1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #define DEBUG_TYPE "scalar-evolution"
62 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/GlobalAlias.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/Operator.h"
70 #include "llvm/Analysis/ConstantFolding.h"
71 #include "llvm/Analysis/Dominators.h"
72 #include "llvm/Analysis/InstructionSimplify.h"
73 #include "llvm/Analysis/LoopInfo.h"
74 #include "llvm/Analysis/ValueTracking.h"
75 #include "llvm/Assembly/Writer.h"
76 #include "llvm/Target/TargetData.h"
77 #include "llvm/Target/TargetLibraryInfo.h"
78 #include "llvm/Support/CommandLine.h"
79 #include "llvm/Support/ConstantRange.h"
80 #include "llvm/Support/Debug.h"
81 #include "llvm/Support/ErrorHandling.h"
82 #include "llvm/Support/GetElementPtrTypeIterator.h"
83 #include "llvm/Support/InstIterator.h"
84 #include "llvm/Support/MathExtras.h"
85 #include "llvm/Support/raw_ostream.h"
86 #include "llvm/ADT/Statistic.h"
87 #include "llvm/ADT/STLExtras.h"
88 #include "llvm/ADT/SmallPtrSet.h"
92 STATISTIC(NumArrayLenItCounts,
93 "Number of trip counts computed with array length");
94 STATISTIC(NumTripCountsComputed,
95 "Number of loops with predictable loop counts");
96 STATISTIC(NumTripCountsNotComputed,
97 "Number of loops without predictable loop counts");
98 STATISTIC(NumBruteForceTripCountsComputed,
99 "Number of loops with trip counts computed by force");
101 static cl::opt<unsigned>
102 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
103 cl::desc("Maximum number of iterations SCEV will "
104 "symbolically execute a constant "
108 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
109 "Scalar Evolution Analysis", false, true)
110 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
111 INITIALIZE_PASS_DEPENDENCY(DominatorTree)
112 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
113 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
114 "Scalar Evolution Analysis", false, true)
115 char ScalarEvolution::ID = 0;
117 //===----------------------------------------------------------------------===//
118 // SCEV class definitions
119 //===----------------------------------------------------------------------===//
121 //===----------------------------------------------------------------------===//
122 // Implementation of the SCEV class.
125 #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 if 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) {
2585 // If we have TargetData, 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(TD->getIntPtrType(getContext()),
2590 TD->getTypeAllocSize(AllocTy));
2592 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2593 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2594 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2596 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2597 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2600 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2601 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2602 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2603 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2605 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2606 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2609 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy,
2611 // If we have TargetData, we can bypass creating a target-independent
2612 // constant expression and then folding it back into a ConstantInt.
2613 // This is just a compile-time optimization.
2615 return getConstant(TD->getIntPtrType(getContext()),
2616 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2618 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2619 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2620 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2622 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2623 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2626 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2627 Constant *FieldNo) {
2628 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2629 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2630 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2632 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2633 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2636 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2637 // Don't attempt to do anything other than create a SCEVUnknown object
2638 // here. createSCEV only calls getUnknown after checking for all other
2639 // interesting possibilities, and any other code that calls getUnknown
2640 // is doing so in order to hide a value from SCEV canonicalization.
2642 FoldingSetNodeID ID;
2643 ID.AddInteger(scUnknown);
2646 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2647 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2648 "Stale SCEVUnknown in uniquing map!");
2651 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2653 FirstUnknown = cast<SCEVUnknown>(S);
2654 UniqueSCEVs.InsertNode(S, IP);
2658 //===----------------------------------------------------------------------===//
2659 // Basic SCEV Analysis and PHI Idiom Recognition Code
2662 /// isSCEVable - Test if values of the given type are analyzable within
2663 /// the SCEV framework. This primarily includes integer types, and it
2664 /// can optionally include pointer types if the ScalarEvolution class
2665 /// has access to target-specific information.
2666 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2667 // Integers and pointers are always SCEVable.
2668 return Ty->isIntegerTy() || Ty->isPointerTy();
2671 /// getTypeSizeInBits - Return the size in bits of the specified type,
2672 /// for which isSCEVable must return true.
2673 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2674 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2676 // If we have a TargetData, use it!
2678 return TD->getTypeSizeInBits(Ty);
2680 // Integer types have fixed sizes.
2681 if (Ty->isIntegerTy())
2682 return Ty->getPrimitiveSizeInBits();
2684 // The only other support type is pointer. Without TargetData, conservatively
2685 // assume pointers are 64-bit.
2686 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2690 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2691 /// the given type and which represents how SCEV will treat the given
2692 /// type, for which isSCEVable must return true. For pointer types,
2693 /// this is the pointer-sized integer type.
2694 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2695 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2697 if (Ty->isIntegerTy())
2700 // The only other support type is pointer.
2701 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2702 if (TD) return TD->getIntPtrType(getContext());
2704 // Without TargetData, conservatively assume pointers are 64-bit.
2705 return Type::getInt64Ty(getContext());
2708 const SCEV *ScalarEvolution::getCouldNotCompute() {
2709 return &CouldNotCompute;
2712 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2713 /// expression and create a new one.
2714 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2715 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2717 ValueExprMapType::const_iterator I = ValueExprMap.find_as(V);
2718 if (I != ValueExprMap.end()) return I->second;
2719 const SCEV *S = createSCEV(V);
2721 // The process of creating a SCEV for V may have caused other SCEVs
2722 // to have been created, so it's necessary to insert the new entry
2723 // from scratch, rather than trying to remember the insert position
2725 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2729 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2731 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2732 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2734 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2736 Type *Ty = V->getType();
2737 Ty = getEffectiveSCEVType(Ty);
2738 return getMulExpr(V,
2739 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2742 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2743 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2744 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2746 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2748 Type *Ty = V->getType();
2749 Ty = getEffectiveSCEVType(Ty);
2750 const SCEV *AllOnes =
2751 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2752 return getMinusSCEV(AllOnes, V);
2755 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2756 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2757 SCEV::NoWrapFlags Flags) {
2758 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2760 // Fast path: X - X --> 0.
2762 return getConstant(LHS->getType(), 0);
2765 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2768 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2769 /// input value to the specified type. If the type must be extended, it is zero
2772 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2773 Type *SrcTy = V->getType();
2774 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2775 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2776 "Cannot truncate or zero extend with non-integer arguments!");
2777 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2778 return V; // No conversion
2779 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2780 return getTruncateExpr(V, Ty);
2781 return getZeroExtendExpr(V, Ty);
2784 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2785 /// input value to the specified type. If the type must be extended, it is sign
2788 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2790 Type *SrcTy = V->getType();
2791 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2792 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2793 "Cannot truncate or zero extend with non-integer arguments!");
2794 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2795 return V; // No conversion
2796 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2797 return getTruncateExpr(V, Ty);
2798 return getSignExtendExpr(V, Ty);
2801 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2802 /// input value to the specified type. If the type must be extended, it is zero
2803 /// extended. The conversion must not be narrowing.
2805 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2806 Type *SrcTy = V->getType();
2807 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2808 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2809 "Cannot noop or zero extend with non-integer arguments!");
2810 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2811 "getNoopOrZeroExtend cannot truncate!");
2812 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2813 return V; // No conversion
2814 return getZeroExtendExpr(V, Ty);
2817 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2818 /// input value to the specified type. If the type must be extended, it is sign
2819 /// extended. The conversion must not be narrowing.
2821 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2822 Type *SrcTy = V->getType();
2823 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2824 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2825 "Cannot noop or sign extend with non-integer arguments!");
2826 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2827 "getNoopOrSignExtend cannot truncate!");
2828 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2829 return V; // No conversion
2830 return getSignExtendExpr(V, Ty);
2833 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2834 /// the input value to the specified type. If the type must be extended,
2835 /// it is extended with unspecified bits. The conversion must not be
2838 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2839 Type *SrcTy = V->getType();
2840 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2841 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2842 "Cannot noop or any extend with non-integer arguments!");
2843 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2844 "getNoopOrAnyExtend cannot truncate!");
2845 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2846 return V; // No conversion
2847 return getAnyExtendExpr(V, Ty);
2850 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2851 /// input value to the specified type. The conversion must not be widening.
2853 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2854 Type *SrcTy = V->getType();
2855 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2856 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2857 "Cannot truncate or noop with non-integer arguments!");
2858 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2859 "getTruncateOrNoop cannot extend!");
2860 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2861 return V; // No conversion
2862 return getTruncateExpr(V, Ty);
2865 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2866 /// the types using zero-extension, and then perform a umax operation
2868 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2870 const SCEV *PromotedLHS = LHS;
2871 const SCEV *PromotedRHS = RHS;
2873 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2874 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2876 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2878 return getUMaxExpr(PromotedLHS, PromotedRHS);
2881 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2882 /// the types using zero-extension, and then perform a umin operation
2884 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2886 const SCEV *PromotedLHS = LHS;
2887 const SCEV *PromotedRHS = RHS;
2889 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2890 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2892 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2894 return getUMinExpr(PromotedLHS, PromotedRHS);
2897 /// getPointerBase - Transitively follow the chain of pointer-type operands
2898 /// until reaching a SCEV that does not have a single pointer operand. This
2899 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2900 /// but corner cases do exist.
2901 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2902 // A pointer operand may evaluate to a nonpointer expression, such as null.
2903 if (!V->getType()->isPointerTy())
2906 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2907 return getPointerBase(Cast->getOperand());
2909 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2910 const SCEV *PtrOp = 0;
2911 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2913 if ((*I)->getType()->isPointerTy()) {
2914 // Cannot find the base of an expression with multiple pointer operands.
2922 return getPointerBase(PtrOp);
2927 /// PushDefUseChildren - Push users of the given Instruction
2928 /// onto the given Worklist.
2930 PushDefUseChildren(Instruction *I,
2931 SmallVectorImpl<Instruction *> &Worklist) {
2932 // Push the def-use children onto the Worklist stack.
2933 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2935 Worklist.push_back(cast<Instruction>(*UI));
2938 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2939 /// instructions that depend on the given instruction and removes them from
2940 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2943 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2944 SmallVector<Instruction *, 16> Worklist;
2945 PushDefUseChildren(PN, Worklist);
2947 SmallPtrSet<Instruction *, 8> Visited;
2949 while (!Worklist.empty()) {
2950 Instruction *I = Worklist.pop_back_val();
2951 if (!Visited.insert(I)) continue;
2953 ValueExprMapType::iterator It =
2954 ValueExprMap.find_as(static_cast<Value *>(I));
2955 if (It != ValueExprMap.end()) {
2956 const SCEV *Old = It->second;
2958 // Short-circuit the def-use traversal if the symbolic name
2959 // ceases to appear in expressions.
2960 if (Old != SymName && !hasOperand(Old, SymName))
2963 // SCEVUnknown for a PHI either means that it has an unrecognized
2964 // structure, it's a PHI that's in the progress of being computed
2965 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2966 // additional loop trip count information isn't going to change anything.
2967 // In the second case, createNodeForPHI will perform the necessary
2968 // updates on its own when it gets to that point. In the third, we do
2969 // want to forget the SCEVUnknown.
2970 if (!isa<PHINode>(I) ||
2971 !isa<SCEVUnknown>(Old) ||
2972 (I != PN && Old == SymName)) {
2973 forgetMemoizedResults(Old);
2974 ValueExprMap.erase(It);
2978 PushDefUseChildren(I, Worklist);
2982 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2983 /// a loop header, making it a potential recurrence, or it doesn't.
2985 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2986 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2987 if (L->getHeader() == PN->getParent()) {
2988 // The loop may have multiple entrances or multiple exits; we can analyze
2989 // this phi as an addrec if it has a unique entry value and a unique
2991 Value *BEValueV = 0, *StartValueV = 0;
2992 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2993 Value *V = PN->getIncomingValue(i);
2994 if (L->contains(PN->getIncomingBlock(i))) {
2997 } else if (BEValueV != V) {
3001 } else if (!StartValueV) {
3003 } else if (StartValueV != V) {
3008 if (BEValueV && StartValueV) {
3009 // While we are analyzing this PHI node, handle its value symbolically.
3010 const SCEV *SymbolicName = getUnknown(PN);
3011 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3012 "PHI node already processed?");
3013 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3015 // Using this symbolic name for the PHI, analyze the value coming around
3017 const SCEV *BEValue = getSCEV(BEValueV);
3019 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3020 // has a special value for the first iteration of the loop.
3022 // If the value coming around the backedge is an add with the symbolic
3023 // value we just inserted, then we found a simple induction variable!
3024 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3025 // If there is a single occurrence of the symbolic value, replace it
3026 // with a recurrence.
3027 unsigned FoundIndex = Add->getNumOperands();
3028 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3029 if (Add->getOperand(i) == SymbolicName)
3030 if (FoundIndex == e) {
3035 if (FoundIndex != Add->getNumOperands()) {
3036 // Create an add with everything but the specified operand.
3037 SmallVector<const SCEV *, 8> Ops;
3038 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3039 if (i != FoundIndex)
3040 Ops.push_back(Add->getOperand(i));
3041 const SCEV *Accum = getAddExpr(Ops);
3043 // This is not a valid addrec if the step amount is varying each
3044 // loop iteration, but is not itself an addrec in this loop.
3045 if (isLoopInvariant(Accum, L) ||
3046 (isa<SCEVAddRecExpr>(Accum) &&
3047 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3048 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3050 // If the increment doesn't overflow, then neither the addrec nor
3051 // the post-increment will overflow.
3052 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3053 if (OBO->hasNoUnsignedWrap())
3054 Flags = setFlags(Flags, SCEV::FlagNUW);
3055 if (OBO->hasNoSignedWrap())
3056 Flags = setFlags(Flags, SCEV::FlagNSW);
3057 } else if (const GEPOperator *GEP =
3058 dyn_cast<GEPOperator>(BEValueV)) {
3059 // If the increment is an inbounds GEP, then we know the address
3060 // space cannot be wrapped around. We cannot make any guarantee
3061 // about signed or unsigned overflow because pointers are
3062 // unsigned but we may have a negative index from the base
3064 if (GEP->isInBounds())
3065 Flags = setFlags(Flags, SCEV::FlagNW);
3068 const SCEV *StartVal = getSCEV(StartValueV);
3069 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3071 // Since the no-wrap flags are on the increment, they apply to the
3072 // post-incremented value as well.
3073 if (isLoopInvariant(Accum, L))
3074 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3077 // Okay, for the entire analysis of this edge we assumed the PHI
3078 // to be symbolic. We now need to go back and purge all of the
3079 // entries for the scalars that use the symbolic expression.
3080 ForgetSymbolicName(PN, SymbolicName);
3081 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3085 } else if (const SCEVAddRecExpr *AddRec =
3086 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3087 // Otherwise, this could be a loop like this:
3088 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3089 // In this case, j = {1,+,1} and BEValue is j.
3090 // Because the other in-value of i (0) fits the evolution of BEValue
3091 // i really is an addrec evolution.
3092 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3093 const SCEV *StartVal = getSCEV(StartValueV);
3095 // If StartVal = j.start - j.stride, we can use StartVal as the
3096 // initial step of the addrec evolution.
3097 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3098 AddRec->getOperand(1))) {
3099 // FIXME: For constant StartVal, we should be able to infer
3101 const SCEV *PHISCEV =
3102 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3105 // Okay, for the entire analysis of this edge we assumed the PHI
3106 // to be symbolic. We now need to go back and purge all of the
3107 // entries for the scalars that use the symbolic expression.
3108 ForgetSymbolicName(PN, SymbolicName);
3109 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3117 // If the PHI has a single incoming value, follow that value, unless the
3118 // PHI's incoming blocks are in a different loop, in which case doing so
3119 // risks breaking LCSSA form. Instcombine would normally zap these, but
3120 // it doesn't have DominatorTree information, so it may miss cases.
3121 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
3122 if (LI->replacementPreservesLCSSAForm(PN, V))
3125 // If it's not a loop phi, we can't handle it yet.
3126 return getUnknown(PN);
3129 /// createNodeForGEP - Expand GEP instructions into add and multiply
3130 /// operations. This allows them to be analyzed by regular SCEV code.
3132 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3134 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3135 // Add expression, because the Instruction may be guarded by control flow
3136 // and the no-overflow bits may not be valid for the expression in any
3138 bool isInBounds = GEP->isInBounds();
3140 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3141 Value *Base = GEP->getOperand(0);
3142 // Don't attempt to analyze GEPs over unsized objects.
3143 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3144 return getUnknown(GEP);
3145 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3146 gep_type_iterator GTI = gep_type_begin(GEP);
3147 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3151 // Compute the (potentially symbolic) offset in bytes for this index.
3152 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3153 // For a struct, add the member offset.
3154 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3155 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
3157 // Add the field offset to the running total offset.
3158 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3160 // For an array, add the element offset, explicitly scaled.
3161 const SCEV *ElementSize = getSizeOfExpr(*GTI);
3162 const SCEV *IndexS = getSCEV(Index);
3163 // Getelementptr indices are signed.
3164 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3166 // Multiply the index by the element size to compute the element offset.
3167 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3168 isInBounds ? SCEV::FlagNSW :
3171 // Add the element offset to the running total offset.
3172 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3176 // Get the SCEV for the GEP base.
3177 const SCEV *BaseS = getSCEV(Base);
3179 // Add the total offset from all the GEP indices to the base.
3180 return getAddExpr(BaseS, TotalOffset,
3181 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3184 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3185 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3186 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3187 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3189 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3190 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3191 return C->getValue()->getValue().countTrailingZeros();
3193 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3194 return std::min(GetMinTrailingZeros(T->getOperand()),
3195 (uint32_t)getTypeSizeInBits(T->getType()));
3197 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3198 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3199 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3200 getTypeSizeInBits(E->getType()) : OpRes;
3203 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3204 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3205 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3206 getTypeSizeInBits(E->getType()) : OpRes;
3209 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3210 // The result is the min of all operands results.
3211 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3212 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3213 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3217 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3218 // The result is the sum of all operands results.
3219 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3220 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3221 for (unsigned i = 1, e = M->getNumOperands();
3222 SumOpRes != BitWidth && i != e; ++i)
3223 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3228 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3229 // The result is the min of all operands results.
3230 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3231 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3232 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3236 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3237 // The result is the min of all operands results.
3238 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3239 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3240 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3244 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3245 // The result is the min of all operands results.
3246 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3247 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3248 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3252 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3253 // For a SCEVUnknown, ask ValueTracking.
3254 unsigned BitWidth = getTypeSizeInBits(U->getType());
3255 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3256 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3257 return Zeros.countTrailingOnes();
3264 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3267 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3268 // See if we've computed this range already.
3269 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3270 if (I != UnsignedRanges.end())
3273 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3274 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3276 unsigned BitWidth = getTypeSizeInBits(S->getType());
3277 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3279 // If the value has known zeros, the maximum unsigned value will have those
3280 // known zeros as well.
3281 uint32_t TZ = GetMinTrailingZeros(S);
3283 ConservativeResult =
3284 ConstantRange(APInt::getMinValue(BitWidth),
3285 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3287 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3288 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3289 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3290 X = X.add(getUnsignedRange(Add->getOperand(i)));
3291 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3294 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3295 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3296 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3297 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3298 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3301 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3302 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3303 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3304 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3305 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3308 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3309 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3310 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3311 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3312 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3315 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3316 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3317 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3318 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3321 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3322 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3323 return setUnsignedRange(ZExt,
3324 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3327 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3328 ConstantRange X = getUnsignedRange(SExt->getOperand());
3329 return setUnsignedRange(SExt,
3330 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3333 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3334 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3335 return setUnsignedRange(Trunc,
3336 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3339 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3340 // If there's no unsigned wrap, the value will never be less than its
3342 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3343 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3344 if (!C->getValue()->isZero())
3345 ConservativeResult =
3346 ConservativeResult.intersectWith(
3347 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3349 // TODO: non-affine addrec
3350 if (AddRec->isAffine()) {
3351 Type *Ty = AddRec->getType();
3352 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3353 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3354 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3355 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3357 const SCEV *Start = AddRec->getStart();
3358 const SCEV *Step = AddRec->getStepRecurrence(*this);
3360 ConstantRange StartRange = getUnsignedRange(Start);
3361 ConstantRange StepRange = getSignedRange(Step);
3362 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3363 ConstantRange EndRange =
3364 StartRange.add(MaxBECountRange.multiply(StepRange));
3366 // Check for overflow. This must be done with ConstantRange arithmetic
3367 // because we could be called from within the ScalarEvolution overflow
3369 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3370 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3371 ConstantRange ExtMaxBECountRange =
3372 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3373 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3374 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3376 return setUnsignedRange(AddRec, ConservativeResult);
3378 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3379 EndRange.getUnsignedMin());
3380 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3381 EndRange.getUnsignedMax());
3382 if (Min.isMinValue() && Max.isMaxValue())
3383 return setUnsignedRange(AddRec, ConservativeResult);
3384 return setUnsignedRange(AddRec,
3385 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3389 return setUnsignedRange(AddRec, ConservativeResult);
3392 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3393 // For a SCEVUnknown, ask ValueTracking.
3394 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3395 ComputeMaskedBits(U->getValue(), Zeros, Ones, TD);
3396 if (Ones == ~Zeros + 1)
3397 return setUnsignedRange(U, ConservativeResult);
3398 return setUnsignedRange(U,
3399 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3402 return setUnsignedRange(S, ConservativeResult);
3405 /// getSignedRange - Determine the signed range for a particular SCEV.
3408 ScalarEvolution::getSignedRange(const SCEV *S) {
3409 // See if we've computed this range already.
3410 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3411 if (I != SignedRanges.end())
3414 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3415 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3417 unsigned BitWidth = getTypeSizeInBits(S->getType());
3418 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3420 // If the value has known zeros, the maximum signed value will have those
3421 // known zeros as well.
3422 uint32_t TZ = GetMinTrailingZeros(S);
3424 ConservativeResult =
3425 ConstantRange(APInt::getSignedMinValue(BitWidth),
3426 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3428 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3429 ConstantRange X = getSignedRange(Add->getOperand(0));
3430 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3431 X = X.add(getSignedRange(Add->getOperand(i)));
3432 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3435 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3436 ConstantRange X = getSignedRange(Mul->getOperand(0));
3437 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3438 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3439 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3442 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3443 ConstantRange X = getSignedRange(SMax->getOperand(0));
3444 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3445 X = X.smax(getSignedRange(SMax->getOperand(i)));
3446 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3449 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3450 ConstantRange X = getSignedRange(UMax->getOperand(0));
3451 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3452 X = X.umax(getSignedRange(UMax->getOperand(i)));
3453 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3456 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3457 ConstantRange X = getSignedRange(UDiv->getLHS());
3458 ConstantRange Y = getSignedRange(UDiv->getRHS());
3459 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3462 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3463 ConstantRange X = getSignedRange(ZExt->getOperand());
3464 return setSignedRange(ZExt,
3465 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3468 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3469 ConstantRange X = getSignedRange(SExt->getOperand());
3470 return setSignedRange(SExt,
3471 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3474 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3475 ConstantRange X = getSignedRange(Trunc->getOperand());
3476 return setSignedRange(Trunc,
3477 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3480 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3481 // If there's no signed wrap, and all the operands have the same sign or
3482 // zero, the value won't ever change sign.
3483 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3484 bool AllNonNeg = true;
3485 bool AllNonPos = true;
3486 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3487 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3488 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3491 ConservativeResult = ConservativeResult.intersectWith(
3492 ConstantRange(APInt(BitWidth, 0),
3493 APInt::getSignedMinValue(BitWidth)));
3495 ConservativeResult = ConservativeResult.intersectWith(
3496 ConstantRange(APInt::getSignedMinValue(BitWidth),
3497 APInt(BitWidth, 1)));
3500 // TODO: non-affine addrec
3501 if (AddRec->isAffine()) {
3502 Type *Ty = AddRec->getType();
3503 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3504 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3505 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3506 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3508 const SCEV *Start = AddRec->getStart();
3509 const SCEV *Step = AddRec->getStepRecurrence(*this);
3511 ConstantRange StartRange = getSignedRange(Start);
3512 ConstantRange StepRange = getSignedRange(Step);
3513 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3514 ConstantRange EndRange =
3515 StartRange.add(MaxBECountRange.multiply(StepRange));
3517 // Check for overflow. This must be done with ConstantRange arithmetic
3518 // because we could be called from within the ScalarEvolution overflow
3520 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3521 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3522 ConstantRange ExtMaxBECountRange =
3523 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3524 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3525 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3527 return setSignedRange(AddRec, ConservativeResult);
3529 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3530 EndRange.getSignedMin());
3531 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3532 EndRange.getSignedMax());
3533 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3534 return setSignedRange(AddRec, ConservativeResult);
3535 return setSignedRange(AddRec,
3536 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3540 return setSignedRange(AddRec, ConservativeResult);
3543 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3544 // For a SCEVUnknown, ask ValueTracking.
3545 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3546 return setSignedRange(U, ConservativeResult);
3547 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3549 return setSignedRange(U, ConservativeResult);
3550 return setSignedRange(U, ConservativeResult.intersectWith(
3551 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3552 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3555 return setSignedRange(S, ConservativeResult);
3558 /// createSCEV - We know that there is no SCEV for the specified value.
3559 /// Analyze the expression.
3561 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3562 if (!isSCEVable(V->getType()))
3563 return getUnknown(V);
3565 unsigned Opcode = Instruction::UserOp1;
3566 if (Instruction *I = dyn_cast<Instruction>(V)) {
3567 Opcode = I->getOpcode();
3569 // Don't attempt to analyze instructions in blocks that aren't
3570 // reachable. Such instructions don't matter, and they aren't required
3571 // to obey basic rules for definitions dominating uses which this
3572 // analysis depends on.
3573 if (!DT->isReachableFromEntry(I->getParent()))
3574 return getUnknown(V);
3575 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3576 Opcode = CE->getOpcode();
3577 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3578 return getConstant(CI);
3579 else if (isa<ConstantPointerNull>(V))
3580 return getConstant(V->getType(), 0);
3581 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3582 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3584 return getUnknown(V);
3586 Operator *U = cast<Operator>(V);
3588 case Instruction::Add: {
3589 // The simple thing to do would be to just call getSCEV on both operands
3590 // and call getAddExpr with the result. However if we're looking at a
3591 // bunch of things all added together, this can be quite inefficient,
3592 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3593 // Instead, gather up all the operands and make a single getAddExpr call.
3594 // LLVM IR canonical form means we need only traverse the left operands.
3596 // Don't apply this instruction's NSW or NUW flags to the new
3597 // expression. The instruction may be guarded by control flow that the
3598 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3599 // mapped to the same SCEV expression, and it would be incorrect to transfer
3600 // NSW/NUW semantics to those operations.
3601 SmallVector<const SCEV *, 4> AddOps;
3602 AddOps.push_back(getSCEV(U->getOperand(1)));
3603 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3604 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3605 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3607 U = cast<Operator>(Op);
3608 const SCEV *Op1 = getSCEV(U->getOperand(1));
3609 if (Opcode == Instruction::Sub)
3610 AddOps.push_back(getNegativeSCEV(Op1));
3612 AddOps.push_back(Op1);
3614 AddOps.push_back(getSCEV(U->getOperand(0)));
3615 return getAddExpr(AddOps);
3617 case Instruction::Mul: {
3618 // Don't transfer NSW/NUW for the same reason as AddExpr.
3619 SmallVector<const SCEV *, 4> MulOps;
3620 MulOps.push_back(getSCEV(U->getOperand(1)));
3621 for (Value *Op = U->getOperand(0);
3622 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3623 Op = U->getOperand(0)) {
3624 U = cast<Operator>(Op);
3625 MulOps.push_back(getSCEV(U->getOperand(1)));
3627 MulOps.push_back(getSCEV(U->getOperand(0)));
3628 return getMulExpr(MulOps);
3630 case Instruction::UDiv:
3631 return getUDivExpr(getSCEV(U->getOperand(0)),
3632 getSCEV(U->getOperand(1)));
3633 case Instruction::Sub:
3634 return getMinusSCEV(getSCEV(U->getOperand(0)),
3635 getSCEV(U->getOperand(1)));
3636 case Instruction::And:
3637 // For an expression like x&255 that merely masks off the high bits,
3638 // use zext(trunc(x)) as the SCEV expression.
3639 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3640 if (CI->isNullValue())
3641 return getSCEV(U->getOperand(1));
3642 if (CI->isAllOnesValue())
3643 return getSCEV(U->getOperand(0));
3644 const APInt &A = CI->getValue();
3646 // Instcombine's ShrinkDemandedConstant may strip bits out of
3647 // constants, obscuring what would otherwise be a low-bits mask.
3648 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3649 // knew about to reconstruct a low-bits mask value.
3650 unsigned LZ = A.countLeadingZeros();
3651 unsigned BitWidth = A.getBitWidth();
3652 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3653 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD);
3655 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3657 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3659 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3660 IntegerType::get(getContext(), BitWidth - LZ)),
3665 case Instruction::Or:
3666 // If the RHS of the Or is a constant, we may have something like:
3667 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3668 // optimizations will transparently handle this case.
3670 // In order for this transformation to be safe, the LHS must be of the
3671 // form X*(2^n) and the Or constant must be less than 2^n.
3672 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3673 const SCEV *LHS = getSCEV(U->getOperand(0));
3674 const APInt &CIVal = CI->getValue();
3675 if (GetMinTrailingZeros(LHS) >=
3676 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3677 // Build a plain add SCEV.
3678 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3679 // If the LHS of the add was an addrec and it has no-wrap flags,
3680 // transfer the no-wrap flags, since an or won't introduce a wrap.
3681 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3682 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3683 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3684 OldAR->getNoWrapFlags());
3690 case Instruction::Xor:
3691 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3692 // If the RHS of the xor is a signbit, then this is just an add.
3693 // Instcombine turns add of signbit into xor as a strength reduction step.
3694 if (CI->getValue().isSignBit())
3695 return getAddExpr(getSCEV(U->getOperand(0)),
3696 getSCEV(U->getOperand(1)));
3698 // If the RHS of xor is -1, then this is a not operation.
3699 if (CI->isAllOnesValue())
3700 return getNotSCEV(getSCEV(U->getOperand(0)));
3702 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3703 // This is a variant of the check for xor with -1, and it handles
3704 // the case where instcombine has trimmed non-demanded bits out
3705 // of an xor with -1.
3706 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3707 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3708 if (BO->getOpcode() == Instruction::And &&
3709 LCI->getValue() == CI->getValue())
3710 if (const SCEVZeroExtendExpr *Z =
3711 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3712 Type *UTy = U->getType();
3713 const SCEV *Z0 = Z->getOperand();
3714 Type *Z0Ty = Z0->getType();
3715 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3717 // If C is a low-bits mask, the zero extend is serving to
3718 // mask off the high bits. Complement the operand and
3719 // re-apply the zext.
3720 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3721 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3723 // If C is a single bit, it may be in the sign-bit position
3724 // before the zero-extend. In this case, represent the xor
3725 // using an add, which is equivalent, and re-apply the zext.
3726 APInt Trunc = CI->getValue().trunc(Z0TySize);
3727 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3729 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3735 case Instruction::Shl:
3736 // Turn shift left of a constant amount into a multiply.
3737 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3738 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3740 // If the shift count is not less than the bitwidth, the result of
3741 // the shift is undefined. Don't try to analyze it, because the
3742 // resolution chosen here may differ from the resolution chosen in
3743 // other parts of the compiler.
3744 if (SA->getValue().uge(BitWidth))
3747 Constant *X = ConstantInt::get(getContext(),
3748 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3749 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3753 case Instruction::LShr:
3754 // Turn logical shift right of a constant into a unsigned divide.
3755 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3756 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3758 // If the shift count is not less than the bitwidth, the result of
3759 // the shift is undefined. Don't try to analyze it, because the
3760 // resolution chosen here may differ from the resolution chosen in
3761 // other parts of the compiler.
3762 if (SA->getValue().uge(BitWidth))
3765 Constant *X = ConstantInt::get(getContext(),
3766 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3767 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3771 case Instruction::AShr:
3772 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3773 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3774 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3775 if (L->getOpcode() == Instruction::Shl &&
3776 L->getOperand(1) == U->getOperand(1)) {
3777 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3779 // If the shift count is not less than the bitwidth, the result of
3780 // the shift is undefined. Don't try to analyze it, because the
3781 // resolution chosen here may differ from the resolution chosen in
3782 // other parts of the compiler.
3783 if (CI->getValue().uge(BitWidth))
3786 uint64_t Amt = BitWidth - CI->getZExtValue();
3787 if (Amt == BitWidth)
3788 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3790 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3791 IntegerType::get(getContext(),
3797 case Instruction::Trunc:
3798 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3800 case Instruction::ZExt:
3801 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3803 case Instruction::SExt:
3804 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3806 case Instruction::BitCast:
3807 // BitCasts are no-op casts so we just eliminate the cast.
3808 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3809 return getSCEV(U->getOperand(0));
3812 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3813 // lead to pointer expressions which cannot safely be expanded to GEPs,
3814 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3815 // simplifying integer expressions.
3817 case Instruction::GetElementPtr:
3818 return createNodeForGEP(cast<GEPOperator>(U));
3820 case Instruction::PHI:
3821 return createNodeForPHI(cast<PHINode>(U));
3823 case Instruction::Select:
3824 // This could be a smax or umax that was lowered earlier.
3825 // Try to recover it.
3826 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3827 Value *LHS = ICI->getOperand(0);
3828 Value *RHS = ICI->getOperand(1);
3829 switch (ICI->getPredicate()) {
3830 case ICmpInst::ICMP_SLT:
3831 case ICmpInst::ICMP_SLE:
3832 std::swap(LHS, RHS);
3834 case ICmpInst::ICMP_SGT:
3835 case ICmpInst::ICMP_SGE:
3836 // a >s b ? a+x : b+x -> smax(a, b)+x
3837 // a >s b ? b+x : a+x -> smin(a, b)+x
3838 if (LHS->getType() == U->getType()) {
3839 const SCEV *LS = getSCEV(LHS);
3840 const SCEV *RS = getSCEV(RHS);
3841 const SCEV *LA = getSCEV(U->getOperand(1));
3842 const SCEV *RA = getSCEV(U->getOperand(2));
3843 const SCEV *LDiff = getMinusSCEV(LA, LS);
3844 const SCEV *RDiff = getMinusSCEV(RA, RS);
3846 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3847 LDiff = getMinusSCEV(LA, RS);
3848 RDiff = getMinusSCEV(RA, LS);
3850 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3853 case ICmpInst::ICMP_ULT:
3854 case ICmpInst::ICMP_ULE:
3855 std::swap(LHS, RHS);
3857 case ICmpInst::ICMP_UGT:
3858 case ICmpInst::ICMP_UGE:
3859 // a >u b ? a+x : b+x -> umax(a, b)+x
3860 // a >u b ? b+x : a+x -> umin(a, b)+x
3861 if (LHS->getType() == U->getType()) {
3862 const SCEV *LS = getSCEV(LHS);
3863 const SCEV *RS = getSCEV(RHS);
3864 const SCEV *LA = getSCEV(U->getOperand(1));
3865 const SCEV *RA = getSCEV(U->getOperand(2));
3866 const SCEV *LDiff = getMinusSCEV(LA, LS);
3867 const SCEV *RDiff = getMinusSCEV(RA, RS);
3869 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3870 LDiff = getMinusSCEV(LA, RS);
3871 RDiff = getMinusSCEV(RA, LS);
3873 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3876 case ICmpInst::ICMP_NE:
3877 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3878 if (LHS->getType() == U->getType() &&
3879 isa<ConstantInt>(RHS) &&
3880 cast<ConstantInt>(RHS)->isZero()) {
3881 const SCEV *One = getConstant(LHS->getType(), 1);
3882 const SCEV *LS = getSCEV(LHS);
3883 const SCEV *LA = getSCEV(U->getOperand(1));
3884 const SCEV *RA = getSCEV(U->getOperand(2));
3885 const SCEV *LDiff = getMinusSCEV(LA, LS);
3886 const SCEV *RDiff = getMinusSCEV(RA, One);
3888 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3891 case ICmpInst::ICMP_EQ:
3892 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3893 if (LHS->getType() == U->getType() &&
3894 isa<ConstantInt>(RHS) &&
3895 cast<ConstantInt>(RHS)->isZero()) {
3896 const SCEV *One = getConstant(LHS->getType(), 1);
3897 const SCEV *LS = getSCEV(LHS);
3898 const SCEV *LA = getSCEV(U->getOperand(1));
3899 const SCEV *RA = getSCEV(U->getOperand(2));
3900 const SCEV *LDiff = getMinusSCEV(LA, One);
3901 const SCEV *RDiff = getMinusSCEV(RA, LS);
3903 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3911 default: // We cannot analyze this expression.
3915 return getUnknown(V);
3920 //===----------------------------------------------------------------------===//
3921 // Iteration Count Computation Code
3924 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3925 /// normal unsigned value. Returns 0 if the trip count is unknown or not
3926 /// constant. Will also return 0 if the maximum trip count is very large (>=
3929 /// This "trip count" assumes that control exits via ExitingBlock. More
3930 /// precisely, it is the number of times that control may reach ExitingBlock
3931 /// before taking the branch. For loops with multiple exits, it may not be the
3932 /// number times that the loop header executes because the loop may exit
3933 /// prematurely via another branch.
3934 unsigned ScalarEvolution::
3935 getSmallConstantTripCount(Loop *L, BasicBlock *ExitingBlock) {
3936 const SCEVConstant *ExitCount =
3937 dyn_cast<SCEVConstant>(getExitCount(L, ExitingBlock));
3941 ConstantInt *ExitConst = ExitCount->getValue();
3943 // Guard against huge trip counts.
3944 if (ExitConst->getValue().getActiveBits() > 32)
3947 // In case of integer overflow, this returns 0, which is correct.
3948 return ((unsigned)ExitConst->getZExtValue()) + 1;
3951 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3952 /// trip count of this loop as a normal unsigned value, if possible. This
3953 /// means that the actual trip count is always a multiple of the returned
3954 /// value (don't forget the trip count could very well be zero as well!).
3956 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3957 /// multiple of a constant (which is also the case if the trip count is simply
3958 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3959 /// if the trip count is very large (>= 2^32).
3961 /// As explained in the comments for getSmallConstantTripCount, this assumes
3962 /// that control exits the loop via ExitingBlock.
3963 unsigned ScalarEvolution::
3964 getSmallConstantTripMultiple(Loop *L, BasicBlock *ExitingBlock) {
3965 const SCEV *ExitCount = getExitCount(L, ExitingBlock);
3966 if (ExitCount == getCouldNotCompute())
3969 // Get the trip count from the BE count by adding 1.
3970 const SCEV *TCMul = getAddExpr(ExitCount,
3971 getConstant(ExitCount->getType(), 1));
3972 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
3973 // to factor simple cases.
3974 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
3975 TCMul = Mul->getOperand(0);
3977 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
3981 ConstantInt *Result = MulC->getValue();
3983 // Guard against huge trip counts.
3984 if (!Result || Result->getValue().getActiveBits() > 32)
3987 return (unsigned)Result->getZExtValue();
3990 // getExitCount - Get the expression for the number of loop iterations for which
3991 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return
3992 // SCEVCouldNotCompute.
3993 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
3994 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
3997 /// getBackedgeTakenCount - If the specified loop has a predictable
3998 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3999 /// object. The backedge-taken count is the number of times the loop header
4000 /// will be branched to from within the loop. This is one less than the
4001 /// trip count of the loop, since it doesn't count the first iteration,
4002 /// when the header is branched to from outside the loop.
4004 /// Note that it is not valid to call this method on a loop without a
4005 /// loop-invariant backedge-taken count (see
4006 /// hasLoopInvariantBackedgeTakenCount).
4008 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4009 return getBackedgeTakenInfo(L).getExact(this);
4012 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4013 /// return the least SCEV value that is known never to be less than the
4014 /// actual backedge taken count.
4015 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4016 return getBackedgeTakenInfo(L).getMax(this);
4019 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4020 /// onto the given Worklist.
4022 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4023 BasicBlock *Header = L->getHeader();
4025 // Push all Loop-header PHIs onto the Worklist stack.
4026 for (BasicBlock::iterator I = Header->begin();
4027 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4028 Worklist.push_back(PN);
4031 const ScalarEvolution::BackedgeTakenInfo &
4032 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4033 // Initially insert an invalid entry for this loop. If the insertion
4034 // succeeds, proceed to actually compute a backedge-taken count and
4035 // update the value. The temporary CouldNotCompute value tells SCEV
4036 // code elsewhere that it shouldn't attempt to request a new
4037 // backedge-taken count, which could result in infinite recursion.
4038 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4039 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4041 return Pair.first->second;
4043 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4044 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4045 // must be cleared in this scope.
4046 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4048 if (Result.getExact(this) != getCouldNotCompute()) {
4049 assert(isLoopInvariant(Result.getExact(this), L) &&
4050 isLoopInvariant(Result.getMax(this), L) &&
4051 "Computed backedge-taken count isn't loop invariant for loop!");
4052 ++NumTripCountsComputed;
4054 else if (Result.getMax(this) == getCouldNotCompute() &&
4055 isa<PHINode>(L->getHeader()->begin())) {
4056 // Only count loops that have phi nodes as not being computable.
4057 ++NumTripCountsNotComputed;
4060 // Now that we know more about the trip count for this loop, forget any
4061 // existing SCEV values for PHI nodes in this loop since they are only
4062 // conservative estimates made without the benefit of trip count
4063 // information. This is similar to the code in forgetLoop, except that
4064 // it handles SCEVUnknown PHI nodes specially.
4065 if (Result.hasAnyInfo()) {
4066 SmallVector<Instruction *, 16> Worklist;
4067 PushLoopPHIs(L, Worklist);
4069 SmallPtrSet<Instruction *, 8> Visited;
4070 while (!Worklist.empty()) {
4071 Instruction *I = Worklist.pop_back_val();
4072 if (!Visited.insert(I)) continue;
4074 ValueExprMapType::iterator It =
4075 ValueExprMap.find_as(static_cast<Value *>(I));
4076 if (It != ValueExprMap.end()) {
4077 const SCEV *Old = It->second;
4079 // SCEVUnknown for a PHI either means that it has an unrecognized
4080 // structure, or it's a PHI that's in the progress of being computed
4081 // by createNodeForPHI. In the former case, additional loop trip
4082 // count information isn't going to change anything. In the later
4083 // case, createNodeForPHI will perform the necessary updates on its
4084 // own when it gets to that point.
4085 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4086 forgetMemoizedResults(Old);
4087 ValueExprMap.erase(It);
4089 if (PHINode *PN = dyn_cast<PHINode>(I))
4090 ConstantEvolutionLoopExitValue.erase(PN);
4093 PushDefUseChildren(I, Worklist);
4097 // Re-lookup the insert position, since the call to
4098 // ComputeBackedgeTakenCount above could result in a
4099 // recusive call to getBackedgeTakenInfo (on a different
4100 // loop), which would invalidate the iterator computed
4102 return BackedgeTakenCounts.find(L)->second = Result;
4105 /// forgetLoop - This method should be called by the client when it has
4106 /// changed a loop in a way that may effect ScalarEvolution's ability to
4107 /// compute a trip count, or if the loop is deleted.
4108 void ScalarEvolution::forgetLoop(const Loop *L) {
4109 // Drop any stored trip count value.
4110 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4111 BackedgeTakenCounts.find(L);
4112 if (BTCPos != BackedgeTakenCounts.end()) {
4113 BTCPos->second.clear();
4114 BackedgeTakenCounts.erase(BTCPos);
4117 // Drop information about expressions based on loop-header PHIs.
4118 SmallVector<Instruction *, 16> Worklist;
4119 PushLoopPHIs(L, Worklist);
4121 SmallPtrSet<Instruction *, 8> Visited;
4122 while (!Worklist.empty()) {
4123 Instruction *I = Worklist.pop_back_val();
4124 if (!Visited.insert(I)) continue;
4126 ValueExprMapType::iterator It =
4127 ValueExprMap.find_as(static_cast<Value *>(I));
4128 if (It != ValueExprMap.end()) {
4129 forgetMemoizedResults(It->second);
4130 ValueExprMap.erase(It);
4131 if (PHINode *PN = dyn_cast<PHINode>(I))
4132 ConstantEvolutionLoopExitValue.erase(PN);
4135 PushDefUseChildren(I, Worklist);
4138 // Forget all contained loops too, to avoid dangling entries in the
4139 // ValuesAtScopes map.
4140 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4144 /// forgetValue - This method should be called by the client when it has
4145 /// changed a value in a way that may effect its value, or which may
4146 /// disconnect it from a def-use chain linking it to a loop.
4147 void ScalarEvolution::forgetValue(Value *V) {
4148 Instruction *I = dyn_cast<Instruction>(V);
4151 // Drop information about expressions based on loop-header PHIs.
4152 SmallVector<Instruction *, 16> Worklist;
4153 Worklist.push_back(I);
4155 SmallPtrSet<Instruction *, 8> Visited;
4156 while (!Worklist.empty()) {
4157 I = Worklist.pop_back_val();
4158 if (!Visited.insert(I)) continue;
4160 ValueExprMapType::iterator It =
4161 ValueExprMap.find_as(static_cast<Value *>(I));
4162 if (It != ValueExprMap.end()) {
4163 forgetMemoizedResults(It->second);
4164 ValueExprMap.erase(It);
4165 if (PHINode *PN = dyn_cast<PHINode>(I))
4166 ConstantEvolutionLoopExitValue.erase(PN);
4169 PushDefUseChildren(I, Worklist);
4173 /// getExact - Get the exact loop backedge taken count considering all loop
4174 /// exits. A computable result can only be return for loops with a single exit.
4175 /// Returning the minimum taken count among all exits is incorrect because one
4176 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4177 /// the limit of each loop test is never skipped. This is a valid assumption as
4178 /// long as the loop exits via that test. For precise results, it is the
4179 /// caller's responsibility to specify the relevant loop exit using
4180 /// getExact(ExitingBlock, SE).
4182 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4183 // If any exits were not computable, the loop is not computable.
4184 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4186 // We need exactly one computable exit.
4187 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4188 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4190 const SCEV *BECount = 0;
4191 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4192 ENT != 0; ENT = ENT->getNextExit()) {
4194 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4197 BECount = ENT->ExactNotTaken;
4198 else if (BECount != ENT->ExactNotTaken)
4199 return SE->getCouldNotCompute();
4201 assert(BECount && "Invalid not taken count for loop exit");
4205 /// getExact - Get the exact not taken count for this loop exit.
4207 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4208 ScalarEvolution *SE) const {
4209 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4210 ENT != 0; ENT = ENT->getNextExit()) {
4212 if (ENT->ExitingBlock == ExitingBlock)
4213 return ENT->ExactNotTaken;
4215 return SE->getCouldNotCompute();
4218 /// getMax - Get the max backedge taken count for the loop.
4220 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4221 return Max ? Max : SE->getCouldNotCompute();
4224 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4225 /// computable exit into a persistent ExitNotTakenInfo array.
4226 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4227 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4228 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4231 ExitNotTaken.setIncomplete();
4233 unsigned NumExits = ExitCounts.size();
4234 if (NumExits == 0) return;
4236 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4237 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4238 if (NumExits == 1) return;
4240 // Handle the rare case of multiple computable exits.
4241 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4243 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4244 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4245 PrevENT->setNextExit(ENT);
4246 ENT->ExitingBlock = ExitCounts[i].first;
4247 ENT->ExactNotTaken = ExitCounts[i].second;
4251 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4252 void ScalarEvolution::BackedgeTakenInfo::clear() {
4253 ExitNotTaken.ExitingBlock = 0;
4254 ExitNotTaken.ExactNotTaken = 0;
4255 delete[] ExitNotTaken.getNextExit();
4258 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4259 /// of the specified loop will execute.
4260 ScalarEvolution::BackedgeTakenInfo
4261 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4262 SmallVector<BasicBlock *, 8> ExitingBlocks;
4263 L->getExitingBlocks(ExitingBlocks);
4265 // Examine all exits and pick the most conservative values.
4266 const SCEV *MaxBECount = getCouldNotCompute();
4267 bool CouldComputeBECount = true;
4268 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4269 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4270 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4271 if (EL.Exact == getCouldNotCompute())
4272 // We couldn't compute an exact value for this exit, so
4273 // we won't be able to compute an exact value for the loop.
4274 CouldComputeBECount = false;
4276 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4278 if (MaxBECount == getCouldNotCompute())
4279 MaxBECount = EL.Max;
4280 else if (EL.Max != getCouldNotCompute()) {
4281 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4282 // skip some loop tests. Taking the max over the exits is sufficiently
4283 // conservative. TODO: We could do better taking into consideration
4284 // that (1) the loop has unit stride (2) the last loop test is
4285 // less-than/greater-than (3) any loop test is less-than/greater-than AND
4286 // falls-through some constant times less then the other tests.
4287 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4291 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4294 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4295 /// loop will execute if it exits via the specified block.
4296 ScalarEvolution::ExitLimit
4297 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4299 // Okay, we've chosen an exiting block. See what condition causes us to
4300 // exit at this block.
4302 // FIXME: we should be able to handle switch instructions (with a single exit)
4303 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4304 if (ExitBr == 0) return getCouldNotCompute();
4305 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4307 // At this point, we know we have a conditional branch that determines whether
4308 // the loop is exited. However, we don't know if the branch is executed each
4309 // time through the loop. If not, then the execution count of the branch will
4310 // not be equal to the trip count of the loop.
4312 // Currently we check for this by checking to see if the Exit branch goes to
4313 // the loop header. If so, we know it will always execute the same number of
4314 // times as the loop. We also handle the case where the exit block *is* the
4315 // loop header. This is common for un-rotated loops.
4317 // If both of those tests fail, walk up the unique predecessor chain to the
4318 // header, stopping if there is an edge that doesn't exit the loop. If the
4319 // header is reached, the execution count of the branch will be equal to the
4320 // trip count of the loop.
4322 // More extensive analysis could be done to handle more cases here.
4324 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4325 ExitBr->getSuccessor(1) != L->getHeader() &&
4326 ExitBr->getParent() != L->getHeader()) {
4327 // The simple checks failed, try climbing the unique predecessor chain
4328 // up to the header.
4330 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4331 BasicBlock *Pred = BB->getUniquePredecessor();
4333 return getCouldNotCompute();
4334 TerminatorInst *PredTerm = Pred->getTerminator();
4335 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4336 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4339 // If the predecessor has a successor that isn't BB and isn't
4340 // outside the loop, assume the worst.
4341 if (L->contains(PredSucc))
4342 return getCouldNotCompute();
4344 if (Pred == L->getHeader()) {
4351 return getCouldNotCompute();
4354 // Proceed to the next level to examine the exit condition expression.
4355 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4356 ExitBr->getSuccessor(0),
4357 ExitBr->getSuccessor(1));
4360 /// ComputeExitLimitFromCond - Compute the number of times the
4361 /// backedge of the specified loop will execute if its exit condition
4362 /// were a conditional branch of ExitCond, TBB, and FBB.
4363 ScalarEvolution::ExitLimit
4364 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4368 // Check if the controlling expression for this loop is an And or Or.
4369 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4370 if (BO->getOpcode() == Instruction::And) {
4371 // Recurse on the operands of the and.
4372 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4373 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4374 const SCEV *BECount = getCouldNotCompute();
4375 const SCEV *MaxBECount = getCouldNotCompute();
4376 if (L->contains(TBB)) {
4377 // Both conditions must be true for the loop to continue executing.
4378 // Choose the less conservative count.
4379 if (EL0.Exact == getCouldNotCompute() ||
4380 EL1.Exact == getCouldNotCompute())
4381 BECount = getCouldNotCompute();
4383 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4384 if (EL0.Max == getCouldNotCompute())
4385 MaxBECount = EL1.Max;
4386 else if (EL1.Max == getCouldNotCompute())
4387 MaxBECount = EL0.Max;
4389 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4391 // Both conditions must be true at the same time for the loop to exit.
4392 // For now, be conservative.
4393 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4394 if (EL0.Max == EL1.Max)
4395 MaxBECount = EL0.Max;
4396 if (EL0.Exact == EL1.Exact)
4397 BECount = EL0.Exact;
4400 return ExitLimit(BECount, MaxBECount);
4402 if (BO->getOpcode() == Instruction::Or) {
4403 // Recurse on the operands of the or.
4404 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4405 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4406 const SCEV *BECount = getCouldNotCompute();
4407 const SCEV *MaxBECount = getCouldNotCompute();
4408 if (L->contains(FBB)) {
4409 // Both conditions must be false for the loop to continue executing.
4410 // Choose the less conservative count.
4411 if (EL0.Exact == getCouldNotCompute() ||
4412 EL1.Exact == getCouldNotCompute())
4413 BECount = getCouldNotCompute();
4415 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4416 if (EL0.Max == getCouldNotCompute())
4417 MaxBECount = EL1.Max;
4418 else if (EL1.Max == getCouldNotCompute())
4419 MaxBECount = EL0.Max;
4421 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4423 // Both conditions must be false at the same time for the loop to exit.
4424 // For now, be conservative.
4425 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4426 if (EL0.Max == EL1.Max)
4427 MaxBECount = EL0.Max;
4428 if (EL0.Exact == EL1.Exact)
4429 BECount = EL0.Exact;
4432 return ExitLimit(BECount, MaxBECount);
4436 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4437 // Proceed to the next level to examine the icmp.
4438 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4439 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB);
4441 // Check for a constant condition. These are normally stripped out by
4442 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4443 // preserve the CFG and is temporarily leaving constant conditions
4445 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4446 if (L->contains(FBB) == !CI->getZExtValue())
4447 // The backedge is always taken.
4448 return getCouldNotCompute();
4450 // The backedge is never taken.
4451 return getConstant(CI->getType(), 0);
4454 // If it's not an integer or pointer comparison then compute it the hard way.
4455 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4458 /// ComputeExitLimitFromICmp - Compute the number of times the
4459 /// backedge of the specified loop will execute if its exit condition
4460 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4461 ScalarEvolution::ExitLimit
4462 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4467 // If the condition was exit on true, convert the condition to exit on false
4468 ICmpInst::Predicate Cond;
4469 if (!L->contains(FBB))
4470 Cond = ExitCond->getPredicate();
4472 Cond = ExitCond->getInversePredicate();
4474 // Handle common loops like: for (X = "string"; *X; ++X)
4475 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4476 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4478 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4479 if (ItCnt.hasAnyInfo())
4483 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4484 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4486 // Try to evaluate any dependencies out of the loop.
4487 LHS = getSCEVAtScope(LHS, L);
4488 RHS = getSCEVAtScope(RHS, L);
4490 // At this point, we would like to compute how many iterations of the
4491 // loop the predicate will return true for these inputs.
4492 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4493 // If there is a loop-invariant, force it into the RHS.
4494 std::swap(LHS, RHS);
4495 Cond = ICmpInst::getSwappedPredicate(Cond);
4498 // Simplify the operands before analyzing them.
4499 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4501 // If we have a comparison of a chrec against a constant, try to use value
4502 // ranges to answer this query.
4503 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4504 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4505 if (AddRec->getLoop() == L) {
4506 // Form the constant range.
4507 ConstantRange CompRange(
4508 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4510 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4511 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4515 case ICmpInst::ICMP_NE: { // while (X != Y)
4516 // Convert to: while (X-Y != 0)
4517 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4518 if (EL.hasAnyInfo()) return EL;
4521 case ICmpInst::ICMP_EQ: { // while (X == Y)
4522 // Convert to: while (X-Y == 0)
4523 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4524 if (EL.hasAnyInfo()) return EL;
4527 case ICmpInst::ICMP_SLT: {
4528 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true);
4529 if (EL.hasAnyInfo()) return EL;
4532 case ICmpInst::ICMP_SGT: {
4533 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4534 getNotSCEV(RHS), L, true);
4535 if (EL.hasAnyInfo()) return EL;
4538 case ICmpInst::ICMP_ULT: {
4539 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false);
4540 if (EL.hasAnyInfo()) return EL;
4543 case ICmpInst::ICMP_UGT: {
4544 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4545 getNotSCEV(RHS), L, false);
4546 if (EL.hasAnyInfo()) return EL;
4551 dbgs() << "ComputeBackedgeTakenCount ";
4552 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4553 dbgs() << "[unsigned] ";
4554 dbgs() << *LHS << " "
4555 << Instruction::getOpcodeName(Instruction::ICmp)
4556 << " " << *RHS << "\n";
4560 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4563 static ConstantInt *
4564 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4565 ScalarEvolution &SE) {
4566 const SCEV *InVal = SE.getConstant(C);
4567 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4568 assert(isa<SCEVConstant>(Val) &&
4569 "Evaluation of SCEV at constant didn't fold correctly?");
4570 return cast<SCEVConstant>(Val)->getValue();
4573 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4574 /// 'icmp op load X, cst', try to see if we can compute the backedge
4575 /// execution count.
4576 ScalarEvolution::ExitLimit
4577 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4581 ICmpInst::Predicate predicate) {
4583 if (LI->isVolatile()) return getCouldNotCompute();
4585 // Check to see if the loaded pointer is a getelementptr of a global.
4586 // TODO: Use SCEV instead of manually grubbing with GEPs.
4587 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4588 if (!GEP) return getCouldNotCompute();
4590 // Make sure that it is really a constant global we are gepping, with an
4591 // initializer, and make sure the first IDX is really 0.
4592 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4593 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4594 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4595 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4596 return getCouldNotCompute();
4598 // Okay, we allow one non-constant index into the GEP instruction.
4600 std::vector<Constant*> Indexes;
4601 unsigned VarIdxNum = 0;
4602 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4603 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4604 Indexes.push_back(CI);
4605 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4606 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4607 VarIdx = GEP->getOperand(i);
4609 Indexes.push_back(0);
4612 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4614 return getCouldNotCompute();
4616 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4617 // Check to see if X is a loop variant variable value now.
4618 const SCEV *Idx = getSCEV(VarIdx);
4619 Idx = getSCEVAtScope(Idx, L);
4621 // We can only recognize very limited forms of loop index expressions, in
4622 // particular, only affine AddRec's like {C1,+,C2}.
4623 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4624 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4625 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4626 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4627 return getCouldNotCompute();
4629 unsigned MaxSteps = MaxBruteForceIterations;
4630 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4631 ConstantInt *ItCst = ConstantInt::get(
4632 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4633 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4635 // Form the GEP offset.
4636 Indexes[VarIdxNum] = Val;
4638 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4640 if (Result == 0) break; // Cannot compute!
4642 // Evaluate the condition for this iteration.
4643 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4644 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4645 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4647 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4648 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4651 ++NumArrayLenItCounts;
4652 return getConstant(ItCst); // Found terminating iteration!
4655 return getCouldNotCompute();
4659 /// CanConstantFold - Return true if we can constant fold an instruction of the
4660 /// specified type, assuming that all operands were constants.
4661 static bool CanConstantFold(const Instruction *I) {
4662 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4663 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4667 if (const CallInst *CI = dyn_cast<CallInst>(I))
4668 if (const Function *F = CI->getCalledFunction())
4669 return canConstantFoldCallTo(F);
4673 /// Determine whether this instruction can constant evolve within this loop
4674 /// assuming its operands can all constant evolve.
4675 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4676 // An instruction outside of the loop can't be derived from a loop PHI.
4677 if (!L->contains(I)) return false;
4679 if (isa<PHINode>(I)) {
4680 if (L->getHeader() == I->getParent())
4683 // We don't currently keep track of the control flow needed to evaluate
4684 // PHIs, so we cannot handle PHIs inside of loops.
4688 // If we won't be able to constant fold this expression even if the operands
4689 // are constants, bail early.
4690 return CanConstantFold(I);
4693 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4694 /// recursing through each instruction operand until reaching a loop header phi.
4696 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4697 DenseMap<Instruction *, PHINode *> &PHIMap) {
4699 // Otherwise, we can evaluate this instruction if all of its operands are
4700 // constant or derived from a PHI node themselves.
4702 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4703 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4705 if (isa<Constant>(*OpI)) continue;
4707 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4708 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4710 PHINode *P = dyn_cast<PHINode>(OpInst);
4712 // If this operand is already visited, reuse the prior result.
4713 // We may have P != PHI if this is the deepest point at which the
4714 // inconsistent paths meet.
4715 P = PHIMap.lookup(OpInst);
4717 // Recurse and memoize the results, whether a phi is found or not.
4718 // This recursive call invalidates pointers into PHIMap.
4719 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4722 if (P == 0) return 0; // Not evolving from PHI
4723 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4726 // This is a expression evolving from a constant PHI!
4730 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4731 /// in the loop that V is derived from. We allow arbitrary operations along the
4732 /// way, but the operands of an operation must either be constants or a value
4733 /// derived from a constant PHI. If this expression does not fit with these
4734 /// constraints, return null.
4735 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4736 Instruction *I = dyn_cast<Instruction>(V);
4737 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4739 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4743 // Record non-constant instructions contained by the loop.
4744 DenseMap<Instruction *, PHINode *> PHIMap;
4745 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4748 /// EvaluateExpression - Given an expression that passes the
4749 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4750 /// in the loop has the value PHIVal. If we can't fold this expression for some
4751 /// reason, return null.
4752 static Constant *EvaluateExpression(Value *V, const Loop *L,
4753 DenseMap<Instruction *, Constant *> &Vals,
4754 const TargetData *TD,
4755 const TargetLibraryInfo *TLI) {
4756 // Convenient constant check, but redundant for recursive calls.
4757 if (Constant *C = dyn_cast<Constant>(V)) return C;
4758 Instruction *I = dyn_cast<Instruction>(V);
4761 if (Constant *C = Vals.lookup(I)) return C;
4763 // An instruction inside the loop depends on a value outside the loop that we
4764 // weren't given a mapping for, or a value such as a call inside the loop.
4765 if (!canConstantEvolve(I, L)) return 0;
4767 // An unmapped PHI can be due to a branch or another loop inside this loop,
4768 // or due to this not being the initial iteration through a loop where we
4769 // couldn't compute the evolution of this particular PHI last time.
4770 if (isa<PHINode>(I)) return 0;
4772 std::vector<Constant*> Operands(I->getNumOperands());
4774 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4775 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4777 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4778 if (!Operands[i]) return 0;
4781 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
4787 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4788 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4789 Operands[1], TD, TLI);
4790 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4791 if (!LI->isVolatile())
4792 return ConstantFoldLoadFromConstPtr(Operands[0], TD);
4794 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
4798 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4799 /// in the header of its containing loop, we know the loop executes a
4800 /// constant number of times, and the PHI node is just a recurrence
4801 /// involving constants, fold it.
4803 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4806 DenseMap<PHINode*, Constant*>::const_iterator I =
4807 ConstantEvolutionLoopExitValue.find(PN);
4808 if (I != ConstantEvolutionLoopExitValue.end())
4811 if (BEs.ugt(MaxBruteForceIterations))
4812 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4814 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4816 DenseMap<Instruction *, Constant *> CurrentIterVals;
4817 BasicBlock *Header = L->getHeader();
4818 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4820 // Since the loop is canonicalized, the PHI node must have two entries. One
4821 // entry must be a constant (coming in from outside of the loop), and the
4822 // second must be derived from the same PHI.
4823 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4825 for (BasicBlock::iterator I = Header->begin();
4826 (PHI = dyn_cast<PHINode>(I)); ++I) {
4827 Constant *StartCST =
4828 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4829 if (StartCST == 0) continue;
4830 CurrentIterVals[PHI] = StartCST;
4832 if (!CurrentIterVals.count(PN))
4835 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4837 // Execute the loop symbolically to determine the exit value.
4838 if (BEs.getActiveBits() >= 32)
4839 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4841 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4842 unsigned IterationNum = 0;
4843 for (; ; ++IterationNum) {
4844 if (IterationNum == NumIterations)
4845 return RetVal = CurrentIterVals[PN]; // Got exit value!
4847 // Compute the value of the PHIs for the next iteration.
4848 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
4849 DenseMap<Instruction *, Constant *> NextIterVals;
4850 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
4853 return 0; // Couldn't evaluate!
4854 NextIterVals[PN] = NextPHI;
4856 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
4858 // Also evaluate the other PHI nodes. However, we don't get to stop if we
4859 // cease to be able to evaluate one of them or if they stop evolving,
4860 // because that doesn't necessarily prevent us from computing PN.
4861 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
4862 for (DenseMap<Instruction *, Constant *>::const_iterator
4863 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4864 PHINode *PHI = dyn_cast<PHINode>(I->first);
4865 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
4866 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
4868 // We use two distinct loops because EvaluateExpression may invalidate any
4869 // iterators into CurrentIterVals.
4870 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
4871 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
4872 PHINode *PHI = I->first;
4873 Constant *&NextPHI = NextIterVals[PHI];
4874 if (!NextPHI) { // Not already computed.
4875 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4876 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4878 if (NextPHI != I->second)
4879 StoppedEvolving = false;
4882 // If all entries in CurrentIterVals == NextIterVals then we can stop
4883 // iterating, the loop can't continue to change.
4884 if (StoppedEvolving)
4885 return RetVal = CurrentIterVals[PN];
4887 CurrentIterVals.swap(NextIterVals);
4891 /// ComputeExitCountExhaustively - If the loop is known to execute a
4892 /// constant number of times (the condition evolves only from constants),
4893 /// try to evaluate a few iterations of the loop until we get the exit
4894 /// condition gets a value of ExitWhen (true or false). If we cannot
4895 /// evaluate the trip count of the loop, return getCouldNotCompute().
4896 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4899 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4900 if (PN == 0) return getCouldNotCompute();
4902 // If the loop is canonicalized, the PHI will have exactly two entries.
4903 // That's the only form we support here.
4904 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4906 DenseMap<Instruction *, Constant *> CurrentIterVals;
4907 BasicBlock *Header = L->getHeader();
4908 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
4910 // One entry must be a constant (coming in from outside of the loop), and the
4911 // second must be derived from the same PHI.
4912 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4914 for (BasicBlock::iterator I = Header->begin();
4915 (PHI = dyn_cast<PHINode>(I)); ++I) {
4916 Constant *StartCST =
4917 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
4918 if (StartCST == 0) continue;
4919 CurrentIterVals[PHI] = StartCST;
4921 if (!CurrentIterVals.count(PN))
4922 return getCouldNotCompute();
4924 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4925 // the loop symbolically to determine when the condition gets a value of
4928 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4929 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
4930 ConstantInt *CondVal =
4931 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
4934 // Couldn't symbolically evaluate.
4935 if (!CondVal) return getCouldNotCompute();
4937 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4938 ++NumBruteForceTripCountsComputed;
4939 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4942 // Update all the PHI nodes for the next iteration.
4943 DenseMap<Instruction *, Constant *> NextIterVals;
4945 // Create a list of which PHIs we need to compute. We want to do this before
4946 // calling EvaluateExpression on them because that may invalidate iterators
4947 // into CurrentIterVals.
4948 SmallVector<PHINode *, 8> PHIsToCompute;
4949 for (DenseMap<Instruction *, Constant *>::const_iterator
4950 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
4951 PHINode *PHI = dyn_cast<PHINode>(I->first);
4952 if (!PHI || PHI->getParent() != Header) continue;
4953 PHIsToCompute.push_back(PHI);
4955 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
4956 E = PHIsToCompute.end(); I != E; ++I) {
4958 Constant *&NextPHI = NextIterVals[PHI];
4959 if (NextPHI) continue; // Already computed!
4961 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
4962 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
4964 CurrentIterVals.swap(NextIterVals);
4967 // Too many iterations were needed to evaluate.
4968 return getCouldNotCompute();
4971 /// getSCEVAtScope - Return a SCEV expression for the specified value
4972 /// at the specified scope in the program. The L value specifies a loop
4973 /// nest to evaluate the expression at, where null is the top-level or a
4974 /// specified loop is immediately inside of the loop.
4976 /// This method can be used to compute the exit value for a variable defined
4977 /// in a loop by querying what the value will hold in the parent loop.
4979 /// In the case that a relevant loop exit value cannot be computed, the
4980 /// original value V is returned.
4981 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4982 // Check to see if we've folded this expression at this loop before.
4983 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4984 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4985 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4987 return Pair.first->second ? Pair.first->second : V;
4989 // Otherwise compute it.
4990 const SCEV *C = computeSCEVAtScope(V, L);
4991 ValuesAtScopes[V][L] = C;
4995 /// This builds up a Constant using the ConstantExpr interface. That way, we
4996 /// will return Constants for objects which aren't represented by a
4997 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
4998 /// Returns NULL if the SCEV isn't representable as a Constant.
4999 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5000 switch (V->getSCEVType()) {
5001 default: // TODO: smax, umax.
5002 case scCouldNotCompute:
5006 return cast<SCEVConstant>(V)->getValue();
5008 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5009 case scSignExtend: {
5010 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5011 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5012 return ConstantExpr::getSExt(CastOp, SS->getType());
5015 case scZeroExtend: {
5016 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5017 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5018 return ConstantExpr::getZExt(CastOp, SZ->getType());
5022 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5023 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5024 return ConstantExpr::getTrunc(CastOp, ST->getType());
5028 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5029 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5030 if (C->getType()->isPointerTy())
5031 C = ConstantExpr::getBitCast(C, Type::getInt8PtrTy(C->getContext()));
5032 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5033 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5037 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5039 // The offsets have been converted to bytes. We can add bytes to an
5040 // i8* by GEP with the byte count in the first index.
5041 C = ConstantExpr::getBitCast(C,Type::getInt8PtrTy(C->getContext()));
5044 // Don't bother trying to sum two pointers. We probably can't
5045 // statically compute a load that results from it anyway.
5046 if (C2->getType()->isPointerTy())
5049 if (C->getType()->isPointerTy()) {
5050 if (cast<PointerType>(C->getType())->getElementType()->isStructTy())
5051 C2 = ConstantExpr::getIntegerCast(
5052 C2, Type::getInt32Ty(C->getContext()), true);
5053 C = ConstantExpr::getGetElementPtr(C, C2);
5055 C = ConstantExpr::getAdd(C, C2);
5062 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5063 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5064 // Don't bother with pointers at all.
5065 if (C->getType()->isPointerTy()) return 0;
5066 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5067 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5068 if (!C2 || C2->getType()->isPointerTy()) return 0;
5069 C = ConstantExpr::getMul(C, C2);
5076 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5077 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5078 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5079 if (LHS->getType() == RHS->getType())
5080 return ConstantExpr::getUDiv(LHS, RHS);
5087 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5088 if (isa<SCEVConstant>(V)) return V;
5090 // If this instruction is evolved from a constant-evolving PHI, compute the
5091 // exit value from the loop without using SCEVs.
5092 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5093 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5094 const Loop *LI = (*this->LI)[I->getParent()];
5095 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5096 if (PHINode *PN = dyn_cast<PHINode>(I))
5097 if (PN->getParent() == LI->getHeader()) {
5098 // Okay, there is no closed form solution for the PHI node. Check
5099 // to see if the loop that contains it has a known backedge-taken
5100 // count. If so, we may be able to force computation of the exit
5102 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5103 if (const SCEVConstant *BTCC =
5104 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5105 // Okay, we know how many times the containing loop executes. If
5106 // this is a constant evolving PHI node, get the final value at
5107 // the specified iteration number.
5108 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5109 BTCC->getValue()->getValue(),
5111 if (RV) return getSCEV(RV);
5115 // Okay, this is an expression that we cannot symbolically evaluate
5116 // into a SCEV. Check to see if it's possible to symbolically evaluate
5117 // the arguments into constants, and if so, try to constant propagate the
5118 // result. This is particularly useful for computing loop exit values.
5119 if (CanConstantFold(I)) {
5120 SmallVector<Constant *, 4> Operands;
5121 bool MadeImprovement = false;
5122 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5123 Value *Op = I->getOperand(i);
5124 if (Constant *C = dyn_cast<Constant>(Op)) {
5125 Operands.push_back(C);
5129 // If any of the operands is non-constant and if they are
5130 // non-integer and non-pointer, don't even try to analyze them
5131 // with scev techniques.
5132 if (!isSCEVable(Op->getType()))
5135 const SCEV *OrigV = getSCEV(Op);
5136 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5137 MadeImprovement |= OrigV != OpV;
5139 Constant *C = BuildConstantFromSCEV(OpV);
5141 if (C->getType() != Op->getType())
5142 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5146 Operands.push_back(C);
5149 // Check to see if getSCEVAtScope actually made an improvement.
5150 if (MadeImprovement) {
5152 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5153 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5154 Operands[0], Operands[1], TD,
5156 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5157 if (!LI->isVolatile())
5158 C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
5160 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5168 // This is some other type of SCEVUnknown, just return it.
5172 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5173 // Avoid performing the look-up in the common case where the specified
5174 // expression has no loop-variant portions.
5175 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5176 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5177 if (OpAtScope != Comm->getOperand(i)) {
5178 // Okay, at least one of these operands is loop variant but might be
5179 // foldable. Build a new instance of the folded commutative expression.
5180 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5181 Comm->op_begin()+i);
5182 NewOps.push_back(OpAtScope);
5184 for (++i; i != e; ++i) {
5185 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5186 NewOps.push_back(OpAtScope);
5188 if (isa<SCEVAddExpr>(Comm))
5189 return getAddExpr(NewOps);
5190 if (isa<SCEVMulExpr>(Comm))
5191 return getMulExpr(NewOps);
5192 if (isa<SCEVSMaxExpr>(Comm))
5193 return getSMaxExpr(NewOps);
5194 if (isa<SCEVUMaxExpr>(Comm))
5195 return getUMaxExpr(NewOps);
5196 llvm_unreachable("Unknown commutative SCEV type!");
5199 // If we got here, all operands are loop invariant.
5203 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5204 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5205 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5206 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5207 return Div; // must be loop invariant
5208 return getUDivExpr(LHS, RHS);
5211 // If this is a loop recurrence for a loop that does not contain L, then we
5212 // are dealing with the final value computed by the loop.
5213 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5214 // First, attempt to evaluate each operand.
5215 // Avoid performing the look-up in the common case where the specified
5216 // expression has no loop-variant portions.
5217 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5218 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5219 if (OpAtScope == AddRec->getOperand(i))
5222 // Okay, at least one of these operands is loop variant but might be
5223 // foldable. Build a new instance of the folded commutative expression.
5224 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5225 AddRec->op_begin()+i);
5226 NewOps.push_back(OpAtScope);
5227 for (++i; i != e; ++i)
5228 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5230 const SCEV *FoldedRec =
5231 getAddRecExpr(NewOps, AddRec->getLoop(),
5232 AddRec->getNoWrapFlags(SCEV::FlagNW));
5233 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5234 // The addrec may be folded to a nonrecurrence, for example, if the
5235 // induction variable is multiplied by zero after constant folding. Go
5236 // ahead and return the folded value.
5242 // If the scope is outside the addrec's loop, evaluate it by using the
5243 // loop exit value of the addrec.
5244 if (!AddRec->getLoop()->contains(L)) {
5245 // To evaluate this recurrence, we need to know how many times the AddRec
5246 // loop iterates. Compute this now.
5247 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5248 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5250 // Then, evaluate the AddRec.
5251 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5257 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5258 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5259 if (Op == Cast->getOperand())
5260 return Cast; // must be loop invariant
5261 return getZeroExtendExpr(Op, Cast->getType());
5264 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5265 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5266 if (Op == Cast->getOperand())
5267 return Cast; // must be loop invariant
5268 return getSignExtendExpr(Op, Cast->getType());
5271 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5272 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5273 if (Op == Cast->getOperand())
5274 return Cast; // must be loop invariant
5275 return getTruncateExpr(Op, Cast->getType());
5278 llvm_unreachable("Unknown SCEV type!");
5281 /// getSCEVAtScope - This is a convenience function which does
5282 /// getSCEVAtScope(getSCEV(V), L).
5283 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5284 return getSCEVAtScope(getSCEV(V), L);
5287 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5288 /// following equation:
5290 /// A * X = B (mod N)
5292 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5293 /// A and B isn't important.
5295 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5296 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5297 ScalarEvolution &SE) {
5298 uint32_t BW = A.getBitWidth();
5299 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5300 assert(A != 0 && "A must be non-zero.");
5304 // The gcd of A and N may have only one prime factor: 2. The number of
5305 // trailing zeros in A is its multiplicity
5306 uint32_t Mult2 = A.countTrailingZeros();
5309 // 2. Check if B is divisible by D.
5311 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5312 // is not less than multiplicity of this prime factor for D.
5313 if (B.countTrailingZeros() < Mult2)
5314 return SE.getCouldNotCompute();
5316 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5319 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5320 // bit width during computations.
5321 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5322 APInt Mod(BW + 1, 0);
5323 Mod.setBit(BW - Mult2); // Mod = N / D
5324 APInt I = AD.multiplicativeInverse(Mod);
5326 // 4. Compute the minimum unsigned root of the equation:
5327 // I * (B / D) mod (N / D)
5328 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5330 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5332 return SE.getConstant(Result.trunc(BW));
5335 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5336 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5337 /// might be the same) or two SCEVCouldNotCompute objects.
5339 static std::pair<const SCEV *,const SCEV *>
5340 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5341 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5342 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5343 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5344 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5346 // We currently can only solve this if the coefficients are constants.
5347 if (!LC || !MC || !NC) {
5348 const SCEV *CNC = SE.getCouldNotCompute();
5349 return std::make_pair(CNC, CNC);
5352 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5353 const APInt &L = LC->getValue()->getValue();
5354 const APInt &M = MC->getValue()->getValue();
5355 const APInt &N = NC->getValue()->getValue();
5356 APInt Two(BitWidth, 2);
5357 APInt Four(BitWidth, 4);
5360 using namespace APIntOps;
5362 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5363 // The B coefficient is M-N/2
5367 // The A coefficient is N/2
5368 APInt A(N.sdiv(Two));
5370 // Compute the B^2-4ac term.
5373 SqrtTerm -= Four * (A * C);
5375 if (SqrtTerm.isNegative()) {
5376 // The loop is provably infinite.
5377 const SCEV *CNC = SE.getCouldNotCompute();
5378 return std::make_pair(CNC, CNC);
5381 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5382 // integer value or else APInt::sqrt() will assert.
5383 APInt SqrtVal(SqrtTerm.sqrt());
5385 // Compute the two solutions for the quadratic formula.
5386 // The divisions must be performed as signed divisions.
5389 if (TwoA.isMinValue()) {
5390 const SCEV *CNC = SE.getCouldNotCompute();
5391 return std::make_pair(CNC, CNC);
5394 LLVMContext &Context = SE.getContext();
5396 ConstantInt *Solution1 =
5397 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5398 ConstantInt *Solution2 =
5399 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5401 return std::make_pair(SE.getConstant(Solution1),
5402 SE.getConstant(Solution2));
5403 } // end APIntOps namespace
5406 /// HowFarToZero - Return the number of times a backedge comparing the specified
5407 /// value to zero will execute. If not computable, return CouldNotCompute.
5409 /// This is only used for loops with a "x != y" exit test. The exit condition is
5410 /// now expressed as a single expression, V = x-y. So the exit test is
5411 /// effectively V != 0. We know and take advantage of the fact that this
5412 /// expression only being used in a comparison by zero context.
5413 ScalarEvolution::ExitLimit
5414 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
5415 // If the value is a constant
5416 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5417 // If the value is already zero, the branch will execute zero times.
5418 if (C->getValue()->isZero()) return C;
5419 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5422 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5423 if (!AddRec || AddRec->getLoop() != L)
5424 return getCouldNotCompute();
5426 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5427 // the quadratic equation to solve it.
5428 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5429 std::pair<const SCEV *,const SCEV *> Roots =
5430 SolveQuadraticEquation(AddRec, *this);
5431 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5432 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5435 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5436 << " sol#2: " << *R2 << "\n";
5438 // Pick the smallest positive root value.
5439 if (ConstantInt *CB =
5440 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5443 if (CB->getZExtValue() == false)
5444 std::swap(R1, R2); // R1 is the minimum root now.
5446 // We can only use this value if the chrec ends up with an exact zero
5447 // value at this index. When solving for "X*X != 5", for example, we
5448 // should not accept a root of 2.
5449 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5451 return R1; // We found a quadratic root!
5454 return getCouldNotCompute();
5457 // Otherwise we can only handle this if it is affine.
5458 if (!AddRec->isAffine())
5459 return getCouldNotCompute();
5461 // If this is an affine expression, the execution count of this branch is
5462 // the minimum unsigned root of the following equation:
5464 // Start + Step*N = 0 (mod 2^BW)
5468 // Step*N = -Start (mod 2^BW)
5470 // where BW is the common bit width of Start and Step.
5472 // Get the initial value for the loop.
5473 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5474 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5476 // For now we handle only constant steps.
5478 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5479 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5480 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5481 // We have not yet seen any such cases.
5482 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5483 if (StepC == 0 || StepC->getValue()->equalsInt(0))
5484 return getCouldNotCompute();
5486 // For positive steps (counting up until unsigned overflow):
5487 // N = -Start/Step (as unsigned)
5488 // For negative steps (counting down to zero):
5490 // First compute the unsigned distance from zero in the direction of Step.
5491 bool CountDown = StepC->getValue()->getValue().isNegative();
5492 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5494 // Handle unitary steps, which cannot wraparound.
5495 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5496 // N = Distance (as unsigned)
5497 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5498 ConstantRange CR = getUnsignedRange(Start);
5499 const SCEV *MaxBECount;
5500 if (!CountDown && CR.getUnsignedMin().isMinValue())
5501 // When counting up, the worst starting value is 1, not 0.
5502 MaxBECount = CR.getUnsignedMax().isMinValue()
5503 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5504 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5506 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5507 : -CR.getUnsignedMin());
5508 return ExitLimit(Distance, MaxBECount);
5511 // If the recurrence is known not to wraparound, unsigned divide computes the
5512 // back edge count. We know that the value will either become zero (and thus
5513 // the loop terminates), that the loop will terminate through some other exit
5514 // condition first, or that the loop has undefined behavior. This means
5515 // we can't "miss" the exit value, even with nonunit stride.
5517 // FIXME: Prove that loops always exhibits *acceptable* undefined
5518 // behavior. Loops must exhibit defined behavior until a wrapped value is
5519 // actually used. So the trip count computed by udiv could be smaller than the
5520 // number of well-defined iterations.
5521 if (AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5522 // FIXME: We really want an "isexact" bit for udiv.
5523 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5525 // Then, try to solve the above equation provided that Start is constant.
5526 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5527 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5528 -StartC->getValue()->getValue(),
5530 return getCouldNotCompute();
5533 /// HowFarToNonZero - Return the number of times a backedge checking the
5534 /// specified value for nonzero will execute. If not computable, return
5536 ScalarEvolution::ExitLimit
5537 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5538 // Loops that look like: while (X == 0) are very strange indeed. We don't
5539 // handle them yet except for the trivial case. This could be expanded in the
5540 // future as needed.
5542 // If the value is a constant, check to see if it is known to be non-zero
5543 // already. If so, the backedge will execute zero times.
5544 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5545 if (!C->getValue()->isNullValue())
5546 return getConstant(C->getType(), 0);
5547 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5550 // We could implement others, but I really doubt anyone writes loops like
5551 // this, and if they did, they would already be constant folded.
5552 return getCouldNotCompute();
5555 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5556 /// (which may not be an immediate predecessor) which has exactly one
5557 /// successor from which BB is reachable, or null if no such block is
5560 std::pair<BasicBlock *, BasicBlock *>
5561 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5562 // If the block has a unique predecessor, then there is no path from the
5563 // predecessor to the block that does not go through the direct edge
5564 // from the predecessor to the block.
5565 if (BasicBlock *Pred = BB->getSinglePredecessor())
5566 return std::make_pair(Pred, BB);
5568 // A loop's header is defined to be a block that dominates the loop.
5569 // If the header has a unique predecessor outside the loop, it must be
5570 // a block that has exactly one successor that can reach the loop.
5571 if (Loop *L = LI->getLoopFor(BB))
5572 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5574 return std::pair<BasicBlock *, BasicBlock *>();
5577 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5578 /// testing whether two expressions are equal, however for the purposes of
5579 /// looking for a condition guarding a loop, it can be useful to be a little
5580 /// more general, since a front-end may have replicated the controlling
5583 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5584 // Quick check to see if they are the same SCEV.
5585 if (A == B) return true;
5587 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5588 // two different instructions with the same value. Check for this case.
5589 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5590 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5591 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5592 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5593 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5596 // Otherwise assume they may have a different value.
5600 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5601 /// predicate Pred. Return true if any changes were made.
5603 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5604 const SCEV *&LHS, const SCEV *&RHS,
5606 bool Changed = false;
5608 // If we hit the max recursion limit bail out.
5612 // Canonicalize a constant to the right side.
5613 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5614 // Check for both operands constant.
5615 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5616 if (ConstantExpr::getICmp(Pred,
5618 RHSC->getValue())->isNullValue())
5619 goto trivially_false;
5621 goto trivially_true;
5623 // Otherwise swap the operands to put the constant on the right.
5624 std::swap(LHS, RHS);
5625 Pred = ICmpInst::getSwappedPredicate(Pred);
5629 // If we're comparing an addrec with a value which is loop-invariant in the
5630 // addrec's loop, put the addrec on the left. Also make a dominance check,
5631 // as both operands could be addrecs loop-invariant in each other's loop.
5632 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5633 const Loop *L = AR->getLoop();
5634 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5635 std::swap(LHS, RHS);
5636 Pred = ICmpInst::getSwappedPredicate(Pred);
5641 // If there's a constant operand, canonicalize comparisons with boundary
5642 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5643 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5644 const APInt &RA = RC->getValue()->getValue();
5646 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5647 case ICmpInst::ICMP_EQ:
5648 case ICmpInst::ICMP_NE:
5649 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5651 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5652 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5653 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5654 ME->getOperand(0)->isAllOnesValue()) {
5655 RHS = AE->getOperand(1);
5656 LHS = ME->getOperand(1);
5660 case ICmpInst::ICMP_UGE:
5661 if ((RA - 1).isMinValue()) {
5662 Pred = ICmpInst::ICMP_NE;
5663 RHS = getConstant(RA - 1);
5667 if (RA.isMaxValue()) {
5668 Pred = ICmpInst::ICMP_EQ;
5672 if (RA.isMinValue()) goto trivially_true;
5674 Pred = ICmpInst::ICMP_UGT;
5675 RHS = getConstant(RA - 1);
5678 case ICmpInst::ICMP_ULE:
5679 if ((RA + 1).isMaxValue()) {
5680 Pred = ICmpInst::ICMP_NE;
5681 RHS = getConstant(RA + 1);
5685 if (RA.isMinValue()) {
5686 Pred = ICmpInst::ICMP_EQ;
5690 if (RA.isMaxValue()) goto trivially_true;
5692 Pred = ICmpInst::ICMP_ULT;
5693 RHS = getConstant(RA + 1);
5696 case ICmpInst::ICMP_SGE:
5697 if ((RA - 1).isMinSignedValue()) {
5698 Pred = ICmpInst::ICMP_NE;
5699 RHS = getConstant(RA - 1);
5703 if (RA.isMaxSignedValue()) {
5704 Pred = ICmpInst::ICMP_EQ;
5708 if (RA.isMinSignedValue()) goto trivially_true;
5710 Pred = ICmpInst::ICMP_SGT;
5711 RHS = getConstant(RA - 1);
5714 case ICmpInst::ICMP_SLE:
5715 if ((RA + 1).isMaxSignedValue()) {
5716 Pred = ICmpInst::ICMP_NE;
5717 RHS = getConstant(RA + 1);
5721 if (RA.isMinSignedValue()) {
5722 Pred = ICmpInst::ICMP_EQ;
5726 if (RA.isMaxSignedValue()) goto trivially_true;
5728 Pred = ICmpInst::ICMP_SLT;
5729 RHS = getConstant(RA + 1);
5732 case ICmpInst::ICMP_UGT:
5733 if (RA.isMinValue()) {
5734 Pred = ICmpInst::ICMP_NE;
5738 if ((RA + 1).isMaxValue()) {
5739 Pred = ICmpInst::ICMP_EQ;
5740 RHS = getConstant(RA + 1);
5744 if (RA.isMaxValue()) goto trivially_false;
5746 case ICmpInst::ICMP_ULT:
5747 if (RA.isMaxValue()) {
5748 Pred = ICmpInst::ICMP_NE;
5752 if ((RA - 1).isMinValue()) {
5753 Pred = ICmpInst::ICMP_EQ;
5754 RHS = getConstant(RA - 1);
5758 if (RA.isMinValue()) goto trivially_false;
5760 case ICmpInst::ICMP_SGT:
5761 if (RA.isMinSignedValue()) {
5762 Pred = ICmpInst::ICMP_NE;
5766 if ((RA + 1).isMaxSignedValue()) {
5767 Pred = ICmpInst::ICMP_EQ;
5768 RHS = getConstant(RA + 1);
5772 if (RA.isMaxSignedValue()) goto trivially_false;
5774 case ICmpInst::ICMP_SLT:
5775 if (RA.isMaxSignedValue()) {
5776 Pred = ICmpInst::ICMP_NE;
5780 if ((RA - 1).isMinSignedValue()) {
5781 Pred = ICmpInst::ICMP_EQ;
5782 RHS = getConstant(RA - 1);
5786 if (RA.isMinSignedValue()) goto trivially_false;
5791 // Check for obvious equality.
5792 if (HasSameValue(LHS, RHS)) {
5793 if (ICmpInst::isTrueWhenEqual(Pred))
5794 goto trivially_true;
5795 if (ICmpInst::isFalseWhenEqual(Pred))
5796 goto trivially_false;
5799 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5800 // adding or subtracting 1 from one of the operands.
5802 case ICmpInst::ICMP_SLE:
5803 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5804 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5806 Pred = ICmpInst::ICMP_SLT;
5808 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5809 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5811 Pred = ICmpInst::ICMP_SLT;
5815 case ICmpInst::ICMP_SGE:
5816 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5817 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5819 Pred = ICmpInst::ICMP_SGT;
5821 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5822 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5824 Pred = ICmpInst::ICMP_SGT;
5828 case ICmpInst::ICMP_ULE:
5829 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5830 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5832 Pred = ICmpInst::ICMP_ULT;
5834 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5835 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5837 Pred = ICmpInst::ICMP_ULT;
5841 case ICmpInst::ICMP_UGE:
5842 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5843 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5845 Pred = ICmpInst::ICMP_UGT;
5847 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5848 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5850 Pred = ICmpInst::ICMP_UGT;
5858 // TODO: More simplifications are possible here.
5860 // Recursively simplify until we either hit a recursion limit or nothing
5863 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
5869 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5870 Pred = ICmpInst::ICMP_EQ;
5875 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5876 Pred = ICmpInst::ICMP_NE;
5880 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5881 return getSignedRange(S).getSignedMax().isNegative();
5884 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5885 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5888 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5889 return !getSignedRange(S).getSignedMin().isNegative();
5892 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5893 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5896 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5897 return isKnownNegative(S) || isKnownPositive(S);
5900 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5901 const SCEV *LHS, const SCEV *RHS) {
5902 // Canonicalize the inputs first.
5903 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5905 // If LHS or RHS is an addrec, check to see if the condition is true in
5906 // every iteration of the loop.
5907 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5908 if (isLoopEntryGuardedByCond(
5909 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5910 isLoopBackedgeGuardedByCond(
5911 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5913 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5914 if (isLoopEntryGuardedByCond(
5915 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5916 isLoopBackedgeGuardedByCond(
5917 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5920 // Otherwise see what can be done with known constant ranges.
5921 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5925 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5926 const SCEV *LHS, const SCEV *RHS) {
5927 if (HasSameValue(LHS, RHS))
5928 return ICmpInst::isTrueWhenEqual(Pred);
5930 // This code is split out from isKnownPredicate because it is called from
5931 // within isLoopEntryGuardedByCond.
5934 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5935 case ICmpInst::ICMP_SGT:
5936 Pred = ICmpInst::ICMP_SLT;
5937 std::swap(LHS, RHS);
5938 case ICmpInst::ICMP_SLT: {
5939 ConstantRange LHSRange = getSignedRange(LHS);
5940 ConstantRange RHSRange = getSignedRange(RHS);
5941 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5943 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5947 case ICmpInst::ICMP_SGE:
5948 Pred = ICmpInst::ICMP_SLE;
5949 std::swap(LHS, RHS);
5950 case ICmpInst::ICMP_SLE: {
5951 ConstantRange LHSRange = getSignedRange(LHS);
5952 ConstantRange RHSRange = getSignedRange(RHS);
5953 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5955 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5959 case ICmpInst::ICMP_UGT:
5960 Pred = ICmpInst::ICMP_ULT;
5961 std::swap(LHS, RHS);
5962 case ICmpInst::ICMP_ULT: {
5963 ConstantRange LHSRange = getUnsignedRange(LHS);
5964 ConstantRange RHSRange = getUnsignedRange(RHS);
5965 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5967 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5971 case ICmpInst::ICMP_UGE:
5972 Pred = ICmpInst::ICMP_ULE;
5973 std::swap(LHS, RHS);
5974 case ICmpInst::ICMP_ULE: {
5975 ConstantRange LHSRange = getUnsignedRange(LHS);
5976 ConstantRange RHSRange = getUnsignedRange(RHS);
5977 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5979 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5983 case ICmpInst::ICMP_NE: {
5984 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5986 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5989 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5990 if (isKnownNonZero(Diff))
5994 case ICmpInst::ICMP_EQ:
5995 // The check at the top of the function catches the case where
5996 // the values are known to be equal.
6002 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6003 /// protected by a conditional between LHS and RHS. This is used to
6004 /// to eliminate casts.
6006 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6007 ICmpInst::Predicate Pred,
6008 const SCEV *LHS, const SCEV *RHS) {
6009 // Interpret a null as meaning no loop, where there is obviously no guard
6010 // (interprocedural conditions notwithstanding).
6011 if (!L) return true;
6013 BasicBlock *Latch = L->getLoopLatch();
6017 BranchInst *LoopContinuePredicate =
6018 dyn_cast<BranchInst>(Latch->getTerminator());
6019 if (!LoopContinuePredicate ||
6020 LoopContinuePredicate->isUnconditional())
6023 return isImpliedCond(Pred, LHS, RHS,
6024 LoopContinuePredicate->getCondition(),
6025 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6028 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6029 /// by a conditional between LHS and RHS. This is used to help avoid max
6030 /// expressions in loop trip counts, and to eliminate casts.
6032 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6033 ICmpInst::Predicate Pred,
6034 const SCEV *LHS, const SCEV *RHS) {
6035 // Interpret a null as meaning no loop, where there is obviously no guard
6036 // (interprocedural conditions notwithstanding).
6037 if (!L) return false;
6039 // Starting at the loop predecessor, climb up the predecessor chain, as long
6040 // as there are predecessors that can be found that have unique successors
6041 // leading to the original header.
6042 for (std::pair<BasicBlock *, BasicBlock *>
6043 Pair(L->getLoopPredecessor(), L->getHeader());
6045 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6047 BranchInst *LoopEntryPredicate =
6048 dyn_cast<BranchInst>(Pair.first->getTerminator());
6049 if (!LoopEntryPredicate ||
6050 LoopEntryPredicate->isUnconditional())
6053 if (isImpliedCond(Pred, LHS, RHS,
6054 LoopEntryPredicate->getCondition(),
6055 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6062 /// RAII wrapper to prevent recursive application of isImpliedCond.
6063 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6064 /// currently evaluating isImpliedCond.
6065 struct MarkPendingLoopPredicate {
6067 DenseSet<Value*> &LoopPreds;
6070 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6071 : Cond(C), LoopPreds(LP) {
6072 Pending = !LoopPreds.insert(Cond).second;
6074 ~MarkPendingLoopPredicate() {
6076 LoopPreds.erase(Cond);
6080 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6081 /// and RHS is true whenever the given Cond value evaluates to true.
6082 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6083 const SCEV *LHS, const SCEV *RHS,
6084 Value *FoundCondValue,
6086 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6090 // Recursively handle And and Or conditions.
6091 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6092 if (BO->getOpcode() == Instruction::And) {
6094 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6095 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6096 } else if (BO->getOpcode() == Instruction::Or) {
6098 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6099 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6103 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6104 if (!ICI) return false;
6106 // Bail if the ICmp's operands' types are wider than the needed type
6107 // before attempting to call getSCEV on them. This avoids infinite
6108 // recursion, since the analysis of widening casts can require loop
6109 // exit condition information for overflow checking, which would
6111 if (getTypeSizeInBits(LHS->getType()) <
6112 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6115 // Now that we found a conditional branch that dominates the loop, check to
6116 // see if it is the comparison we are looking for.
6117 ICmpInst::Predicate FoundPred;
6119 FoundPred = ICI->getInversePredicate();
6121 FoundPred = ICI->getPredicate();
6123 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6124 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6126 // Balance the types. The case where FoundLHS' type is wider than
6127 // LHS' type is checked for above.
6128 if (getTypeSizeInBits(LHS->getType()) >
6129 getTypeSizeInBits(FoundLHS->getType())) {
6130 if (CmpInst::isSigned(Pred)) {
6131 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6132 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6134 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6135 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6139 // Canonicalize the query to match the way instcombine will have
6140 // canonicalized the comparison.
6141 if (SimplifyICmpOperands(Pred, LHS, RHS))
6143 return CmpInst::isTrueWhenEqual(Pred);
6144 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6145 if (FoundLHS == FoundRHS)
6146 return CmpInst::isFalseWhenEqual(Pred);
6148 // Check to see if we can make the LHS or RHS match.
6149 if (LHS == FoundRHS || RHS == FoundLHS) {
6150 if (isa<SCEVConstant>(RHS)) {
6151 std::swap(FoundLHS, FoundRHS);
6152 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6154 std::swap(LHS, RHS);
6155 Pred = ICmpInst::getSwappedPredicate(Pred);
6159 // Check whether the found predicate is the same as the desired predicate.
6160 if (FoundPred == Pred)
6161 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6163 // Check whether swapping the found predicate makes it the same as the
6164 // desired predicate.
6165 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6166 if (isa<SCEVConstant>(RHS))
6167 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6169 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6170 RHS, LHS, FoundLHS, FoundRHS);
6173 // Check whether the actual condition is beyond sufficient.
6174 if (FoundPred == ICmpInst::ICMP_EQ)
6175 if (ICmpInst::isTrueWhenEqual(Pred))
6176 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6178 if (Pred == ICmpInst::ICMP_NE)
6179 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6180 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6183 // Otherwise assume the worst.
6187 /// isImpliedCondOperands - Test whether the condition described by Pred,
6188 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6189 /// and FoundRHS is true.
6190 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6191 const SCEV *LHS, const SCEV *RHS,
6192 const SCEV *FoundLHS,
6193 const SCEV *FoundRHS) {
6194 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6195 FoundLHS, FoundRHS) ||
6196 // ~x < ~y --> x > y
6197 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6198 getNotSCEV(FoundRHS),
6199 getNotSCEV(FoundLHS));
6202 /// isImpliedCondOperandsHelper - Test whether the condition described by
6203 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6204 /// FoundLHS, and FoundRHS is true.
6206 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6207 const SCEV *LHS, const SCEV *RHS,
6208 const SCEV *FoundLHS,
6209 const SCEV *FoundRHS) {
6211 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6212 case ICmpInst::ICMP_EQ:
6213 case ICmpInst::ICMP_NE:
6214 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6217 case ICmpInst::ICMP_SLT:
6218 case ICmpInst::ICMP_SLE:
6219 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6220 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6223 case ICmpInst::ICMP_SGT:
6224 case ICmpInst::ICMP_SGE:
6225 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6226 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6229 case ICmpInst::ICMP_ULT:
6230 case ICmpInst::ICMP_ULE:
6231 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6232 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6235 case ICmpInst::ICMP_UGT:
6236 case ICmpInst::ICMP_UGE:
6237 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6238 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6246 /// getBECount - Subtract the end and start values and divide by the step,
6247 /// rounding up, to get the number of times the backedge is executed. Return
6248 /// CouldNotCompute if an intermediate computation overflows.
6249 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
6253 assert(!isKnownNegative(Step) &&
6254 "This code doesn't handle negative strides yet!");
6256 Type *Ty = Start->getType();
6258 // When Start == End, we have an exact BECount == 0. Short-circuit this case
6259 // here because SCEV may not be able to determine that the unsigned division
6260 // after rounding is zero.
6262 return getConstant(Ty, 0);
6264 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
6265 const SCEV *Diff = getMinusSCEV(End, Start);
6266 const SCEV *RoundUp = getAddExpr(Step, NegOne);
6268 // Add an adjustment to the difference between End and Start so that
6269 // the division will effectively round up.
6270 const SCEV *Add = getAddExpr(Diff, RoundUp);
6273 // Check Add for unsigned overflow.
6274 // TODO: More sophisticated things could be done here.
6275 Type *WideTy = IntegerType::get(getContext(),
6276 getTypeSizeInBits(Ty) + 1);
6277 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
6278 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
6279 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
6280 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
6281 return getCouldNotCompute();
6284 return getUDivExpr(Add, Step);
6287 /// HowManyLessThans - Return the number of times a backedge containing the
6288 /// specified less-than comparison will execute. If not computable, return
6289 /// CouldNotCompute.
6290 ScalarEvolution::ExitLimit
6291 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6292 const Loop *L, bool isSigned) {
6293 // Only handle: "ADDREC < LoopInvariant".
6294 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
6296 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
6297 if (!AddRec || AddRec->getLoop() != L)
6298 return getCouldNotCompute();
6300 // Check to see if we have a flag which makes analysis easy.
6301 bool NoWrap = isSigned ?
6302 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNSW | SCEV::FlagNW)) :
6303 AddRec->getNoWrapFlags((SCEV::NoWrapFlags)(SCEV::FlagNUW | SCEV::FlagNW));
6305 if (AddRec->isAffine()) {
6306 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
6307 const SCEV *Step = AddRec->getStepRecurrence(*this);
6310 return getCouldNotCompute();
6311 if (Step->isOne()) {
6312 // With unit stride, the iteration never steps past the limit value.
6313 } else if (isKnownPositive(Step)) {
6314 // Test whether a positive iteration can step past the limit
6315 // value and past the maximum value for its type in a single step.
6316 // Note that it's not sufficient to check NoWrap here, because even
6317 // though the value after a wrap is undefined, it's not undefined
6318 // behavior, so if wrap does occur, the loop could either terminate or
6319 // loop infinitely, but in either case, the loop is guaranteed to
6320 // iterate at least until the iteration where the wrapping occurs.
6321 const SCEV *One = getConstant(Step->getType(), 1);
6323 APInt Max = APInt::getSignedMaxValue(BitWidth);
6324 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
6325 .slt(getSignedRange(RHS).getSignedMax()))
6326 return getCouldNotCompute();
6328 APInt Max = APInt::getMaxValue(BitWidth);
6329 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
6330 .ult(getUnsignedRange(RHS).getUnsignedMax()))
6331 return getCouldNotCompute();
6334 // TODO: Handle negative strides here and below.
6335 return getCouldNotCompute();
6337 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
6338 // m. So, we count the number of iterations in which {n,+,s} < m is true.
6339 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
6340 // treat m-n as signed nor unsigned due to overflow possibility.
6342 // First, we get the value of the LHS in the first iteration: n
6343 const SCEV *Start = AddRec->getOperand(0);
6345 // Determine the minimum constant start value.
6346 const SCEV *MinStart = getConstant(isSigned ?
6347 getSignedRange(Start).getSignedMin() :
6348 getUnsignedRange(Start).getUnsignedMin());
6350 // If we know that the condition is true in order to enter the loop,
6351 // then we know that it will run exactly (m-n)/s times. Otherwise, we
6352 // only know that it will execute (max(m,n)-n)/s times. In both cases,
6353 // the division must round up.
6354 const SCEV *End = RHS;
6355 if (!isLoopEntryGuardedByCond(L,
6356 isSigned ? ICmpInst::ICMP_SLT :
6358 getMinusSCEV(Start, Step), RHS))
6359 End = isSigned ? getSMaxExpr(RHS, Start)
6360 : getUMaxExpr(RHS, Start);
6362 // Determine the maximum constant end value.
6363 const SCEV *MaxEnd = getConstant(isSigned ?
6364 getSignedRange(End).getSignedMax() :
6365 getUnsignedRange(End).getUnsignedMax());
6367 // If MaxEnd is within a step of the maximum integer value in its type,
6368 // adjust it down to the minimum value which would produce the same effect.
6369 // This allows the subsequent ceiling division of (N+(step-1))/step to
6370 // compute the correct value.
6371 const SCEV *StepMinusOne = getMinusSCEV(Step,
6372 getConstant(Step->getType(), 1));
6375 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6378 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6381 // Finally, we subtract these two values and divide, rounding up, to get
6382 // the number of times the backedge is executed.
6383 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6385 // The maximum backedge count is similar, except using the minimum start
6386 // value and the maximum end value.
6387 // If we already have an exact constant BECount, use it instead.
6388 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6389 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6391 // If the stride is nonconstant, and NoWrap == true, then
6392 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6393 // exact BECount and invalid MaxBECount, which should be avoided to catch
6394 // more optimization opportunities.
6395 if (isa<SCEVCouldNotCompute>(MaxBECount))
6396 MaxBECount = BECount;
6398 return ExitLimit(BECount, MaxBECount);
6401 return getCouldNotCompute();
6404 /// getNumIterationsInRange - Return the number of iterations of this loop that
6405 /// produce values in the specified constant range. Another way of looking at
6406 /// this is that it returns the first iteration number where the value is not in
6407 /// the condition, thus computing the exit count. If the iteration count can't
6408 /// be computed, an instance of SCEVCouldNotCompute is returned.
6409 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6410 ScalarEvolution &SE) const {
6411 if (Range.isFullSet()) // Infinite loop.
6412 return SE.getCouldNotCompute();
6414 // If the start is a non-zero constant, shift the range to simplify things.
6415 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6416 if (!SC->getValue()->isZero()) {
6417 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6418 Operands[0] = SE.getConstant(SC->getType(), 0);
6419 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6420 getNoWrapFlags(FlagNW));
6421 if (const SCEVAddRecExpr *ShiftedAddRec =
6422 dyn_cast<SCEVAddRecExpr>(Shifted))
6423 return ShiftedAddRec->getNumIterationsInRange(
6424 Range.subtract(SC->getValue()->getValue()), SE);
6425 // This is strange and shouldn't happen.
6426 return SE.getCouldNotCompute();
6429 // The only time we can solve this is when we have all constant indices.
6430 // Otherwise, we cannot determine the overflow conditions.
6431 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6432 if (!isa<SCEVConstant>(getOperand(i)))
6433 return SE.getCouldNotCompute();
6436 // Okay at this point we know that all elements of the chrec are constants and
6437 // that the start element is zero.
6439 // First check to see if the range contains zero. If not, the first
6441 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6442 if (!Range.contains(APInt(BitWidth, 0)))
6443 return SE.getConstant(getType(), 0);
6446 // If this is an affine expression then we have this situation:
6447 // Solve {0,+,A} in Range === Ax in Range
6449 // We know that zero is in the range. If A is positive then we know that
6450 // the upper value of the range must be the first possible exit value.
6451 // If A is negative then the lower of the range is the last possible loop
6452 // value. Also note that we already checked for a full range.
6453 APInt One(BitWidth,1);
6454 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6455 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6457 // The exit value should be (End+A)/A.
6458 APInt ExitVal = (End + A).udiv(A);
6459 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6461 // Evaluate at the exit value. If we really did fall out of the valid
6462 // range, then we computed our trip count, otherwise wrap around or other
6463 // things must have happened.
6464 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6465 if (Range.contains(Val->getValue()))
6466 return SE.getCouldNotCompute(); // Something strange happened
6468 // Ensure that the previous value is in the range. This is a sanity check.
6469 assert(Range.contains(
6470 EvaluateConstantChrecAtConstant(this,
6471 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6472 "Linear scev computation is off in a bad way!");
6473 return SE.getConstant(ExitValue);
6474 } else if (isQuadratic()) {
6475 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6476 // quadratic equation to solve it. To do this, we must frame our problem in
6477 // terms of figuring out when zero is crossed, instead of when
6478 // Range.getUpper() is crossed.
6479 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6480 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6481 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6482 // getNoWrapFlags(FlagNW)
6485 // Next, solve the constructed addrec
6486 std::pair<const SCEV *,const SCEV *> Roots =
6487 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6488 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6489 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6491 // Pick the smallest positive root value.
6492 if (ConstantInt *CB =
6493 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6494 R1->getValue(), R2->getValue()))) {
6495 if (CB->getZExtValue() == false)
6496 std::swap(R1, R2); // R1 is the minimum root now.
6498 // Make sure the root is not off by one. The returned iteration should
6499 // not be in the range, but the previous one should be. When solving
6500 // for "X*X < 5", for example, we should not return a root of 2.
6501 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6504 if (Range.contains(R1Val->getValue())) {
6505 // The next iteration must be out of the range...
6506 ConstantInt *NextVal =
6507 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6509 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6510 if (!Range.contains(R1Val->getValue()))
6511 return SE.getConstant(NextVal);
6512 return SE.getCouldNotCompute(); // Something strange happened
6515 // If R1 was not in the range, then it is a good return value. Make
6516 // sure that R1-1 WAS in the range though, just in case.
6517 ConstantInt *NextVal =
6518 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6519 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6520 if (Range.contains(R1Val->getValue()))
6522 return SE.getCouldNotCompute(); // Something strange happened
6527 return SE.getCouldNotCompute();
6532 //===----------------------------------------------------------------------===//
6533 // SCEVCallbackVH Class Implementation
6534 //===----------------------------------------------------------------------===//
6536 void ScalarEvolution::SCEVCallbackVH::deleted() {
6537 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6538 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6539 SE->ConstantEvolutionLoopExitValue.erase(PN);
6540 SE->ValueExprMap.erase(getValPtr());
6541 // this now dangles!
6544 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6545 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6547 // Forget all the expressions associated with users of the old value,
6548 // so that future queries will recompute the expressions using the new
6550 Value *Old = getValPtr();
6551 SmallVector<User *, 16> Worklist;
6552 SmallPtrSet<User *, 8> Visited;
6553 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6555 Worklist.push_back(*UI);
6556 while (!Worklist.empty()) {
6557 User *U = Worklist.pop_back_val();
6558 // Deleting the Old value will cause this to dangle. Postpone
6559 // that until everything else is done.
6562 if (!Visited.insert(U))
6564 if (PHINode *PN = dyn_cast<PHINode>(U))
6565 SE->ConstantEvolutionLoopExitValue.erase(PN);
6566 SE->ValueExprMap.erase(U);
6567 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6569 Worklist.push_back(*UI);
6571 // Delete the Old value.
6572 if (PHINode *PN = dyn_cast<PHINode>(Old))
6573 SE->ConstantEvolutionLoopExitValue.erase(PN);
6574 SE->ValueExprMap.erase(Old);
6575 // this now dangles!
6578 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6579 : CallbackVH(V), SE(se) {}
6581 //===----------------------------------------------------------------------===//
6582 // ScalarEvolution Class Implementation
6583 //===----------------------------------------------------------------------===//
6585 ScalarEvolution::ScalarEvolution()
6586 : FunctionPass(ID), FirstUnknown(0) {
6587 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6590 bool ScalarEvolution::runOnFunction(Function &F) {
6592 LI = &getAnalysis<LoopInfo>();
6593 TD = getAnalysisIfAvailable<TargetData>();
6594 TLI = &getAnalysis<TargetLibraryInfo>();
6595 DT = &getAnalysis<DominatorTree>();
6599 void ScalarEvolution::releaseMemory() {
6600 // Iterate through all the SCEVUnknown instances and call their
6601 // destructors, so that they release their references to their values.
6602 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6606 ValueExprMap.clear();
6608 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6609 // that a loop had multiple computable exits.
6610 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6611 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6616 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
6618 BackedgeTakenCounts.clear();
6619 ConstantEvolutionLoopExitValue.clear();
6620 ValuesAtScopes.clear();
6621 LoopDispositions.clear();
6622 BlockDispositions.clear();
6623 UnsignedRanges.clear();
6624 SignedRanges.clear();
6625 UniqueSCEVs.clear();
6626 SCEVAllocator.Reset();
6629 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6630 AU.setPreservesAll();
6631 AU.addRequiredTransitive<LoopInfo>();
6632 AU.addRequiredTransitive<DominatorTree>();
6633 AU.addRequired<TargetLibraryInfo>();
6636 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6637 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6640 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6642 // Print all inner loops first
6643 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6644 PrintLoopInfo(OS, SE, *I);
6647 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6650 SmallVector<BasicBlock *, 8> ExitBlocks;
6651 L->getExitBlocks(ExitBlocks);
6652 if (ExitBlocks.size() != 1)
6653 OS << "<multiple exits> ";
6655 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6656 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6658 OS << "Unpredictable backedge-taken count. ";
6663 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6666 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6667 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6669 OS << "Unpredictable max backedge-taken count. ";
6675 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6676 // ScalarEvolution's implementation of the print method is to print
6677 // out SCEV values of all instructions that are interesting. Doing
6678 // this potentially causes it to create new SCEV objects though,
6679 // which technically conflicts with the const qualifier. This isn't
6680 // observable from outside the class though, so casting away the
6681 // const isn't dangerous.
6682 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6684 OS << "Classifying expressions for: ";
6685 WriteAsOperand(OS, F, /*PrintType=*/false);
6687 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6688 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6691 const SCEV *SV = SE.getSCEV(&*I);
6694 const Loop *L = LI->getLoopFor((*I).getParent());
6696 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6703 OS << "\t\t" "Exits: ";
6704 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6705 if (!SE.isLoopInvariant(ExitValue, L)) {
6706 OS << "<<Unknown>>";
6715 OS << "Determining loop execution counts for: ";
6716 WriteAsOperand(OS, F, /*PrintType=*/false);
6718 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6719 PrintLoopInfo(OS, &SE, *I);
6722 ScalarEvolution::LoopDisposition
6723 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6724 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6725 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6726 Values.insert(std::make_pair(L, LoopVariant));
6728 return Pair.first->second;
6730 LoopDisposition D = computeLoopDisposition(S, L);
6731 return LoopDispositions[S][L] = D;
6734 ScalarEvolution::LoopDisposition
6735 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6736 switch (S->getSCEVType()) {
6738 return LoopInvariant;
6742 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6743 case scAddRecExpr: {
6744 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6746 // If L is the addrec's loop, it's computable.
6747 if (AR->getLoop() == L)
6748 return LoopComputable;
6750 // Add recurrences are never invariant in the function-body (null loop).
6754 // This recurrence is variant w.r.t. L if L contains AR's loop.
6755 if (L->contains(AR->getLoop()))
6758 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6759 if (AR->getLoop()->contains(L))
6760 return LoopInvariant;
6762 // This recurrence is variant w.r.t. L if any of its operands
6764 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6766 if (!isLoopInvariant(*I, L))
6769 // Otherwise it's loop-invariant.
6770 return LoopInvariant;
6776 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6777 bool HasVarying = false;
6778 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6780 LoopDisposition D = getLoopDisposition(*I, L);
6781 if (D == LoopVariant)
6783 if (D == LoopComputable)
6786 return HasVarying ? LoopComputable : LoopInvariant;
6789 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6790 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6791 if (LD == LoopVariant)
6793 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6794 if (RD == LoopVariant)
6796 return (LD == LoopInvariant && RD == LoopInvariant) ?
6797 LoopInvariant : LoopComputable;
6800 // All non-instruction values are loop invariant. All instructions are loop
6801 // invariant if they are not contained in the specified loop.
6802 // Instructions are never considered invariant in the function body
6803 // (null loop) because they are defined within the "loop".
6804 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6805 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6806 return LoopInvariant;
6807 case scCouldNotCompute:
6808 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6809 default: llvm_unreachable("Unknown SCEV kind!");
6813 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6814 return getLoopDisposition(S, L) == LoopInvariant;
6817 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6818 return getLoopDisposition(S, L) == LoopComputable;
6821 ScalarEvolution::BlockDisposition
6822 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6823 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6824 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6825 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6827 return Pair.first->second;
6829 BlockDisposition D = computeBlockDisposition(S, BB);
6830 return BlockDispositions[S][BB] = D;
6833 ScalarEvolution::BlockDisposition
6834 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6835 switch (S->getSCEVType()) {
6837 return ProperlyDominatesBlock;
6841 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6842 case scAddRecExpr: {
6843 // This uses a "dominates" query instead of "properly dominates" query
6844 // to test for proper dominance too, because the instruction which
6845 // produces the addrec's value is a PHI, and a PHI effectively properly
6846 // dominates its entire containing block.
6847 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6848 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6849 return DoesNotDominateBlock;
6851 // FALL THROUGH into SCEVNAryExpr handling.
6856 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6858 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6860 BlockDisposition D = getBlockDisposition(*I, BB);
6861 if (D == DoesNotDominateBlock)
6862 return DoesNotDominateBlock;
6863 if (D == DominatesBlock)
6866 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6869 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6870 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6871 BlockDisposition LD = getBlockDisposition(LHS, BB);
6872 if (LD == DoesNotDominateBlock)
6873 return DoesNotDominateBlock;
6874 BlockDisposition RD = getBlockDisposition(RHS, BB);
6875 if (RD == DoesNotDominateBlock)
6876 return DoesNotDominateBlock;
6877 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6878 ProperlyDominatesBlock : DominatesBlock;
6881 if (Instruction *I =
6882 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6883 if (I->getParent() == BB)
6884 return DominatesBlock;
6885 if (DT->properlyDominates(I->getParent(), BB))
6886 return ProperlyDominatesBlock;
6887 return DoesNotDominateBlock;
6889 return ProperlyDominatesBlock;
6890 case scCouldNotCompute:
6891 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6893 llvm_unreachable("Unknown SCEV kind!");
6897 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6898 return getBlockDisposition(S, BB) >= DominatesBlock;
6901 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6902 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6906 // Search for a SCEV expression node within an expression tree.
6907 // Implements SCEVTraversal::Visitor.
6912 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
6914 bool follow(const SCEV *S) {
6915 IsFound |= (S == Node);
6918 bool isDone() const { return IsFound; }
6922 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6923 SCEVSearch Search(Op);
6924 visitAll(S, Search);
6925 return Search.IsFound;
6928 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6929 ValuesAtScopes.erase(S);
6930 LoopDispositions.erase(S);
6931 BlockDispositions.erase(S);
6932 UnsignedRanges.erase(S);
6933 SignedRanges.erase(S);