790 ScalarEvolution::BlockDisposition
6791 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6792 switch (S->getSCEVType()) {
6794 return ProperlyDominatesBlock;
6798 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6799 case scAddRecExpr: {
6800 // This uses a "dominates" query instead of "properly dominates" query
6801 // to test for proper dominance too, because the instruction which
6802 // produces the addrec's value is a PHI, and a PHI effectively properly
6803 // dominates its entire containing block.
6804 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6805 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6806 return DoesNotDominateBlock;
6808 // FALL THROUGH into SCEVNAryExpr handling.
6813 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6815 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6817 BlockDisposition D = getBlockDisposition(*I, BB);
6818 if (D == DoesNotDominateBlock)
6819 return DoesNotDominateBlock;
6820 if (D == DominatesBlock)
6823 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6826 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6827 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6828 BlockDisposition LD = getBlockDisposition(LHS, BB);
6829 if (LD == DoesNotDominateBlock)
6830 return DoesNotDominateBlock;
6831 BlockDisposition RD = getBlockDisposition(RHS, BB);
6832 if (RD == DoesNotDominateBlock)
6833 return DoesNotDominateBlock;
6834 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6835 ProperlyDominatesBlock : DominatesBlock;
6838 if (Instruction *I =
6839 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6840 if (I->getParent() == BB)
6841 return DominatesBlock;
6842 if (DT->properlyDominates(I->getParent(), BB))
6843 return ProperlyDominatesBlock;
6844 return DoesNotDominateBlock;
6846 return ProperlyDominatesBlock;
6847 case scCouldNotCompute:
6848 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6850 llvm_unreachable("Unknown SCEV kind!");
6854 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6855 return getBlockDisposition(S, BB) >= DominatesBlock;
6858 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6859 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6862 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6863 switch (S->getSCEVType()) {
6868 case scSignExtend: {
6869 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
6870 const SCEV *CastOp = Cast->getOperand();
6871 return Op == CastOp || hasOperand(CastOp, Op);
6878 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6879 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6881 const SCEV *NAryOp = *I;
6882 if (NAryOp == Op || hasOperand(NAryOp, Op))
6888 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6889 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6890 return LHS == Op || hasOperand(LHS, Op) ||
6891 RHS == Op || hasOperand(RHS, Op);
6895 case scCouldNotCompute:
6896 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6898 llvm_unreachable("Unknown SCEV kind!");
6902 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6903 ValuesAtScopes.erase(S);
6904 LoopDispositions.erase(S);
6905 BlockDispositions.erase(S);
6906 UnsignedRanges.erase(S);
6907 SignedRanges.erase(S);