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/DataLayout.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 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
126 void SCEV::dump() const {
132 void SCEV::print(raw_ostream &OS) const {
133 switch (getSCEVType()) {
135 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false);
138 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
139 const SCEV *Op = Trunc->getOperand();
140 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
141 << *Trunc->getType() << ")";
145 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
146 const SCEV *Op = ZExt->getOperand();
147 OS << "(zext " << *Op->getType() << " " << *Op << " to "
148 << *ZExt->getType() << ")";
152 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
153 const SCEV *Op = SExt->getOperand();
154 OS << "(sext " << *Op->getType() << " " << *Op << " to "
155 << *SExt->getType() << ")";
159 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
160 OS << "{" << *AR->getOperand(0);
161 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
162 OS << ",+," << *AR->getOperand(i);
164 if (AR->getNoWrapFlags(FlagNUW))
166 if (AR->getNoWrapFlags(FlagNSW))
168 if (AR->getNoWrapFlags(FlagNW) &&
169 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
171 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false);
179 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
180 const char *OpStr = 0;
181 switch (NAry->getSCEVType()) {
182 case scAddExpr: OpStr = " + "; break;
183 case scMulExpr: OpStr = " * "; break;
184 case scUMaxExpr: OpStr = " umax "; break;
185 case scSMaxExpr: OpStr = " smax "; break;
188 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
191 if (llvm::next(I) != E)
195 switch (NAry->getSCEVType()) {
198 if (NAry->getNoWrapFlags(FlagNUW))
200 if (NAry->getNoWrapFlags(FlagNSW))
206 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
207 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
211 const SCEVUnknown *U = cast<SCEVUnknown>(this);
213 if (U->isSizeOf(AllocTy)) {
214 OS << "sizeof(" << *AllocTy << ")";
217 if (U->isAlignOf(AllocTy)) {
218 OS << "alignof(" << *AllocTy << ")";
224 if (U->isOffsetOf(CTy, FieldNo)) {
225 OS << "offsetof(" << *CTy << ", ";
226 WriteAsOperand(OS, FieldNo, false);
231 // Otherwise just print it normally.
232 WriteAsOperand(OS, U->getValue(), false);
235 case scCouldNotCompute:
236 OS << "***COULDNOTCOMPUTE***";
240 llvm_unreachable("Unknown SCEV kind!");
243 Type *SCEV::getType() const {
244 switch (getSCEVType()) {
246 return cast<SCEVConstant>(this)->getType();
250 return cast<SCEVCastExpr>(this)->getType();
255 return cast<SCEVNAryExpr>(this)->getType();
257 return cast<SCEVAddExpr>(this)->getType();
259 return cast<SCEVUDivExpr>(this)->getType();
261 return cast<SCEVUnknown>(this)->getType();
262 case scCouldNotCompute:
263 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
265 llvm_unreachable("Unknown SCEV kind!");
269 bool SCEV::isZero() const {
270 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
271 return SC->getValue()->isZero();
275 bool SCEV::isOne() const {
276 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
277 return SC->getValue()->isOne();
281 bool SCEV::isAllOnesValue() const {
282 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
283 return SC->getValue()->isAllOnesValue();
287 /// isNonConstantNegative - Return true if the specified scev is negated, but
289 bool SCEV::isNonConstantNegative() const {
290 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
291 if (!Mul) return false;
293 // If there is a constant factor, it will be first.
294 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
295 if (!SC) return false;
297 // Return true if the value is negative, this matches things like (-42 * V).
298 return SC->getValue()->getValue().isNegative();
301 SCEVCouldNotCompute::SCEVCouldNotCompute() :
302 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
304 bool SCEVCouldNotCompute::classof(const SCEV *S) {
305 return S->getSCEVType() == scCouldNotCompute;
308 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
310 ID.AddInteger(scConstant);
313 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
314 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
315 UniqueSCEVs.InsertNode(S, IP);
319 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
320 return getConstant(ConstantInt::get(getContext(), Val));
324 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
325 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
326 return getConstant(ConstantInt::get(ITy, V, isSigned));
329 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
330 unsigned SCEVTy, const SCEV *op, Type *ty)
331 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
333 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
334 const SCEV *op, Type *ty)
335 : SCEVCastExpr(ID, scTruncate, op, ty) {
336 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
337 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
338 "Cannot truncate non-integer value!");
341 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
342 const SCEV *op, Type *ty)
343 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
344 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
345 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
346 "Cannot zero extend non-integer value!");
349 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
350 const SCEV *op, Type *ty)
351 : SCEVCastExpr(ID, scSignExtend, op, ty) {
352 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
353 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
354 "Cannot sign extend non-integer value!");
357 void SCEVUnknown::deleted() {
358 // Clear this SCEVUnknown from various maps.
359 SE->forgetMemoizedResults(this);
361 // Remove this SCEVUnknown from the uniquing map.
362 SE->UniqueSCEVs.RemoveNode(this);
364 // Release the value.
368 void SCEVUnknown::allUsesReplacedWith(Value *New) {
369 // Clear this SCEVUnknown from various maps.
370 SE->forgetMemoizedResults(this);
372 // Remove this SCEVUnknown from the uniquing map.
373 SE->UniqueSCEVs.RemoveNode(this);
375 // Update this SCEVUnknown to point to the new value. This is needed
376 // because there may still be outstanding SCEVs which still point to
381 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
382 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
383 if (VCE->getOpcode() == Instruction::PtrToInt)
384 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
385 if (CE->getOpcode() == Instruction::GetElementPtr &&
386 CE->getOperand(0)->isNullValue() &&
387 CE->getNumOperands() == 2)
388 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
390 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
398 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
399 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
400 if (VCE->getOpcode() == Instruction::PtrToInt)
401 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
402 if (CE->getOpcode() == Instruction::GetElementPtr &&
403 CE->getOperand(0)->isNullValue()) {
405 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
406 if (StructType *STy = dyn_cast<StructType>(Ty))
407 if (!STy->isPacked() &&
408 CE->getNumOperands() == 3 &&
409 CE->getOperand(1)->isNullValue()) {
410 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
412 STy->getNumElements() == 2 &&
413 STy->getElementType(0)->isIntegerTy(1)) {
414 AllocTy = STy->getElementType(1);
423 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
424 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
425 if (VCE->getOpcode() == Instruction::PtrToInt)
426 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
427 if (CE->getOpcode() == Instruction::GetElementPtr &&
428 CE->getNumOperands() == 3 &&
429 CE->getOperand(0)->isNullValue() &&
430 CE->getOperand(1)->isNullValue()) {
432 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
433 // Ignore vector types here so that ScalarEvolutionExpander doesn't
434 // emit getelementptrs that index into vectors.
435 if (Ty->isStructTy() || Ty->isArrayTy()) {
437 FieldNo = CE->getOperand(2);
445 //===----------------------------------------------------------------------===//
447 //===----------------------------------------------------------------------===//
450 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
451 /// than the complexity of the RHS. This comparator is used to canonicalize
453 class SCEVComplexityCompare {
454 const LoopInfo *const LI;
456 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
458 // Return true or false if LHS is less than, or at least RHS, respectively.
459 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
460 return compare(LHS, RHS) < 0;
463 // Return negative, zero, or positive, if LHS is less than, equal to, or
464 // greater than RHS, respectively. A three-way result allows recursive
465 // comparisons to be more efficient.
466 int compare(const SCEV *LHS, const SCEV *RHS) const {
467 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
471 // Primarily, sort the SCEVs by their getSCEVType().
472 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
474 return (int)LType - (int)RType;
476 // Aside from the getSCEVType() ordering, the particular ordering
477 // isn't very important except that it's beneficial to be consistent,
478 // so that (a + b) and (b + a) don't end up as different expressions.
481 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
482 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
484 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
485 // not as complete as it could be.
486 const Value *LV = LU->getValue(), *RV = RU->getValue();
488 // Order pointer values after integer values. This helps SCEVExpander
490 bool LIsPointer = LV->getType()->isPointerTy(),
491 RIsPointer = RV->getType()->isPointerTy();
492 if (LIsPointer != RIsPointer)
493 return (int)LIsPointer - (int)RIsPointer;
495 // Compare getValueID values.
496 unsigned LID = LV->getValueID(),
497 RID = RV->getValueID();
499 return (int)LID - (int)RID;
501 // Sort arguments by their position.
502 if (const Argument *LA = dyn_cast<Argument>(LV)) {
503 const Argument *RA = cast<Argument>(RV);
504 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
505 return (int)LArgNo - (int)RArgNo;
508 // For instructions, compare their loop depth, and their operand
509 // count. This is pretty loose.
510 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
511 const Instruction *RInst = cast<Instruction>(RV);
513 // Compare loop depths.
514 const BasicBlock *LParent = LInst->getParent(),
515 *RParent = RInst->getParent();
516 if (LParent != RParent) {
517 unsigned LDepth = LI->getLoopDepth(LParent),
518 RDepth = LI->getLoopDepth(RParent);
519 if (LDepth != RDepth)
520 return (int)LDepth - (int)RDepth;
523 // Compare the number of operands.
524 unsigned LNumOps = LInst->getNumOperands(),
525 RNumOps = RInst->getNumOperands();
526 return (int)LNumOps - (int)RNumOps;
533 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
534 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
536 // Compare constant values.
537 const APInt &LA = LC->getValue()->getValue();
538 const APInt &RA = RC->getValue()->getValue();
539 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
540 if (LBitWidth != RBitWidth)
541 return (int)LBitWidth - (int)RBitWidth;
542 return LA.ult(RA) ? -1 : 1;
546 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
547 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
549 // Compare addrec loop depths.
550 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
551 if (LLoop != RLoop) {
552 unsigned LDepth = LLoop->getLoopDepth(),
553 RDepth = RLoop->getLoopDepth();
554 if (LDepth != RDepth)
555 return (int)LDepth - (int)RDepth;
558 // Addrec complexity grows with operand count.
559 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
560 if (LNumOps != RNumOps)
561 return (int)LNumOps - (int)RNumOps;
563 // Lexicographically compare.
564 for (unsigned i = 0; i != LNumOps; ++i) {
565 long X = compare(LA->getOperand(i), RA->getOperand(i));
577 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
578 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
580 // Lexicographically compare n-ary expressions.
581 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
582 for (unsigned i = 0; i != LNumOps; ++i) {
585 long X = compare(LC->getOperand(i), RC->getOperand(i));
589 return (int)LNumOps - (int)RNumOps;
593 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
594 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
596 // Lexicographically compare udiv expressions.
597 long X = compare(LC->getLHS(), RC->getLHS());
600 return compare(LC->getRHS(), RC->getRHS());
606 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
607 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
609 // Compare cast expressions by operand.
610 return compare(LC->getOperand(), RC->getOperand());
614 llvm_unreachable("Unknown SCEV kind!");
620 /// GroupByComplexity - Given a list of SCEV objects, order them by their
621 /// complexity, and group objects of the same complexity together by value.
622 /// When this routine is finished, we know that any duplicates in the vector are
623 /// consecutive and that complexity is monotonically increasing.
625 /// Note that we go take special precautions to ensure that we get deterministic
626 /// results from this routine. In other words, we don't want the results of
627 /// this to depend on where the addresses of various SCEV objects happened to
630 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
632 if (Ops.size() < 2) return; // Noop
633 if (Ops.size() == 2) {
634 // This is the common case, which also happens to be trivially simple.
636 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
637 if (SCEVComplexityCompare(LI)(RHS, LHS))
642 // Do the rough sort by complexity.
643 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
645 // Now that we are sorted by complexity, group elements of the same
646 // complexity. Note that this is, at worst, N^2, but the vector is likely to
647 // be extremely short in practice. Note that we take this approach because we
648 // do not want to depend on the addresses of the objects we are grouping.
649 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
650 const SCEV *S = Ops[i];
651 unsigned Complexity = S->getSCEVType();
653 // If there are any objects of the same complexity and same value as this
655 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
656 if (Ops[j] == S) { // Found a duplicate.
657 // Move it to immediately after i'th element.
658 std::swap(Ops[i+1], Ops[j]);
659 ++i; // no need to rescan it.
660 if (i == e-2) return; // Done!
668 //===----------------------------------------------------------------------===//
669 // Simple SCEV method implementations
670 //===----------------------------------------------------------------------===//
672 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
674 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
677 // Handle the simplest case efficiently.
679 return SE.getTruncateOrZeroExtend(It, ResultTy);
681 // We are using the following formula for BC(It, K):
683 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
685 // Suppose, W is the bitwidth of the return value. We must be prepared for
686 // overflow. Hence, we must assure that the result of our computation is
687 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
688 // safe in modular arithmetic.
690 // However, this code doesn't use exactly that formula; the formula it uses
691 // is something like the following, where T is the number of factors of 2 in
692 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
695 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
697 // This formula is trivially equivalent to the previous formula. However,
698 // this formula can be implemented much more efficiently. The trick is that
699 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
700 // arithmetic. To do exact division in modular arithmetic, all we have
701 // to do is multiply by the inverse. Therefore, this step can be done at
704 // The next issue is how to safely do the division by 2^T. The way this
705 // is done is by doing the multiplication step at a width of at least W + T
706 // bits. This way, the bottom W+T bits of the product are accurate. Then,
707 // when we perform the division by 2^T (which is equivalent to a right shift
708 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
709 // truncated out after the division by 2^T.
711 // In comparison to just directly using the first formula, this technique
712 // is much more efficient; using the first formula requires W * K bits,
713 // but this formula less than W + K bits. Also, the first formula requires
714 // a division step, whereas this formula only requires multiplies and shifts.
716 // It doesn't matter whether the subtraction step is done in the calculation
717 // width or the input iteration count's width; if the subtraction overflows,
718 // the result must be zero anyway. We prefer here to do it in the width of
719 // the induction variable because it helps a lot for certain cases; CodeGen
720 // isn't smart enough to ignore the overflow, which leads to much less
721 // efficient code if the width of the subtraction is wider than the native
724 // (It's possible to not widen at all by pulling out factors of 2 before
725 // the multiplication; for example, K=2 can be calculated as
726 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
727 // extra arithmetic, so it's not an obvious win, and it gets
728 // much more complicated for K > 3.)
730 // Protection from insane SCEVs; this bound is conservative,
731 // but it probably doesn't matter.
733 return SE.getCouldNotCompute();
735 unsigned W = SE.getTypeSizeInBits(ResultTy);
737 // Calculate K! / 2^T and T; we divide out the factors of two before
738 // multiplying for calculating K! / 2^T to avoid overflow.
739 // Other overflow doesn't matter because we only care about the bottom
740 // W bits of the result.
741 APInt OddFactorial(W, 1);
743 for (unsigned i = 3; i <= K; ++i) {
745 unsigned TwoFactors = Mult.countTrailingZeros();
747 Mult = Mult.lshr(TwoFactors);
748 OddFactorial *= Mult;
751 // We need at least W + T bits for the multiplication step
752 unsigned CalculationBits = W + T;
754 // Calculate 2^T, at width T+W.
755 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
757 // Calculate the multiplicative inverse of K! / 2^T;
758 // this multiplication factor will perform the exact division by
760 APInt Mod = APInt::getSignedMinValue(W+1);
761 APInt MultiplyFactor = OddFactorial.zext(W+1);
762 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
763 MultiplyFactor = MultiplyFactor.trunc(W);
765 // Calculate the product, at width T+W
766 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
768 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
769 for (unsigned i = 1; i != K; ++i) {
770 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
771 Dividend = SE.getMulExpr(Dividend,
772 SE.getTruncateOrZeroExtend(S, CalculationTy));
776 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
778 // Truncate the result, and divide by K! / 2^T.
780 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
781 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
784 /// evaluateAtIteration - Return the value of this chain of recurrences at
785 /// the specified iteration number. We can evaluate this recurrence by
786 /// multiplying each element in the chain by the binomial coefficient
787 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
789 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
791 /// where BC(It, k) stands for binomial coefficient.
793 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
794 ScalarEvolution &SE) const {
795 const SCEV *Result = getStart();
796 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
797 // The computation is correct in the face of overflow provided that the
798 // multiplication is performed _after_ the evaluation of the binomial
800 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
801 if (isa<SCEVCouldNotCompute>(Coeff))
804 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
809 //===----------------------------------------------------------------------===//
810 // SCEV Expression folder implementations
811 //===----------------------------------------------------------------------===//
813 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
815 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
816 "This is not a truncating conversion!");
817 assert(isSCEVable(Ty) &&
818 "This is not a conversion to a SCEVable type!");
819 Ty = getEffectiveSCEVType(Ty);
822 ID.AddInteger(scTruncate);
826 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
828 // Fold if the operand is constant.
829 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
831 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
833 // trunc(trunc(x)) --> trunc(x)
834 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
835 return getTruncateExpr(ST->getOperand(), Ty);
837 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
838 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
839 return getTruncateOrSignExtend(SS->getOperand(), Ty);
841 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
842 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
843 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
845 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
846 // eliminate all the truncates.
847 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
848 SmallVector<const SCEV *, 4> Operands;
849 bool hasTrunc = false;
850 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
851 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
852 hasTrunc = isa<SCEVTruncateExpr>(S);
853 Operands.push_back(S);
856 return getAddExpr(Operands);
857 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
860 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
861 // eliminate all the truncates.
862 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
863 SmallVector<const SCEV *, 4> Operands;
864 bool hasTrunc = false;
865 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
866 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
867 hasTrunc = isa<SCEVTruncateExpr>(S);
868 Operands.push_back(S);
871 return getMulExpr(Operands);
872 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
875 // If the input value is a chrec scev, truncate the chrec's operands.
876 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
877 SmallVector<const SCEV *, 4> Operands;
878 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
879 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
880 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
883 // The cast wasn't folded; create an explicit cast node. We can reuse
884 // the existing insert position since if we get here, we won't have
885 // made any changes which would invalidate it.
886 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
888 UniqueSCEVs.InsertNode(S, IP);
892 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
894 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
895 "This is not an extending conversion!");
896 assert(isSCEVable(Ty) &&
897 "This is not a conversion to a SCEVable type!");
898 Ty = getEffectiveSCEVType(Ty);
900 // Fold if the operand is constant.
901 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
903 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
905 // zext(zext(x)) --> zext(x)
906 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
907 return getZeroExtendExpr(SZ->getOperand(), Ty);
909 // Before doing any expensive analysis, check to see if we've already
910 // computed a SCEV for this Op and Ty.
912 ID.AddInteger(scZeroExtend);
916 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
918 // zext(trunc(x)) --> zext(x) or x or trunc(x)
919 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
920 // It's possible the bits taken off by the truncate were all zero bits. If
921 // so, we should be able to simplify this further.
922 const SCEV *X = ST->getOperand();
923 ConstantRange CR = getUnsignedRange(X);
924 unsigned TruncBits = getTypeSizeInBits(ST->getType());
925 unsigned NewBits = getTypeSizeInBits(Ty);
926 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
927 CR.zextOrTrunc(NewBits)))
928 return getTruncateOrZeroExtend(X, Ty);
931 // If the input value is a chrec scev, and we can prove that the value
932 // did not overflow the old, smaller, value, we can zero extend all of the
933 // operands (often constants). This allows analysis of something like
934 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
935 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
936 if (AR->isAffine()) {
937 const SCEV *Start = AR->getStart();
938 const SCEV *Step = AR->getStepRecurrence(*this);
939 unsigned BitWidth = getTypeSizeInBits(AR->getType());
940 const Loop *L = AR->getLoop();
942 // If we have special knowledge that this addrec won't overflow,
943 // we don't need to do any further analysis.
944 if (AR->getNoWrapFlags(SCEV::FlagNUW))
945 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
946 getZeroExtendExpr(Step, Ty),
947 L, AR->getNoWrapFlags());
949 // Check whether the backedge-taken count is SCEVCouldNotCompute.
950 // Note that this serves two purposes: It filters out loops that are
951 // simply not analyzable, and it covers the case where this code is
952 // being called from within backedge-taken count analysis, such that
953 // attempting to ask for the backedge-taken count would likely result
954 // in infinite recursion. In the later case, the analysis code will
955 // cope with a conservative value, and it will take care to purge
956 // that value once it has finished.
957 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
958 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
959 // Manually compute the final value for AR, checking for
962 // Check whether the backedge-taken count can be losslessly casted to
963 // the addrec's type. The count is always unsigned.
964 const SCEV *CastedMaxBECount =
965 getTruncateOrZeroExtend(MaxBECount, Start->getType());
966 const SCEV *RecastedMaxBECount =
967 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
968 if (MaxBECount == RecastedMaxBECount) {
969 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
970 // Check whether Start+Step*MaxBECount has no unsigned overflow.
971 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
972 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
973 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
974 const SCEV *WideMaxBECount =
975 getZeroExtendExpr(CastedMaxBECount, WideTy);
976 const SCEV *OperandExtendedAdd =
977 getAddExpr(WideStart,
978 getMulExpr(WideMaxBECount,
979 getZeroExtendExpr(Step, WideTy)));
980 if (ZAdd == OperandExtendedAdd) {
981 // Cache knowledge of AR NUW, which is propagated to this AddRec.
982 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
983 // Return the expression with the addrec on the outside.
984 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
985 getZeroExtendExpr(Step, Ty),
986 L, AR->getNoWrapFlags());
988 // Similar to above, only this time treat the step value as signed.
989 // This covers loops that count down.
991 getAddExpr(WideStart,
992 getMulExpr(WideMaxBECount,
993 getSignExtendExpr(Step, WideTy)));
994 if (ZAdd == OperandExtendedAdd) {
995 // Cache knowledge of AR NW, which is propagated to this AddRec.
996 // Negative step causes unsigned wrap, but it still can't self-wrap.
997 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
998 // Return the expression with the addrec on the outside.
999 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1000 getSignExtendExpr(Step, Ty),
1001 L, AR->getNoWrapFlags());
1005 // If the backedge is guarded by a comparison with the pre-inc value
1006 // the addrec is safe. Also, if the entry is guarded by a comparison
1007 // with the start value and the backedge is guarded by a comparison
1008 // with the post-inc value, the addrec is safe.
1009 if (isKnownPositive(Step)) {
1010 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1011 getUnsignedRange(Step).getUnsignedMax());
1012 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1013 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1014 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1015 AR->getPostIncExpr(*this), N))) {
1016 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1017 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1018 // Return the expression with the addrec on the outside.
1019 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1020 getZeroExtendExpr(Step, Ty),
1021 L, AR->getNoWrapFlags());
1023 } else if (isKnownNegative(Step)) {
1024 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1025 getSignedRange(Step).getSignedMin());
1026 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1027 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1028 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1029 AR->getPostIncExpr(*this), N))) {
1030 // Cache knowledge of AR NW, which is propagated to this AddRec.
1031 // Negative step causes unsigned wrap, but it still can't self-wrap.
1032 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1033 // Return the expression with the addrec on the outside.
1034 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1035 getSignExtendExpr(Step, Ty),
1036 L, AR->getNoWrapFlags());
1042 // The cast wasn't folded; create an explicit cast node.
1043 // Recompute the insert position, as it may have been invalidated.
1044 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1045 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1047 UniqueSCEVs.InsertNode(S, IP);
1051 // Get the limit of a recurrence such that incrementing by Step cannot cause
1052 // signed overflow as long as the value of the recurrence within the loop does
1053 // not exceed this limit before incrementing.
1054 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1055 ICmpInst::Predicate *Pred,
1056 ScalarEvolution *SE) {
1057 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1058 if (SE->isKnownPositive(Step)) {
1059 *Pred = ICmpInst::ICMP_SLT;
1060 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1061 SE->getSignedRange(Step).getSignedMax());
1063 if (SE->isKnownNegative(Step)) {
1064 *Pred = ICmpInst::ICMP_SGT;
1065 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1066 SE->getSignedRange(Step).getSignedMin());
1071 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1072 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1073 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1074 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1075 // result, the expression "Step + sext(PreIncAR)" is congruent with
1076 // "sext(PostIncAR)"
1077 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1079 ScalarEvolution *SE) {
1080 const Loop *L = AR->getLoop();
1081 const SCEV *Start = AR->getStart();
1082 const SCEV *Step = AR->getStepRecurrence(*SE);
1084 // Check for a simple looking step prior to loop entry.
1085 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1089 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1090 // subtraction is expensive. For this purpose, perform a quick and dirty
1091 // difference, by checking for Step in the operand list.
1092 SmallVector<const SCEV *, 4> DiffOps;
1093 for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end();
1096 DiffOps.push_back(*I);
1098 if (DiffOps.size() == SA->getNumOperands())
1101 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1102 // same three conditions that getSignExtendedExpr checks.
1104 // 1. NSW flags on the step increment.
1105 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1106 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1107 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1109 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1112 // 2. Direct overflow check on the step operation's expression.
1113 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1114 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1115 const SCEV *OperandExtendedStart =
1116 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1117 SE->getSignExtendExpr(Step, WideTy));
1118 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1119 // Cache knowledge of PreAR NSW.
1121 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1122 // FIXME: this optimization needs a unit test
1123 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1127 // 3. Loop precondition.
1128 ICmpInst::Predicate Pred;
1129 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1131 if (OverflowLimit &&
1132 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1138 // Get the normalized sign-extended expression for this AddRec's Start.
1139 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1141 ScalarEvolution *SE) {
1142 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1144 return SE->getSignExtendExpr(AR->getStart(), Ty);
1146 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1147 SE->getSignExtendExpr(PreStart, Ty));
1150 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1152 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1153 "This is not an extending conversion!");
1154 assert(isSCEVable(Ty) &&
1155 "This is not a conversion to a SCEVable type!");
1156 Ty = getEffectiveSCEVType(Ty);
1158 // Fold if the operand is constant.
1159 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1161 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1163 // sext(sext(x)) --> sext(x)
1164 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1165 return getSignExtendExpr(SS->getOperand(), Ty);
1167 // sext(zext(x)) --> zext(x)
1168 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1169 return getZeroExtendExpr(SZ->getOperand(), Ty);
1171 // Before doing any expensive analysis, check to see if we've already
1172 // computed a SCEV for this Op and Ty.
1173 FoldingSetNodeID ID;
1174 ID.AddInteger(scSignExtend);
1178 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1180 // If the input value is provably positive, build a zext instead.
1181 if (isKnownNonNegative(Op))
1182 return getZeroExtendExpr(Op, Ty);
1184 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1185 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1186 // It's possible the bits taken off by the truncate were all sign bits. If
1187 // so, we should be able to simplify this further.
1188 const SCEV *X = ST->getOperand();
1189 ConstantRange CR = getSignedRange(X);
1190 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1191 unsigned NewBits = getTypeSizeInBits(Ty);
1192 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1193 CR.sextOrTrunc(NewBits)))
1194 return getTruncateOrSignExtend(X, Ty);
1197 // If the input value is a chrec scev, and we can prove that the value
1198 // did not overflow the old, smaller, value, we can sign extend all of the
1199 // operands (often constants). This allows analysis of something like
1200 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1201 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1202 if (AR->isAffine()) {
1203 const SCEV *Start = AR->getStart();
1204 const SCEV *Step = AR->getStepRecurrence(*this);
1205 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1206 const Loop *L = AR->getLoop();
1208 // If we have special knowledge that this addrec won't overflow,
1209 // we don't need to do any further analysis.
1210 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1211 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1212 getSignExtendExpr(Step, Ty),
1215 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1216 // Note that this serves two purposes: It filters out loops that are
1217 // simply not analyzable, and it covers the case where this code is
1218 // being called from within backedge-taken count analysis, such that
1219 // attempting to ask for the backedge-taken count would likely result
1220 // in infinite recursion. In the later case, the analysis code will
1221 // cope with a conservative value, and it will take care to purge
1222 // that value once it has finished.
1223 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1224 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1225 // Manually compute the final value for AR, checking for
1228 // Check whether the backedge-taken count can be losslessly casted to
1229 // the addrec's type. The count is always unsigned.
1230 const SCEV *CastedMaxBECount =
1231 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1232 const SCEV *RecastedMaxBECount =
1233 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1234 if (MaxBECount == RecastedMaxBECount) {
1235 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1236 // Check whether Start+Step*MaxBECount has no signed overflow.
1237 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1238 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1239 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1240 const SCEV *WideMaxBECount =
1241 getZeroExtendExpr(CastedMaxBECount, WideTy);
1242 const SCEV *OperandExtendedAdd =
1243 getAddExpr(WideStart,
1244 getMulExpr(WideMaxBECount,
1245 getSignExtendExpr(Step, WideTy)));
1246 if (SAdd == OperandExtendedAdd) {
1247 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1248 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1249 // Return the expression with the addrec on the outside.
1250 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1251 getSignExtendExpr(Step, Ty),
1252 L, AR->getNoWrapFlags());
1254 // Similar to above, only this time treat the step value as unsigned.
1255 // This covers loops that count up with an unsigned step.
1256 OperandExtendedAdd =
1257 getAddExpr(WideStart,
1258 getMulExpr(WideMaxBECount,
1259 getZeroExtendExpr(Step, WideTy)));
1260 if (SAdd == OperandExtendedAdd) {
1261 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1262 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1263 // Return the expression with the addrec on the outside.
1264 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1265 getZeroExtendExpr(Step, Ty),
1266 L, AR->getNoWrapFlags());
1270 // If the backedge is guarded by a comparison with the pre-inc value
1271 // the addrec is safe. Also, if the entry is guarded by a comparison
1272 // with the start value and the backedge is guarded by a comparison
1273 // with the post-inc value, the addrec is safe.
1274 ICmpInst::Predicate Pred;
1275 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1276 if (OverflowLimit &&
1277 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1278 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1279 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1281 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1282 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1283 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1284 getSignExtendExpr(Step, Ty),
1285 L, AR->getNoWrapFlags());
1290 // The cast wasn't folded; create an explicit cast node.
1291 // Recompute the insert position, as it may have been invalidated.
1292 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1293 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1295 UniqueSCEVs.InsertNode(S, IP);
1299 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1300 /// unspecified bits out to the given type.
1302 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1304 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1305 "This is not an extending conversion!");
1306 assert(isSCEVable(Ty) &&
1307 "This is not a conversion to a SCEVable type!");
1308 Ty = getEffectiveSCEVType(Ty);
1310 // Sign-extend negative constants.
1311 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1312 if (SC->getValue()->getValue().isNegative())
1313 return getSignExtendExpr(Op, Ty);
1315 // Peel off a truncate cast.
1316 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1317 const SCEV *NewOp = T->getOperand();
1318 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1319 return getAnyExtendExpr(NewOp, Ty);
1320 return getTruncateOrNoop(NewOp, Ty);
1323 // Next try a zext cast. If the cast is folded, use it.
1324 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1325 if (!isa<SCEVZeroExtendExpr>(ZExt))
1328 // Next try a sext cast. If the cast is folded, use it.
1329 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1330 if (!isa<SCEVSignExtendExpr>(SExt))
1333 // Force the cast to be folded into the operands of an addrec.
1334 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1335 SmallVector<const SCEV *, 4> Ops;
1336 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1338 Ops.push_back(getAnyExtendExpr(*I, Ty));
1339 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1342 // If the expression is obviously signed, use the sext cast value.
1343 if (isa<SCEVSMaxExpr>(Op))
1346 // Absent any other information, use the zext cast value.
1350 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1351 /// a list of operands to be added under the given scale, update the given
1352 /// map. This is a helper function for getAddRecExpr. As an example of
1353 /// what it does, given a sequence of operands that would form an add
1354 /// expression like this:
1356 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1358 /// where A and B are constants, update the map with these values:
1360 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1362 /// and add 13 + A*B*29 to AccumulatedConstant.
1363 /// This will allow getAddRecExpr to produce this:
1365 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1367 /// This form often exposes folding opportunities that are hidden in
1368 /// the original operand list.
1370 /// Return true iff it appears that any interesting folding opportunities
1371 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1372 /// the common case where no interesting opportunities are present, and
1373 /// is also used as a check to avoid infinite recursion.
1376 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1377 SmallVector<const SCEV *, 8> &NewOps,
1378 APInt &AccumulatedConstant,
1379 const SCEV *const *Ops, size_t NumOperands,
1381 ScalarEvolution &SE) {
1382 bool Interesting = false;
1384 // Iterate over the add operands. They are sorted, with constants first.
1386 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1388 // Pull a buried constant out to the outside.
1389 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1391 AccumulatedConstant += Scale * C->getValue()->getValue();
1394 // Next comes everything else. We're especially interested in multiplies
1395 // here, but they're in the middle, so just visit the rest with one loop.
1396 for (; i != NumOperands; ++i) {
1397 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1398 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1400 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1401 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1402 // A multiplication of a constant with another add; recurse.
1403 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1405 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1406 Add->op_begin(), Add->getNumOperands(),
1409 // A multiplication of a constant with some other value. Update
1411 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1412 const SCEV *Key = SE.getMulExpr(MulOps);
1413 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1414 M.insert(std::make_pair(Key, NewScale));
1416 NewOps.push_back(Pair.first->first);
1418 Pair.first->second += NewScale;
1419 // The map already had an entry for this value, which may indicate
1420 // a folding opportunity.
1425 // An ordinary operand. Update the map.
1426 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1427 M.insert(std::make_pair(Ops[i], Scale));
1429 NewOps.push_back(Pair.first->first);
1431 Pair.first->second += Scale;
1432 // The map already had an entry for this value, which may indicate
1433 // a folding opportunity.
1443 struct APIntCompare {
1444 bool operator()(const APInt &LHS, const APInt &RHS) const {
1445 return LHS.ult(RHS);
1450 /// getAddExpr - Get a canonical add expression, or something simpler if
1452 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1453 SCEV::NoWrapFlags Flags) {
1454 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1455 "only nuw or nsw allowed");
1456 assert(!Ops.empty() && "Cannot get empty add!");
1457 if (Ops.size() == 1) return Ops[0];
1459 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1460 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1461 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1462 "SCEVAddExpr operand types don't match!");
1465 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1467 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1468 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1469 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1471 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1472 E = Ops.end(); I != E; ++I)
1473 if (!isKnownNonNegative(*I)) {
1477 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1480 // Sort by complexity, this groups all similar expression types together.
1481 GroupByComplexity(Ops, LI);
1483 // If there are any constants, fold them together.
1485 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1487 assert(Idx < Ops.size());
1488 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1489 // We found two constants, fold them together!
1490 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1491 RHSC->getValue()->getValue());
1492 if (Ops.size() == 2) return Ops[0];
1493 Ops.erase(Ops.begin()+1); // Erase the folded element
1494 LHSC = cast<SCEVConstant>(Ops[0]);
1497 // If we are left with a constant zero being added, strip it off.
1498 if (LHSC->getValue()->isZero()) {
1499 Ops.erase(Ops.begin());
1503 if (Ops.size() == 1) return Ops[0];
1506 // Okay, check to see if the same value occurs in the operand list more than
1507 // once. If so, merge them together into an multiply expression. Since we
1508 // sorted the list, these values are required to be adjacent.
1509 Type *Ty = Ops[0]->getType();
1510 bool FoundMatch = false;
1511 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1512 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1513 // Scan ahead to count how many equal operands there are.
1515 while (i+Count != e && Ops[i+Count] == Ops[i])
1517 // Merge the values into a multiply.
1518 const SCEV *Scale = getConstant(Ty, Count);
1519 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1520 if (Ops.size() == Count)
1523 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1524 --i; e -= Count - 1;
1528 return getAddExpr(Ops, Flags);
1530 // Check for truncates. If all the operands are truncated from the same
1531 // type, see if factoring out the truncate would permit the result to be
1532 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1533 // if the contents of the resulting outer trunc fold to something simple.
1534 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1535 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1536 Type *DstType = Trunc->getType();
1537 Type *SrcType = Trunc->getOperand()->getType();
1538 SmallVector<const SCEV *, 8> LargeOps;
1540 // Check all the operands to see if they can be represented in the
1541 // source type of the truncate.
1542 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1543 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1544 if (T->getOperand()->getType() != SrcType) {
1548 LargeOps.push_back(T->getOperand());
1549 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1550 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1551 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1552 SmallVector<const SCEV *, 8> LargeMulOps;
1553 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1554 if (const SCEVTruncateExpr *T =
1555 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1556 if (T->getOperand()->getType() != SrcType) {
1560 LargeMulOps.push_back(T->getOperand());
1561 } else if (const SCEVConstant *C =
1562 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1563 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1570 LargeOps.push_back(getMulExpr(LargeMulOps));
1577 // Evaluate the expression in the larger type.
1578 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1579 // If it folds to something simple, use it. Otherwise, don't.
1580 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1581 return getTruncateExpr(Fold, DstType);
1585 // Skip past any other cast SCEVs.
1586 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1589 // If there are add operands they would be next.
1590 if (Idx < Ops.size()) {
1591 bool DeletedAdd = false;
1592 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1593 // If we have an add, expand the add operands onto the end of the operands
1595 Ops.erase(Ops.begin()+Idx);
1596 Ops.append(Add->op_begin(), Add->op_end());
1600 // If we deleted at least one add, we added operands to the end of the list,
1601 // and they are not necessarily sorted. Recurse to resort and resimplify
1602 // any operands we just acquired.
1604 return getAddExpr(Ops);
1607 // Skip over the add expression until we get to a multiply.
1608 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1611 // Check to see if there are any folding opportunities present with
1612 // operands multiplied by constant values.
1613 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1614 uint64_t BitWidth = getTypeSizeInBits(Ty);
1615 DenseMap<const SCEV *, APInt> M;
1616 SmallVector<const SCEV *, 8> NewOps;
1617 APInt AccumulatedConstant(BitWidth, 0);
1618 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1619 Ops.data(), Ops.size(),
1620 APInt(BitWidth, 1), *this)) {
1621 // Some interesting folding opportunity is present, so its worthwhile to
1622 // re-generate the operands list. Group the operands by constant scale,
1623 // to avoid multiplying by the same constant scale multiple times.
1624 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1625 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1626 E = NewOps.end(); I != E; ++I)
1627 MulOpLists[M.find(*I)->second].push_back(*I);
1628 // Re-generate the operands list.
1630 if (AccumulatedConstant != 0)
1631 Ops.push_back(getConstant(AccumulatedConstant));
1632 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1633 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1635 Ops.push_back(getMulExpr(getConstant(I->first),
1636 getAddExpr(I->second)));
1638 return getConstant(Ty, 0);
1639 if (Ops.size() == 1)
1641 return getAddExpr(Ops);
1645 // If we are adding something to a multiply expression, make sure the
1646 // something is not already an operand of the multiply. If so, merge it into
1648 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1649 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1650 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1651 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1652 if (isa<SCEVConstant>(MulOpSCEV))
1654 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1655 if (MulOpSCEV == Ops[AddOp]) {
1656 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1657 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1658 if (Mul->getNumOperands() != 2) {
1659 // If the multiply has more than two operands, we must get the
1661 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1662 Mul->op_begin()+MulOp);
1663 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1664 InnerMul = getMulExpr(MulOps);
1666 const SCEV *One = getConstant(Ty, 1);
1667 const SCEV *AddOne = getAddExpr(One, InnerMul);
1668 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1669 if (Ops.size() == 2) return OuterMul;
1671 Ops.erase(Ops.begin()+AddOp);
1672 Ops.erase(Ops.begin()+Idx-1);
1674 Ops.erase(Ops.begin()+Idx);
1675 Ops.erase(Ops.begin()+AddOp-1);
1677 Ops.push_back(OuterMul);
1678 return getAddExpr(Ops);
1681 // Check this multiply against other multiplies being added together.
1682 for (unsigned OtherMulIdx = Idx+1;
1683 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1685 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1686 // If MulOp occurs in OtherMul, we can fold the two multiplies
1688 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1689 OMulOp != e; ++OMulOp)
1690 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1691 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1692 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1693 if (Mul->getNumOperands() != 2) {
1694 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1695 Mul->op_begin()+MulOp);
1696 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1697 InnerMul1 = getMulExpr(MulOps);
1699 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1700 if (OtherMul->getNumOperands() != 2) {
1701 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1702 OtherMul->op_begin()+OMulOp);
1703 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1704 InnerMul2 = getMulExpr(MulOps);
1706 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1707 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1708 if (Ops.size() == 2) return OuterMul;
1709 Ops.erase(Ops.begin()+Idx);
1710 Ops.erase(Ops.begin()+OtherMulIdx-1);
1711 Ops.push_back(OuterMul);
1712 return getAddExpr(Ops);
1718 // If there are any add recurrences in the operands list, see if any other
1719 // added values are loop invariant. If so, we can fold them into the
1721 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1724 // Scan over all recurrences, trying to fold loop invariants into them.
1725 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1726 // Scan all of the other operands to this add and add them to the vector if
1727 // they are loop invariant w.r.t. the recurrence.
1728 SmallVector<const SCEV *, 8> LIOps;
1729 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1730 const Loop *AddRecLoop = AddRec->getLoop();
1731 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1732 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1733 LIOps.push_back(Ops[i]);
1734 Ops.erase(Ops.begin()+i);
1738 // If we found some loop invariants, fold them into the recurrence.
1739 if (!LIOps.empty()) {
1740 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1741 LIOps.push_back(AddRec->getStart());
1743 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1745 AddRecOps[0] = getAddExpr(LIOps);
1747 // Build the new addrec. Propagate the NUW and NSW flags if both the
1748 // outer add and the inner addrec are guaranteed to have no overflow.
1749 // Always propagate NW.
1750 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1751 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1753 // If all of the other operands were loop invariant, we are done.
1754 if (Ops.size() == 1) return NewRec;
1756 // Otherwise, add the folded AddRec by the non-invariant parts.
1757 for (unsigned i = 0;; ++i)
1758 if (Ops[i] == AddRec) {
1762 return getAddExpr(Ops);
1765 // Okay, if there weren't any loop invariants to be folded, check to see if
1766 // there are multiple AddRec's with the same loop induction variable being
1767 // added together. If so, we can fold them.
1768 for (unsigned OtherIdx = Idx+1;
1769 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1771 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1772 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1773 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1775 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1777 if (const SCEVAddRecExpr *OtherAddRec =
1778 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1779 if (OtherAddRec->getLoop() == AddRecLoop) {
1780 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1782 if (i >= AddRecOps.size()) {
1783 AddRecOps.append(OtherAddRec->op_begin()+i,
1784 OtherAddRec->op_end());
1787 AddRecOps[i] = getAddExpr(AddRecOps[i],
1788 OtherAddRec->getOperand(i));
1790 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1792 // Step size has changed, so we cannot guarantee no self-wraparound.
1793 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1794 return getAddExpr(Ops);
1797 // Otherwise couldn't fold anything into this recurrence. Move onto the
1801 // Okay, it looks like we really DO need an add expr. Check to see if we
1802 // already have one, otherwise create a new one.
1803 FoldingSetNodeID ID;
1804 ID.AddInteger(scAddExpr);
1805 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1806 ID.AddPointer(Ops[i]);
1809 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1811 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1812 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1813 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1815 UniqueSCEVs.InsertNode(S, IP);
1817 S->setNoWrapFlags(Flags);
1821 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1823 if (j > 1 && k / j != i) Overflow = true;
1827 /// Compute the result of "n choose k", the binomial coefficient. If an
1828 /// intermediate computation overflows, Overflow will be set and the return will
1829 /// be garbage. Overflow is not cleared on absence of overflow.
1830 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1831 // We use the multiplicative formula:
1832 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1833 // At each iteration, we take the n-th term of the numeral and divide by the
1834 // (k-n)th term of the denominator. This division will always produce an
1835 // integral result, and helps reduce the chance of overflow in the
1836 // intermediate computations. However, we can still overflow even when the
1837 // final result would fit.
1839 if (n == 0 || n == k) return 1;
1840 if (k > n) return 0;
1846 for (uint64_t i = 1; i <= k; ++i) {
1847 r = umul_ov(r, n-(i-1), Overflow);
1853 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1855 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1856 SCEV::NoWrapFlags Flags) {
1857 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1858 "only nuw or nsw allowed");
1859 assert(!Ops.empty() && "Cannot get empty mul!");
1860 if (Ops.size() == 1) return Ops[0];
1862 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1863 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1864 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1865 "SCEVMulExpr operand types don't match!");
1868 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1870 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1871 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1872 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1874 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1875 E = Ops.end(); I != E; ++I)
1876 if (!isKnownNonNegative(*I)) {
1880 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1883 // Sort by complexity, this groups all similar expression types together.
1884 GroupByComplexity(Ops, LI);
1886 // If there are any constants, fold them together.
1888 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1890 // C1*(C2+V) -> C1*C2 + C1*V
1891 if (Ops.size() == 2)
1892 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1893 if (Add->getNumOperands() == 2 &&
1894 isa<SCEVConstant>(Add->getOperand(0)))
1895 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1896 getMulExpr(LHSC, Add->getOperand(1)));
1899 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1900 // We found two constants, fold them together!
1901 ConstantInt *Fold = ConstantInt::get(getContext(),
1902 LHSC->getValue()->getValue() *
1903 RHSC->getValue()->getValue());
1904 Ops[0] = getConstant(Fold);
1905 Ops.erase(Ops.begin()+1); // Erase the folded element
1906 if (Ops.size() == 1) return Ops[0];
1907 LHSC = cast<SCEVConstant>(Ops[0]);
1910 // If we are left with a constant one being multiplied, strip it off.
1911 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1912 Ops.erase(Ops.begin());
1914 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1915 // If we have a multiply of zero, it will always be zero.
1917 } else if (Ops[0]->isAllOnesValue()) {
1918 // If we have a mul by -1 of an add, try distributing the -1 among the
1920 if (Ops.size() == 2) {
1921 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1922 SmallVector<const SCEV *, 4> NewOps;
1923 bool AnyFolded = false;
1924 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1925 E = Add->op_end(); I != E; ++I) {
1926 const SCEV *Mul = getMulExpr(Ops[0], *I);
1927 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1928 NewOps.push_back(Mul);
1931 return getAddExpr(NewOps);
1933 else if (const SCEVAddRecExpr *
1934 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1935 // Negation preserves a recurrence's no self-wrap property.
1936 SmallVector<const SCEV *, 4> Operands;
1937 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1938 E = AddRec->op_end(); I != E; ++I) {
1939 Operands.push_back(getMulExpr(Ops[0], *I));
1941 return getAddRecExpr(Operands, AddRec->getLoop(),
1942 AddRec->getNoWrapFlags(SCEV::FlagNW));
1947 if (Ops.size() == 1)
1951 // Skip over the add expression until we get to a multiply.
1952 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1955 // If there are mul operands inline them all into this expression.
1956 if (Idx < Ops.size()) {
1957 bool DeletedMul = false;
1958 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1959 // If we have an mul, expand the mul operands onto the end of the operands
1961 Ops.erase(Ops.begin()+Idx);
1962 Ops.append(Mul->op_begin(), Mul->op_end());
1966 // If we deleted at least one mul, we added operands to the end of the list,
1967 // and they are not necessarily sorted. Recurse to resort and resimplify
1968 // any operands we just acquired.
1970 return getMulExpr(Ops);
1973 // If there are any add recurrences in the operands list, see if any other
1974 // added values are loop invariant. If so, we can fold them into the
1976 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1979 // Scan over all recurrences, trying to fold loop invariants into them.
1980 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1981 // Scan all of the other operands to this mul and add them to the vector if
1982 // they are loop invariant w.r.t. the recurrence.
1983 SmallVector<const SCEV *, 8> LIOps;
1984 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1985 const Loop *AddRecLoop = AddRec->getLoop();
1986 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1987 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1988 LIOps.push_back(Ops[i]);
1989 Ops.erase(Ops.begin()+i);
1993 // If we found some loop invariants, fold them into the recurrence.
1994 if (!LIOps.empty()) {
1995 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1996 SmallVector<const SCEV *, 4> NewOps;
1997 NewOps.reserve(AddRec->getNumOperands());
1998 const SCEV *Scale = getMulExpr(LIOps);
1999 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2000 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2002 // Build the new addrec. Propagate the NUW and NSW flags if both the
2003 // outer mul and the inner addrec are guaranteed to have no overflow.
2005 // No self-wrap cannot be guaranteed after changing the step size, but
2006 // will be inferred if either NUW or NSW is true.
2007 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2008 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2010 // If all of the other operands were loop invariant, we are done.
2011 if (Ops.size() == 1) return NewRec;
2013 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2014 for (unsigned i = 0;; ++i)
2015 if (Ops[i] == AddRec) {
2019 return getMulExpr(Ops);
2022 // Okay, if there weren't any loop invariants to be folded, check to see if
2023 // there are multiple AddRec's with the same loop induction variable being
2024 // multiplied together. If so, we can fold them.
2025 for (unsigned OtherIdx = Idx+1;
2026 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2028 if (AddRecLoop != cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop())
2031 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2032 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2033 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2034 // ]]],+,...up to x=2n}.
2035 // Note that the arguments to choose() are always integers with values
2036 // known at compile time, never SCEV objects.
2038 // The implementation avoids pointless extra computations when the two
2039 // addrec's are of different length (mathematically, it's equivalent to
2040 // an infinite stream of zeros on the right).
2041 bool OpsModified = false;
2042 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2044 const SCEVAddRecExpr *OtherAddRec =
2045 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2046 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2049 bool Overflow = false;
2050 Type *Ty = AddRec->getType();
2051 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2052 SmallVector<const SCEV*, 7> AddRecOps;
2053 for (int x = 0, xe = AddRec->getNumOperands() +
2054 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2055 const SCEV *Term = getConstant(Ty, 0);
2056 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2057 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2058 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2059 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2060 z < ze && !Overflow; ++z) {
2061 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2063 if (LargerThan64Bits)
2064 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2066 Coeff = Coeff1*Coeff2;
2067 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2068 const SCEV *Term1 = AddRec->getOperand(y-z);
2069 const SCEV *Term2 = OtherAddRec->getOperand(z);
2070 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2073 AddRecOps.push_back(Term);
2076 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2078 if (Ops.size() == 2) return NewAddRec;
2079 Ops[Idx] = NewAddRec;
2080 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2082 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2088 return getMulExpr(Ops);
2091 // Otherwise couldn't fold anything into this recurrence. Move onto the
2095 // Okay, it looks like we really DO need an mul expr. Check to see if we
2096 // already have one, otherwise create a new one.
2097 FoldingSetNodeID ID;
2098 ID.AddInteger(scMulExpr);
2099 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2100 ID.AddPointer(Ops[i]);
2103 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2105 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2106 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2107 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2109 UniqueSCEVs.InsertNode(S, IP);
2111 S->setNoWrapFlags(Flags);
2115 /// getUDivExpr - Get a canonical unsigned division expression, or something
2116 /// simpler if possible.
2117 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2119 assert(getEffectiveSCEVType(LHS->getType()) ==
2120 getEffectiveSCEVType(RHS->getType()) &&
2121 "SCEVUDivExpr operand types don't match!");
2123 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2124 if (RHSC->getValue()->equalsInt(1))
2125 return LHS; // X udiv 1 --> x
2126 // If the denominator is zero, the result of the udiv is undefined. Don't
2127 // try to analyze it, because the resolution chosen here may differ from
2128 // the resolution chosen in other parts of the compiler.
2129 if (!RHSC->getValue()->isZero()) {
2130 // Determine if the division can be folded into the operands of
2132 // TODO: Generalize this to non-constants by using known-bits information.
2133 Type *Ty = LHS->getType();
2134 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2135 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2136 // For non-power-of-two values, effectively round the value up to the
2137 // nearest power of two.
2138 if (!RHSC->getValue()->getValue().isPowerOf2())
2140 IntegerType *ExtTy =
2141 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2142 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2143 if (const SCEVConstant *Step =
2144 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2145 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2146 const APInt &StepInt = Step->getValue()->getValue();
2147 const APInt &DivInt = RHSC->getValue()->getValue();
2148 if (!StepInt.urem(DivInt) &&
2149 getZeroExtendExpr(AR, ExtTy) ==
2150 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2151 getZeroExtendExpr(Step, ExtTy),
2152 AR->getLoop(), SCEV::FlagAnyWrap)) {
2153 SmallVector<const SCEV *, 4> Operands;
2154 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2155 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2156 return getAddRecExpr(Operands, AR->getLoop(),
2159 /// Get a canonical UDivExpr for a recurrence.
2160 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2161 // We can currently only fold X%N if X is constant.
2162 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2163 if (StartC && !DivInt.urem(StepInt) &&
2164 getZeroExtendExpr(AR, ExtTy) ==
2165 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2166 getZeroExtendExpr(Step, ExtTy),
2167 AR->getLoop(), SCEV::FlagAnyWrap)) {
2168 const APInt &StartInt = StartC->getValue()->getValue();
2169 const APInt &StartRem = StartInt.urem(StepInt);
2171 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2172 AR->getLoop(), SCEV::FlagNW);
2175 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2176 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2177 SmallVector<const SCEV *, 4> Operands;
2178 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2179 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2180 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2181 // Find an operand that's safely divisible.
2182 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2183 const SCEV *Op = M->getOperand(i);
2184 const SCEV *Div = getUDivExpr(Op, RHSC);
2185 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2186 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2189 return getMulExpr(Operands);
2193 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2194 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2195 SmallVector<const SCEV *, 4> Operands;
2196 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2197 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2198 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2200 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2201 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2202 if (isa<SCEVUDivExpr>(Op) ||
2203 getMulExpr(Op, RHS) != A->getOperand(i))
2205 Operands.push_back(Op);
2207 if (Operands.size() == A->getNumOperands())
2208 return getAddExpr(Operands);
2212 // Fold if both operands are constant.
2213 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2214 Constant *LHSCV = LHSC->getValue();
2215 Constant *RHSCV = RHSC->getValue();
2216 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2222 FoldingSetNodeID ID;
2223 ID.AddInteger(scUDivExpr);
2227 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2228 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2230 UniqueSCEVs.InsertNode(S, IP);
2235 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2236 /// Simplify the expression as much as possible.
2237 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2239 SCEV::NoWrapFlags Flags) {
2240 SmallVector<const SCEV *, 4> Operands;
2241 Operands.push_back(Start);
2242 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2243 if (StepChrec->getLoop() == L) {
2244 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2245 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2248 Operands.push_back(Step);
2249 return getAddRecExpr(Operands, L, Flags);
2252 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2253 /// Simplify the expression as much as possible.
2255 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2256 const Loop *L, SCEV::NoWrapFlags Flags) {
2257 if (Operands.size() == 1) return Operands[0];
2259 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2260 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2261 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2262 "SCEVAddRecExpr operand types don't match!");
2263 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2264 assert(isLoopInvariant(Operands[i], L) &&
2265 "SCEVAddRecExpr operand is not loop-invariant!");
2268 if (Operands.back()->isZero()) {
2269 Operands.pop_back();
2270 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2273 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2274 // use that information to infer NUW and NSW flags. However, computing a
2275 // BE count requires calling getAddRecExpr, so we may not yet have a
2276 // meaningful BE count at this point (and if we don't, we'd be stuck
2277 // with a SCEVCouldNotCompute as the cached BE count).
2279 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2281 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2282 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2283 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2285 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2286 E = Operands.end(); I != E; ++I)
2287 if (!isKnownNonNegative(*I)) {
2291 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2294 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2295 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2296 const Loop *NestedLoop = NestedAR->getLoop();
2297 if (L->contains(NestedLoop) ?
2298 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2299 (!NestedLoop->contains(L) &&
2300 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2301 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2302 NestedAR->op_end());
2303 Operands[0] = NestedAR->getStart();
2304 // AddRecs require their operands be loop-invariant with respect to their
2305 // loops. Don't perform this transformation if it would break this
2307 bool AllInvariant = true;
2308 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2309 if (!isLoopInvariant(Operands[i], L)) {
2310 AllInvariant = false;
2314 // Create a recurrence for the outer loop with the same step size.
2316 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2317 // inner recurrence has the same property.
2318 SCEV::NoWrapFlags OuterFlags =
2319 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2321 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2322 AllInvariant = true;
2323 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2324 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2325 AllInvariant = false;
2329 // Ok, both add recurrences are valid after the transformation.
2331 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2332 // the outer recurrence has the same property.
2333 SCEV::NoWrapFlags InnerFlags =
2334 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2335 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2338 // Reset Operands to its original state.
2339 Operands[0] = NestedAR;
2343 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2344 // already have one, otherwise create a new one.
2345 FoldingSetNodeID ID;
2346 ID.AddInteger(scAddRecExpr);
2347 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2348 ID.AddPointer(Operands[i]);
2352 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2354 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2355 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2356 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2357 O, Operands.size(), L);
2358 UniqueSCEVs.InsertNode(S, IP);
2360 S->setNoWrapFlags(Flags);
2364 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2366 SmallVector<const SCEV *, 2> Ops;
2369 return getSMaxExpr(Ops);
2373 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2374 assert(!Ops.empty() && "Cannot get empty smax!");
2375 if (Ops.size() == 1) return Ops[0];
2377 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2378 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2379 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2380 "SCEVSMaxExpr operand types don't match!");
2383 // Sort by complexity, this groups all similar expression types together.
2384 GroupByComplexity(Ops, LI);
2386 // If there are any constants, fold them together.
2388 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2390 assert(Idx < Ops.size());
2391 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2392 // We found two constants, fold them together!
2393 ConstantInt *Fold = ConstantInt::get(getContext(),
2394 APIntOps::smax(LHSC->getValue()->getValue(),
2395 RHSC->getValue()->getValue()));
2396 Ops[0] = getConstant(Fold);
2397 Ops.erase(Ops.begin()+1); // Erase the folded element
2398 if (Ops.size() == 1) return Ops[0];
2399 LHSC = cast<SCEVConstant>(Ops[0]);
2402 // If we are left with a constant minimum-int, strip it off.
2403 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2404 Ops.erase(Ops.begin());
2406 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2407 // If we have an smax with a constant maximum-int, it will always be
2412 if (Ops.size() == 1) return Ops[0];
2415 // Find the first SMax
2416 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2419 // Check to see if one of the operands is an SMax. If so, expand its operands
2420 // onto our operand list, and recurse to simplify.
2421 if (Idx < Ops.size()) {
2422 bool DeletedSMax = false;
2423 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2424 Ops.erase(Ops.begin()+Idx);
2425 Ops.append(SMax->op_begin(), SMax->op_end());
2430 return getSMaxExpr(Ops);
2433 // Okay, check to see if the same value occurs in the operand list twice. If
2434 // so, delete one. Since we sorted the list, these values are required to
2436 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2437 // X smax Y smax Y --> X smax Y
2438 // X smax Y --> X, if X is always greater than Y
2439 if (Ops[i] == Ops[i+1] ||
2440 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2441 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2443 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2444 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2448 if (Ops.size() == 1) return Ops[0];
2450 assert(!Ops.empty() && "Reduced smax down to nothing!");
2452 // Okay, it looks like we really DO need an smax expr. Check to see if we
2453 // already have one, otherwise create a new one.
2454 FoldingSetNodeID ID;
2455 ID.AddInteger(scSMaxExpr);
2456 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2457 ID.AddPointer(Ops[i]);
2459 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2460 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2461 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2462 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2464 UniqueSCEVs.InsertNode(S, IP);
2468 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2470 SmallVector<const SCEV *, 2> Ops;
2473 return getUMaxExpr(Ops);
2477 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2478 assert(!Ops.empty() && "Cannot get empty umax!");
2479 if (Ops.size() == 1) return Ops[0];
2481 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2482 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2483 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2484 "SCEVUMaxExpr operand types don't match!");
2487 // Sort by complexity, this groups all similar expression types together.
2488 GroupByComplexity(Ops, LI);
2490 // If there are any constants, fold them together.
2492 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2494 assert(Idx < Ops.size());
2495 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2496 // We found two constants, fold them together!
2497 ConstantInt *Fold = ConstantInt::get(getContext(),
2498 APIntOps::umax(LHSC->getValue()->getValue(),
2499 RHSC->getValue()->getValue()));
2500 Ops[0] = getConstant(Fold);
2501 Ops.erase(Ops.begin()+1); // Erase the folded element
2502 if (Ops.size() == 1) return Ops[0];
2503 LHSC = cast<SCEVConstant>(Ops[0]);
2506 // If we are left with a constant minimum-int, strip it off.
2507 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2508 Ops.erase(Ops.begin());
2510 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2511 // If we have an umax with a constant maximum-int, it will always be
2516 if (Ops.size() == 1) return Ops[0];
2519 // Find the first UMax
2520 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2523 // Check to see if one of the operands is a UMax. If so, expand its operands
2524 // onto our operand list, and recurse to simplify.
2525 if (Idx < Ops.size()) {
2526 bool DeletedUMax = false;
2527 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2528 Ops.erase(Ops.begin()+Idx);
2529 Ops.append(UMax->op_begin(), UMax->op_end());
2534 return getUMaxExpr(Ops);
2537 // Okay, check to see if the same value occurs in the operand list twice. If
2538 // so, delete one. Since we sorted the list, these values are required to
2540 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2541 // X umax Y umax Y --> X umax Y
2542 // X umax Y --> X, if X is always greater than Y
2543 if (Ops[i] == Ops[i+1] ||
2544 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2545 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2547 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2548 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2552 if (Ops.size() == 1) return Ops[0];
2554 assert(!Ops.empty() && "Reduced umax down to nothing!");
2556 // Okay, it looks like we really DO need a umax expr. Check to see if we
2557 // already have one, otherwise create a new one.
2558 FoldingSetNodeID ID;
2559 ID.AddInteger(scUMaxExpr);
2560 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2561 ID.AddPointer(Ops[i]);
2563 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2564 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2565 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2566 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2568 UniqueSCEVs.InsertNode(S, IP);
2572 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2574 // ~smax(~x, ~y) == smin(x, y).
2575 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2578 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2580 // ~umax(~x, ~y) == umin(x, y)
2581 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2584 const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy, Type *IntPtrTy) {
2585 // If we have DataLayout, we can bypass creating a target-independent
2586 // constant expression and then folding it back into a ConstantInt.
2587 // This is just a compile-time optimization.
2589 return getConstant(IntPtrTy, TD->getTypeAllocSize(AllocTy));
2591 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2592 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2593 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2595 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2596 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2599 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2600 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2601 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2602 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2604 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2605 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2608 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy, Type *IntPtrTy,
2610 // If we have DataLayout, we can bypass creating a target-independent
2611 // constant expression and then folding it back into a ConstantInt.
2612 // This is just a compile-time optimization.
2614 return getConstant(IntPtrTy,
2615 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2617 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2618 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2619 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2621 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2622 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2625 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2626 Constant *FieldNo) {
2627 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2628 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2629 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2631 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2632 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2635 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2636 // Don't attempt to do anything other than create a SCEVUnknown object
2637 // here. createSCEV only calls getUnknown after checking for all other
2638 // interesting possibilities, and any other code that calls getUnknown
2639 // is doing so in order to hide a value from SCEV canonicalization.
2641 FoldingSetNodeID ID;
2642 ID.AddInteger(scUnknown);
2645 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2646 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2647 "Stale SCEVUnknown in uniquing map!");
2650 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2652 FirstUnknown = cast<SCEVUnknown>(S);
2653 UniqueSCEVs.InsertNode(S, IP);
2657 //===----------------------------------------------------------------------===//
2658 // Basic SCEV Analysis and PHI Idiom Recognition Code
2661 /// isSCEVable - Test if values of the given type are analyzable within
2662 /// the SCEV framework. This primarily includes integer types, and it
2663 /// can optionally include pointer types if the ScalarEvolution class
2664 /// has access to target-specific information.
2665 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2666 // Integers and pointers are always SCEVable.
2667 return Ty->isIntegerTy() || Ty->isPointerTy();
2670 /// getTypeSizeInBits - Return the size in bits of the specified type,
2671 /// for which isSCEVable must return true.
2672 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2673 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2675 // If we have a DataLayout, use it!
2677 return TD->getTypeSizeInBits(Ty);
2679 // Integer types have fixed sizes.
2680 if (Ty->isIntegerTy())
2681 return Ty->getPrimitiveSizeInBits();
2683 // The only other support type is pointer. Without DataLayout, conservatively
2684 // assume pointers are 64-bit.
2685 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2689 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2690 /// the given type and which represents how SCEV will treat the given
2691 /// type, for which isSCEVable must return true. For pointer types,
2692 /// this is the pointer-sized integer type.
2693 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2694 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2696 if (Ty->isIntegerTy())
2699 // The only other support type is pointer.
2700 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2701 if (TD) return TD->getIntPtrType(Ty);
2703 // Without DataLayout, conservatively assume pointers are 64-bit.
2704 return Type::getInt64Ty(getContext());
2707 const SCEV *ScalarEvolution::getCouldNotCompute() {
2708 return &CouldNotCompute;
2711 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2712 /// expression and create a new one.
2713 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2714 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2716 ValueExprMapType::const_iterator I = ValueExprMap.find_as(V);
2717 if (I != ValueExprMap.end()) return I->second;
2718 const SCEV *S = createSCEV(V);
2720 // The process of creating a SCEV for V may have caused other SCEVs
2721 // to have been created, so it's necessary to insert the new entry
2722 // from scratch, rather than trying to remember the insert position
2724 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2728 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2730 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2731 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2733 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2735 Type *Ty = V->getType();
2736 Ty = getEffectiveSCEVType(Ty);
2737 return getMulExpr(V,
2738 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2741 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2742 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2743 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2745 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2747 Type *Ty = V->getType();
2748 Ty = getEffectiveSCEVType(Ty);
2749 const SCEV *AllOnes =
2750 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2751 return getMinusSCEV(AllOnes, V);
2754 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2755 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2756 SCEV::NoWrapFlags Flags) {
2757 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2759 // Fast path: X - X --> 0.
2761 return getConstant(LHS->getType(), 0);
2764 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2767 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2768 /// input value to the specified type. If the type must be extended, it is zero
2771 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2772 Type *SrcTy = V->getType();
2773 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2774 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2775 "Cannot truncate or zero extend with non-integer arguments!");
2776 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2777 return V; // No conversion
2778 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2779 return getTruncateExpr(V, Ty);
2780 return getZeroExtendExpr(V, Ty);
2783 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2784 /// input value to the specified type. If the type must be extended, it is sign
2787 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2789 Type *SrcTy = V->getType();
2790 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2791 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2792 "Cannot truncate or zero extend with non-integer arguments!");
2793 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2794 return V; // No conversion
2795 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2796 return getTruncateExpr(V, Ty);
2797 return getSignExtendExpr(V, Ty);
2800 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2801 /// input value to the specified type. If the type must be extended, it is zero
2802 /// extended. The conversion must not be narrowing.
2804 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2805 Type *SrcTy = V->getType();
2806 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2807 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2808 "Cannot noop or zero extend with non-integer arguments!");
2809 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2810 "getNoopOrZeroExtend cannot truncate!");
2811 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2812 return V; // No conversion
2813 return getZeroExtendExpr(V, Ty);
2816 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2817 /// input value to the specified type. If the type must be extended, it is sign
2818 /// extended. The conversion must not be narrowing.
2820 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2821 Type *SrcTy = V->getType();
2822 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2823 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2824 "Cannot noop or sign extend with non-integer arguments!");
2825 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2826 "getNoopOrSignExtend cannot truncate!");
2827 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2828 return V; // No conversion
2829 return getSignExtendExpr(V, Ty);
2832 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2833 /// the input value to the specified type. If the type must be extended,
2834 /// it is extended with unspecified bits. The conversion must not be
2837 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2838 Type *SrcTy = V->getType();
2839 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2840 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2841 "Cannot noop or any extend with non-integer arguments!");
2842 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2843 "getNoopOrAnyExtend cannot truncate!");
2844 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2845 return V; // No conversion
2846 return getAnyExtendExpr(V, Ty);
2849 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2850 /// input value to the specified type. The conversion must not be widening.
2852 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2853 Type *SrcTy = V->getType();
2854 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2855 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2856 "Cannot truncate or noop with non-integer arguments!");
2857 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2858 "getTruncateOrNoop cannot extend!");
2859 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2860 return V; // No conversion
2861 return getTruncateExpr(V, Ty);
2864 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2865 /// the types using zero-extension, and then perform a umax operation
2867 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2869 const SCEV *PromotedLHS = LHS;
2870 const SCEV *PromotedRHS = RHS;
2872 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2873 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2875 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2877 return getUMaxExpr(PromotedLHS, PromotedRHS);
2880 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2881 /// the types using zero-extension, and then perform a umin operation
2883 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2885 const SCEV *PromotedLHS = LHS;
2886 const SCEV *PromotedRHS = RHS;
2888 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2889 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2891 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2893 return getUMinExpr(PromotedLHS, PromotedRHS);
2896 /// getPointerBase - Transitively follow the chain of pointer-type operands
2897 /// until reaching a SCEV that does not have a single pointer operand. This
2898 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2899 /// but corner cases do exist.
2900 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2901 // A pointer operand may evaluate to a nonpointer expression, such as null.
2902 if (!V->getType()->isPointerTy())
2905 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2906 return getPointerBase(Cast->getOperand());
2908 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2909 const SCEV *PtrOp = 0;
2910 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2912 if ((*I)->getType()->isPointerTy()) {
2913 // Cannot find the base of an expression with multiple pointer operands.
2921 return getPointerBase(PtrOp);
2926 /// PushDefUseChildren - Push users of the given Instruction
2927 /// onto the given Worklist.
2929 PushDefUseChildren(Instruction *I,
2930 SmallVectorImpl<Instruction *> &Worklist) {
2931 // Push the def-use children onto the Worklist stack.
2932 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2934 Worklist.push_back(cast<Instruction>(*UI));
2937 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2938 /// instructions that depend on the given instruction and removes them from
2939 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2942 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2943 SmallVector<Instruction *, 16> Worklist;
2944 PushDefUseChildren(PN, Worklist);
2946 SmallPtrSet<Instruction *, 8> Visited;
2948 while (!Worklist.empty()) {
2949 Instruction *I = Worklist.pop_back_val();
2950 if (!Visited.insert(I)) continue;
2952 ValueExprMapType::iterator It =
2953 ValueExprMap.find_as(static_cast<Value *>(I));
2954 if (It != ValueExprMap.end()) {
2955 const SCEV *Old = It->second;
2957 // Short-circuit the def-use traversal if the symbolic name
2958 // ceases to appear in expressions.
2959 if (Old != SymName && !hasOperand(Old, SymName))
2962 // SCEVUnknown for a PHI either means that it has an unrecognized
2963 // structure, it's a PHI that's in the progress of being computed
2964 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2965 // additional loop trip count information isn't going to change anything.
2966 // In the second case, createNodeForPHI will perform the necessary
2967 // updates on its own when it gets to that point. In the third, we do
2968 // want to forget the SCEVUnknown.
2969 if (!isa<PHINode>(I) ||
2970 !isa<SCEVUnknown>(Old) ||
2971 (I != PN && Old == SymName)) {
2972 forgetMemoizedResults(Old);
2973 ValueExprMap.erase(It);
2977 PushDefUseChildren(I, Worklist);
2981 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2982 /// a loop header, making it a potential recurrence, or it doesn't.
2984 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2985 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2986 if (L->getHeader() == PN->getParent()) {
2987 // The loop may have multiple entrances or multiple exits; we can analyze
2988 // this phi as an addrec if it has a unique entry value and a unique
2990 Value *BEValueV = 0, *StartValueV = 0;
2991 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2992 Value *V = PN->getIncomingValue(i);
2993 if (L->contains(PN->getIncomingBlock(i))) {
2996 } else if (BEValueV != V) {
3000 } else if (!StartValueV) {
3002 } else if (StartValueV != V) {
3007 if (BEValueV && StartValueV) {
3008 // While we are analyzing this PHI node, handle its value symbolically.
3009 const SCEV *SymbolicName = getUnknown(PN);
3010 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3011 "PHI node already processed?");
3012 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3014 // Using this symbolic name for the PHI, analyze the value coming around
3016 const SCEV *BEValue = getSCEV(BEValueV);
3018 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3019 // has a special value for the first iteration of the loop.
3021 // If the value coming around the backedge is an add with the symbolic
3022 // value we just inserted, then we found a simple induction variable!
3023 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3024 // If there is a single occurrence of the symbolic value, replace it
3025 // with a recurrence.
3026 unsigned FoundIndex = Add->getNumOperands();
3027 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3028 if (Add->getOperand(i) == SymbolicName)
3029 if (FoundIndex == e) {
3034 if (FoundIndex != Add->getNumOperands()) {
3035 // Create an add with everything but the specified operand.
3036 SmallVector<const SCEV *, 8> Ops;
3037 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3038 if (i != FoundIndex)
3039 Ops.push_back(Add->getOperand(i));
3040 const SCEV *Accum = getAddExpr(Ops);
3042 // This is not a valid addrec if the step amount is varying each
3043 // loop iteration, but is not itself an addrec in this loop.
3044 if (isLoopInvariant(Accum, L) ||
3045 (isa<SCEVAddRecExpr>(Accum) &&
3046 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3047 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3049 // If the increment doesn't overflow, then neither the addrec nor
3050 // the post-increment will overflow.
3051 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3052 if (OBO->hasNoUnsignedWrap())
3053 Flags = setFlags(Flags, SCEV::FlagNUW);
3054 if (OBO->hasNoSignedWrap())
3055 Flags = setFlags(Flags, SCEV::FlagNSW);
3056 } else if (const GEPOperator *GEP =
3057 dyn_cast<GEPOperator>(BEValueV)) {
3058 // If the increment is an inbounds GEP, then we know the address
3059 // space cannot be wrapped around. We cannot make any guarantee
3060 // about signed or unsigned overflow because pointers are
3061 // unsigned but we may have a negative index from the base
3063 if (GEP->isInBounds())
3064 Flags = setFlags(Flags, SCEV::FlagNW);
3067 const SCEV *StartVal = getSCEV(StartValueV);
3068 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3070 // Since the no-wrap flags are on the increment, they apply to the
3071 // post-incremented value as well.
3072 if (isLoopInvariant(Accum, L))
3073 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3076 // Okay, for the entire analysis of this edge we assumed the PHI
3077 // to be symbolic. We now need to go back and purge all of the
3078 // entries for the scalars that use the symbolic expression.
3079 ForgetSymbolicName(PN, SymbolicName);
3080 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3084 } else if (const SCEVAddRecExpr *AddRec =
3085 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3086 // Otherwise, this could be a loop like this:
3087 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3088 // In this case, j = {1,+,1} and BEValue is j.
3089 // Because the other in-value of i (0) fits the evolution of BEValue
3090 // i really is an addrec evolution.
3091 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3092 const SCEV *StartVal = getSCEV(StartValueV);
3094 // If StartVal = j.start - j.stride, we can use StartVal as the
3095 // initial step of the addrec evolution.
3096 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3097 AddRec->getOperand(1))) {
3098 // FIXME: For constant StartVal, we should be able to infer
3100 const SCEV *PHISCEV =
3101 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3104 // Okay, for the entire analysis of this edge we assumed the PHI
3105 // to be symbolic. We now need to go back and purge all of the
3106 // entries for the scalars that use the symbolic expression.
3107 ForgetSymbolicName(PN, SymbolicName);
3108 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3116 // If the PHI has a single incoming value, follow that value, unless the
3117 // PHI's incoming blocks are in a different loop, in which case doing so
3118 // risks breaking LCSSA form. Instcombine would normally zap these, but
3119 // it doesn't have DominatorTree information, so it may miss cases.
3120 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
3121 if (LI->replacementPreservesLCSSAForm(PN, V))
3124 // If it's not a loop phi, we can't handle it yet.
3125 return getUnknown(PN);
3128 /// createNodeForGEP - Expand GEP instructions into add and multiply
3129 /// operations. This allows them to be analyzed by regular SCEV code.
3131 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3133 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3134 // Add expression, because the Instruction may be guarded by control flow
3135 // and the no-overflow bits may not be valid for the expression in any
3137 bool isInBounds = GEP->isInBounds();
3139 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3140 Value *Base = GEP->getOperand(0);
3141 // Don't attempt to analyze GEPs over unsized objects.
3142 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3143 return getUnknown(GEP);
3144 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3145 gep_type_iterator GTI = gep_type_begin(GEP);
3146 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3150 // Compute the (potentially symbolic) offset in bytes for this index.
3151 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3152 // For a struct, add the member offset.
3153 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3154 const SCEV *FieldOffset = getOffsetOfExpr(STy, IntPtrTy, FieldNo);
3156 // Add the field offset to the running total offset.
3157 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3159 // For an array, add the element offset, explicitly scaled.
3160 const SCEV *ElementSize = getSizeOfExpr(*GTI, IntPtrTy);
3161 const SCEV *IndexS = getSCEV(Index);
3162 // Getelementptr indices are signed.
3163 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3165 // Multiply the index by the element size to compute the element offset.
3166 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3167 isInBounds ? SCEV::FlagNSW :
3170 // Add the element offset to the running total offset.
3171 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3175 // Get the SCEV for the GEP base.
3176 const SCEV *BaseS = getSCEV(Base);
3178 // Add the total offset from all the GEP indices to the base.
3179 return getAddExpr(BaseS, TotalOffset,
3180 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3183 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3184 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3185 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3186 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3188 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3189 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3190 return C->getValue()->getValue().countTrailingZeros();
3192 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3193 return std::min(GetMinTrailingZeros(T->getOperand()),
3194 (uint32_t)getTypeSizeInBits(T->getType()));
3196 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3197 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3198 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3199 getTypeSizeInBits(E->getType()) : OpRes;
3202 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3203 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3204 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3205 getTypeSizeInBits(E->getType()) : OpRes;
3208 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3209 // The result is the min of all operands results.
3210 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3211 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3212 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3216 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3217 // The result is the sum of all operands results.
3218 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3219 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3220 for (unsigned i = 1, e = M->getNumOperands();
3221 SumOpRes != BitWidth && i != e; ++i)
3222 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3227 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3228 // The result is the min of all operands results.
3229 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3230 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3231 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3235 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3236 // The result is the min of all operands results.
3237 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3238 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3239 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3243 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3244 // The result is the min of all operands results.
3245 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3246 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3247 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3251 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3252 // For a SCEVUnknown, ask ValueTracking.
3253 unsigned BitWidth = getTypeSizeInBits(U->getType());
3254 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3255 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3256 return Zeros.countTrailingOnes();
3263 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3266 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3267 // See if we've computed this range already.
3268 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3269 if (I != UnsignedRanges.end())
3272 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3273 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3275 unsigned BitWidth = getTypeSizeInBits(S->getType());
3276 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3278 // If the value has known zeros, the maximum unsigned value will have those
3279 // known zeros as well.
3280 uint32_t TZ = GetMinTrailingZeros(S);
3282 ConservativeResult =
3283 ConstantRange(APInt::getMinValue(BitWidth),
3284 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3286 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3287 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3288 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3289 X = X.add(getUnsignedRange(Add->getOperand(i)));
3290 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3293 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3294 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3295 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3296 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3297 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3300 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3301 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3302 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3303 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3304 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3307 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3308 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3309 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3310 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3311 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3314 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3315 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3316 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3317 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3320 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3321 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3322 return setUnsignedRange(ZExt,
3323 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3326 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3327 ConstantRange X = getUnsignedRange(SExt->getOperand());
3328 return setUnsignedRange(SExt,
3329 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3332 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3333 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3334 return setUnsignedRange(Trunc,
3335 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3338 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3339 // If there's no unsigned wrap, the value will never be less than its
3341 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3342 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3343 if (!C->getValue()->isZero())
3344 ConservativeResult =
3345 ConservativeResult.intersectWith(
3346 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3348 // TODO: non-affine addrec
3349 if (AddRec->isAffine()) {
3350 Type *Ty = AddRec->getType();
3351 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3352 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3353 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3354 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3356 const SCEV *Start = AddRec->getStart();
3357 const SCEV *Step = AddRec->getStepRecurrence(*this);
3359 ConstantRange StartRange = getUnsignedRange(Start);
3360 ConstantRange StepRange = getSignedRange(Step);
3361 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3362 ConstantRange EndRange =
3363 StartRange.add(MaxBECountRange.multiply(StepRange));
3365 // Check for overflow. This must be done with ConstantRange arithmetic
3366 // because we could be called from within the ScalarEvolution overflow
3368 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3369 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3370 ConstantRange ExtMaxBECountRange =
3371 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3372 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3373 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3375 return setUnsignedRange(AddRec, ConservativeResult);
3377 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3378 EndRange.getUnsignedMin());
3379 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3380 EndRange.getUnsignedMax());
3381 if (Min.isMinValue() && Max.isMaxValue())
3382 return setUnsignedRange(AddRec, ConservativeResult);
3383 return setUnsignedRange(AddRec,
3384 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3388 return setUnsignedRange(AddRec, ConservativeResult);
3391 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3392 // For a SCEVUnknown, ask ValueTracking.
3393 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3394 ComputeMaskedBits(U->getValue(), Zeros, Ones, TD);
3395 if (Ones == ~Zeros + 1)
3396 return setUnsignedRange(U, ConservativeResult);
3397 return setUnsignedRange(U,
3398 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3401 return setUnsignedRange(S, ConservativeResult);
3404 /// getSignedRange - Determine the signed range for a particular SCEV.
3407 ScalarEvolution::getSignedRange(const SCEV *S) {
3408 // See if we've computed this range already.
3409 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3410 if (I != SignedRanges.end())
3413 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3414 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3416 unsigned BitWidth = getTypeSizeInBits(S->getType());
3417 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3419 // If the value has known zeros, the maximum signed value will have those
3420 // known zeros as well.
3421 uint32_t TZ = GetMinTrailingZeros(S);
3423 ConservativeResult =
3424 ConstantRange(APInt::getSignedMinValue(BitWidth),
3425 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3427 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3428 ConstantRange X = getSignedRange(Add->getOperand(0));
3429 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3430 X = X.add(getSignedRange(Add->getOperand(i)));
3431 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3434 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3435 ConstantRange X = getSignedRange(Mul->getOperand(0));
3436 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3437 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3438 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3441 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3442 ConstantRange X = getSignedRange(SMax->getOperand(0));
3443 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3444 X = X.smax(getSignedRange(SMax->getOperand(i)));
3445 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3448 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3449 ConstantRange X = getSignedRange(UMax->getOperand(0));
3450 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3451 X = X.umax(getSignedRange(UMax->getOperand(i)));
3452 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3455 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3456 ConstantRange X = getSignedRange(UDiv->getLHS());
3457 ConstantRange Y = getSignedRange(UDiv->getRHS());
3458 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3461 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3462 ConstantRange X = getSignedRange(ZExt->getOperand());
3463 return setSignedRange(ZExt,
3464 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3467 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3468 ConstantRange X = getSignedRange(SExt->getOperand());
3469 return setSignedRange(SExt,
3470 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3473 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3474 ConstantRange X = getSignedRange(Trunc->getOperand());
3475 return setSignedRange(Trunc,
3476 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3479 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3480 // If there's no signed wrap, and all the operands have the same sign or
3481 // zero, the value won't ever change sign.
3482 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3483 bool AllNonNeg = true;
3484 bool AllNonPos = true;
3485 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3486 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3487 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3490 ConservativeResult = ConservativeResult.intersectWith(
3491 ConstantRange(APInt(BitWidth, 0),
3492 APInt::getSignedMinValue(BitWidth)));
3494 ConservativeResult = ConservativeResult.intersectWith(
3495 ConstantRange(APInt::getSignedMinValue(BitWidth),
3496 APInt(BitWidth, 1)));
3499 // TODO: non-affine addrec
3500 if (AddRec->isAffine()) {
3501 Type *Ty = AddRec->getType();
3502 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3503 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3504 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3505 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3507 const SCEV *Start = AddRec->getStart();
3508 const SCEV *Step = AddRec->getStepRecurrence(*this);
3510 ConstantRange StartRange = getSignedRange(Start);
3511 ConstantRange StepRange = getSignedRange(Step);
3512 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3513 ConstantRange EndRange =
3514 StartRange.add(MaxBECountRange.multiply(StepRange));
3516 // Check for overflow. This must be done with ConstantRange arithmetic
3517 // because we could be called from within the ScalarEvolution overflow
3519 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3520 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3521 ConstantRange ExtMaxBECountRange =
3522 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3523 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3524 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3526 return setSignedRange(AddRec, ConservativeResult);
3528 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3529 EndRange.getSignedMin());
3530 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3531 EndRange.getSignedMax());
3532 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3533 return setSignedRange(AddRec, ConservativeResult);
3534 return setSignedRange(AddRec,
3535 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3539 return setSignedRange(AddRec, ConservativeResult);
3542 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3543 // For a SCEVUnknown, ask ValueTracking.
3544 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3545 return setSignedRange(U, ConservativeResult);
3546 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3548 return setSignedRange(U, ConservativeResult);
3549 return setSignedRange(U, ConservativeResult.intersectWith(
3550 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3551 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3554 return setSignedRange(S, ConservativeResult);
3557 /// createSCEV - We know that there is no SCEV for the specified value.
3558 /// Analyze the expression.
3560 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3561 if (!isSCEVable(V->getType()))
3562 return getUnknown(V);
3564 unsigned Opcode = Instruction::UserOp1;
3565 if (Instruction *I = dyn_cast<Instruction>(V)) {
3566 Opcode = I->getOpcode();
3568 // Don't attempt to analyze instructions in blocks that aren't
3569 // reachable. Such instructions don't matter, and they aren't required
3570 // to obey basic rules for definitions dominating uses which this
3571 // analysis depends on.
3572 if (!DT->isReachableFromEntry(I->getParent()))
3573 return getUnknown(V);
3574 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3575 Opcode = CE->getOpcode();
3576 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3577 return getConstant(CI);
3578 else if (isa<ConstantPointerNull>(V))
3579 return getConstant(V->getType(), 0);
3580 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3581 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3583 return getUnknown(V);
3585 Operator *U = cast<Operator>(V);
3587 case Instruction::Add: {
3588 // The simple thing to do would be to just call getSCEV on both operands
3589 // and call getAddExpr with the result. However if we're looking at a
3590 // bunch of things all added together, this can be quite inefficient,
3591 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3592 // Instead, gather up all the operands and make a single getAddExpr call.
3593 // LLVM IR canonical form means we need only traverse the left operands.
3595 // Don't apply this instruction's NSW or NUW flags to the new
3596 // expression. The instruction may be guarded by control flow that the
3597 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3598 // mapped to the same SCEV expression, and it would be incorrect to transfer
3599 // NSW/NUW semantics to those operations.
3600 SmallVector<const SCEV *, 4> AddOps;
3601 AddOps.push_back(getSCEV(U->getOperand(1)));
3602 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3603 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3604 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3606 U = cast<Operator>(Op);
3607 const SCEV *Op1 = getSCEV(U->getOperand(1));
3608 if (Opcode == Instruction::Sub)
3609 AddOps.push_back(getNegativeSCEV(Op1));
3611 AddOps.push_back(Op1);
3613 AddOps.push_back(getSCEV(U->getOperand(0)));
3614 return getAddExpr(AddOps);
3616 case Instruction::Mul: {
3617 // Don't transfer NSW/NUW for the same reason as AddExpr.
3618 SmallVector<const SCEV *, 4> MulOps;
3619 MulOps.push_back(getSCEV(U->getOperand(1)));
3620 for (Value *Op = U->getOperand(0);
3621 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3622 Op = U->getOperand(0)) {
3623 U = cast<Operator>(Op);
3624 MulOps.push_back(getSCEV(U->getOperand(1)));
3626 MulOps.push_back(getSCEV(U->getOperand(0)));
3627 return getMulExpr(MulOps);
3629 case Instruction::UDiv:
3630 return getUDivExpr(getSCEV(U->getOperand(0)),
3631 getSCEV(U->getOperand(1)));
3632 case Instruction::Sub:
3633 return getMinusSCEV(getSCEV(U->getOperand(0)),
3634 getSCEV(U->getOperand(1)));
3635 case Instruction::And:
3636 // For an expression like x&255 that merely masks off the high bits,
3637 // use zext(trunc(x)) as the SCEV expression.
3638 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3639 if (CI->isNullValue())
3640 return getSCEV(U->getOperand(1));
3641 if (CI->isAllOnesValue())
3642 return getSCEV(U->getOperand(0));
3643 const APInt &A = CI->getValue();
3645 // Instcombine's ShrinkDemandedConstant may strip bits out of
3646 // constants, obscuring what would otherwise be a low-bits mask.
3647 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3648 // knew about to reconstruct a low-bits mask value.
3649 unsigned LZ = A.countLeadingZeros();
3650 unsigned BitWidth = A.getBitWidth();
3651 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3652 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD);
3654 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3656 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3658 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3659 IntegerType::get(getContext(), BitWidth - LZ)),
3664 case Instruction::Or:
3665 // If the RHS of the Or is a constant, we may have something like:
3666 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3667 // optimizations will transparently handle this case.
3669 // In order for this transformation to be safe, the LHS must be of the
3670 // form X*(2^n) and the Or constant must be less than 2^n.
3671 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3672 const SCEV *LHS = getSCEV(U->getOperand(0));
3673 const APInt &CIVal = CI->getValue();
3674 if (GetMinTrailingZeros(LHS) >=
3675 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3676 // Build a plain add SCEV.
3677 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3678 // If the LHS of the add was an addrec and it has no-wrap flags,
3679 // transfer the no-wrap flags, since an or won't introduce a wrap.
3680 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3681 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3682 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3683 OldAR->getNoWrapFlags());
3689 case Instruction::Xor:
3690 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3691 // If the RHS of the xor is a signbit, then this is just an add.
3692 // Instcombine turns add of signbit into xor as a strength reduction step.
3693 if (CI->getValue().isSignBit())
3694 return getAddExpr(getSCEV(U->getOperand(0)),
3695 getSCEV(U->getOperand(1)));
3697 // If the RHS of xor is -1, then this is a not operation.
3698 if (CI->isAllOnesValue())
3699 return getNotSCEV(getSCEV(U->getOperand(0)));
3701 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3702 // This is a variant of the check for xor with -1, and it handles
3703 // the case where instcombine has trimmed non-demanded bits out
3704 // of an xor with -1.
3705 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3706 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3707 if (BO->getOpcode() == Instruction::And &&
3708 LCI->getValue() == CI->getValue())
3709 if (const SCEVZeroExtendExpr *Z =
3710 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3711 Type *UTy = U->getType();
3712 const SCEV *Z0 = Z->getOperand();
3713 Type *Z0Ty = Z0->getType();
3714 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3716 // If C is a low-bits mask, the zero extend is serving to
3717 // mask off the high bits. Complement the operand and
3718 // re-apply the zext.
3719 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3720 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3722 // If C is a single bit, it may be in the sign-bit position
3723 // before the zero-extend. In this case, represent the xor
3724 // using an add, which is equivalent, and re-apply the zext.
3725 APInt Trunc = CI->getValue().trunc(Z0TySize);
3726 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3728 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3734 case Instruction::Shl:
3735 // Turn shift left of a constant amount into a multiply.
3736 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3737 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3739 // If the shift count is not less than the bitwidth, the result of
3740 // the shift is undefined. Don't try to analyze it, because the
3741 // resolution chosen here may differ from the resolution chosen in
3742 // other parts of the compiler.
3743 if (SA->getValue().uge(BitWidth))
3746 Constant *X = ConstantInt::get(getContext(),
3747 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3748 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3752 case Instruction::LShr:
3753 // Turn logical shift right of a constant into a unsigned divide.
3754 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3755 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3757 // If the shift count is not less than the bitwidth, the result of
3758 // the shift is undefined. Don't try to analyze it, because the
3759 // resolution chosen here may differ from the resolution chosen in
3760 // other parts of the compiler.
3761 if (SA->getValue().uge(BitWidth))
3764 Constant *X = ConstantInt::get(getContext(),
3765 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3766 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3770 case Instruction::AShr:
3771 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3772 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3773 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3774 if (L->getOpcode() == Instruction::Shl &&
3775 L->getOperand(1) == U->getOperand(1)) {
3776 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3778 // If the shift count is not less than the bitwidth, the result of
3779 // the shift is undefined. Don't try to analyze it, because the
3780 // resolution chosen here may differ from the resolution chosen in
3781 // other parts of the compiler.
3782 if (CI->getValue().uge(BitWidth))
3785 uint64_t Amt = BitWidth - CI->getZExtValue();
3786 if (Amt == BitWidth)
3787 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3789 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3790 IntegerType::get(getContext(),
3796 case Instruction::Trunc:
3797 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3799 case Instruction::ZExt:
3800 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3802 case Instruction::SExt:
3803 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3805 case Instruction::BitCast:
3806 // BitCasts are no-op casts so we just eliminate the cast.
3807 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3808 return getSCEV(U->getOperand(0));
3811 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3812 // lead to pointer expressions which cannot safely be expanded to GEPs,
3813 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3814 // simplifying integer expressions.
3816 case Instruction::GetElementPtr:
3817 return createNodeForGEP(cast<GEPOperator>(U));
3819 case Instruction::PHI:
3820 return createNodeForPHI(cast<PHINode>(U));
3822 case Instruction::Select:
3823 // This could be a smax or umax that was lowered earlier.
3824 // Try to recover it.
3825 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3826 Value *LHS = ICI->getOperand(0);
3827 Value *RHS = ICI->getOperand(1);
3828 switch (ICI->getPredicate()) {
3829 case ICmpInst::ICMP_SLT:
3830 case ICmpInst::ICMP_SLE:
3831 std::swap(LHS, RHS);
3833 case ICmpInst::ICMP_SGT:
3834 case ICmpInst::ICMP_SGE:
3835 // a >s b ? a+x : b+x -> smax(a, b)+x
3836 // a >s b ? b+x : a+x -> smin(a, b)+x
3837 if (LHS->getType() == U->getType()) {
3838 const SCEV *LS = getSCEV(LHS);
3839 const SCEV *RS = getSCEV(RHS);
3840 const SCEV *LA = getSCEV(U->getOperand(1));
3841 const SCEV *RA = getSCEV(U->getOperand(2));
3842 const SCEV *LDiff = getMinusSCEV(LA, LS);
3843 const SCEV *RDiff = getMinusSCEV(RA, RS);
3845 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3846 LDiff = getMinusSCEV(LA, RS);
3847 RDiff = getMinusSCEV(RA, LS);
3849 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3852 case ICmpInst::ICMP_ULT:
3853 case ICmpInst::ICMP_ULE:
3854 std::swap(LHS, RHS);
3856 case ICmpInst::ICMP_UGT:
3857 case ICmpInst::ICMP_UGE:
3858 // a >u b ? a+x : b+x -> umax(a, b)+x
3859 // a >u b ? b+x : a+x -> umin(a, b)+x
3860 if (LHS->getType() == U->getType()) {
3861 const SCEV *LS = getSCEV(LHS);
3862 const SCEV *RS = getSCEV(RHS);
3863 const SCEV *LA = getSCEV(U->getOperand(1));
3864 const SCEV *RA = getSCEV(U->getOperand(2));
3865 const SCEV *LDiff = getMinusSCEV(LA, LS);
3866 const SCEV *RDiff = getMinusSCEV(RA, RS);
3868 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3869 LDiff = getMinusSCEV(LA, RS);
3870 RDiff = getMinusSCEV(RA, LS);
3872 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3875 case ICmpInst::ICMP_NE:
3876 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3877 if (LHS->getType() == U->getType() &&
3878 isa<ConstantInt>(RHS) &&
3879 cast<ConstantInt>(RHS)->isZero()) {
3880 const SCEV *One = getConstant(LHS->getType(), 1);
3881 const SCEV *LS = getSCEV(LHS);
3882 const SCEV *LA = getSCEV(U->getOperand(1));
3883 const SCEV *RA = getSCEV(U->getOperand(2));
3884 const SCEV *LDiff = getMinusSCEV(LA, LS);
3885 const SCEV *RDiff = getMinusSCEV(RA, One);
3887 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3890 case ICmpInst::ICMP_EQ:
3891 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3892 if (LHS->getType() == U->getType() &&
3893 isa<ConstantInt>(RHS) &&
3894 cast<ConstantInt>(RHS)->isZero()) {
3895 const SCEV *One = getConstant(LHS->getType(), 1);
3896 const SCEV *LS = getSCEV(LHS);
3897 const SCEV *LA = getSCEV(U->getOperand(1));
3898 const SCEV *RA = getSCEV(U->getOperand(2));
3899 const SCEV *LDiff = getMinusSCEV(LA, One);
3900 const SCEV *RDiff = getMinusSCEV(RA, LS);
3902 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3910 default: // We cannot analyze this expression.
3914 return getUnknown(V);
3919 //===----------------------------------------------------------------------===//
3920 // Iteration Count Computation Code
3923 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3924 /// normal unsigned value. Returns 0 if the trip count is unknown or not
3925 /// constant. Will also return 0 if the maximum trip count is very large (>=
3928 /// This "trip count" assumes that control exits via ExitingBlock. More
3929 /// precisely, it is the number of times that control may reach ExitingBlock
3930 /// before taking the branch. For loops with multiple exits, it may not be the
3931 /// number times that the loop header executes because the loop may exit
3932 /// prematurely via another branch.
3933 unsigned ScalarEvolution::
3934 getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock) {
3935 const SCEVConstant *ExitCount =
3936 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
3940 ConstantInt *ExitConst = ExitCount->getValue();
3942 // Guard against huge trip counts.
3943 if (ExitConst->getValue().getActiveBits() > 32)
3946 // In case of integer overflow, this returns 0, which is correct.
3947 return ((unsigned)ExitConst->getZExtValue()) + 1;
3950 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3951 /// trip count of this loop as a normal unsigned value, if possible. This
3952 /// means that the actual trip count is always a multiple of the returned
3953 /// value (don't forget the trip count could very well be zero as well!).
3955 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3956 /// multiple of a constant (which is also the case if the trip count is simply
3957 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3958 /// if the trip count is very large (>= 2^32).
3960 /// As explained in the comments for getSmallConstantTripCount, this assumes
3961 /// that control exits the loop via ExitingBlock.
3962 unsigned ScalarEvolution::
3963 getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock) {
3964 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
3965 if (ExitCount == getCouldNotCompute())
3968 // Get the trip count from the BE count by adding 1.
3969 const SCEV *TCMul = getAddExpr(ExitCount,
3970 getConstant(ExitCount->getType(), 1));
3971 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
3972 // to factor simple cases.
3973 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
3974 TCMul = Mul->getOperand(0);
3976 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
3980 ConstantInt *Result = MulC->getValue();
3982 // Guard against huge trip counts (this requires checking
3983 // for zero to handle the case where the trip count == -1 and the
3985 if (!Result || Result->getValue().getActiveBits() > 32 ||
3986 Result->getValue().getActiveBits() == 0)
3989 return (unsigned)Result->getZExtValue();
3992 // getExitCount - Get the expression for the number of loop iterations for which
3993 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return
3994 // SCEVCouldNotCompute.
3995 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
3996 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
3999 /// getBackedgeTakenCount - If the specified loop has a predictable
4000 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4001 /// object. The backedge-taken count is the number of times the loop header
4002 /// will be branched to from within the loop. This is one less than the
4003 /// trip count of the loop, since it doesn't count the first iteration,
4004 /// when the header is branched to from outside the loop.
4006 /// Note that it is not valid to call this method on a loop without a
4007 /// loop-invariant backedge-taken count (see
4008 /// hasLoopInvariantBackedgeTakenCount).
4010 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4011 return getBackedgeTakenInfo(L).getExact(this);
4014 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4015 /// return the least SCEV value that is known never to be less than the
4016 /// actual backedge taken count.
4017 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4018 return getBackedgeTakenInfo(L).getMax(this);
4021 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4022 /// onto the given Worklist.
4024 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4025 BasicBlock *Header = L->getHeader();
4027 // Push all Loop-header PHIs onto the Worklist stack.
4028 for (BasicBlock::iterator I = Header->begin();
4029 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4030 Worklist.push_back(PN);
4033 const ScalarEvolution::BackedgeTakenInfo &
4034 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4035 // Initially insert an invalid entry for this loop. If the insertion
4036 // succeeds, proceed to actually compute a backedge-taken count and
4037 // update the value. The temporary CouldNotCompute value tells SCEV
4038 // code elsewhere that it shouldn't attempt to request a new
4039 // backedge-taken count, which could result in infinite recursion.
4040 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4041 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4043 return Pair.first->second;
4045 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4046 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4047 // must be cleared in this scope.
4048 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4050 if (Result.getExact(this) != getCouldNotCompute()) {
4051 assert(isLoopInvariant(Result.getExact(this), L) &&
4052 isLoopInvariant(Result.getMax(this), L) &&
4053 "Computed backedge-taken count isn't loop invariant for loop!");
4054 ++NumTripCountsComputed;
4056 else if (Result.getMax(this) == getCouldNotCompute() &&
4057 isa<PHINode>(L->getHeader()->begin())) {
4058 // Only count loops that have phi nodes as not being computable.
4059 ++NumTripCountsNotComputed;
4062 // Now that we know more about the trip count for this loop, forget any
4063 // existing SCEV values for PHI nodes in this loop since they are only
4064 // conservative estimates made without the benefit of trip count
4065 // information. This is similar to the code in forgetLoop, except that
4066 // it handles SCEVUnknown PHI nodes specially.
4067 if (Result.hasAnyInfo()) {
4068 SmallVector<Instruction *, 16> Worklist;
4069 PushLoopPHIs(L, Worklist);
4071 SmallPtrSet<Instruction *, 8> Visited;
4072 while (!Worklist.empty()) {
4073 Instruction *I = Worklist.pop_back_val();
4074 if (!Visited.insert(I)) continue;
4076 ValueExprMapType::iterator It =
4077 ValueExprMap.find_as(static_cast<Value *>(I));
4078 if (It != ValueExprMap.end()) {
4079 const SCEV *Old = It->second;
4081 // SCEVUnknown for a PHI either means that it has an unrecognized
4082 // structure, or it's a PHI that's in the progress of being computed
4083 // by createNodeForPHI. In the former case, additional loop trip
4084 // count information isn't going to change anything. In the later
4085 // case, createNodeForPHI will perform the necessary updates on its
4086 // own when it gets to that point.
4087 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4088 forgetMemoizedResults(Old);
4089 ValueExprMap.erase(It);
4091 if (PHINode *PN = dyn_cast<PHINode>(I))
4092 ConstantEvolutionLoopExitValue.erase(PN);
4095 PushDefUseChildren(I, Worklist);
4099 // Re-lookup the insert position, since the call to
4100 // ComputeBackedgeTakenCount above could result in a
4101 // recusive call to getBackedgeTakenInfo (on a different
4102 // loop), which would invalidate the iterator computed
4104 return BackedgeTakenCounts.find(L)->second = Result;
4107 /// forgetLoop - This method should be called by the client when it has
4108 /// changed a loop in a way that may effect ScalarEvolution's ability to
4109 /// compute a trip count, or if the loop is deleted.
4110 void ScalarEvolution::forgetLoop(const Loop *L) {
4111 // Drop any stored trip count value.
4112 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4113 BackedgeTakenCounts.find(L);
4114 if (BTCPos != BackedgeTakenCounts.end()) {
4115 BTCPos->second.clear();
4116 BackedgeTakenCounts.erase(BTCPos);
4119 // Drop information about expressions based on loop-header PHIs.
4120 SmallVector<Instruction *, 16> Worklist;
4121 PushLoopPHIs(L, Worklist);
4123 SmallPtrSet<Instruction *, 8> Visited;
4124 while (!Worklist.empty()) {
4125 Instruction *I = Worklist.pop_back_val();
4126 if (!Visited.insert(I)) continue;
4128 ValueExprMapType::iterator It =
4129 ValueExprMap.find_as(static_cast<Value *>(I));
4130 if (It != ValueExprMap.end()) {
4131 forgetMemoizedResults(It->second);
4132 ValueExprMap.erase(It);
4133 if (PHINode *PN = dyn_cast<PHINode>(I))
4134 ConstantEvolutionLoopExitValue.erase(PN);
4137 PushDefUseChildren(I, Worklist);
4140 // Forget all contained loops too, to avoid dangling entries in the
4141 // ValuesAtScopes map.
4142 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4146 /// forgetValue - This method should be called by the client when it has
4147 /// changed a value in a way that may effect its value, or which may
4148 /// disconnect it from a def-use chain linking it to a loop.
4149 void ScalarEvolution::forgetValue(Value *V) {
4150 Instruction *I = dyn_cast<Instruction>(V);
4153 // Drop information about expressions based on loop-header PHIs.
4154 SmallVector<Instruction *, 16> Worklist;
4155 Worklist.push_back(I);
4157 SmallPtrSet<Instruction *, 8> Visited;
4158 while (!Worklist.empty()) {
4159 I = Worklist.pop_back_val();
4160 if (!Visited.insert(I)) continue;
4162 ValueExprMapType::iterator It =
4163 ValueExprMap.find_as(static_cast<Value *>(I));
4164 if (It != ValueExprMap.end()) {
4165 forgetMemoizedResults(It->second);
4166 ValueExprMap.erase(It);
4167 if (PHINode *PN = dyn_cast<PHINode>(I))
4168 ConstantEvolutionLoopExitValue.erase(PN);
4171 PushDefUseChildren(I, Worklist);
4175 /// getExact - Get the exact loop backedge taken count considering all loop
4176 /// exits. A computable result can only be return for loops with a single exit.
4177 /// Returning the minimum taken count among all exits is incorrect because one
4178 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4179 /// the limit of each loop test is never skipped. This is a valid assumption as
4180 /// long as the loop exits via that test. For precise results, it is the
4181 /// caller's responsibility to specify the relevant loop exit using
4182 /// getExact(ExitingBlock, SE).
4184 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4185 // If any exits were not computable, the loop is not computable.
4186 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4188 // We need exactly one computable exit.
4189 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4190 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4192 const SCEV *BECount = 0;
4193 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4194 ENT != 0; ENT = ENT->getNextExit()) {
4196 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4199 BECount = ENT->ExactNotTaken;
4200 else if (BECount != ENT->ExactNotTaken)
4201 return SE->getCouldNotCompute();
4203 assert(BECount && "Invalid not taken count for loop exit");
4207 /// getExact - Get the exact not taken count for this loop exit.
4209 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4210 ScalarEvolution *SE) const {
4211 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4212 ENT != 0; ENT = ENT->getNextExit()) {
4214 if (ENT->ExitingBlock == ExitingBlock)
4215 return ENT->ExactNotTaken;
4217 return SE->getCouldNotCompute();
4220 /// getMax - Get the max backedge taken count for the loop.
4222 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4223 return Max ? Max : SE->getCouldNotCompute();
4226 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4227 /// computable exit into a persistent ExitNotTakenInfo array.
4228 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4229 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4230 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4233 ExitNotTaken.setIncomplete();
4235 unsigned NumExits = ExitCounts.size();
4236 if (NumExits == 0) return;
4238 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4239 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4240 if (NumExits == 1) return;
4242 // Handle the rare case of multiple computable exits.
4243 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4245 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4246 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4247 PrevENT->setNextExit(ENT);
4248 ENT->ExitingBlock = ExitCounts[i].first;
4249 ENT->ExactNotTaken = ExitCounts[i].second;
4253 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4254 void ScalarEvolution::BackedgeTakenInfo::clear() {
4255 ExitNotTaken.ExitingBlock = 0;
4256 ExitNotTaken.ExactNotTaken = 0;
4257 delete[] ExitNotTaken.getNextExit();
4260 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4261 /// of the specified loop will execute.
4262 ScalarEvolution::BackedgeTakenInfo
4263 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4264 SmallVector<BasicBlock *, 8> ExitingBlocks;
4265 L->getExitingBlocks(ExitingBlocks);
4267 // Examine all exits and pick the most conservative values.
4268 const SCEV *MaxBECount = getCouldNotCompute();
4269 bool CouldComputeBECount = true;
4270 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4271 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4272 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4273 if (EL.Exact == getCouldNotCompute())
4274 // We couldn't compute an exact value for this exit, so
4275 // we won't be able to compute an exact value for the loop.
4276 CouldComputeBECount = false;
4278 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4280 if (MaxBECount == getCouldNotCompute())
4281 MaxBECount = EL.Max;
4282 else if (EL.Max != getCouldNotCompute()) {
4283 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4284 // skip some loop tests. Taking the max over the exits is sufficiently
4285 // conservative. TODO: We could do better taking into consideration
4286 // that (1) the loop has unit stride (2) the last loop test is
4287 // less-than/greater-than (3) any loop test is less-than/greater-than AND
4288 // falls-through some constant times less then the other tests.
4289 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4293 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4296 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4297 /// loop will execute if it exits via the specified block.
4298 ScalarEvolution::ExitLimit
4299 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4301 // Okay, we've chosen an exiting block. See what condition causes us to
4302 // exit at this block.
4304 // FIXME: we should be able to handle switch instructions (with a single exit)
4305 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4306 if (ExitBr == 0) return getCouldNotCompute();
4307 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4309 // At this point, we know we have a conditional branch that determines whether
4310 // the loop is exited. However, we don't know if the branch is executed each
4311 // time through the loop. If not, then the execution count of the branch will
4312 // not be equal to the trip count of the loop.
4314 // Currently we check for this by checking to see if the Exit branch goes to
4315 // the loop header. If so, we know it will always execute the same number of
4316 // times as the loop. We also handle the case where the exit block *is* the
4317 // loop header. This is common for un-rotated loops.
4319 // If both of those tests fail, walk up the unique predecessor chain to the
4320 // header, stopping if there is an edge that doesn't exit the loop. If the
4321 // header is reached, the execution count of the branch will be equal to the
4322 // trip count of the loop.
4324 // More extensive analysis could be done to handle more cases here.
4326 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4327 ExitBr->getSuccessor(1) != L->getHeader() &&
4328 ExitBr->getParent() != L->getHeader()) {
4329 // The simple checks failed, try climbing the unique predecessor chain
4330 // up to the header.
4332 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4333 BasicBlock *Pred = BB->getUniquePredecessor();
4335 return getCouldNotCompute();
4336 TerminatorInst *PredTerm = Pred->getTerminator();
4337 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4338 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4341 // If the predecessor has a successor that isn't BB and isn't
4342 // outside the loop, assume the worst.
4343 if (L->contains(PredSucc))
4344 return getCouldNotCompute();
4346 if (Pred == L->getHeader()) {
4353 return getCouldNotCompute();
4356 // Proceed to the next level to examine the exit condition expression.
4357 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4358 ExitBr->getSuccessor(0),
4359 ExitBr->getSuccessor(1));
4362 /// ComputeExitLimitFromCond - Compute the number of times the
4363 /// backedge of the specified loop will execute if its exit condition
4364 /// were a conditional branch of ExitCond, TBB, and FBB.
4365 ScalarEvolution::ExitLimit
4366 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4370 // Check if the controlling expression for this loop is an And or Or.
4371 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4372 if (BO->getOpcode() == Instruction::And) {
4373 // Recurse on the operands of the and.
4374 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4375 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4376 const SCEV *BECount = getCouldNotCompute();
4377 const SCEV *MaxBECount = getCouldNotCompute();
4378 if (L->contains(TBB)) {
4379 // Both conditions must be true for the loop to continue executing.
4380 // Choose the less conservative count.
4381 if (EL0.Exact == getCouldNotCompute() ||
4382 EL1.Exact == getCouldNotCompute())
4383 BECount = getCouldNotCompute();
4385 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4386 if (EL0.Max == getCouldNotCompute())
4387 MaxBECount = EL1.Max;
4388 else if (EL1.Max == getCouldNotCompute())
4389 MaxBECount = EL0.Max;
4391 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4393 // Both conditions must be true at the same time for the loop to exit.
4394 // For now, be conservative.
4395 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4396 if (EL0.Max == EL1.Max)
4397 MaxBECount = EL0.Max;
4398 if (EL0.Exact == EL1.Exact)
4399 BECount = EL0.Exact;
4402 return ExitLimit(BECount, MaxBECount);
4404 if (BO->getOpcode() == Instruction::Or) {
4405 // Recurse on the operands of the or.
4406 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4407 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4408 const SCEV *BECount = getCouldNotCompute();
4409 const SCEV *MaxBECount = getCouldNotCompute();
4410 if (L->contains(FBB)) {
4411 // Both conditions must be false for the loop to continue executing.
4412 // Choose the less conservative count.
4413 if (EL0.Exact == getCouldNotCompute() ||
4414 EL1.Exact == getCouldNotCompute())
4415 BECount = getCouldNotCompute();
4417 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4418 if (EL0.Max == getCouldNotCompute())
4419 MaxBECount = EL1.Max;
4420 else if (EL1.Max == getCouldNotCompute())
4421 MaxBECount = EL0.Max;
4423 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4425 // Both conditions must be false at the same time for the loop to exit.
4426 // For now, be conservative.
4427 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4428 if (EL0.Max == EL1.Max)
4429 MaxBECount = EL0.Max;
4430 if (EL0.Exact == EL1.Exact)
4431 BECount = EL0.Exact;
4434 return ExitLimit(BECount, MaxBECount);
4438 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4439 // Proceed to the next level to examine the icmp.
4440 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4441 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB);
4443 // Check for a constant condition. These are normally stripped out by
4444 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4445 // preserve the CFG and is temporarily leaving constant conditions
4447 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4448 if (L->contains(FBB) == !CI->getZExtValue())
4449 // The backedge is always taken.
4450 return getCouldNotCompute();
4452 // The backedge is never taken.
4453 return getConstant(CI->getType(), 0);
4456 // If it's not an integer or pointer comparison then compute it the hard way.
4457 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4460 /// ComputeExitLimitFromICmp - Compute the number of times the
4461 /// backedge of the specified loop will execute if its exit condition
4462 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4463 ScalarEvolution::ExitLimit
4464 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4469 // If the condition was exit on true, convert the condition to exit on false
4470 ICmpInst::Predicate Cond;
4471 if (!L->contains(FBB))
4472 Cond = ExitCond->getPredicate();
4474 Cond = ExitCond->getInversePredicate();
4476 // Handle common loops like: for (X = "string"; *X; ++X)
4477 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4478 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4480 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4481 if (ItCnt.hasAnyInfo())
4485 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4486 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4488 // Try to evaluate any dependencies out of the loop.
4489 LHS = getSCEVAtScope(LHS, L);
4490 RHS = getSCEVAtScope(RHS, L);
4492 // At this point, we would like to compute how many iterations of the
4493 // loop the predicate will return true for these inputs.
4494 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4495 // If there is a loop-invariant, force it into the RHS.
4496 std::swap(LHS, RHS);
4497 Cond = ICmpInst::getSwappedPredicate(Cond);
4500 // Simplify the operands before analyzing them.
4501 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4503 // If we have a comparison of a chrec against a constant, try to use value
4504 // ranges to answer this query.
4505 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4506 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4507 if (AddRec->getLoop() == L) {
4508 // Form the constant range.
4509 ConstantRange CompRange(
4510 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4512 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4513 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4517 case ICmpInst::ICMP_NE: { // while (X != Y)
4518 // Convert to: while (X-Y != 0)
4519 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4520 if (EL.hasAnyInfo()) return EL;
4523 case ICmpInst::ICMP_EQ: { // while (X == Y)
4524 // Convert to: while (X-Y == 0)
4525 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4526 if (EL.hasAnyInfo()) return EL;
4529 case ICmpInst::ICMP_SLT: {
4530 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true);
4531 if (EL.hasAnyInfo()) return EL;
4534 case ICmpInst::ICMP_SGT: {
4535 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4536 getNotSCEV(RHS), L, true);
4537 if (EL.hasAnyInfo()) return EL;
4540 case ICmpInst::ICMP_ULT: {
4541 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false);
4542 if (EL.hasAnyInfo()) return EL;
4545 case ICmpInst::ICMP_UGT: {
4546 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4547 getNotSCEV(RHS), L, false);
4548 if (EL.hasAnyInfo()) return EL;
4553 dbgs() << "ComputeBackedgeTakenCount ";
4554 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4555 dbgs() << "[unsigned] ";
4556 dbgs() << *LHS << " "
4557 << Instruction::getOpcodeName(Instruction::ICmp)
4558 << " " << *RHS << "\n";
4562 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4565 static ConstantInt *
4566 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4567 ScalarEvolution &SE) {
4568 const SCEV *InVal = SE.getConstant(C);
4569 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4570 assert(isa<SCEVConstant>(Val) &&
4571 "Evaluation of SCEV at constant didn't fold correctly?");
4572 return cast<SCEVConstant>(Val)->getValue();
4575 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4576 /// 'icmp op load X, cst', try to see if we can compute the backedge
4577 /// execution count.
4578 ScalarEvolution::ExitLimit
4579 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4583 ICmpInst::Predicate predicate) {
4585 if (LI->isVolatile()) return getCouldNotCompute();
4587 // Check to see if the loaded pointer is a getelementptr of a global.
4588 // TODO: Use SCEV instead of manually grubbing with GEPs.
4589 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4590 if (!GEP) return getCouldNotCompute();
4592 // Make sure that it is really a constant global we are gepping, with an
4593 // initializer, and make sure the first IDX is really 0.
4594 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4595 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4596 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4597 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4598 return getCouldNotCompute();
4600 // Okay, we allow one non-constant index into the GEP instruction.
4602 std::vector<Constant*> Indexes;
4603 unsigned VarIdxNum = 0;
4604 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4605 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4606 Indexes.push_back(CI);
4607 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4608 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4609 VarIdx = GEP->getOperand(i);
4611 Indexes.push_back(0);
4614 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4616 return getCouldNotCompute();
4618 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4619 // Check to see if X is a loop variant variable value now.
4620 const SCEV *Idx = getSCEV(VarIdx);
4621 Idx = getSCEVAtScope(Idx, L);
4623 // We can only recognize very limited forms of loop index expressions, in
4624 // particular, only affine AddRec's like {C1,+,C2}.
4625 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4626 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4627 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4628 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4629 return getCouldNotCompute();
4631 unsigned MaxSteps = MaxBruteForceIterations;
4632 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4633 ConstantInt *ItCst = ConstantInt::get(
4634 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4635 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4637 // Form the GEP offset.
4638 Indexes[VarIdxNum] = Val;
4640 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4642 if (Result == 0) break; // Cannot compute!
4644 // Evaluate the condition for this iteration.
4645 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4646 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4647 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4649 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4650 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4653 ++NumArrayLenItCounts;
4654 return getConstant(ItCst); // Found terminating iteration!
4657 return getCouldNotCompute();
4661 /// CanConstantFold - Return true if we can constant fold an instruction of the
4662 /// specified type, assuming that all operands were constants.
4663 static bool CanConstantFold(const Instruction *I) {
4664 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4665 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4669 if (const CallInst *CI = dyn_cast<CallInst>(I))
4670 if (const Function *F = CI->getCalledFunction())
4671 return canConstantFoldCallTo(F);
4675 /// Determine whether this instruction can constant evolve within this loop
4676 /// assuming its operands can all constant evolve.
4677 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4678 // An instruction outside of the loop can't be derived from a loop PHI.
4679 if (!L->contains(I)) return false;
4681 if (isa<PHINode>(I)) {
4682 if (L->getHeader() == I->getParent())
4685 // We don't currently keep track of the control flow needed to evaluate
4686 // PHIs, so we cannot handle PHIs inside of loops.
4690 // If we won't be able to constant fold this expression even if the operands
4691 // are constants, bail early.
4692 return CanConstantFold(I);
4695 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4696 /// recursing through each instruction operand until reaching a loop header phi.
4698 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4699 DenseMap<Instruction *, PHINode *> &PHIMap) {
4701 // Otherwise, we can evaluate this instruction if all of its operands are
4702 // constant or derived from a PHI node themselves.
4704 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4705 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4707 if (isa<Constant>(*OpI)) continue;
4709 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4710 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4712 PHINode *P = dyn_cast<PHINode>(OpInst);
4714 // If this operand is already visited, reuse the prior result.
4715 // We may have P != PHI if this is the deepest point at which the
4716 // inconsistent paths meet.
4717 P = PHIMap.lookup(OpInst);
4719 // Recurse and memoize the results, whether a phi is found or not.
4720 // This recursive call invalidates pointers into PHIMap.
4721 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4724 if (P == 0) return 0; // Not evolving from PHI
4725 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4728 // This is a expression evolving from a constant PHI!
4732 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4733 /// in the loop that V is derived from. We allow arbitrary operations along the
4734 /// way, but the operands of an operation must either be constants or a value
4735 /// derived from a constant PHI. If this expression does not fit with these
4736 /// constraints, return null.
4737 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4738 Instruction *I = dyn_cast<Instruction>(V);
4739 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4741 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4745 // Record non-constant instructions contained by the loop.
4746 DenseMap<Instruction *, PHINode *> PHIMap;
4747 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4750 /// EvaluateExpression - Given an expression that passes the
4751 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4752 /// in the loop has the value PHIVal. If we can't fold this expression for some
4753 /// reason, return null.
4754 static Constant *EvaluateExpression(Value *V, const Loop *L,
4755 DenseMap<Instruction *, Constant *> &Vals,
4756 const DataLayout *TD,
4757 const TargetLibraryInfo *TLI) {
4758 // Convenient constant check, but redundant for recursive calls.
4759 if (Constant *C = dyn_cast<Constant>(V)) return C;
4760 Instruction *I = dyn_cast<Instruction>(V);
4763 if (Constant *C = Vals.lookup(I)) return C;
4765 // An instruction inside the loop depends on a value outside the loop that we
4766 // weren't given a mapping for, or a value such as a call inside the loop.
4767 if (!canConstantEvolve(I, L)) return 0;
4769 // An unmapped PHI can be due to a branch or another loop inside this loop,
4770 // or due to this not being the initial iteration through a loop where we
4771 // couldn't compute the evolution of this particular PHI last time.
4772 if (isa<PHINode>(I)) return 0;
4774 std::vector<Constant*> Operands(I->getNumOperands());
4776 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4777 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4779 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4780 if (!Operands[i]) return 0;
4783 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
4789 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4790 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4791 Operands[1], TD, TLI);
4792 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4793 if (!LI->isVolatile())
4794 return ConstantFoldLoadFromConstPtr(Operands[0], TD);
4796 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
4800 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4801 /// in the header of its containing loop, we know the loop executes a
4802 /// constant number of times, and the PHI node is just a recurrence
4803 /// involving constants, fold it.
4805 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4808 DenseMap<PHINode*, Constant*>::const_iterator I =
4809 ConstantEvolutionLoopExitValue.find(PN);
4810 if (I != ConstantEvolutionLoopExitValue.end())
4813 if (BEs.ugt(MaxBruteForceIterations))
4814 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4816 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4818 DenseMap<Instruction *, Constant *> CurrentIterVals;
4819 BasicBlock *Header = L->getHeader();
4820 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4822 // Since the loop is canonicalized, the PHI node must have two entries. One
4823 // entry must be a constant (coming in from outside of the loop), and the
4824 // second must be derived from the same PHI.
4825 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4827 for (BasicBlock::iterator I = Header->begin();
4828 (PHI = dyn_cast<PHINode>(I)); ++I) {
4829 Constant *StartCST =
4830 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4831 if (StartCST == 0) continue;
4832 CurrentIterVals[PHI] = StartCST;
4834 if (!CurrentIterVals.count(PN))
4837 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4839 // Execute the loop symbolically to determine the exit value.
4840 if (BEs.getActiveBits() >= 32)
4841 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4843 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4844 unsigned IterationNum = 0;
4845 for (; ; ++IterationNum) {
4846 if (IterationNum == NumIterations)
4847 return RetVal = CurrentIterVals[PN]; // Got exit value!
4849 // Compute the value of the PHIs for the next iteration.
4850 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
4851 DenseMap<Instruction *, Constant *> NextIterVals;
4852 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
4855 return 0; // Couldn't evaluate!
4856 NextIterVals[PN] = NextPHI;
4858 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
4860 // Also evaluate the other PHI nodes. However, we don't get to stop if we
4861 // cease to be able to evaluate one of them or if they stop evolving,
4862 // because that doesn't necessarily prevent us from computing PN.
4863 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
4864 for (DenseMap<Instruction *, Constant *>::const_iterator
4865 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4866 PHINode *PHI = dyn_cast<PHINode>(I->first);
4867 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
4868 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
4870 // We use two distinct loops because EvaluateExpression may invalidate any
4871 // iterators into CurrentIterVals.
4872 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
4873 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
4874 PHINode *PHI = I->first;
4875 Constant *&NextPHI = NextIterVals[PHI];
4876 if (!NextPHI) { // Not already computed.
4877 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4878 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4880 if (NextPHI != I->second)
4881 StoppedEvolving = false;
4884 // If all entries in CurrentIterVals == NextIterVals then we can stop
4885 // iterating, the loop can't continue to change.
4886 if (StoppedEvolving)
4887 return RetVal = CurrentIterVals[PN];
4889 CurrentIterVals.swap(NextIterVals);
4893 /// ComputeExitCountExhaustively - If the loop is known to execute a
4894 /// constant number of times (the condition evolves only from constants),
4895 /// try to evaluate a few iterations of the loop until we get the exit
4896 /// condition gets a value of ExitWhen (true or false). If we cannot
4897 /// evaluate the trip count of the loop, return getCouldNotCompute().
4898 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4901 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4902 if (PN == 0) return getCouldNotCompute();
4904 // If the loop is canonicalized, the PHI will have exactly two entries.
4905 // That's the only form we support here.
4906 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4908 DenseMap<Instruction *, Constant *> CurrentIterVals;
4909 BasicBlock *Header = L->getHeader();
4910 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4912 // One entry must be a constant (coming in from outside of the loop), and the
4913 // second must be derived from the same PHI.
4914 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4916 for (BasicBlock::iterator I = Header->begin();
4917 (PHI = dyn_cast<PHINode>(I)); ++I) {
4918 Constant *StartCST =
4919 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4920 if (StartCST == 0) continue;
4921 CurrentIterVals[PHI] = StartCST;
4923 if (!CurrentIterVals.count(PN))
4924 return getCouldNotCompute();
4926 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4927 // the loop symbolically to determine when the condition gets a value of
4930 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4931 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
4932 ConstantInt *CondVal =
4933 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
4936 // Couldn't symbolically evaluate.
4937 if (!CondVal) return getCouldNotCompute();
4939 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4940 ++NumBruteForceTripCountsComputed;
4941 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4944 // Update all the PHI nodes for the next iteration.
4945 DenseMap<Instruction *, Constant *> NextIterVals;
4947 // Create a list of which PHIs we need to compute. We want to do this before
4948 // calling EvaluateExpression on them because that may invalidate iterators
4949 // into CurrentIterVals.
4950 SmallVector<PHINode *, 8> PHIsToCompute;
4951 for (DenseMap<Instruction *, Constant *>::const_iterator
4952 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4953 PHINode *PHI = dyn_cast<PHINode>(I->first);
4954 if (!PHI || PHI->getParent() != Header) continue;
4955 PHIsToCompute.push_back(PHI);
4957 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
4958 E = PHIsToCompute.end(); I != E; ++I) {
4960 Constant *&NextPHI = NextIterVals[PHI];
4961 if (NextPHI) continue; // Already computed!
4963 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4964 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4966 CurrentIterVals.swap(NextIterVals);
4969 // Too many iterations were needed to evaluate.
4970 return getCouldNotCompute();
4973 /// getSCEVAtScope - Return a SCEV expression for the specified value
4974 /// at the specified scope in the program. The L value specifies a loop
4975 /// nest to evaluate the expression at, where null is the top-level or a
4976 /// specified loop is immediately inside of the loop.
4978 /// This method can be used to compute the exit value for a variable defined
4979 /// in a loop by querying what the value will hold in the parent loop.
4981 /// In the case that a relevant loop exit value cannot be computed, the
4982 /// original value V is returned.
4983 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4984 // Check to see if we've folded this expression at this loop before.
4985 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4986 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4987 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4989 return Pair.first->second ? Pair.first->second : V;
4991 // Otherwise compute it.
4992 const SCEV *C = computeSCEVAtScope(V, L);
4993 ValuesAtScopes[V][L] = C;
4997 /// This builds up a Constant using the ConstantExpr interface. That way, we
4998 /// will return Constants for objects which aren't represented by a
4999 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5000 /// Returns NULL if the SCEV isn't representable as a Constant.
5001 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5002 switch (V->getSCEVType()) {
5003 default: // TODO: smax, umax.
5004 case scCouldNotCompute:
5008 return cast<SCEVConstant>(V)->getValue();
5010 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5011 case scSignExtend: {
5012 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5013 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5014 return ConstantExpr::getSExt(CastOp, SS->getType());
5017 case scZeroExtend: {
5018 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5019 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5020 return ConstantExpr::getZExt(CastOp, SZ->getType());
5024 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5025 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5026 return ConstantExpr::getTrunc(CastOp, ST->getType());
5030 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5031 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5032 if (C->getType()->isPointerTy())
5033 C = ConstantExpr::getBitCast(C, Type::getInt8PtrTy(C->getContext()));
5034 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5035 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5039 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5041 // The offsets have been converted to bytes. We can add bytes to an
5042 // i8* by GEP with the byte count in the first index.
5043 C = ConstantExpr::getBitCast(C,Type::getInt8PtrTy(C->getContext()));
5046 // Don't bother trying to sum two pointers. We probably can't
5047 // statically compute a load that results from it anyway.
5048 if (C2->getType()->isPointerTy())
5051 if (C->getType()->isPointerTy()) {
5052 if (cast<PointerType>(C->getType())->getElementType()->isStructTy())
5053 C2 = ConstantExpr::getIntegerCast(
5054 C2, Type::getInt32Ty(C->getContext()), true);
5055 C = ConstantExpr::getGetElementPtr(C, C2);
5057 C = ConstantExpr::getAdd(C, C2);
5064 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5065 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5066 // Don't bother with pointers at all.
5067 if (C->getType()->isPointerTy()) return 0;
5068 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5069 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5070 if (!C2 || C2->getType()->isPointerTy()) return 0;
5071 C = ConstantExpr::getMul(C, C2);
5078 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5079 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5080 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5081 if (LHS->getType() == RHS->getType())
5082 return ConstantExpr::getUDiv(LHS, RHS);
5089 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5090 if (isa<SCEVConstant>(V)) return V;
5092 // If this instruction is evolved from a constant-evolving PHI, compute the
5093 // exit value from the loop without using SCEVs.
5094 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5095 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5096 const Loop *LI = (*this->LI)[I->getParent()];
5097 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5098 if (PHINode *PN = dyn_cast<PHINode>(I))
5099 if (PN->getParent() == LI->getHeader()) {
5100 // Okay, there is no closed form solution for the PHI node. Check
5101 // to see if the loop that contains it has a known backedge-taken
5102 // count. If so, we may be able to force computation of the exit
5104 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5105 if (const SCEVConstant *BTCC =
5106 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5107 // Okay, we know how many times the containing loop executes. If
5108 // this is a constant evolving PHI node, get the final value at
5109 // the specified iteration number.
5110 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5111 BTCC->getValue()->getValue(),
5113 if (RV) return getSCEV(RV);
5117 // Okay, this is an expression that we cannot symbolically evaluate
5118 // into a SCEV. Check to see if it's possible to symbolically evaluate
5119 // the arguments into constants, and if so, try to constant propagate the
5120 // result. This is particularly useful for computing loop exit values.
5121 if (CanConstantFold(I)) {
5122 SmallVector<Constant *, 4> Operands;
5123 bool MadeImprovement = false;
5124 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5125 Value *Op = I->getOperand(i);
5126 if (Constant *C = dyn_cast<Constant>(Op)) {
5127 Operands.push_back(C);
5131 // If any of the operands is non-constant and if they are
5132 // non-integer and non-pointer, don't even try to analyze them
5133 // with scev techniques.
5134 if (!isSCEVable(Op->getType()))
5137 const SCEV *OrigV = getSCEV(Op);
5138 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5139 MadeImprovement |= OrigV != OpV;
5141 Constant *C = BuildConstantFromSCEV(OpV);
5143 if (C->getType() != Op->getType())
5144 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5148 Operands.push_back(C);
5151 // Check to see if getSCEVAtScope actually made an improvement.
5152 if (MadeImprovement) {
5154 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5155 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5156 Operands[0], Operands[1], TD,
5158 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5159 if (!LI->isVolatile())
5160 C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
5162 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5170 // This is some other type of SCEVUnknown, just return it.
5174 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5175 // Avoid performing the look-up in the common case where the specified
5176 // expression has no loop-variant portions.
5177 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5178 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5179 if (OpAtScope != Comm->getOperand(i)) {
5180 // Okay, at least one of these operands is loop variant but might be
5181 // foldable. Build a new instance of the folded commutative expression.
5182 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5183 Comm->op_begin()+i);
5184 NewOps.push_back(OpAtScope);
5186 for (++i; i != e; ++i) {
5187 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5188 NewOps.push_back(OpAtScope);
5190 if (isa<SCEVAddExpr>(Comm))
5191 return getAddExpr(NewOps);
5192 if (isa<SCEVMulExpr>(Comm))
5193 return getMulExpr(NewOps);
5194 if (isa<SCEVSMaxExpr>(Comm))
5195 return getSMaxExpr(NewOps);
5196 if (isa<SCEVUMaxExpr>(Comm))
5197 return getUMaxExpr(NewOps);
5198 llvm_unreachable("Unknown commutative SCEV type!");
5201 // If we got here, all operands are loop invariant.
5205 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5206 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5207 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5208 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5209 return Div; // must be loop invariant
5210 return getUDivExpr(LHS, RHS);
5213 // If this is a loop recurrence for a loop that does not contain L, then we
5214 // are dealing with the final value computed by the loop.
5215 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5216 // First, attempt to evaluate each operand.
5217 // Avoid performing the look-up in the common case where the specified
5218 // expression has no loop-variant portions.
5219 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5220 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5221 if (OpAtScope == AddRec->getOperand(i))
5224 // Okay, at least one of these operands is loop variant but might be
5225 // foldable. Build a new instance of the folded commutative expression.
5226 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5227 AddRec->op_begin()+i);
5228 NewOps.push_back(OpAtScope);
5229 for (++i; i != e; ++i)
5230 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5232 const SCEV *FoldedRec =
5233 getAddRecExpr(NewOps, AddRec->getLoop(),
5234 AddRec->getNoWrapFlags(SCEV::FlagNW));
5235 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5236 // The addrec may be folded to a nonrecurrence, for example, if the
5237 // induction variable is multiplied by zero after constant folding. Go
5238 // ahead and return the folded value.
5244 // If the scope is outside the addrec's loop, evaluate it by using the
5245 // loop exit value of the addrec.
5246 if (!AddRec->getLoop()->contains(L)) {
5247 // To evaluate this recurrence, we need to know how many times the AddRec
5248 // loop iterates. Compute this now.
5249 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5250 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5252 // Then, evaluate the AddRec.
5253 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5259 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5260 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5261 if (Op == Cast->getOperand())
5262 return Cast; // must be loop invariant
5263 return getZeroExtendExpr(Op, Cast->getType());
5266 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5267 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5268 if (Op == Cast->getOperand())
5269 return Cast; // must be loop invariant
5270 return getSignExtendExpr(Op, Cast->getType());
5273 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5274 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5275 if (Op == Cast->getOperand())
5276 return Cast; // must be loop invariant
5277 return getTruncateExpr(Op, Cast->getType());
5280 llvm_unreachable("Unknown SCEV type!");
5283 /// getSCEVAtScope - This is a convenience function which does
5284 /// getSCEVAtScope(getSCEV(V), L).
5285 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5286 return getSCEVAtScope(getSCEV(V), L);
5289 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5290 /// following equation:
5292 /// A * X = B (mod N)
5294 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5295 /// A and B isn't important.
5297 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5298 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5299 ScalarEvolution &SE) {
5300 uint32_t BW = A.getBitWidth();
5301 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5302 assert(A != 0 && "A must be non-zero.");
5306 // The gcd of A and N may have only one prime factor: 2. The number of
5307 // trailing zeros in A is its multiplicity
5308 uint32_t Mult2 = A.countTrailingZeros();
5311 // 2. Check if B is divisible by D.
5313 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5314 // is not less than multiplicity of this prime factor for D.
5315 if (B.countTrailingZeros() < Mult2)
5316 return SE.getCouldNotCompute();
5318 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5321 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5322 // bit width during computations.
5323 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5324 APInt Mod(BW + 1, 0);
5325 Mod.setBit(BW - Mult2); // Mod = N / D
5326 APInt I = AD.multiplicativeInverse(Mod);
5328 // 4. Compute the minimum unsigned root of the equation:
5329 // I * (B / D) mod (N / D)
5330 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5332 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5334 return SE.getConstant(Result.trunc(BW));
5337 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5338 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5339 /// might be the same) or two SCEVCouldNotCompute objects.
5341 static std::pair<const SCEV *,const SCEV *>
5342 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5343 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5344 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5345 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5346 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5348 // We currently can only solve this if the coefficients are constants.
5349 if (!LC || !MC || !NC) {
5350 const SCEV *CNC = SE.getCouldNotCompute();
5351 return std::make_pair(CNC, CNC);
5354 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5355 const APInt &L = LC->getValue()->getValue();
5356 const APInt &M = MC->getValue()->getValue();
5357 const APInt &N = NC->getValue()->getValue();
5358 APInt Two(BitWidth, 2);
5359 APInt Four(BitWidth, 4);
5362 using namespace APIntOps;
5364 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5365 // The B coefficient is M-N/2
5369 // The A coefficient is N/2
5370 APInt A(N.sdiv(Two));
5372 // Compute the B^2-4ac term.
5375 SqrtTerm -= Four * (A * C);
5377 if (SqrtTerm.isNegative()) {
5378 // The loop is provably infinite.
5379 const SCEV *CNC = SE.getCouldNotCompute();
5380 return std::make_pair(CNC, CNC);
5383 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5384 // integer value or else APInt::sqrt() will assert.
5385 APInt SqrtVal(SqrtTerm.sqrt());
5387 // Compute the two solutions for the quadratic formula.
5388 // The divisions must be performed as signed divisions.
5391 if (TwoA.isMinValue()) {
5392 const SCEV *CNC = SE.getCouldNotCompute();
5393 return std::make_pair(CNC, CNC);
5396 LLVMContext &Context = SE.getContext();
5398 ConstantInt *Solution1 =
5399 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5400 ConstantInt *Solution2 =
5401 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5403 return std::make_pair(SE.getConstant(Solution1),
5404 SE.getConstant(Solution2));
5405 } // end APIntOps namespace
5408 /// HowFarToZero - Return the number of times a backedge comparing the specified
5409 /// value to zero will execute. If not computable, return CouldNotCompute.
5411 /// This is only used for loops with a "x != y" exit test. The exit condition is
5412 /// now expressed as a single expression, V = x-y. So the exit test is
5413 /// effectively V != 0. We know and take advantage of the fact that this
5414 /// expression only being used in a comparison by zero context.
5415 ScalarEvolution::ExitLimit
5416 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
5417 // If the value is a constant
5418 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5419 // If the value is already zero, the branch will execute zero times.
5420 if (C->getValue()->isZero()) return C;
5421 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5424 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5425 if (!AddRec || AddRec->getLoop() != L)
5426 return getCouldNotCompute();
5428 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5429 // the quadratic equation to solve it.
5430 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5431 std::pair<const SCEV *,const SCEV *> Roots =
5432 SolveQuadraticEquation(AddRec, *this);
5433 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5434 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5437 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5438 << " sol#2: " << *R2 << "\n";
5440 // Pick the smallest positive root value.
5441 if (ConstantInt *CB =
5442 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5445 if (CB->getZExtValue() == false)
5446 std::swap(R1, R2); // R1 is the minimum root now.
5448 // We can only use this value if the chrec ends up with an exact zero
5449 // value at this index. When solving for "X*X != 5", for example, we
5450 // should not accept a root of 2.
5451 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5453 return R1; // We found a quadratic root!
5456 return getCouldNotCompute();
5459 // Otherwise we can only handle this if it is affine.
5460 if (!AddRec->isAffine())
5461 return getCouldNotCompute();
5463 // If this is an affine expression, the execution count of this branch is
5464 // the minimum unsigned root of the following equation:
5466 // Start + Step*N = 0 (mod 2^BW)
5470 // Step*N = -Start (mod 2^BW)
5472 // where BW is the common bit width of Start and Step.
5474 // Get the initial value for the loop.
5475 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5476 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5478 // For now we handle only constant steps.
5480 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5481 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5482 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5483 // We have not yet seen any such cases.
5484 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5485 if (StepC == 0 || StepC->getValue()->equalsInt(0))
5486 return getCouldNotCompute();
5488 // For positive steps (counting up until unsigned overflow):
5489 // N = -Start/Step (as unsigned)
5490 // For negative steps (counting down to zero):
5492 // First compute the unsigned distance from zero in the direction of Step.
5493 bool CountDown = StepC->getValue()->getValue().isNegative();
5494 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5496 // Handle unitary steps, which cannot wraparound.
5497 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5498 // N = Distance (as unsigned)
5499 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5500 ConstantRange CR = getUnsignedRange(Start);
5501 const SCEV *MaxBECount;
5502 if (!CountDown && CR.getUnsignedMin().isMinValue())
5503 // When counting up, the worst starting value is 1, not 0.
5504 MaxBECount = CR.getUnsignedMax().isMinValue()
5505 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5506 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5508 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5509 : -CR.getUnsignedMin());
5510 return ExitLimit(Distance, MaxBECount);
5513 // If the recurrence is known not to wraparound, unsigned divide computes the
5514 // back edge count. We know that the value will either become zero (and thus
5515 // the loop terminates), that the loop will terminate through some other exit
5516 // condition first, or that the loop has undefined behavior. This means
5517 // we can't "miss" the exit value, even with nonunit stride.
5519 // FIXME: Prove that loops always exhibits *acceptable* undefined
5520 // behavior. Loops must exhibit defined behavior until a wrapped value is
5521 // actually used. So the trip count computed by udiv could be smaller than the
5522 // number of well-defined iterations.
5523 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5524 // FIXME: We really want an "isexact" bit for udiv.
5525 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5527 // Then, try to solve the above equation provided that Start is constant.
5528 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5529 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5530 -StartC->getValue()->getValue(),
5532 return getCouldNotCompute();
5535 /// HowFarToNonZero - Return the number of times a backedge checking the
5536 /// specified value for nonzero will execute. If not computable, return
5538 ScalarEvolution::ExitLimit
5539 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5540 // Loops that look like: while (X == 0) are very strange indeed. We don't
5541 // handle them yet except for the trivial case. This could be expanded in the
5542 // future as needed.
5544 // If the value is a constant, check to see if it is known to be non-zero
5545 // already. If so, the backedge will execute zero times.
5546 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5547 if (!C->getValue()->isNullValue())
5548 return getConstant(C->getType(), 0);
5549 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5552 // We could implement others, but I really doubt anyone writes loops like
5553 // this, and if they did, they would already be constant folded.
5554 return getCouldNotCompute();
5557 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5558 /// (which may not be an immediate predecessor) which has exactly one
5559 /// successor from which BB is reachable, or null if no such block is
5562 std::pair<BasicBlock *, BasicBlock *>
5563 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5564 // If the block has a unique predecessor, then there is no path from the
5565 // predecessor to the block that does not go through the direct edge
5566 // from the predecessor to the block.
5567 if (BasicBlock *Pred = BB->getSinglePredecessor())
5568 return std::make_pair(Pred, BB);
5570 // A loop's header is defined to be a block that dominates the loop.
5571 // If the header has a unique predecessor outside the loop, it must be
5572 // a block that has exactly one successor that can reach the loop.
5573 if (Loop *L = LI->getLoopFor(BB))
5574 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5576 return std::pair<BasicBlock *, BasicBlock *>();
5579 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5580 /// testing whether two expressions are equal, however for the purposes of
5581 /// looking for a condition guarding a loop, it can be useful to be a little
5582 /// more general, since a front-end may have replicated the controlling
5585 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5586 // Quick check to see if they are the same SCEV.
5587 if (A == B) return true;
5589 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5590 // two different instructions with the same value. Check for this case.
5591 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5592 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5593 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5594 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5595 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5598 // Otherwise assume they may have a different value.
5602 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5603 /// predicate Pred. Return true iff any changes were made.
5605 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5606 const SCEV *&LHS, const SCEV *&RHS,
5608 bool Changed = false;
5610 // If we hit the max recursion limit bail out.
5614 // Canonicalize a constant to the right side.
5615 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5616 // Check for both operands constant.
5617 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5618 if (ConstantExpr::getICmp(Pred,
5620 RHSC->getValue())->isNullValue())
5621 goto trivially_false;
5623 goto trivially_true;
5625 // Otherwise swap the operands to put the constant on the right.
5626 std::swap(LHS, RHS);
5627 Pred = ICmpInst::getSwappedPredicate(Pred);
5631 // If we're comparing an addrec with a value which is loop-invariant in the
5632 // addrec's loop, put the addrec on the left. Also make a dominance check,
5633 // as both operands could be addrecs loop-invariant in each other's loop.
5634 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5635 const Loop *L = AR->getLoop();
5636 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5637 std::swap(LHS, RHS);
5638 Pred = ICmpInst::getSwappedPredicate(Pred);
5643 // If there's a constant operand, canonicalize comparisons with boundary
5644 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5645 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5646 const APInt &RA = RC->getValue()->getValue();
5648 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5649 case ICmpInst::ICMP_EQ:
5650 case ICmpInst::ICMP_NE:
5651 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5653 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5654 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5655 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5656 ME->getOperand(0)->isAllOnesValue()) {
5657 RHS = AE->getOperand(1);
5658 LHS = ME->getOperand(1);
5662 case ICmpInst::ICMP_UGE:
5663 if ((RA - 1).isMinValue()) {
5664 Pred = ICmpInst::ICMP_NE;
5665 RHS = getConstant(RA - 1);
5669 if (RA.isMaxValue()) {
5670 Pred = ICmpInst::ICMP_EQ;
5674 if (RA.isMinValue()) goto trivially_true;
5676 Pred = ICmpInst::ICMP_UGT;
5677 RHS = getConstant(RA - 1);
5680 case ICmpInst::ICMP_ULE:
5681 if ((RA + 1).isMaxValue()) {
5682 Pred = ICmpInst::ICMP_NE;
5683 RHS = getConstant(RA + 1);
5687 if (RA.isMinValue()) {
5688 Pred = ICmpInst::ICMP_EQ;
5692 if (RA.isMaxValue()) goto trivially_true;
5694 Pred = ICmpInst::ICMP_ULT;
5695 RHS = getConstant(RA + 1);
5698 case ICmpInst::ICMP_SGE:
5699 if ((RA - 1).isMinSignedValue()) {
5700 Pred = ICmpInst::ICMP_NE;
5701 RHS = getConstant(RA - 1);
5705 if (RA.isMaxSignedValue()) {
5706 Pred = ICmpInst::ICMP_EQ;
5710 if (RA.isMinSignedValue()) goto trivially_true;
5712 Pred = ICmpInst::ICMP_SGT;
5713 RHS = getConstant(RA - 1);
5716 case ICmpInst::ICMP_SLE:
5717 if ((RA + 1).isMaxSignedValue()) {
5718 Pred = ICmpInst::ICMP_NE;
5719 RHS = getConstant(RA + 1);
5723 if (RA.isMinSignedValue()) {
5724 Pred = ICmpInst::ICMP_EQ;
5728 if (RA.isMaxSignedValue()) goto trivially_true;
5730 Pred = ICmpInst::ICMP_SLT;
5731 RHS = getConstant(RA + 1);
5734 case ICmpInst::ICMP_UGT:
5735 if (RA.isMinValue()) {
5736 Pred = ICmpInst::ICMP_NE;
5740 if ((RA + 1).isMaxValue()) {
5741 Pred = ICmpInst::ICMP_EQ;
5742 RHS = getConstant(RA + 1);
5746 if (RA.isMaxValue()) goto trivially_false;
5748 case ICmpInst::ICMP_ULT:
5749 if (RA.isMaxValue()) {
5750 Pred = ICmpInst::ICMP_NE;
5754 if ((RA - 1).isMinValue()) {
5755 Pred = ICmpInst::ICMP_EQ;
5756 RHS = getConstant(RA - 1);
5760 if (RA.isMinValue()) goto trivially_false;
5762 case ICmpInst::ICMP_SGT:
5763 if (RA.isMinSignedValue()) {
5764 Pred = ICmpInst::ICMP_NE;
5768 if ((RA + 1).isMaxSignedValue()) {
5769 Pred = ICmpInst::ICMP_EQ;
5770 RHS = getConstant(RA + 1);
5774 if (RA.isMaxSignedValue()) goto trivially_false;
5776 case ICmpInst::ICMP_SLT:
5777 if (RA.isMaxSignedValue()) {
5778 Pred = ICmpInst::ICMP_NE;
5782 if ((RA - 1).isMinSignedValue()) {
5783 Pred = ICmpInst::ICMP_EQ;
5784 RHS = getConstant(RA - 1);
5788 if (RA.isMinSignedValue()) goto trivially_false;
5793 // Check for obvious equality.
5794 if (HasSameValue(LHS, RHS)) {
5795 if (ICmpInst::isTrueWhenEqual(Pred))
5796 goto trivially_true;
5797 if (ICmpInst::isFalseWhenEqual(Pred))
5798 goto trivially_false;
5801 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5802 // adding or subtracting 1 from one of the operands.
5804 case ICmpInst::ICMP_SLE:
5805 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5806 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5808 Pred = ICmpInst::ICMP_SLT;
5810 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5811 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5813 Pred = ICmpInst::ICMP_SLT;
5817 case ICmpInst::ICMP_SGE:
5818 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5819 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5821 Pred = ICmpInst::ICMP_SGT;
5823 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5824 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5826 Pred = ICmpInst::ICMP_SGT;
5830 case ICmpInst::ICMP_ULE:
5831 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5832 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5834 Pred = ICmpInst::ICMP_ULT;
5836 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5837 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5839 Pred = ICmpInst::ICMP_ULT;
5843 case ICmpInst::ICMP_UGE:
5844 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5845 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5847 Pred = ICmpInst::ICMP_UGT;
5849 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5850 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5852 Pred = ICmpInst::ICMP_UGT;
5860 // TODO: More simplifications are possible here.
5862 // Recursively simplify until we either hit a recursion limit or nothing
5865 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
5871 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5872 Pred = ICmpInst::ICMP_EQ;
5877 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5878 Pred = ICmpInst::ICMP_NE;
5882 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5883 return getSignedRange(S).getSignedMax().isNegative();
5886 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5887 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5890 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5891 return !getSignedRange(S).getSignedMin().isNegative();
5894 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5895 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5898 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5899 return isKnownNegative(S) || isKnownPositive(S);
5902 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5903 const SCEV *LHS, const SCEV *RHS) {
5904 // Canonicalize the inputs first.
5905 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5907 // If LHS or RHS is an addrec, check to see if the condition is true in
5908 // every iteration of the loop.
5909 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5910 if (isLoopEntryGuardedByCond(
5911 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5912 isLoopBackedgeGuardedByCond(
5913 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5915 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5916 if (isLoopEntryGuardedByCond(
5917 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5918 isLoopBackedgeGuardedByCond(
5919 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5922 // Otherwise see what can be done with known constant ranges.
5923 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5927 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5928 const SCEV *LHS, const SCEV *RHS) {
5929 if (HasSameValue(LHS, RHS))
5930 return ICmpInst::isTrueWhenEqual(Pred);
5932 // This code is split out from isKnownPredicate because it is called from
5933 // within isLoopEntryGuardedByCond.
5936 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5937 case ICmpInst::ICMP_SGT:
5938 Pred = ICmpInst::ICMP_SLT;
5939 std::swap(LHS, RHS);
5940 case ICmpInst::ICMP_SLT: {
5941 ConstantRange LHSRange = getSignedRange(LHS);
5942 ConstantRange RHSRange = getSignedRange(RHS);
5943 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5945 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5949 case ICmpInst::ICMP_SGE:
5950 Pred = ICmpInst::ICMP_SLE;
5951 std::swap(LHS, RHS);
5952 case ICmpInst::ICMP_SLE: {
5953 ConstantRange LHSRange = getSignedRange(LHS);
5954 ConstantRange RHSRange = getSignedRange(RHS);
5955 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5957 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5961 case ICmpInst::ICMP_UGT:
5962 Pred = ICmpInst::ICMP_ULT;
5963 std::swap(LHS, RHS);
5964 case ICmpInst::ICMP_ULT: {
5965 ConstantRange LHSRange = getUnsignedRange(LHS);
5966 ConstantRange RHSRange = getUnsignedRange(RHS);
5967 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5969 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5973 case ICmpInst::ICMP_UGE:
5974 Pred = ICmpInst::ICMP_ULE;
5975 std::swap(LHS, RHS);
5976 case ICmpInst::ICMP_ULE: {
5977 ConstantRange LHSRange = getUnsignedRange(LHS);
5978 ConstantRange RHSRange = getUnsignedRange(RHS);
5979 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5981 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5985 case ICmpInst::ICMP_NE: {
5986 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5988 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5991 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5992 if (isKnownNonZero(Diff))
5996 case ICmpInst::ICMP_EQ:
5997 // The check at the top of the function catches the case where
5998 // the values are known to be equal.
6004 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6005 /// protected by a conditional between LHS and RHS. This is used to
6006 /// to eliminate casts.
6008 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6009 ICmpInst::Predicate Pred,
6010 const SCEV *LHS, const SCEV *RHS) {
6011 // Interpret a null as meaning no loop, where there is obviously no guard
6012 // (interprocedural conditions notwithstanding).
6013 if (!L) return true;
6015 BasicBlock *Latch = L->getLoopLatch();
6019 BranchInst *LoopContinuePredicate =
6020 dyn_cast<BranchInst>(Latch->getTerminator());
6021 if (!LoopContinuePredicate ||
6022 LoopContinuePredicate->isUnconditional())
6025 return isImpliedCond(Pred, LHS, RHS,
6026 LoopContinuePredicate->getCondition(),
6027 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6030 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6031 /// by a conditional between LHS and RHS. This is used to help avoid max
6032 /// expressions in loop trip counts, and to eliminate casts.
6034 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6035 ICmpInst::Predicate Pred,
6036 const SCEV *LHS, const SCEV *RHS) {
6037 // Interpret a null as meaning no loop, where there is obviously no guard
6038 // (interprocedural conditions notwithstanding).
6039 if (!L) return false;
6041 // Starting at the loop predecessor, climb up the predecessor chain, as long
6042 // as there are predecessors that can be found that have unique successors
6043 // leading to the original header.
6044 for (std::pair<BasicBlock *, BasicBlock *>
6045 Pair(L->getLoopPredecessor(), L->getHeader());
6047 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6049 BranchInst *LoopEntryPredicate =
6050 dyn_cast<BranchInst>(Pair.first->getTerminator());
6051 if (!LoopEntryPredicate ||
6052 LoopEntryPredicate->isUnconditional())
6055 if (isImpliedCond(Pred, LHS, RHS,
6056 LoopEntryPredicate->getCondition(),
6057 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6064 /// RAII wrapper to prevent recursive application of isImpliedCond.
6065 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6066 /// currently evaluating isImpliedCond.
6067 struct MarkPendingLoopPredicate {
6069 DenseSet<Value*> &LoopPreds;
6072 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6073 : Cond(C), LoopPreds(LP) {
6074 Pending = !LoopPreds.insert(Cond).second;
6076 ~MarkPendingLoopPredicate() {
6078 LoopPreds.erase(Cond);
6082 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6083 /// and RHS is true whenever the given Cond value evaluates to true.
6084 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6085 const SCEV *LHS, const SCEV *RHS,
6086 Value *FoundCondValue,
6088 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6092 // Recursively handle And and Or conditions.
6093 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6094 if (BO->getOpcode() == Instruction::And) {
6096 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6097 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6098 } else if (BO->getOpcode() == Instruction::Or) {
6100 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6101 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6105 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6106 if (!ICI) return false;
6108 // Bail if the ICmp's operands' types are wider than the needed type
6109 // before attempting to call getSCEV on them. This avoids infinite
6110 // recursion, since the analysis of widening casts can require loop
6111 // exit condition information for overflow checking, which would
6113 if (getTypeSizeInBits(LHS->getType()) <
6114 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6117 // Now that we found a conditional branch that dominates the loop, check to
6118 // see if it is the comparison we are looking for.
6119 ICmpInst::Predicate FoundPred;
6121 FoundPred = ICI->getInversePredicate();
6123 FoundPred = ICI->getPredicate();
6125 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6126 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6128 // Balance the types. The case where FoundLHS' type is wider than
6129 // LHS' type is checked for above.
6130 if (getTypeSizeInBits(LHS->getType()) >
6131 getTypeSizeInBits(FoundLHS->getType())) {
6132 if (CmpInst::isSigned(Pred)) {
6133 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6134 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6136 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6137 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6141 // Canonicalize the query to match the way instcombine will have
6142 // canonicalized the comparison.
6143 if (SimplifyICmpOperands(Pred, LHS, RHS))
6145 return CmpInst::isTrueWhenEqual(Pred);
6146 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6147 if (FoundLHS == FoundRHS)
6148 return CmpInst::isFalseWhenEqual(Pred);
6150 // Check to see if we can make the LHS or RHS match.
6151 if (LHS == FoundRHS || RHS == FoundLHS) {
6152 if (isa<SCEVConstant>(RHS)) {
6153 std::swap(FoundLHS, FoundRHS);
6154 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6156 std::swap(LHS, RHS);
6157 Pred = ICmpInst::getSwappedPredicate(Pred);
6161 // Check whether the found predicate is the same as the desired predicate.
6162 if (FoundPred == Pred)
6163 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6165 // Check whether swapping the found predicate makes it the same as the
6166 // desired predicate.
6167 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6168 if (isa<SCEVConstant>(RHS))
6169 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6171 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6172 RHS, LHS, FoundLHS, FoundRHS);
6175 // Check whether the actual condition is beyond sufficient.
6176 if (FoundPred == ICmpInst::ICMP_EQ)
6177 if (ICmpInst::isTrueWhenEqual(Pred))
6178 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6180 if (Pred == ICmpInst::ICMP_NE)
6181 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6182 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6185 // Otherwise assume the worst.
6189 /// isImpliedCondOperands - Test whether the condition described by Pred,
6190 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6191 /// and FoundRHS is true.
6192 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6193 const SCEV *LHS, const SCEV *RHS,
6194 const SCEV *FoundLHS,
6195 const SCEV *FoundRHS) {
6196 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6197 FoundLHS, FoundRHS) ||
6198 // ~x < ~y --> x > y
6199 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6200 getNotSCEV(FoundRHS),
6201 getNotSCEV(FoundLHS));
6204 /// isImpliedCondOperandsHelper - Test whether the condition described by
6205 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6206 /// FoundLHS, and FoundRHS is true.
6208 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6209 const SCEV *LHS, const SCEV *RHS,
6210 const SCEV *FoundLHS,
6211 const SCEV *FoundRHS) {
6213 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6214 case ICmpInst::ICMP_EQ:
6215 case ICmpInst::ICMP_NE:
6216 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6219 case ICmpInst::ICMP_SLT:
6220 case ICmpInst::ICMP_SLE:
6221 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6222 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6225 case ICmpInst::ICMP_SGT:
6226 case ICmpInst::ICMP_SGE:
6227 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6228 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6231 case ICmpInst::ICMP_ULT:
6232 case ICmpInst::ICMP_ULE:
6233 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6234 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6237 case ICmpInst::ICMP_UGT:
6238 case ICmpInst::ICMP_UGE:
6239 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6240 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6248 /// getBECount - Subtract the end and start values and divide by the step,
6249 /// rounding up, to get the number of times the backedge is executed. Return
6250 /// CouldNotCompute if an intermediate computation overflows.
6251 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
6255 assert(!isKnownNegative(Step) &&
6256 "This code doesn't handle negative strides yet!");
6258 Type *Ty = Start->getType();
6260 // When Start == End, we have an exact BECount == 0. Short-circuit this case
6261 // here because SCEV may not be able to determine that the unsigned division
6262 // after rounding is zero.
6264 return getConstant(Ty, 0);
6266 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
6267 const SCEV *Diff = getMinusSCEV(End, Start);
6268 const SCEV *RoundUp = getAddExpr(Step, NegOne);
6270 // Add an adjustment to the difference between End and Start so that
6271 // the division will effectively round up.
6272 const SCEV *Add = getAddExpr(Diff, RoundUp);
6275 // Check Add for unsigned overflow.
6276 // TODO: More sophisticated things could be done here.
6277 Type *WideTy = IntegerType::get(getContext(),
6278 getTypeSizeInBits(Ty) + 1);
6279 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
6280 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
6281 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
6282 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
6283 return getCouldNotCompute();
6286 return getUDivExpr(Add, Step);
6289 /// HowManyLessThans - Return the number of times a backedge containing the
6290 /// specified less-than comparison will execute. If not computable, return
6291 /// CouldNotCompute.
6292 ScalarEvolution::ExitLimit
6293 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6294 const Loop *L, bool isSigned) {
6295 // Only handle: "ADDREC < LoopInvariant".
6296 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
6298 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
6299 if (!AddRec || AddRec->getLoop() != L)
6300 return getCouldNotCompute();
6302 // Check to see if we have a flag which makes analysis easy.
6303 bool NoWrap = isSigned ?
6304 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNW)) :
6305 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNW));
6307 if (AddRec->isAffine()) {
6308 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
6309 const SCEV *Step = AddRec->getStepRecurrence(*this);
6312 return getCouldNotCompute();
6313 if (Step->isOne()) {
6314 // With unit stride, the iteration never steps past the limit value.
6315 } else if (isKnownPositive(Step)) {
6316 // Test whether a positive iteration can step past the limit
6317 // value and past the maximum value for its type in a single step.
6318 // Note that it's not sufficient to check NoWrap here, because even
6319 // though the value after a wrap is undefined, it's not undefined
6320 // behavior, so if wrap does occur, the loop could either terminate or
6321 // loop infinitely, but in either case, the loop is guaranteed to
6322 // iterate at least until the iteration where the wrapping occurs.
6323 const SCEV *One = getConstant(Step->getType(), 1);
6325 APInt Max = APInt::getSignedMaxValue(BitWidth);
6326 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
6327 .slt(getSignedRange(RHS).getSignedMax()))
6328 return getCouldNotCompute();
6330 APInt Max = APInt::getMaxValue(BitWidth);
6331 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
6332 .ult(getUnsignedRange(RHS).getUnsignedMax()))
6333 return getCouldNotCompute();
6336 // TODO: Handle negative strides here and below.
6337 return getCouldNotCompute();
6339 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6340 // m. So, we count the number of iterations in which {n,+,s} < m is true.
6341 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6342 // treat m-n as signed nor unsigned due to overflow possibility.
6344 // First, we get the value of the LHS in the first iteration: n
6345 const SCEV *Start = AddRec->getOperand(0);
6347 // Determine the minimum constant start value.
6348 const SCEV *MinStart = getConstant(isSigned ?
6349 getSignedRange(Start).getSignedMin() :
6350 getUnsignedRange(Start).getUnsignedMin());
6352 // If we know that the condition is true in order to enter the loop,
6353 // then we know that it will run exactly (m-n)/s times. Otherwise, we
6354 // only know that it will execute (max(m,n)-n)/s times. In both cases,
6355 // the division must round up.
6356 const SCEV *End = RHS;
6357 if (!isLoopEntryGuardedByCond(L,
6358 isSigned ? ICmpInst::ICMP_SLT :
6360 getMinusSCEV(Start, Step), RHS))
6361 End = isSigned ? getSMaxExpr(RHS, Start)
6362 : getUMaxExpr(RHS, Start);
6364 // Determine the maximum constant end value.
6365 const SCEV *MaxEnd = getConstant(isSigned ?
6366 getSignedRange(End).getSignedMax() :
6367 getUnsignedRange(End).getUnsignedMax());
6369 // If MaxEnd is within a step of the maximum integer value in its type,
6370 // adjust it down to the minimum value which would produce the same effect.
6371 // This allows the subsequent ceiling division of (N+(step-1))/step to
6372 // compute the correct value.
6373 const SCEV *StepMinusOne = getMinusSCEV(Step,
6374 getConstant(Step->getType(), 1));
6377 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6380 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6383 // Finally, we subtract these two values and divide, rounding up, to get
6384 // the number of times the backedge is executed.
6385 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6387 // The maximum backedge count is similar, except using the minimum start
6388 // value and the maximum end value.
6389 // If we already have an exact constant BECount, use it instead.
6390 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6391 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6393 // If the stride is nonconstant, and NoWrap == true, then
6394 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6395 // exact BECount and invalid MaxBECount, which should be avoided to catch
6396 // more optimization opportunities.
6397 if (isa<SCEVCouldNotCompute>(MaxBECount))
6398 MaxBECount = BECount;
6400 return ExitLimit(BECount, MaxBECount);
6403 return getCouldNotCompute();
6406 /// getNumIterationsInRange - Return the number of iterations of this loop that
6407 /// produce values in the specified constant range. Another way of looking at
6408 /// this is that it returns the first iteration number where the value is not in
6409 /// the condition, thus computing the exit count. If the iteration count can't
6410 /// be computed, an instance of SCEVCouldNotCompute is returned.
6411 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6412 ScalarEvolution &SE) const {
6413 if (Range.isFullSet()) // Infinite loop.
6414 return SE.getCouldNotCompute();
6416 // If the start is a non-zero constant, shift the range to simplify things.
6417 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6418 if (!SC->getValue()->isZero()) {
6419 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6420 Operands[0] = SE.getConstant(SC->getType(), 0);
6421 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6422 getNoWrapFlags(FlagNW));
6423 if (const SCEVAddRecExpr *ShiftedAddRec =
6424 dyn_cast<SCEVAddRecExpr>(Shifted))
6425 return ShiftedAddRec->getNumIterationsInRange(
6426 Range.subtract(SC->getValue()->getValue()), SE);
6427 // This is strange and shouldn't happen.
6428 return SE.getCouldNotCompute();
6431 // The only time we can solve this is when we have all constant indices.
6432 // Otherwise, we cannot determine the overflow conditions.
6433 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6434 if (!isa<SCEVConstant>(getOperand(i)))
6435 return SE.getCouldNotCompute();
6438 // Okay at this point we know that all elements of the chrec are constants and
6439 // that the start element is zero.
6441 // First check to see if the range contains zero. If not, the first
6443 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6444 if (!Range.contains(APInt(BitWidth, 0)))
6445 return SE.getConstant(getType(), 0);
6448 // If this is an affine expression then we have this situation:
6449 // Solve {0,+,A} in Range === Ax in Range
6451 // We know that zero is in the range. If A is positive then we know that
6452 // the upper value of the range must be the first possible exit value.
6453 // If A is negative then the lower of the range is the last possible loop
6454 // value. Also note that we already checked for a full range.
6455 APInt One(BitWidth,1);
6456 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6457 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6459 // The exit value should be (End+A)/A.
6460 APInt ExitVal = (End + A).udiv(A);
6461 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6463 // Evaluate at the exit value. If we really did fall out of the valid
6464 // range, then we computed our trip count, otherwise wrap around or other
6465 // things must have happened.
6466 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6467 if (Range.contains(Val->getValue()))
6468 return SE.getCouldNotCompute(); // Something strange happened
6470 // Ensure that the previous value is in the range. This is a sanity check.
6471 assert(Range.contains(
6472 EvaluateConstantChrecAtConstant(this,
6473 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6474 "Linear scev computation is off in a bad way!");
6475 return SE.getConstant(ExitValue);
6476 } else if (isQuadratic()) {
6477 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6478 // quadratic equation to solve it. To do this, we must frame our problem in
6479 // terms of figuring out when zero is crossed, instead of when
6480 // Range.getUpper() is crossed.
6481 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6482 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6483 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6484 // getNoWrapFlags(FlagNW)
6487 // Next, solve the constructed addrec
6488 std::pair<const SCEV *,const SCEV *> Roots =
6489 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6490 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6491 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6493 // Pick the smallest positive root value.
6494 if (ConstantInt *CB =
6495 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6496 R1->getValue(), R2->getValue()))) {
6497 if (CB->getZExtValue() == false)
6498 std::swap(R1, R2); // R1 is the minimum root now.
6500 // Make sure the root is not off by one. The returned iteration should
6501 // not be in the range, but the previous one should be. When solving
6502 // for "X*X < 5", for example, we should not return a root of 2.
6503 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6506 if (Range.contains(R1Val->getValue())) {
6507 // The next iteration must be out of the range...
6508 ConstantInt *NextVal =
6509 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6511 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6512 if (!Range.contains(R1Val->getValue()))
6513 return SE.getConstant(NextVal);
6514 return SE.getCouldNotCompute(); // Something strange happened
6517 // If R1 was not in the range, then it is a good return value. Make
6518 // sure that R1-1 WAS in the range though, just in case.
6519 ConstantInt *NextVal =
6520 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6521 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6522 if (Range.contains(R1Val->getValue()))
6524 return SE.getCouldNotCompute(); // Something strange happened
6529 return SE.getCouldNotCompute();
6534 //===----------------------------------------------------------------------===//
6535 // SCEVCallbackVH Class Implementation
6536 //===----------------------------------------------------------------------===//
6538 void ScalarEvolution::SCEVCallbackVH::deleted() {
6539 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6540 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6541 SE->ConstantEvolutionLoopExitValue.erase(PN);
6542 SE->ValueExprMap.erase(getValPtr());
6543 // this now dangles!
6546 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6547 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6549 // Forget all the expressions associated with users of the old value,
6550 // so that future queries will recompute the expressions using the new
6552 Value *Old = getValPtr();
6553 SmallVector<User *, 16> Worklist;
6554 SmallPtrSet<User *, 8> Visited;
6555 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6557 Worklist.push_back(*UI);
6558 while (!Worklist.empty()) {
6559 User *U = Worklist.pop_back_val();
6560 // Deleting the Old value will cause this to dangle. Postpone
6561 // that until everything else is done.
6564 if (!Visited.insert(U))
6566 if (PHINode *PN = dyn_cast<PHINode>(U))
6567 SE->ConstantEvolutionLoopExitValue.erase(PN);
6568 SE->ValueExprMap.erase(U);
6569 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6571 Worklist.push_back(*UI);
6573 // Delete the Old value.
6574 if (PHINode *PN = dyn_cast<PHINode>(Old))
6575 SE->ConstantEvolutionLoopExitValue.erase(PN);
6576 SE->ValueExprMap.erase(Old);
6577 // this now dangles!
6580 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6581 : CallbackVH(V), SE(se) {}
6583 //===----------------------------------------------------------------------===//
6584 // ScalarEvolution Class Implementation
6585 //===----------------------------------------------------------------------===//
6587 ScalarEvolution::ScalarEvolution()
6588 : FunctionPass(ID), FirstUnknown(0) {
6589 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6592 bool ScalarEvolution::runOnFunction(Function &F) {
6594 LI = &getAnalysis<LoopInfo>();
6595 TD = getAnalysisIfAvailable<DataLayout>();
6596 TLI = &getAnalysis<TargetLibraryInfo>();
6597 DT = &getAnalysis<DominatorTree>();
6601 void ScalarEvolution::releaseMemory() {
6602 // Iterate through all the SCEVUnknown instances and call their
6603 // destructors, so that they release their references to their values.
6604 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6608 ValueExprMap.clear();
6610 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6611 // that a loop had multiple computable exits.
6612 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6613 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6618 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
6620 BackedgeTakenCounts.clear();
6621 ConstantEvolutionLoopExitValue.clear();
6622 ValuesAtScopes.clear();
6623 LoopDispositions.clear();
6624 BlockDispositions.clear();
6625 UnsignedRanges.clear();
6626 SignedRanges.clear();
6627 UniqueSCEVs.clear();
6628 SCEVAllocator.Reset();
6631 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6632 AU.setPreservesAll();
6633 AU.addRequiredTransitive<LoopInfo>();
6634 AU.addRequiredTransitive<DominatorTree>();
6635 AU.addRequired<TargetLibraryInfo>();
6638 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6639 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6642 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6644 // Print all inner loops first
6645 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6646 PrintLoopInfo(OS, SE, *I);
6649 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6652 SmallVector<BasicBlock *, 8> ExitBlocks;
6653 L->getExitBlocks(ExitBlocks);
6654 if (ExitBlocks.size() != 1)
6655 OS << "<multiple exits> ";
6657 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6658 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6660 OS << "Unpredictable backedge-taken count. ";
6665 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6668 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6669 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6671 OS << "Unpredictable max backedge-taken count. ";
6677 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6678 // ScalarEvolution's implementation of the print method is to print
6679 // out SCEV values of all instructions that are interesting. Doing
6680 // this potentially causes it to create new SCEV objects though,
6681 // which technically conflicts with the const qualifier. This isn't
6682 // observable from outside the class though, so casting away the
6683 // const isn't dangerous.
6684 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6686 OS << "Classifying expressions for: ";
6687 WriteAsOperand(OS, F, /*PrintType=*/false);
6689 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6690 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6693 const SCEV *SV = SE.getSCEV(&*I);
6696 const Loop *L = LI->getLoopFor((*I).getParent());
6698 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6705 OS << "\t\t" "Exits: ";
6706 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6707 if (!SE.isLoopInvariant(ExitValue, L)) {
6708 OS << "<<Unknown>>";
6717 OS << "Determining loop execution counts for: ";
6718 WriteAsOperand(OS, F, /*PrintType=*/false);
6720 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6721 PrintLoopInfo(OS, &SE, *I);
6724 ScalarEvolution::LoopDisposition
6725 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6726 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6727 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6728 Values.insert(std::make_pair(L, LoopVariant));
6730 return Pair.first->second;
6732 LoopDisposition D = computeLoopDisposition(S, L);
6733 return LoopDispositions[S][L] = D;
6736 ScalarEvolution::LoopDisposition
6737 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6738 switch (S->getSCEVType()) {
6740 return LoopInvariant;
6744 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6745 case scAddRecExpr: {
6746 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6748 // If L is the addrec's loop, it's computable.
6749 if (AR->getLoop() == L)
6750 return LoopComputable;
6752 // Add recurrences are never invariant in the function-body (null loop).
6756 // This recurrence is variant w.r.t. L if L contains AR's loop.
6757 if (L->contains(AR->getLoop()))
6760 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6761 if (AR->getLoop()->contains(L))
6762 return LoopInvariant;
6764 // This recurrence is variant w.r.t. L if any of its operands
6766 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6768 if (!isLoopInvariant(*I, L))
6771 // Otherwise it's loop-invariant.
6772 return LoopInvariant;
6778 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6779 bool HasVarying = false;
6780 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6782 LoopDisposition D = getLoopDisposition(*I, L);
6783 if (D == LoopVariant)
6785 if (D == LoopComputable)
6788 return HasVarying ? LoopComputable : LoopInvariant;
6791 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6792 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6793 if (LD == LoopVariant)
6795 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6796 if (RD == LoopVariant)
6798 return (LD == LoopInvariant && RD == LoopInvariant) ?
6799 LoopInvariant : LoopComputable;
6802 // All non-instruction values are loop invariant. All instructions are loop
6803 // invariant if they are not contained in the specified loop.
6804 // Instructions are never considered invariant in the function body
6805 // (null loop) because they are defined within the "loop".
6806 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6807 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6808 return LoopInvariant;
6809 case scCouldNotCompute:
6810 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6811 default: llvm_unreachable("Unknown SCEV kind!");
6815 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6816 return getLoopDisposition(S, L) == LoopInvariant;
6819 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6820 return getLoopDisposition(S, L) == LoopComputable;
6823 ScalarEvolution::BlockDisposition
6824 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6825 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6826 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6827 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6829 return Pair.first->second;
6831 BlockDisposition D = computeBlockDisposition(S, BB);
6832 return BlockDispositions[S][BB] = D;
6835 ScalarEvolution::BlockDisposition
6836 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6837 switch (S->getSCEVType()) {
6839 return ProperlyDominatesBlock;
6843 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6844 case scAddRecExpr: {
6845 // This uses a "dominates" query instead of "properly dominates" query
6846 // to test for proper dominance too, because the instruction which
6847 // produces the addrec's value is a PHI, and a PHI effectively properly
6848 // dominates its entire containing block.
6849 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6850 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6851 return DoesNotDominateBlock;
6853 // FALL THROUGH into SCEVNAryExpr handling.
6858 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6860 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6862 BlockDisposition D = getBlockDisposition(*I, BB);
6863 if (D == DoesNotDominateBlock)
6864 return DoesNotDominateBlock;
6865 if (D == DominatesBlock)
6868 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6871 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6872 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6873 BlockDisposition LD = getBlockDisposition(LHS, BB);
6874 if (LD == DoesNotDominateBlock)
6875 return DoesNotDominateBlock;
6876 BlockDisposition RD = getBlockDisposition(RHS, BB);
6877 if (RD == DoesNotDominateBlock)
6878 return DoesNotDominateBlock;
6879 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6880 ProperlyDominatesBlock : DominatesBlock;
6883 if (Instruction *I =
6884 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6885 if (I->getParent() == BB)
6886 return DominatesBlock;
6887 if (DT->properlyDominates(I->getParent(), BB))
6888 return ProperlyDominatesBlock;
6889 return DoesNotDominateBlock;
6891 return ProperlyDominatesBlock;
6892 case scCouldNotCompute:
6893 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6895 llvm_unreachable("Unknown SCEV kind!");
6899 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6900 return getBlockDisposition(S, BB) >= DominatesBlock;
6903 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6904 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6908 // Search for a SCEV expression node within an expression tree.
6909 // Implements SCEVTraversal::Visitor.
6914 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
6916 bool follow(const SCEV *S) {
6917 IsFound |= (S == Node);
6920 bool isDone() const { return IsFound; }
6924 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6925 SCEVSearch Search(Op);
6926 visitAll(S, Search);
6927 return Search.IsFound;
6930 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6931 ValuesAtScopes.erase(S);
6932 LoopDispositions.erase(S);
6933 BlockDispositions.erase(S);
6934 UnsignedRanges.erase(S);
6935 SignedRanges.erase(S);