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/Support/CommandLine.h"
78 #include "llvm/Support/ConstantRange.h"
79 #include "llvm/Support/Debug.h"
80 #include "llvm/Support/ErrorHandling.h"
81 #include "llvm/Support/GetElementPtrTypeIterator.h"
82 #include "llvm/Support/InstIterator.h"
83 #include "llvm/Support/MathExtras.h"
84 #include "llvm/Support/raw_ostream.h"
85 #include "llvm/ADT/Statistic.h"
86 #include "llvm/ADT/STLExtras.h"
87 #include "llvm/ADT/SmallPtrSet.h"
91 STATISTIC(NumArrayLenItCounts,
92 "Number of trip counts computed with array length");
93 STATISTIC(NumTripCountsComputed,
94 "Number of loops with predictable loop counts");
95 STATISTIC(NumTripCountsNotComputed,
96 "Number of loops without predictable loop counts");
97 STATISTIC(NumBruteForceTripCountsComputed,
98 "Number of loops with trip counts computed by force");
100 static cl::opt<unsigned>
101 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
102 cl::desc("Maximum number of iterations SCEV will "
103 "symbolically execute a constant "
107 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
108 "Scalar Evolution Analysis", false, true)
109 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
110 INITIALIZE_PASS_DEPENDENCY(DominatorTree)
111 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
112 "Scalar Evolution Analysis", false, true)
113 char ScalarEvolution::ID = 0;
115 //===----------------------------------------------------------------------===//
116 // SCEV class definitions
117 //===----------------------------------------------------------------------===//
119 //===----------------------------------------------------------------------===//
120 // Implementation of the SCEV class.
123 void SCEV::dump() const {
128 void SCEV::print(raw_ostream &OS) const {
129 switch (getSCEVType()) {
131 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false);
134 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
135 const SCEV *Op = Trunc->getOperand();
136 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
137 << *Trunc->getType() << ")";
141 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
142 const SCEV *Op = ZExt->getOperand();
143 OS << "(zext " << *Op->getType() << " " << *Op << " to "
144 << *ZExt->getType() << ")";
148 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
149 const SCEV *Op = SExt->getOperand();
150 OS << "(sext " << *Op->getType() << " " << *Op << " to "
151 << *SExt->getType() << ")";
155 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
156 OS << "{" << *AR->getOperand(0);
157 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
158 OS << ",+," << *AR->getOperand(i);
160 if (AR->getNoWrapFlags(FlagNUW))
162 if (AR->getNoWrapFlags(FlagNSW))
164 if (AR->getNoWrapFlags(FlagNW) &&
165 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
167 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false);
175 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
176 const char *OpStr = 0;
177 switch (NAry->getSCEVType()) {
178 case scAddExpr: OpStr = " + "; break;
179 case scMulExpr: OpStr = " * "; break;
180 case scUMaxExpr: OpStr = " umax "; break;
181 case scSMaxExpr: OpStr = " smax "; break;
184 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
187 if (llvm::next(I) != E)
194 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
195 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
199 const SCEVUnknown *U = cast<SCEVUnknown>(this);
201 if (U->isSizeOf(AllocTy)) {
202 OS << "sizeof(" << *AllocTy << ")";
205 if (U->isAlignOf(AllocTy)) {
206 OS << "alignof(" << *AllocTy << ")";
212 if (U->isOffsetOf(CTy, FieldNo)) {
213 OS << "offsetof(" << *CTy << ", ";
214 WriteAsOperand(OS, FieldNo, false);
219 // Otherwise just print it normally.
220 WriteAsOperand(OS, U->getValue(), false);
223 case scCouldNotCompute:
224 OS << "***COULDNOTCOMPUTE***";
228 llvm_unreachable("Unknown SCEV kind!");
231 const Type *SCEV::getType() const {
232 switch (getSCEVType()) {
234 return cast<SCEVConstant>(this)->getType();
238 return cast<SCEVCastExpr>(this)->getType();
243 return cast<SCEVNAryExpr>(this)->getType();
245 return cast<SCEVAddExpr>(this)->getType();
247 return cast<SCEVUDivExpr>(this)->getType();
249 return cast<SCEVUnknown>(this)->getType();
250 case scCouldNotCompute:
251 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
255 llvm_unreachable("Unknown SCEV kind!");
259 bool SCEV::isZero() const {
260 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
261 return SC->getValue()->isZero();
265 bool SCEV::isOne() const {
266 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
267 return SC->getValue()->isOne();
271 bool SCEV::isAllOnesValue() const {
272 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
273 return SC->getValue()->isAllOnesValue();
277 SCEVCouldNotCompute::SCEVCouldNotCompute() :
278 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
280 bool SCEVCouldNotCompute::classof(const SCEV *S) {
281 return S->getSCEVType() == scCouldNotCompute;
284 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
286 ID.AddInteger(scConstant);
289 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
290 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
291 UniqueSCEVs.InsertNode(S, IP);
295 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
296 return getConstant(ConstantInt::get(getContext(), Val));
300 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
301 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
302 return getConstant(ConstantInt::get(ITy, V, isSigned));
305 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
306 unsigned SCEVTy, const SCEV *op, const Type *ty)
307 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
309 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
310 const SCEV *op, const Type *ty)
311 : SCEVCastExpr(ID, scTruncate, op, ty) {
312 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
313 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
314 "Cannot truncate non-integer value!");
317 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
318 const SCEV *op, const Type *ty)
319 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
320 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
321 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
322 "Cannot zero extend non-integer value!");
325 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
326 const SCEV *op, const Type *ty)
327 : SCEVCastExpr(ID, scSignExtend, op, ty) {
328 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
329 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
330 "Cannot sign extend non-integer value!");
333 void SCEVUnknown::deleted() {
334 // Clear this SCEVUnknown from various maps.
335 SE->forgetMemoizedResults(this);
337 // Remove this SCEVUnknown from the uniquing map.
338 SE->UniqueSCEVs.RemoveNode(this);
340 // Release the value.
344 void SCEVUnknown::allUsesReplacedWith(Value *New) {
345 // Clear this SCEVUnknown from various maps.
346 SE->forgetMemoizedResults(this);
348 // Remove this SCEVUnknown from the uniquing map.
349 SE->UniqueSCEVs.RemoveNode(this);
351 // Update this SCEVUnknown to point to the new value. This is needed
352 // because there may still be outstanding SCEVs which still point to
357 bool SCEVUnknown::isSizeOf(const Type *&AllocTy) const {
358 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
359 if (VCE->getOpcode() == Instruction::PtrToInt)
360 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
361 if (CE->getOpcode() == Instruction::GetElementPtr &&
362 CE->getOperand(0)->isNullValue() &&
363 CE->getNumOperands() == 2)
364 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
366 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
374 bool SCEVUnknown::isAlignOf(const Type *&AllocTy) const {
375 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
376 if (VCE->getOpcode() == Instruction::PtrToInt)
377 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
378 if (CE->getOpcode() == Instruction::GetElementPtr &&
379 CE->getOperand(0)->isNullValue()) {
381 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
382 if (const StructType *STy = dyn_cast<StructType>(Ty))
383 if (!STy->isPacked() &&
384 CE->getNumOperands() == 3 &&
385 CE->getOperand(1)->isNullValue()) {
386 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
388 STy->getNumElements() == 2 &&
389 STy->getElementType(0)->isIntegerTy(1)) {
390 AllocTy = STy->getElementType(1);
399 bool SCEVUnknown::isOffsetOf(const Type *&CTy, Constant *&FieldNo) const {
400 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
401 if (VCE->getOpcode() == Instruction::PtrToInt)
402 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
403 if (CE->getOpcode() == Instruction::GetElementPtr &&
404 CE->getNumOperands() == 3 &&
405 CE->getOperand(0)->isNullValue() &&
406 CE->getOperand(1)->isNullValue()) {
408 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
409 // Ignore vector types here so that ScalarEvolutionExpander doesn't
410 // emit getelementptrs that index into vectors.
411 if (Ty->isStructTy() || Ty->isArrayTy()) {
413 FieldNo = CE->getOperand(2);
421 //===----------------------------------------------------------------------===//
423 //===----------------------------------------------------------------------===//
426 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
427 /// than the complexity of the RHS. This comparator is used to canonicalize
429 class SCEVComplexityCompare {
430 const LoopInfo *const LI;
432 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
434 // Return true or false if LHS is less than, or at least RHS, respectively.
435 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
436 return compare(LHS, RHS) < 0;
439 // Return negative, zero, or positive, if LHS is less than, equal to, or
440 // greater than RHS, respectively. A three-way result allows recursive
441 // comparisons to be more efficient.
442 int compare(const SCEV *LHS, const SCEV *RHS) const {
443 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
447 // Primarily, sort the SCEVs by their getSCEVType().
448 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
450 return (int)LType - (int)RType;
452 // Aside from the getSCEVType() ordering, the particular ordering
453 // isn't very important except that it's beneficial to be consistent,
454 // so that (a + b) and (b + a) don't end up as different expressions.
457 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
458 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
460 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
461 // not as complete as it could be.
462 const Value *LV = LU->getValue(), *RV = RU->getValue();
464 // Order pointer values after integer values. This helps SCEVExpander
466 bool LIsPointer = LV->getType()->isPointerTy(),
467 RIsPointer = RV->getType()->isPointerTy();
468 if (LIsPointer != RIsPointer)
469 return (int)LIsPointer - (int)RIsPointer;
471 // Compare getValueID values.
472 unsigned LID = LV->getValueID(),
473 RID = RV->getValueID();
475 return (int)LID - (int)RID;
477 // Sort arguments by their position.
478 if (const Argument *LA = dyn_cast<Argument>(LV)) {
479 const Argument *RA = cast<Argument>(RV);
480 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
481 return (int)LArgNo - (int)RArgNo;
484 // For instructions, compare their loop depth, and their operand
485 // count. This is pretty loose.
486 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
487 const Instruction *RInst = cast<Instruction>(RV);
489 // Compare loop depths.
490 const BasicBlock *LParent = LInst->getParent(),
491 *RParent = RInst->getParent();
492 if (LParent != RParent) {
493 unsigned LDepth = LI->getLoopDepth(LParent),
494 RDepth = LI->getLoopDepth(RParent);
495 if (LDepth != RDepth)
496 return (int)LDepth - (int)RDepth;
499 // Compare the number of operands.
500 unsigned LNumOps = LInst->getNumOperands(),
501 RNumOps = RInst->getNumOperands();
502 return (int)LNumOps - (int)RNumOps;
509 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
510 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
512 // Compare constant values.
513 const APInt &LA = LC->getValue()->getValue();
514 const APInt &RA = RC->getValue()->getValue();
515 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
516 if (LBitWidth != RBitWidth)
517 return (int)LBitWidth - (int)RBitWidth;
518 return LA.ult(RA) ? -1 : 1;
522 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
523 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
525 // Compare addrec loop depths.
526 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
527 if (LLoop != RLoop) {
528 unsigned LDepth = LLoop->getLoopDepth(),
529 RDepth = RLoop->getLoopDepth();
530 if (LDepth != RDepth)
531 return (int)LDepth - (int)RDepth;
534 // Addrec complexity grows with operand count.
535 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
536 if (LNumOps != RNumOps)
537 return (int)LNumOps - (int)RNumOps;
539 // Lexicographically compare.
540 for (unsigned i = 0; i != LNumOps; ++i) {
541 long X = compare(LA->getOperand(i), RA->getOperand(i));
553 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
554 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
556 // Lexicographically compare n-ary expressions.
557 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
558 for (unsigned i = 0; i != LNumOps; ++i) {
561 long X = compare(LC->getOperand(i), RC->getOperand(i));
565 return (int)LNumOps - (int)RNumOps;
569 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
570 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
572 // Lexicographically compare udiv expressions.
573 long X = compare(LC->getLHS(), RC->getLHS());
576 return compare(LC->getRHS(), RC->getRHS());
582 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
583 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
585 // Compare cast expressions by operand.
586 return compare(LC->getOperand(), RC->getOperand());
593 llvm_unreachable("Unknown SCEV kind!");
599 /// GroupByComplexity - Given a list of SCEV objects, order them by their
600 /// complexity, and group objects of the same complexity together by value.
601 /// When this routine is finished, we know that any duplicates in the vector are
602 /// consecutive and that complexity is monotonically increasing.
604 /// Note that we go take special precautions to ensure that we get deterministic
605 /// results from this routine. In other words, we don't want the results of
606 /// this to depend on where the addresses of various SCEV objects happened to
609 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
611 if (Ops.size() < 2) return; // Noop
612 if (Ops.size() == 2) {
613 // This is the common case, which also happens to be trivially simple.
615 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
616 if (SCEVComplexityCompare(LI)(RHS, LHS))
621 // Do the rough sort by complexity.
622 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
624 // Now that we are sorted by complexity, group elements of the same
625 // complexity. Note that this is, at worst, N^2, but the vector is likely to
626 // be extremely short in practice. Note that we take this approach because we
627 // do not want to depend on the addresses of the objects we are grouping.
628 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
629 const SCEV *S = Ops[i];
630 unsigned Complexity = S->getSCEVType();
632 // If there are any objects of the same complexity and same value as this
634 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
635 if (Ops[j] == S) { // Found a duplicate.
636 // Move it to immediately after i'th element.
637 std::swap(Ops[i+1], Ops[j]);
638 ++i; // no need to rescan it.
639 if (i == e-2) return; // Done!
647 //===----------------------------------------------------------------------===//
648 // Simple SCEV method implementations
649 //===----------------------------------------------------------------------===//
651 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
653 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
655 const Type* ResultTy) {
656 // Handle the simplest case efficiently.
658 return SE.getTruncateOrZeroExtend(It, ResultTy);
660 // We are using the following formula for BC(It, K):
662 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
664 // Suppose, W is the bitwidth of the return value. We must be prepared for
665 // overflow. Hence, we must assure that the result of our computation is
666 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
667 // safe in modular arithmetic.
669 // However, this code doesn't use exactly that formula; the formula it uses
670 // is something like the following, where T is the number of factors of 2 in
671 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
674 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
676 // This formula is trivially equivalent to the previous formula. However,
677 // this formula can be implemented much more efficiently. The trick is that
678 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
679 // arithmetic. To do exact division in modular arithmetic, all we have
680 // to do is multiply by the inverse. Therefore, this step can be done at
683 // The next issue is how to safely do the division by 2^T. The way this
684 // is done is by doing the multiplication step at a width of at least W + T
685 // bits. This way, the bottom W+T bits of the product are accurate. Then,
686 // when we perform the division by 2^T (which is equivalent to a right shift
687 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
688 // truncated out after the division by 2^T.
690 // In comparison to just directly using the first formula, this technique
691 // is much more efficient; using the first formula requires W * K bits,
692 // but this formula less than W + K bits. Also, the first formula requires
693 // a division step, whereas this formula only requires multiplies and shifts.
695 // It doesn't matter whether the subtraction step is done in the calculation
696 // width or the input iteration count's width; if the subtraction overflows,
697 // the result must be zero anyway. We prefer here to do it in the width of
698 // the induction variable because it helps a lot for certain cases; CodeGen
699 // isn't smart enough to ignore the overflow, which leads to much less
700 // efficient code if the width of the subtraction is wider than the native
703 // (It's possible to not widen at all by pulling out factors of 2 before
704 // the multiplication; for example, K=2 can be calculated as
705 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
706 // extra arithmetic, so it's not an obvious win, and it gets
707 // much more complicated for K > 3.)
709 // Protection from insane SCEVs; this bound is conservative,
710 // but it probably doesn't matter.
712 return SE.getCouldNotCompute();
714 unsigned W = SE.getTypeSizeInBits(ResultTy);
716 // Calculate K! / 2^T and T; we divide out the factors of two before
717 // multiplying for calculating K! / 2^T to avoid overflow.
718 // Other overflow doesn't matter because we only care about the bottom
719 // W bits of the result.
720 APInt OddFactorial(W, 1);
722 for (unsigned i = 3; i <= K; ++i) {
724 unsigned TwoFactors = Mult.countTrailingZeros();
726 Mult = Mult.lshr(TwoFactors);
727 OddFactorial *= Mult;
730 // We need at least W + T bits for the multiplication step
731 unsigned CalculationBits = W + T;
733 // Calculate 2^T, at width T+W.
734 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
736 // Calculate the multiplicative inverse of K! / 2^T;
737 // this multiplication factor will perform the exact division by
739 APInt Mod = APInt::getSignedMinValue(W+1);
740 APInt MultiplyFactor = OddFactorial.zext(W+1);
741 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
742 MultiplyFactor = MultiplyFactor.trunc(W);
744 // Calculate the product, at width T+W
745 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
747 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
748 for (unsigned i = 1; i != K; ++i) {
749 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
750 Dividend = SE.getMulExpr(Dividend,
751 SE.getTruncateOrZeroExtend(S, CalculationTy));
755 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
757 // Truncate the result, and divide by K! / 2^T.
759 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
760 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
763 /// evaluateAtIteration - Return the value of this chain of recurrences at
764 /// the specified iteration number. We can evaluate this recurrence by
765 /// multiplying each element in the chain by the binomial coefficient
766 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
768 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
770 /// where BC(It, k) stands for binomial coefficient.
772 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
773 ScalarEvolution &SE) const {
774 const SCEV *Result = getStart();
775 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
776 // The computation is correct in the face of overflow provided that the
777 // multiplication is performed _after_ the evaluation of the binomial
779 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
780 if (isa<SCEVCouldNotCompute>(Coeff))
783 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
788 //===----------------------------------------------------------------------===//
789 // SCEV Expression folder implementations
790 //===----------------------------------------------------------------------===//
792 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
794 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
795 "This is not a truncating conversion!");
796 assert(isSCEVable(Ty) &&
797 "This is not a conversion to a SCEVable type!");
798 Ty = getEffectiveSCEVType(Ty);
801 ID.AddInteger(scTruncate);
805 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
807 // Fold if the operand is constant.
808 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
810 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(),
811 getEffectiveSCEVType(Ty))));
813 // trunc(trunc(x)) --> trunc(x)
814 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
815 return getTruncateExpr(ST->getOperand(), Ty);
817 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
818 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
819 return getTruncateOrSignExtend(SS->getOperand(), Ty);
821 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
822 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
823 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
825 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
826 // eliminate all the truncates.
827 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
828 SmallVector<const SCEV *, 4> Operands;
829 bool hasTrunc = false;
830 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
831 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
832 hasTrunc = isa<SCEVTruncateExpr>(S);
833 Operands.push_back(S);
836 return getAddExpr(Operands);
837 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
840 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
841 // eliminate all the truncates.
842 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
843 SmallVector<const SCEV *, 4> Operands;
844 bool hasTrunc = false;
845 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
846 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
847 hasTrunc = isa<SCEVTruncateExpr>(S);
848 Operands.push_back(S);
851 return getMulExpr(Operands);
852 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
855 // If the input value is a chrec scev, truncate the chrec's operands.
856 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
857 SmallVector<const SCEV *, 4> Operands;
858 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
859 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
860 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
863 // As a special case, fold trunc(undef) to undef. We don't want to
864 // know too much about SCEVUnknowns, but this special case is handy
866 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
867 if (isa<UndefValue>(U->getValue()))
868 return getSCEV(UndefValue::get(Ty));
870 // The cast wasn't folded; create an explicit cast node. We can reuse
871 // the existing insert position since if we get here, we won't have
872 // made any changes which would invalidate it.
873 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
875 UniqueSCEVs.InsertNode(S, IP);
879 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
881 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
882 "This is not an extending conversion!");
883 assert(isSCEVable(Ty) &&
884 "This is not a conversion to a SCEVable type!");
885 Ty = getEffectiveSCEVType(Ty);
887 // Fold if the operand is constant.
888 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
890 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
891 getEffectiveSCEVType(Ty))));
893 // zext(zext(x)) --> zext(x)
894 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
895 return getZeroExtendExpr(SZ->getOperand(), Ty);
897 // Before doing any expensive analysis, check to see if we've already
898 // computed a SCEV for this Op and Ty.
900 ID.AddInteger(scZeroExtend);
904 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
906 // zext(trunc(x)) --> zext(x) or x or trunc(x)
907 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
908 // It's possible the bits taken off by the truncate were all zero bits. If
909 // so, we should be able to simplify this further.
910 const SCEV *X = ST->getOperand();
911 ConstantRange CR = getUnsignedRange(X);
912 unsigned TruncBits = getTypeSizeInBits(ST->getType());
913 unsigned NewBits = getTypeSizeInBits(Ty);
914 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
915 CR.zextOrTrunc(NewBits)))
916 return getTruncateOrZeroExtend(X, Ty);
919 // If the input value is a chrec scev, and we can prove that the value
920 // did not overflow the old, smaller, value, we can zero extend all of the
921 // operands (often constants). This allows analysis of something like
922 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
923 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
924 if (AR->isAffine()) {
925 const SCEV *Start = AR->getStart();
926 const SCEV *Step = AR->getStepRecurrence(*this);
927 unsigned BitWidth = getTypeSizeInBits(AR->getType());
928 const Loop *L = AR->getLoop();
930 // If we have special knowledge that this addrec won't overflow,
931 // we don't need to do any further analysis.
932 if (AR->getNoWrapFlags(SCEV::FlagNUW))
933 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
934 getZeroExtendExpr(Step, Ty),
935 L, AR->getNoWrapFlags());
937 // Check whether the backedge-taken count is SCEVCouldNotCompute.
938 // Note that this serves two purposes: It filters out loops that are
939 // simply not analyzable, and it covers the case where this code is
940 // being called from within backedge-taken count analysis, such that
941 // attempting to ask for the backedge-taken count would likely result
942 // in infinite recursion. In the later case, the analysis code will
943 // cope with a conservative value, and it will take care to purge
944 // that value once it has finished.
945 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
946 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
947 // Manually compute the final value for AR, checking for
950 // Check whether the backedge-taken count can be losslessly casted to
951 // the addrec's type. The count is always unsigned.
952 const SCEV *CastedMaxBECount =
953 getTruncateOrZeroExtend(MaxBECount, Start->getType());
954 const SCEV *RecastedMaxBECount =
955 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
956 if (MaxBECount == RecastedMaxBECount) {
957 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
958 // Check whether Start+Step*MaxBECount has no unsigned overflow.
959 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
960 const SCEV *Add = getAddExpr(Start, ZMul);
961 const SCEV *OperandExtendedAdd =
962 getAddExpr(getZeroExtendExpr(Start, WideTy),
963 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
964 getZeroExtendExpr(Step, WideTy)));
965 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
966 // Cache knowledge of AR NUW, which is propagated to this AddRec.
967 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
968 // Return the expression with the addrec on the outside.
969 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
970 getZeroExtendExpr(Step, Ty),
971 L, AR->getNoWrapFlags());
973 // Similar to above, only this time treat the step value as signed.
974 // This covers loops that count down.
975 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
976 Add = getAddExpr(Start, SMul);
978 getAddExpr(getZeroExtendExpr(Start, WideTy),
979 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
980 getSignExtendExpr(Step, WideTy)));
981 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
982 // Cache knowledge of AR NW, which is propagated to this AddRec.
983 // Negative step causes unsigned wrap, but it still can't self-wrap.
984 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
985 // Return the expression with the addrec on the outside.
986 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
987 getSignExtendExpr(Step, Ty),
988 L, AR->getNoWrapFlags());
992 // If the backedge is guarded by a comparison with the pre-inc value
993 // the addrec is safe. Also, if the entry is guarded by a comparison
994 // with the start value and the backedge is guarded by a comparison
995 // with the post-inc value, the addrec is safe.
996 if (isKnownPositive(Step)) {
997 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
998 getUnsignedRange(Step).getUnsignedMax());
999 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1000 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1001 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1002 AR->getPostIncExpr(*this), N))) {
1003 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1004 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1005 // Return the expression with the addrec on the outside.
1006 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1007 getZeroExtendExpr(Step, Ty),
1008 L, AR->getNoWrapFlags());
1010 } else if (isKnownNegative(Step)) {
1011 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1012 getSignedRange(Step).getSignedMin());
1013 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1014 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1015 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1016 AR->getPostIncExpr(*this), N))) {
1017 // Cache knowledge of AR NW, which is propagated to this AddRec.
1018 // Negative step causes unsigned wrap, but it still can't self-wrap.
1019 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1020 // Return the expression with the addrec on the outside.
1021 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1022 getSignExtendExpr(Step, Ty),
1023 L, AR->getNoWrapFlags());
1029 // The cast wasn't folded; create an explicit cast node.
1030 // Recompute the insert position, as it may have been invalidated.
1031 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1032 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1034 UniqueSCEVs.InsertNode(S, IP);
1038 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1040 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1041 "This is not an extending conversion!");
1042 assert(isSCEVable(Ty) &&
1043 "This is not a conversion to a SCEVable type!");
1044 Ty = getEffectiveSCEVType(Ty);
1046 // Fold if the operand is constant.
1047 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1049 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1050 getEffectiveSCEVType(Ty))));
1052 // sext(sext(x)) --> sext(x)
1053 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1054 return getSignExtendExpr(SS->getOperand(), Ty);
1056 // sext(zext(x)) --> zext(x)
1057 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1058 return getZeroExtendExpr(SZ->getOperand(), Ty);
1060 // Before doing any expensive analysis, check to see if we've already
1061 // computed a SCEV for this Op and Ty.
1062 FoldingSetNodeID ID;
1063 ID.AddInteger(scSignExtend);
1067 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1069 // If the input value is provably positive, build a zext instead.
1070 if (isKnownNonNegative(Op))
1071 return getZeroExtendExpr(Op, Ty);
1073 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1074 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1075 // It's possible the bits taken off by the truncate were all sign bits. If
1076 // so, we should be able to simplify this further.
1077 const SCEV *X = ST->getOperand();
1078 ConstantRange CR = getSignedRange(X);
1079 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1080 unsigned NewBits = getTypeSizeInBits(Ty);
1081 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1082 CR.sextOrTrunc(NewBits)))
1083 return getTruncateOrSignExtend(X, Ty);
1086 // If the input value is a chrec scev, and we can prove that the value
1087 // did not overflow the old, smaller, value, we can sign extend all of the
1088 // operands (often constants). This allows analysis of something like
1089 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1090 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1091 if (AR->isAffine()) {
1092 const SCEV *Start = AR->getStart();
1093 const SCEV *Step = AR->getStepRecurrence(*this);
1094 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1095 const Loop *L = AR->getLoop();
1097 // If we have special knowledge that this addrec won't overflow,
1098 // we don't need to do any further analysis.
1099 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1100 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1101 getSignExtendExpr(Step, Ty),
1104 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1105 // Note that this serves two purposes: It filters out loops that are
1106 // simply not analyzable, and it covers the case where this code is
1107 // being called from within backedge-taken count analysis, such that
1108 // attempting to ask for the backedge-taken count would likely result
1109 // in infinite recursion. In the later case, the analysis code will
1110 // cope with a conservative value, and it will take care to purge
1111 // that value once it has finished.
1112 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1113 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1114 // Manually compute the final value for AR, checking for
1117 // Check whether the backedge-taken count can be losslessly casted to
1118 // the addrec's type. The count is always unsigned.
1119 const SCEV *CastedMaxBECount =
1120 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1121 const SCEV *RecastedMaxBECount =
1122 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1123 if (MaxBECount == RecastedMaxBECount) {
1124 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1125 // Check whether Start+Step*MaxBECount has no signed overflow.
1126 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1127 const SCEV *Add = getAddExpr(Start, SMul);
1128 const SCEV *OperandExtendedAdd =
1129 getAddExpr(getSignExtendExpr(Start, WideTy),
1130 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1131 getSignExtendExpr(Step, WideTy)));
1132 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1133 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1134 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1135 // Return the expression with the addrec on the outside.
1136 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1137 getSignExtendExpr(Step, Ty),
1138 L, AR->getNoWrapFlags());
1140 // Similar to above, only this time treat the step value as unsigned.
1141 // This covers loops that count up with an unsigned step.
1142 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1143 Add = getAddExpr(Start, UMul);
1144 OperandExtendedAdd =
1145 getAddExpr(getSignExtendExpr(Start, WideTy),
1146 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1147 getZeroExtendExpr(Step, WideTy)));
1148 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1149 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1150 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1151 // Return the expression with the addrec on the outside.
1152 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1153 getZeroExtendExpr(Step, Ty),
1154 L, AR->getNoWrapFlags());
1158 // If the backedge is guarded by a comparison with the pre-inc value
1159 // the addrec is safe. Also, if the entry is guarded by a comparison
1160 // with the start value and the backedge is guarded by a comparison
1161 // with the post-inc value, the addrec is safe.
1162 if (isKnownPositive(Step)) {
1163 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
1164 getSignedRange(Step).getSignedMax());
1165 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
1166 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
1167 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
1168 AR->getPostIncExpr(*this), N))) {
1169 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1170 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1171 // Return the expression with the addrec on the outside.
1172 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1173 getSignExtendExpr(Step, Ty),
1174 L, AR->getNoWrapFlags());
1176 } else if (isKnownNegative(Step)) {
1177 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
1178 getSignedRange(Step).getSignedMin());
1179 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1180 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1181 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1182 AR->getPostIncExpr(*this), N))) {
1183 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1184 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1185 // Return the expression with the addrec on the outside.
1186 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1187 getSignExtendExpr(Step, Ty),
1188 L, AR->getNoWrapFlags());
1194 // The cast wasn't folded; create an explicit cast node.
1195 // Recompute the insert position, as it may have been invalidated.
1196 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1197 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1199 UniqueSCEVs.InsertNode(S, IP);
1203 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1204 /// unspecified bits out to the given type.
1206 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1208 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1209 "This is not an extending conversion!");
1210 assert(isSCEVable(Ty) &&
1211 "This is not a conversion to a SCEVable type!");
1212 Ty = getEffectiveSCEVType(Ty);
1214 // Sign-extend negative constants.
1215 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1216 if (SC->getValue()->getValue().isNegative())
1217 return getSignExtendExpr(Op, Ty);
1219 // Peel off a truncate cast.
1220 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1221 const SCEV *NewOp = T->getOperand();
1222 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1223 return getAnyExtendExpr(NewOp, Ty);
1224 return getTruncateOrNoop(NewOp, Ty);
1227 // Next try a zext cast. If the cast is folded, use it.
1228 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1229 if (!isa<SCEVZeroExtendExpr>(ZExt))
1232 // Next try a sext cast. If the cast is folded, use it.
1233 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1234 if (!isa<SCEVSignExtendExpr>(SExt))
1237 // Force the cast to be folded into the operands of an addrec.
1238 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1239 SmallVector<const SCEV *, 4> Ops;
1240 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1242 Ops.push_back(getAnyExtendExpr(*I, Ty));
1243 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1246 // As a special case, fold anyext(undef) to undef. We don't want to
1247 // know too much about SCEVUnknowns, but this special case is handy
1249 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1250 if (isa<UndefValue>(U->getValue()))
1251 return getSCEV(UndefValue::get(Ty));
1253 // If the expression is obviously signed, use the sext cast value.
1254 if (isa<SCEVSMaxExpr>(Op))
1257 // Absent any other information, use the zext cast value.
1261 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1262 /// a list of operands to be added under the given scale, update the given
1263 /// map. This is a helper function for getAddRecExpr. As an example of
1264 /// what it does, given a sequence of operands that would form an add
1265 /// expression like this:
1267 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1269 /// where A and B are constants, update the map with these values:
1271 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1273 /// and add 13 + A*B*29 to AccumulatedConstant.
1274 /// This will allow getAddRecExpr to produce this:
1276 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1278 /// This form often exposes folding opportunities that are hidden in
1279 /// the original operand list.
1281 /// Return true iff it appears that any interesting folding opportunities
1282 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1283 /// the common case where no interesting opportunities are present, and
1284 /// is also used as a check to avoid infinite recursion.
1287 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1288 SmallVector<const SCEV *, 8> &NewOps,
1289 APInt &AccumulatedConstant,
1290 const SCEV *const *Ops, size_t NumOperands,
1292 ScalarEvolution &SE) {
1293 bool Interesting = false;
1295 // Iterate over the add operands. They are sorted, with constants first.
1297 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1299 // Pull a buried constant out to the outside.
1300 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1302 AccumulatedConstant += Scale * C->getValue()->getValue();
1305 // Next comes everything else. We're especially interested in multiplies
1306 // here, but they're in the middle, so just visit the rest with one loop.
1307 for (; i != NumOperands; ++i) {
1308 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1309 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1311 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1312 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1313 // A multiplication of a constant with another add; recurse.
1314 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1316 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1317 Add->op_begin(), Add->getNumOperands(),
1320 // A multiplication of a constant with some other value. Update
1322 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1323 const SCEV *Key = SE.getMulExpr(MulOps);
1324 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1325 M.insert(std::make_pair(Key, NewScale));
1327 NewOps.push_back(Pair.first->first);
1329 Pair.first->second += NewScale;
1330 // The map already had an entry for this value, which may indicate
1331 // a folding opportunity.
1336 // An ordinary operand. Update the map.
1337 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1338 M.insert(std::make_pair(Ops[i], Scale));
1340 NewOps.push_back(Pair.first->first);
1342 Pair.first->second += Scale;
1343 // The map already had an entry for this value, which may indicate
1344 // a folding opportunity.
1354 struct APIntCompare {
1355 bool operator()(const APInt &LHS, const APInt &RHS) const {
1356 return LHS.ult(RHS);
1361 /// getAddExpr - Get a canonical add expression, or something simpler if
1363 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1364 SCEV::NoWrapFlags Flags) {
1365 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1366 "only nuw or nsw allowed");
1367 assert(!Ops.empty() && "Cannot get empty add!");
1368 if (Ops.size() == 1) return Ops[0];
1370 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1371 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1372 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1373 "SCEVAddExpr operand types don't match!");
1376 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1378 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1379 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1380 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1382 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1383 E = Ops.end(); I != E; ++I)
1384 if (!isKnownNonNegative(*I)) {
1388 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1391 // Sort by complexity, this groups all similar expression types together.
1392 GroupByComplexity(Ops, LI);
1394 // If there are any constants, fold them together.
1396 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1398 assert(Idx < Ops.size());
1399 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1400 // We found two constants, fold them together!
1401 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1402 RHSC->getValue()->getValue());
1403 if (Ops.size() == 2) return Ops[0];
1404 Ops.erase(Ops.begin()+1); // Erase the folded element
1405 LHSC = cast<SCEVConstant>(Ops[0]);
1408 // If we are left with a constant zero being added, strip it off.
1409 if (LHSC->getValue()->isZero()) {
1410 Ops.erase(Ops.begin());
1414 if (Ops.size() == 1) return Ops[0];
1417 // Okay, check to see if the same value occurs in the operand list more than
1418 // once. If so, merge them together into an multiply expression. Since we
1419 // sorted the list, these values are required to be adjacent.
1420 const Type *Ty = Ops[0]->getType();
1421 bool FoundMatch = false;
1422 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1423 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1424 // Scan ahead to count how many equal operands there are.
1426 while (i+Count != e && Ops[i+Count] == Ops[i])
1428 // Merge the values into a multiply.
1429 const SCEV *Scale = getConstant(Ty, Count);
1430 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1431 if (Ops.size() == Count)
1434 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1435 --i; e -= Count - 1;
1439 return getAddExpr(Ops, Flags);
1441 // Check for truncates. If all the operands are truncated from the same
1442 // type, see if factoring out the truncate would permit the result to be
1443 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1444 // if the contents of the resulting outer trunc fold to something simple.
1445 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1446 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1447 const Type *DstType = Trunc->getType();
1448 const Type *SrcType = Trunc->getOperand()->getType();
1449 SmallVector<const SCEV *, 8> LargeOps;
1451 // Check all the operands to see if they can be represented in the
1452 // source type of the truncate.
1453 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1454 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1455 if (T->getOperand()->getType() != SrcType) {
1459 LargeOps.push_back(T->getOperand());
1460 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1461 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1462 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1463 SmallVector<const SCEV *, 8> LargeMulOps;
1464 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1465 if (const SCEVTruncateExpr *T =
1466 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1467 if (T->getOperand()->getType() != SrcType) {
1471 LargeMulOps.push_back(T->getOperand());
1472 } else if (const SCEVConstant *C =
1473 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1474 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1481 LargeOps.push_back(getMulExpr(LargeMulOps));
1488 // Evaluate the expression in the larger type.
1489 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1490 // If it folds to something simple, use it. Otherwise, don't.
1491 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1492 return getTruncateExpr(Fold, DstType);
1496 // Skip past any other cast SCEVs.
1497 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1500 // If there are add operands they would be next.
1501 if (Idx < Ops.size()) {
1502 bool DeletedAdd = false;
1503 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1504 // If we have an add, expand the add operands onto the end of the operands
1506 Ops.erase(Ops.begin()+Idx);
1507 Ops.append(Add->op_begin(), Add->op_end());
1511 // If we deleted at least one add, we added operands to the end of the list,
1512 // and they are not necessarily sorted. Recurse to resort and resimplify
1513 // any operands we just acquired.
1515 return getAddExpr(Ops);
1518 // Skip over the add expression until we get to a multiply.
1519 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1522 // Check to see if there are any folding opportunities present with
1523 // operands multiplied by constant values.
1524 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1525 uint64_t BitWidth = getTypeSizeInBits(Ty);
1526 DenseMap<const SCEV *, APInt> M;
1527 SmallVector<const SCEV *, 8> NewOps;
1528 APInt AccumulatedConstant(BitWidth, 0);
1529 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1530 Ops.data(), Ops.size(),
1531 APInt(BitWidth, 1), *this)) {
1532 // Some interesting folding opportunity is present, so its worthwhile to
1533 // re-generate the operands list. Group the operands by constant scale,
1534 // to avoid multiplying by the same constant scale multiple times.
1535 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1536 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1537 E = NewOps.end(); I != E; ++I)
1538 MulOpLists[M.find(*I)->second].push_back(*I);
1539 // Re-generate the operands list.
1541 if (AccumulatedConstant != 0)
1542 Ops.push_back(getConstant(AccumulatedConstant));
1543 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1544 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1546 Ops.push_back(getMulExpr(getConstant(I->first),
1547 getAddExpr(I->second)));
1549 return getConstant(Ty, 0);
1550 if (Ops.size() == 1)
1552 return getAddExpr(Ops);
1556 // If we are adding something to a multiply expression, make sure the
1557 // something is not already an operand of the multiply. If so, merge it into
1559 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1560 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1561 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1562 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1563 if (isa<SCEVConstant>(MulOpSCEV))
1565 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1566 if (MulOpSCEV == Ops[AddOp]) {
1567 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1568 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1569 if (Mul->getNumOperands() != 2) {
1570 // If the multiply has more than two operands, we must get the
1572 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1573 Mul->op_begin()+MulOp);
1574 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1575 InnerMul = getMulExpr(MulOps);
1577 const SCEV *One = getConstant(Ty, 1);
1578 const SCEV *AddOne = getAddExpr(One, InnerMul);
1579 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1580 if (Ops.size() == 2) return OuterMul;
1582 Ops.erase(Ops.begin()+AddOp);
1583 Ops.erase(Ops.begin()+Idx-1);
1585 Ops.erase(Ops.begin()+Idx);
1586 Ops.erase(Ops.begin()+AddOp-1);
1588 Ops.push_back(OuterMul);
1589 return getAddExpr(Ops);
1592 // Check this multiply against other multiplies being added together.
1593 for (unsigned OtherMulIdx = Idx+1;
1594 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1596 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1597 // If MulOp occurs in OtherMul, we can fold the two multiplies
1599 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1600 OMulOp != e; ++OMulOp)
1601 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1602 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1603 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1604 if (Mul->getNumOperands() != 2) {
1605 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1606 Mul->op_begin()+MulOp);
1607 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1608 InnerMul1 = getMulExpr(MulOps);
1610 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1611 if (OtherMul->getNumOperands() != 2) {
1612 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1613 OtherMul->op_begin()+OMulOp);
1614 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1615 InnerMul2 = getMulExpr(MulOps);
1617 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1618 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1619 if (Ops.size() == 2) return OuterMul;
1620 Ops.erase(Ops.begin()+Idx);
1621 Ops.erase(Ops.begin()+OtherMulIdx-1);
1622 Ops.push_back(OuterMul);
1623 return getAddExpr(Ops);
1629 // If there are any add recurrences in the operands list, see if any other
1630 // added values are loop invariant. If so, we can fold them into the
1632 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1635 // Scan over all recurrences, trying to fold loop invariants into them.
1636 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1637 // Scan all of the other operands to this add and add them to the vector if
1638 // they are loop invariant w.r.t. the recurrence.
1639 SmallVector<const SCEV *, 8> LIOps;
1640 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1641 const Loop *AddRecLoop = AddRec->getLoop();
1642 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1643 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1644 LIOps.push_back(Ops[i]);
1645 Ops.erase(Ops.begin()+i);
1649 // If we found some loop invariants, fold them into the recurrence.
1650 if (!LIOps.empty()) {
1651 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1652 LIOps.push_back(AddRec->getStart());
1654 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1656 AddRecOps[0] = getAddExpr(LIOps);
1658 // Build the new addrec. Propagate the NUW and NSW flags if both the
1659 // outer add and the inner addrec are guaranteed to have no overflow.
1660 // Always propagate NW.
1661 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1662 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1664 // If all of the other operands were loop invariant, we are done.
1665 if (Ops.size() == 1) return NewRec;
1667 // Otherwise, add the folded AddRec by the non-liv parts.
1668 for (unsigned i = 0;; ++i)
1669 if (Ops[i] == AddRec) {
1673 return getAddExpr(Ops);
1676 // Okay, if there weren't any loop invariants to be folded, check to see if
1677 // there are multiple AddRec's with the same loop induction variable being
1678 // added together. If so, we can fold them.
1679 for (unsigned OtherIdx = Idx+1;
1680 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1682 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1683 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1684 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1686 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1688 if (const SCEVAddRecExpr *OtherAddRec =
1689 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1690 if (OtherAddRec->getLoop() == AddRecLoop) {
1691 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1693 if (i >= AddRecOps.size()) {
1694 AddRecOps.append(OtherAddRec->op_begin()+i,
1695 OtherAddRec->op_end());
1698 AddRecOps[i] = getAddExpr(AddRecOps[i],
1699 OtherAddRec->getOperand(i));
1701 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1703 // Step size has changed, so we cannot guarantee no self-wraparound.
1704 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1705 return getAddExpr(Ops);
1708 // Otherwise couldn't fold anything into this recurrence. Move onto the
1712 // Okay, it looks like we really DO need an add expr. Check to see if we
1713 // already have one, otherwise create a new one.
1714 FoldingSetNodeID ID;
1715 ID.AddInteger(scAddExpr);
1716 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1717 ID.AddPointer(Ops[i]);
1720 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1722 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1723 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1724 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1726 UniqueSCEVs.InsertNode(S, IP);
1728 S->setNoWrapFlags(Flags);
1732 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1734 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1735 SCEV::NoWrapFlags Flags) {
1736 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1737 "only nuw or nsw allowed");
1738 assert(!Ops.empty() && "Cannot get empty mul!");
1739 if (Ops.size() == 1) return Ops[0];
1741 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1742 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1743 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1744 "SCEVMulExpr operand types don't match!");
1747 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1749 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1750 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1751 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1753 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1754 E = Ops.end(); I != E; ++I)
1755 if (!isKnownNonNegative(*I)) {
1759 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1762 // Sort by complexity, this groups all similar expression types together.
1763 GroupByComplexity(Ops, LI);
1765 // If there are any constants, fold them together.
1767 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1769 // C1*(C2+V) -> C1*C2 + C1*V
1770 if (Ops.size() == 2)
1771 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1772 if (Add->getNumOperands() == 2 &&
1773 isa<SCEVConstant>(Add->getOperand(0)))
1774 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1775 getMulExpr(LHSC, Add->getOperand(1)));
1778 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1779 // We found two constants, fold them together!
1780 ConstantInt *Fold = ConstantInt::get(getContext(),
1781 LHSC->getValue()->getValue() *
1782 RHSC->getValue()->getValue());
1783 Ops[0] = getConstant(Fold);
1784 Ops.erase(Ops.begin()+1); // Erase the folded element
1785 if (Ops.size() == 1) return Ops[0];
1786 LHSC = cast<SCEVConstant>(Ops[0]);
1789 // If we are left with a constant one being multiplied, strip it off.
1790 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1791 Ops.erase(Ops.begin());
1793 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1794 // If we have a multiply of zero, it will always be zero.
1796 } else if (Ops[0]->isAllOnesValue()) {
1797 // If we have a mul by -1 of an add, try distributing the -1 among the
1799 if (Ops.size() == 2) {
1800 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1801 SmallVector<const SCEV *, 4> NewOps;
1802 bool AnyFolded = false;
1803 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1804 E = Add->op_end(); I != E; ++I) {
1805 const SCEV *Mul = getMulExpr(Ops[0], *I);
1806 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1807 NewOps.push_back(Mul);
1810 return getAddExpr(NewOps);
1812 else if (const SCEVAddRecExpr *
1813 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1814 // Negation preserves a recurrence's no self-wrap property.
1815 SmallVector<const SCEV *, 4> Operands;
1816 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1817 E = AddRec->op_end(); I != E; ++I) {
1818 Operands.push_back(getMulExpr(Ops[0], *I));
1820 return getAddRecExpr(Operands, AddRec->getLoop(),
1821 AddRec->getNoWrapFlags(SCEV::FlagNW));
1826 if (Ops.size() == 1)
1830 // Skip over the add expression until we get to a multiply.
1831 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1834 // If there are mul operands inline them all into this expression.
1835 if (Idx < Ops.size()) {
1836 bool DeletedMul = false;
1837 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1838 // If we have an mul, expand the mul operands onto the end of the operands
1840 Ops.erase(Ops.begin()+Idx);
1841 Ops.append(Mul->op_begin(), Mul->op_end());
1845 // If we deleted at least one mul, we added operands to the end of the list,
1846 // and they are not necessarily sorted. Recurse to resort and resimplify
1847 // any operands we just acquired.
1849 return getMulExpr(Ops);
1852 // If there are any add recurrences in the operands list, see if any other
1853 // added values are loop invariant. If so, we can fold them into the
1855 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1858 // Scan over all recurrences, trying to fold loop invariants into them.
1859 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1860 // Scan all of the other operands to this mul and add them to the vector if
1861 // they are loop invariant w.r.t. the recurrence.
1862 SmallVector<const SCEV *, 8> LIOps;
1863 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1864 const Loop *AddRecLoop = AddRec->getLoop();
1865 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1866 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1867 LIOps.push_back(Ops[i]);
1868 Ops.erase(Ops.begin()+i);
1872 // If we found some loop invariants, fold them into the recurrence.
1873 if (!LIOps.empty()) {
1874 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1875 SmallVector<const SCEV *, 4> NewOps;
1876 NewOps.reserve(AddRec->getNumOperands());
1877 const SCEV *Scale = getMulExpr(LIOps);
1878 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1879 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1881 // Build the new addrec. Propagate the NUW and NSW flags if both the
1882 // outer mul and the inner addrec are guaranteed to have no overflow.
1884 // No self-wrap cannot be guaranteed after changing the step size, but
1885 // will be inferred if either NUW or NSW is true.
1886 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
1887 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
1889 // If all of the other operands were loop invariant, we are done.
1890 if (Ops.size() == 1) return NewRec;
1892 // Otherwise, multiply the folded AddRec by the non-liv parts.
1893 for (unsigned i = 0;; ++i)
1894 if (Ops[i] == AddRec) {
1898 return getMulExpr(Ops);
1901 // Okay, if there weren't any loop invariants to be folded, check to see if
1902 // there are multiple AddRec's with the same loop induction variable being
1903 // multiplied together. If so, we can fold them.
1904 for (unsigned OtherIdx = Idx+1;
1905 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1907 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1908 // F * G, where F = {A,+,B}<L> and G = {C,+,D}<L> -->
1909 // {A*C,+,F*D + G*B + B*D}<L>
1910 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1912 if (const SCEVAddRecExpr *OtherAddRec =
1913 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1914 if (OtherAddRec->getLoop() == AddRecLoop) {
1915 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1916 const SCEV *NewStart = getMulExpr(F->getStart(), G->getStart());
1917 const SCEV *B = F->getStepRecurrence(*this);
1918 const SCEV *D = G->getStepRecurrence(*this);
1919 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1922 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1925 if (Ops.size() == 2) return NewAddRec;
1926 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
1927 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1929 return getMulExpr(Ops);
1932 // Otherwise couldn't fold anything into this recurrence. Move onto the
1936 // Okay, it looks like we really DO need an mul expr. Check to see if we
1937 // already have one, otherwise create a new one.
1938 FoldingSetNodeID ID;
1939 ID.AddInteger(scMulExpr);
1940 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1941 ID.AddPointer(Ops[i]);
1944 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1946 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1947 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1948 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
1950 UniqueSCEVs.InsertNode(S, IP);
1952 S->setNoWrapFlags(Flags);
1956 /// getUDivExpr - Get a canonical unsigned division expression, or something
1957 /// simpler if possible.
1958 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1960 assert(getEffectiveSCEVType(LHS->getType()) ==
1961 getEffectiveSCEVType(RHS->getType()) &&
1962 "SCEVUDivExpr operand types don't match!");
1964 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1965 if (RHSC->getValue()->equalsInt(1))
1966 return LHS; // X udiv 1 --> x
1967 // If the denominator is zero, the result of the udiv is undefined. Don't
1968 // try to analyze it, because the resolution chosen here may differ from
1969 // the resolution chosen in other parts of the compiler.
1970 if (!RHSC->getValue()->isZero()) {
1971 // Determine if the division can be folded into the operands of
1973 // TODO: Generalize this to non-constants by using known-bits information.
1974 const Type *Ty = LHS->getType();
1975 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1976 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
1977 // For non-power-of-two values, effectively round the value up to the
1978 // nearest power of two.
1979 if (!RHSC->getValue()->getValue().isPowerOf2())
1981 const IntegerType *ExtTy =
1982 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1983 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1984 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1985 if (const SCEVConstant *Step =
1986 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1987 if (!Step->getValue()->getValue()
1988 .urem(RHSC->getValue()->getValue()) &&
1989 getZeroExtendExpr(AR, ExtTy) ==
1990 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1991 getZeroExtendExpr(Step, ExtTy),
1992 AR->getLoop(), SCEV::FlagAnyWrap)) {
1993 SmallVector<const SCEV *, 4> Operands;
1994 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1995 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1996 return getAddRecExpr(Operands, AR->getLoop(),
1999 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2000 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2001 SmallVector<const SCEV *, 4> Operands;
2002 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2003 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2004 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2005 // Find an operand that's safely divisible.
2006 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2007 const SCEV *Op = M->getOperand(i);
2008 const SCEV *Div = getUDivExpr(Op, RHSC);
2009 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2010 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2013 return getMulExpr(Operands);
2017 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2018 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
2019 SmallVector<const SCEV *, 4> Operands;
2020 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2021 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2022 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2024 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2025 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2026 if (isa<SCEVUDivExpr>(Op) ||
2027 getMulExpr(Op, RHS) != A->getOperand(i))
2029 Operands.push_back(Op);
2031 if (Operands.size() == A->getNumOperands())
2032 return getAddExpr(Operands);
2036 // Fold if both operands are constant.
2037 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2038 Constant *LHSCV = LHSC->getValue();
2039 Constant *RHSCV = RHSC->getValue();
2040 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2046 FoldingSetNodeID ID;
2047 ID.AddInteger(scUDivExpr);
2051 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2052 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2054 UniqueSCEVs.InsertNode(S, IP);
2059 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2060 /// Simplify the expression as much as possible.
2061 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2063 SCEV::NoWrapFlags Flags) {
2064 SmallVector<const SCEV *, 4> Operands;
2065 Operands.push_back(Start);
2066 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2067 if (StepChrec->getLoop() == L) {
2068 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2069 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2072 Operands.push_back(Step);
2073 return getAddRecExpr(Operands, L, Flags);
2076 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2077 /// Simplify the expression as much as possible.
2079 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2080 const Loop *L, SCEV::NoWrapFlags Flags) {
2081 if (Operands.size() == 1) return Operands[0];
2083 const Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2084 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2085 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2086 "SCEVAddRecExpr operand types don't match!");
2087 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2088 assert(isLoopInvariant(Operands[i], L) &&
2089 "SCEVAddRecExpr operand is not loop-invariant!");
2092 if (Operands.back()->isZero()) {
2093 Operands.pop_back();
2094 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2097 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2098 // use that information to infer NUW and NSW flags. However, computing a
2099 // BE count requires calling getAddRecExpr, so we may not yet have a
2100 // meaningful BE count at this point (and if we don't, we'd be stuck
2101 // with a SCEVCouldNotCompute as the cached BE count).
2103 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2105 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2106 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2107 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2109 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2110 E = Operands.end(); I != E; ++I)
2111 if (!isKnownNonNegative(*I)) {
2115 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2118 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2119 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2120 const Loop *NestedLoop = NestedAR->getLoop();
2121 if (L->contains(NestedLoop) ?
2122 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2123 (!NestedLoop->contains(L) &&
2124 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2125 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2126 NestedAR->op_end());
2127 Operands[0] = NestedAR->getStart();
2128 // AddRecs require their operands be loop-invariant with respect to their
2129 // loops. Don't perform this transformation if it would break this
2131 bool AllInvariant = true;
2132 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2133 if (!isLoopInvariant(Operands[i], L)) {
2134 AllInvariant = false;
2138 // Create a recurrence for the outer loop with the same step size.
2140 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2141 // inner recurrence has the same property.
2142 SCEV::NoWrapFlags OuterFlags =
2143 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2145 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2146 AllInvariant = true;
2147 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2148 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2149 AllInvariant = false;
2153 // Ok, both add recurrences are valid after the transformation.
2155 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2156 // the outer recurrence has the same property.
2157 SCEV::NoWrapFlags InnerFlags =
2158 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2159 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2162 // Reset Operands to its original state.
2163 Operands[0] = NestedAR;
2167 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2168 // already have one, otherwise create a new one.
2169 FoldingSetNodeID ID;
2170 ID.AddInteger(scAddRecExpr);
2171 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2172 ID.AddPointer(Operands[i]);
2176 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2178 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2179 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2180 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2181 O, Operands.size(), L);
2182 UniqueSCEVs.InsertNode(S, IP);
2184 S->setNoWrapFlags(Flags);
2188 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2190 SmallVector<const SCEV *, 2> Ops;
2193 return getSMaxExpr(Ops);
2197 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2198 assert(!Ops.empty() && "Cannot get empty smax!");
2199 if (Ops.size() == 1) return Ops[0];
2201 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2202 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2203 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2204 "SCEVSMaxExpr operand types don't match!");
2207 // Sort by complexity, this groups all similar expression types together.
2208 GroupByComplexity(Ops, LI);
2210 // If there are any constants, fold them together.
2212 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2214 assert(Idx < Ops.size());
2215 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2216 // We found two constants, fold them together!
2217 ConstantInt *Fold = ConstantInt::get(getContext(),
2218 APIntOps::smax(LHSC->getValue()->getValue(),
2219 RHSC->getValue()->getValue()));
2220 Ops[0] = getConstant(Fold);
2221 Ops.erase(Ops.begin()+1); // Erase the folded element
2222 if (Ops.size() == 1) return Ops[0];
2223 LHSC = cast<SCEVConstant>(Ops[0]);
2226 // If we are left with a constant minimum-int, strip it off.
2227 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2228 Ops.erase(Ops.begin());
2230 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2231 // If we have an smax with a constant maximum-int, it will always be
2236 if (Ops.size() == 1) return Ops[0];
2239 // Find the first SMax
2240 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2243 // Check to see if one of the operands is an SMax. If so, expand its operands
2244 // onto our operand list, and recurse to simplify.
2245 if (Idx < Ops.size()) {
2246 bool DeletedSMax = false;
2247 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2248 Ops.erase(Ops.begin()+Idx);
2249 Ops.append(SMax->op_begin(), SMax->op_end());
2254 return getSMaxExpr(Ops);
2257 // Okay, check to see if the same value occurs in the operand list twice. If
2258 // so, delete one. Since we sorted the list, these values are required to
2260 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2261 // X smax Y smax Y --> X smax Y
2262 // X smax Y --> X, if X is always greater than Y
2263 if (Ops[i] == Ops[i+1] ||
2264 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2265 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2267 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2268 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2272 if (Ops.size() == 1) return Ops[0];
2274 assert(!Ops.empty() && "Reduced smax down to nothing!");
2276 // Okay, it looks like we really DO need an smax expr. Check to see if we
2277 // already have one, otherwise create a new one.
2278 FoldingSetNodeID ID;
2279 ID.AddInteger(scSMaxExpr);
2280 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2281 ID.AddPointer(Ops[i]);
2283 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2284 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2285 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2286 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2288 UniqueSCEVs.InsertNode(S, IP);
2292 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2294 SmallVector<const SCEV *, 2> Ops;
2297 return getUMaxExpr(Ops);
2301 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2302 assert(!Ops.empty() && "Cannot get empty umax!");
2303 if (Ops.size() == 1) return Ops[0];
2305 const Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2306 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2307 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2308 "SCEVUMaxExpr operand types don't match!");
2311 // Sort by complexity, this groups all similar expression types together.
2312 GroupByComplexity(Ops, LI);
2314 // If there are any constants, fold them together.
2316 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2318 assert(Idx < Ops.size());
2319 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2320 // We found two constants, fold them together!
2321 ConstantInt *Fold = ConstantInt::get(getContext(),
2322 APIntOps::umax(LHSC->getValue()->getValue(),
2323 RHSC->getValue()->getValue()));
2324 Ops[0] = getConstant(Fold);
2325 Ops.erase(Ops.begin()+1); // Erase the folded element
2326 if (Ops.size() == 1) return Ops[0];
2327 LHSC = cast<SCEVConstant>(Ops[0]);
2330 // If we are left with a constant minimum-int, strip it off.
2331 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2332 Ops.erase(Ops.begin());
2334 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2335 // If we have an umax with a constant maximum-int, it will always be
2340 if (Ops.size() == 1) return Ops[0];
2343 // Find the first UMax
2344 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2347 // Check to see if one of the operands is a UMax. If so, expand its operands
2348 // onto our operand list, and recurse to simplify.
2349 if (Idx < Ops.size()) {
2350 bool DeletedUMax = false;
2351 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2352 Ops.erase(Ops.begin()+Idx);
2353 Ops.append(UMax->op_begin(), UMax->op_end());
2358 return getUMaxExpr(Ops);
2361 // Okay, check to see if the same value occurs in the operand list twice. If
2362 // so, delete one. Since we sorted the list, these values are required to
2364 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2365 // X umax Y umax Y --> X umax Y
2366 // X umax Y --> X, if X is always greater than Y
2367 if (Ops[i] == Ops[i+1] ||
2368 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2369 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2371 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2372 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2376 if (Ops.size() == 1) return Ops[0];
2378 assert(!Ops.empty() && "Reduced umax down to nothing!");
2380 // Okay, it looks like we really DO need a umax expr. Check to see if we
2381 // already have one, otherwise create a new one.
2382 FoldingSetNodeID ID;
2383 ID.AddInteger(scUMaxExpr);
2384 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2385 ID.AddPointer(Ops[i]);
2387 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2388 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2389 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2390 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2392 UniqueSCEVs.InsertNode(S, IP);
2396 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2398 // ~smax(~x, ~y) == smin(x, y).
2399 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2402 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2404 // ~umax(~x, ~y) == umin(x, y)
2405 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2408 const SCEV *ScalarEvolution::getSizeOfExpr(const Type *AllocTy) {
2409 // If we have TargetData, we can bypass creating a target-independent
2410 // constant expression and then folding it back into a ConstantInt.
2411 // This is just a compile-time optimization.
2413 return getConstant(TD->getIntPtrType(getContext()),
2414 TD->getTypeAllocSize(AllocTy));
2416 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2417 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2418 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2420 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2421 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2424 const SCEV *ScalarEvolution::getAlignOfExpr(const Type *AllocTy) {
2425 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2426 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2427 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2429 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2430 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2433 const SCEV *ScalarEvolution::getOffsetOfExpr(const StructType *STy,
2435 // If we have TargetData, we can bypass creating a target-independent
2436 // constant expression and then folding it back into a ConstantInt.
2437 // This is just a compile-time optimization.
2439 return getConstant(TD->getIntPtrType(getContext()),
2440 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2442 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2443 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2444 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2446 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2447 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2450 const SCEV *ScalarEvolution::getOffsetOfExpr(const Type *CTy,
2451 Constant *FieldNo) {
2452 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2453 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2454 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2456 const Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2457 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2460 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2461 // Don't attempt to do anything other than create a SCEVUnknown object
2462 // here. createSCEV only calls getUnknown after checking for all other
2463 // interesting possibilities, and any other code that calls getUnknown
2464 // is doing so in order to hide a value from SCEV canonicalization.
2466 FoldingSetNodeID ID;
2467 ID.AddInteger(scUnknown);
2470 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2471 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2472 "Stale SCEVUnknown in uniquing map!");
2475 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2477 FirstUnknown = cast<SCEVUnknown>(S);
2478 UniqueSCEVs.InsertNode(S, IP);
2482 //===----------------------------------------------------------------------===//
2483 // Basic SCEV Analysis and PHI Idiom Recognition Code
2486 /// isSCEVable - Test if values of the given type are analyzable within
2487 /// the SCEV framework. This primarily includes integer types, and it
2488 /// can optionally include pointer types if the ScalarEvolution class
2489 /// has access to target-specific information.
2490 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2491 // Integers and pointers are always SCEVable.
2492 return Ty->isIntegerTy() || Ty->isPointerTy();
2495 /// getTypeSizeInBits - Return the size in bits of the specified type,
2496 /// for which isSCEVable must return true.
2497 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2498 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2500 // If we have a TargetData, use it!
2502 return TD->getTypeSizeInBits(Ty);
2504 // Integer types have fixed sizes.
2505 if (Ty->isIntegerTy())
2506 return Ty->getPrimitiveSizeInBits();
2508 // The only other support type is pointer. Without TargetData, conservatively
2509 // assume pointers are 64-bit.
2510 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2514 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2515 /// the given type and which represents how SCEV will treat the given
2516 /// type, for which isSCEVable must return true. For pointer types,
2517 /// this is the pointer-sized integer type.
2518 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2519 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2521 if (Ty->isIntegerTy())
2524 // The only other support type is pointer.
2525 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2526 if (TD) return TD->getIntPtrType(getContext());
2528 // Without TargetData, conservatively assume pointers are 64-bit.
2529 return Type::getInt64Ty(getContext());
2532 const SCEV *ScalarEvolution::getCouldNotCompute() {
2533 return &CouldNotCompute;
2536 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2537 /// expression and create a new one.
2538 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2539 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2541 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2542 if (I != ValueExprMap.end()) return I->second;
2543 const SCEV *S = createSCEV(V);
2545 // The process of creating a SCEV for V may have caused other SCEVs
2546 // to have been created, so it's necessary to insert the new entry
2547 // from scratch, rather than trying to remember the insert position
2549 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2553 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2555 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2556 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2558 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2560 const Type *Ty = V->getType();
2561 Ty = getEffectiveSCEVType(Ty);
2562 return getMulExpr(V,
2563 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2566 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2567 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2568 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2570 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2572 const Type *Ty = V->getType();
2573 Ty = getEffectiveSCEVType(Ty);
2574 const SCEV *AllOnes =
2575 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2576 return getMinusSCEV(AllOnes, V);
2579 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2580 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2581 SCEV::NoWrapFlags Flags) {
2582 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2584 // Fast path: X - X --> 0.
2586 return getConstant(LHS->getType(), 0);
2589 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2592 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2593 /// input value to the specified type. If the type must be extended, it is zero
2596 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, const Type *Ty) {
2597 const Type *SrcTy = V->getType();
2598 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2599 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2600 "Cannot truncate or zero extend with non-integer arguments!");
2601 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2602 return V; // No conversion
2603 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2604 return getTruncateExpr(V, Ty);
2605 return getZeroExtendExpr(V, Ty);
2608 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2609 /// input value to the specified type. If the type must be extended, it is sign
2612 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2614 const Type *SrcTy = V->getType();
2615 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2616 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2617 "Cannot truncate or zero extend with non-integer arguments!");
2618 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2619 return V; // No conversion
2620 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2621 return getTruncateExpr(V, Ty);
2622 return getSignExtendExpr(V, Ty);
2625 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2626 /// input value to the specified type. If the type must be extended, it is zero
2627 /// extended. The conversion must not be narrowing.
2629 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2630 const Type *SrcTy = V->getType();
2631 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2632 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2633 "Cannot noop or zero extend with non-integer arguments!");
2634 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2635 "getNoopOrZeroExtend cannot truncate!");
2636 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2637 return V; // No conversion
2638 return getZeroExtendExpr(V, Ty);
2641 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2642 /// input value to the specified type. If the type must be extended, it is sign
2643 /// extended. The conversion must not be narrowing.
2645 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2646 const Type *SrcTy = V->getType();
2647 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2648 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2649 "Cannot noop or sign extend with non-integer arguments!");
2650 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2651 "getNoopOrSignExtend cannot truncate!");
2652 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2653 return V; // No conversion
2654 return getSignExtendExpr(V, Ty);
2657 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2658 /// the input value to the specified type. If the type must be extended,
2659 /// it is extended with unspecified bits. The conversion must not be
2662 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2663 const Type *SrcTy = V->getType();
2664 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2665 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2666 "Cannot noop or any extend with non-integer arguments!");
2667 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2668 "getNoopOrAnyExtend cannot truncate!");
2669 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2670 return V; // No conversion
2671 return getAnyExtendExpr(V, Ty);
2674 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2675 /// input value to the specified type. The conversion must not be widening.
2677 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2678 const Type *SrcTy = V->getType();
2679 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2680 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2681 "Cannot truncate or noop with non-integer arguments!");
2682 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2683 "getTruncateOrNoop cannot extend!");
2684 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2685 return V; // No conversion
2686 return getTruncateExpr(V, Ty);
2689 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2690 /// the types using zero-extension, and then perform a umax operation
2692 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2694 const SCEV *PromotedLHS = LHS;
2695 const SCEV *PromotedRHS = RHS;
2697 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2698 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2700 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2702 return getUMaxExpr(PromotedLHS, PromotedRHS);
2705 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2706 /// the types using zero-extension, and then perform a umin operation
2708 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2710 const SCEV *PromotedLHS = LHS;
2711 const SCEV *PromotedRHS = RHS;
2713 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2714 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2716 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2718 return getUMinExpr(PromotedLHS, PromotedRHS);
2721 /// getPointerBase - Transitively follow the chain of pointer-type operands
2722 /// until reaching a SCEV that does not have a single pointer operand. This
2723 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2724 /// but corner cases do exist.
2725 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2726 // A pointer operand may evaluate to a nonpointer expression, such as null.
2727 if (!V->getType()->isPointerTy())
2730 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2731 return getPointerBase(Cast->getOperand());
2733 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2734 const SCEV *PtrOp = 0;
2735 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2737 if ((*I)->getType()->isPointerTy()) {
2738 // Cannot find the base of an expression with multiple pointer operands.
2746 return getPointerBase(PtrOp);
2751 /// PushDefUseChildren - Push users of the given Instruction
2752 /// onto the given Worklist.
2754 PushDefUseChildren(Instruction *I,
2755 SmallVectorImpl<Instruction *> &Worklist) {
2756 // Push the def-use children onto the Worklist stack.
2757 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2759 Worklist.push_back(cast<Instruction>(*UI));
2762 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2763 /// instructions that depend on the given instruction and removes them from
2764 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2767 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2768 SmallVector<Instruction *, 16> Worklist;
2769 PushDefUseChildren(PN, Worklist);
2771 SmallPtrSet<Instruction *, 8> Visited;
2773 while (!Worklist.empty()) {
2774 Instruction *I = Worklist.pop_back_val();
2775 if (!Visited.insert(I)) continue;
2777 ValueExprMapType::iterator It =
2778 ValueExprMap.find(static_cast<Value *>(I));
2779 if (It != ValueExprMap.end()) {
2780 const SCEV *Old = It->second;
2782 // Short-circuit the def-use traversal if the symbolic name
2783 // ceases to appear in expressions.
2784 if (Old != SymName && !hasOperand(Old, SymName))
2787 // SCEVUnknown for a PHI either means that it has an unrecognized
2788 // structure, it's a PHI that's in the progress of being computed
2789 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2790 // additional loop trip count information isn't going to change anything.
2791 // In the second case, createNodeForPHI will perform the necessary
2792 // updates on its own when it gets to that point. In the third, we do
2793 // want to forget the SCEVUnknown.
2794 if (!isa<PHINode>(I) ||
2795 !isa<SCEVUnknown>(Old) ||
2796 (I != PN && Old == SymName)) {
2797 forgetMemoizedResults(Old);
2798 ValueExprMap.erase(It);
2802 PushDefUseChildren(I, Worklist);
2806 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2807 /// a loop header, making it a potential recurrence, or it doesn't.
2809 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2810 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2811 if (L->getHeader() == PN->getParent()) {
2812 // The loop may have multiple entrances or multiple exits; we can analyze
2813 // this phi as an addrec if it has a unique entry value and a unique
2815 Value *BEValueV = 0, *StartValueV = 0;
2816 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2817 Value *V = PN->getIncomingValue(i);
2818 if (L->contains(PN->getIncomingBlock(i))) {
2821 } else if (BEValueV != V) {
2825 } else if (!StartValueV) {
2827 } else if (StartValueV != V) {
2832 if (BEValueV && StartValueV) {
2833 // While we are analyzing this PHI node, handle its value symbolically.
2834 const SCEV *SymbolicName = getUnknown(PN);
2835 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
2836 "PHI node already processed?");
2837 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2839 // Using this symbolic name for the PHI, analyze the value coming around
2841 const SCEV *BEValue = getSCEV(BEValueV);
2843 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2844 // has a special value for the first iteration of the loop.
2846 // If the value coming around the backedge is an add with the symbolic
2847 // value we just inserted, then we found a simple induction variable!
2848 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2849 // If there is a single occurrence of the symbolic value, replace it
2850 // with a recurrence.
2851 unsigned FoundIndex = Add->getNumOperands();
2852 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2853 if (Add->getOperand(i) == SymbolicName)
2854 if (FoundIndex == e) {
2859 if (FoundIndex != Add->getNumOperands()) {
2860 // Create an add with everything but the specified operand.
2861 SmallVector<const SCEV *, 8> Ops;
2862 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2863 if (i != FoundIndex)
2864 Ops.push_back(Add->getOperand(i));
2865 const SCEV *Accum = getAddExpr(Ops);
2867 // This is not a valid addrec if the step amount is varying each
2868 // loop iteration, but is not itself an addrec in this loop.
2869 if (isLoopInvariant(Accum, L) ||
2870 (isa<SCEVAddRecExpr>(Accum) &&
2871 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2872 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
2874 // If the increment doesn't overflow, then neither the addrec nor
2875 // the post-increment will overflow.
2876 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2877 if (OBO->hasNoUnsignedWrap())
2878 Flags = setFlags(Flags, SCEV::FlagNUW);
2879 if (OBO->hasNoSignedWrap())
2880 Flags = setFlags(Flags, SCEV::FlagNSW);
2881 } else if (const GEPOperator *GEP =
2882 dyn_cast<GEPOperator>(BEValueV)) {
2883 // If the increment is an inbounds GEP, then we know the address
2884 // space cannot be wrapped around. We cannot make any guarantee
2885 // about signed or unsigned overflow because pointers are
2886 // unsigned but we may have a negative index from the base
2888 if (GEP->isInBounds())
2889 Flags = setFlags(Flags, SCEV::FlagNW);
2892 const SCEV *StartVal = getSCEV(StartValueV);
2893 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
2895 // Since the no-wrap flags are on the increment, they apply to the
2896 // post-incremented value as well.
2897 if (isLoopInvariant(Accum, L))
2898 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2901 // Okay, for the entire analysis of this edge we assumed the PHI
2902 // to be symbolic. We now need to go back and purge all of the
2903 // entries for the scalars that use the symbolic expression.
2904 ForgetSymbolicName(PN, SymbolicName);
2905 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2909 } else if (const SCEVAddRecExpr *AddRec =
2910 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2911 // Otherwise, this could be a loop like this:
2912 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2913 // In this case, j = {1,+,1} and BEValue is j.
2914 // Because the other in-value of i (0) fits the evolution of BEValue
2915 // i really is an addrec evolution.
2916 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2917 const SCEV *StartVal = getSCEV(StartValueV);
2919 // If StartVal = j.start - j.stride, we can use StartVal as the
2920 // initial step of the addrec evolution.
2921 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2922 AddRec->getOperand(1))) {
2923 // FIXME: For constant StartVal, we should be able to infer
2925 const SCEV *PHISCEV =
2926 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
2929 // Okay, for the entire analysis of this edge we assumed the PHI
2930 // to be symbolic. We now need to go back and purge all of the
2931 // entries for the scalars that use the symbolic expression.
2932 ForgetSymbolicName(PN, SymbolicName);
2933 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
2941 // If the PHI has a single incoming value, follow that value, unless the
2942 // PHI's incoming blocks are in a different loop, in which case doing so
2943 // risks breaking LCSSA form. Instcombine would normally zap these, but
2944 // it doesn't have DominatorTree information, so it may miss cases.
2945 if (Value *V = SimplifyInstruction(PN, TD, DT))
2946 if (LI->replacementPreservesLCSSAForm(PN, V))
2949 // If it's not a loop phi, we can't handle it yet.
2950 return getUnknown(PN);
2953 /// createNodeForGEP - Expand GEP instructions into add and multiply
2954 /// operations. This allows them to be analyzed by regular SCEV code.
2956 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
2958 // Don't blindly transfer the inbounds flag from the GEP instruction to the
2959 // Add expression, because the Instruction may be guarded by control flow
2960 // and the no-overflow bits may not be valid for the expression in any
2962 bool isInBounds = GEP->isInBounds();
2964 const Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
2965 Value *Base = GEP->getOperand(0);
2966 // Don't attempt to analyze GEPs over unsized objects.
2967 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2968 return getUnknown(GEP);
2969 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
2970 gep_type_iterator GTI = gep_type_begin(GEP);
2971 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
2975 // Compute the (potentially symbolic) offset in bytes for this index.
2976 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2977 // For a struct, add the member offset.
2978 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2979 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
2981 // Add the field offset to the running total offset.
2982 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
2984 // For an array, add the element offset, explicitly scaled.
2985 const SCEV *ElementSize = getSizeOfExpr(*GTI);
2986 const SCEV *IndexS = getSCEV(Index);
2987 // Getelementptr indices are signed.
2988 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
2990 // Multiply the index by the element size to compute the element offset.
2991 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
2992 isInBounds ? SCEV::FlagNSW :
2995 // Add the element offset to the running total offset.
2996 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3000 // Get the SCEV for the GEP base.
3001 const SCEV *BaseS = getSCEV(Base);
3003 // Add the total offset from all the GEP indices to the base.
3004 return getAddExpr(BaseS, TotalOffset,
3005 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3008 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3009 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3010 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3011 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3013 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3014 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3015 return C->getValue()->getValue().countTrailingZeros();
3017 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3018 return std::min(GetMinTrailingZeros(T->getOperand()),
3019 (uint32_t)getTypeSizeInBits(T->getType()));
3021 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3022 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3023 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3024 getTypeSizeInBits(E->getType()) : OpRes;
3027 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3028 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3029 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3030 getTypeSizeInBits(E->getType()) : OpRes;
3033 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3034 // The result is the min of all operands results.
3035 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3036 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3037 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3041 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3042 // The result is the sum of all operands results.
3043 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3044 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3045 for (unsigned i = 1, e = M->getNumOperands();
3046 SumOpRes != BitWidth && i != e; ++i)
3047 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3052 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3053 // The result is the min of all operands results.
3054 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3055 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3056 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3060 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3061 // The result is the min of all operands results.
3062 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3063 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3064 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3068 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3069 // The result is the min of all operands results.
3070 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3071 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3072 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3076 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3077 // For a SCEVUnknown, ask ValueTracking.
3078 unsigned BitWidth = getTypeSizeInBits(U->getType());
3079 APInt Mask = APInt::getAllOnesValue(BitWidth);
3080 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3081 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
3082 return Zeros.countTrailingOnes();
3089 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3092 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3093 // See if we've computed this range already.
3094 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3095 if (I != UnsignedRanges.end())
3098 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3099 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3101 unsigned BitWidth = getTypeSizeInBits(S->getType());
3102 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3104 // If the value has known zeros, the maximum unsigned value will have those
3105 // known zeros as well.
3106 uint32_t TZ = GetMinTrailingZeros(S);
3108 ConservativeResult =
3109 ConstantRange(APInt::getMinValue(BitWidth),
3110 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3112 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3113 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3114 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3115 X = X.add(getUnsignedRange(Add->getOperand(i)));
3116 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3119 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3120 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3121 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3122 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3123 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3126 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3127 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3128 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3129 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3130 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3133 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3134 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3135 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3136 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3137 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3140 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3141 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3142 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3143 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3146 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3147 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3148 return setUnsignedRange(ZExt,
3149 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3152 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3153 ConstantRange X = getUnsignedRange(SExt->getOperand());
3154 return setUnsignedRange(SExt,
3155 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3158 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3159 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3160 return setUnsignedRange(Trunc,
3161 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3164 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3165 // If there's no unsigned wrap, the value will never be less than its
3167 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3168 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3169 if (!C->getValue()->isZero())
3170 ConservativeResult =
3171 ConservativeResult.intersectWith(
3172 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3174 // TODO: non-affine addrec
3175 if (AddRec->isAffine()) {
3176 const Type *Ty = AddRec->getType();
3177 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3178 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3179 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3180 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3182 const SCEV *Start = AddRec->getStart();
3183 const SCEV *Step = AddRec->getStepRecurrence(*this);
3185 ConstantRange StartRange = getUnsignedRange(Start);
3186 ConstantRange StepRange = getSignedRange(Step);
3187 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3188 ConstantRange EndRange =
3189 StartRange.add(MaxBECountRange.multiply(StepRange));
3191 // Check for overflow. This must be done with ConstantRange arithmetic
3192 // because we could be called from within the ScalarEvolution overflow
3194 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3195 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3196 ConstantRange ExtMaxBECountRange =
3197 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3198 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3199 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3201 return setUnsignedRange(AddRec, ConservativeResult);
3203 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3204 EndRange.getUnsignedMin());
3205 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3206 EndRange.getUnsignedMax());
3207 if (Min.isMinValue() && Max.isMaxValue())
3208 return setUnsignedRange(AddRec, ConservativeResult);
3209 return setUnsignedRange(AddRec,
3210 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3214 return setUnsignedRange(AddRec, ConservativeResult);
3217 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3218 // For a SCEVUnknown, ask ValueTracking.
3219 APInt Mask = APInt::getAllOnesValue(BitWidth);
3220 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3221 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3222 if (Ones == ~Zeros + 1)
3223 return setUnsignedRange(U, ConservativeResult);
3224 return setUnsignedRange(U,
3225 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3228 return setUnsignedRange(S, ConservativeResult);
3231 /// getSignedRange - Determine the signed range for a particular SCEV.
3234 ScalarEvolution::getSignedRange(const SCEV *S) {
3235 // See if we've computed this range already.
3236 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3237 if (I != SignedRanges.end())
3240 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3241 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3243 unsigned BitWidth = getTypeSizeInBits(S->getType());
3244 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3246 // If the value has known zeros, the maximum signed value will have those
3247 // known zeros as well.
3248 uint32_t TZ = GetMinTrailingZeros(S);
3250 ConservativeResult =
3251 ConstantRange(APInt::getSignedMinValue(BitWidth),
3252 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3254 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3255 ConstantRange X = getSignedRange(Add->getOperand(0));
3256 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3257 X = X.add(getSignedRange(Add->getOperand(i)));
3258 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3261 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3262 ConstantRange X = getSignedRange(Mul->getOperand(0));
3263 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3264 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3265 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3268 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3269 ConstantRange X = getSignedRange(SMax->getOperand(0));
3270 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3271 X = X.smax(getSignedRange(SMax->getOperand(i)));
3272 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3275 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3276 ConstantRange X = getSignedRange(UMax->getOperand(0));
3277 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3278 X = X.umax(getSignedRange(UMax->getOperand(i)));
3279 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3282 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3283 ConstantRange X = getSignedRange(UDiv->getLHS());
3284 ConstantRange Y = getSignedRange(UDiv->getRHS());
3285 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3288 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3289 ConstantRange X = getSignedRange(ZExt->getOperand());
3290 return setSignedRange(ZExt,
3291 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3294 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3295 ConstantRange X = getSignedRange(SExt->getOperand());
3296 return setSignedRange(SExt,
3297 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3300 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3301 ConstantRange X = getSignedRange(Trunc->getOperand());
3302 return setSignedRange(Trunc,
3303 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3306 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3307 // If there's no signed wrap, and all the operands have the same sign or
3308 // zero, the value won't ever change sign.
3309 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3310 bool AllNonNeg = true;
3311 bool AllNonPos = true;
3312 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3313 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3314 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3317 ConservativeResult = ConservativeResult.intersectWith(
3318 ConstantRange(APInt(BitWidth, 0),
3319 APInt::getSignedMinValue(BitWidth)));
3321 ConservativeResult = ConservativeResult.intersectWith(
3322 ConstantRange(APInt::getSignedMinValue(BitWidth),
3323 APInt(BitWidth, 1)));
3326 // TODO: non-affine addrec
3327 if (AddRec->isAffine()) {
3328 const Type *Ty = AddRec->getType();
3329 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3330 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3331 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3332 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3334 const SCEV *Start = AddRec->getStart();
3335 const SCEV *Step = AddRec->getStepRecurrence(*this);
3337 ConstantRange StartRange = getSignedRange(Start);
3338 ConstantRange StepRange = getSignedRange(Step);
3339 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3340 ConstantRange EndRange =
3341 StartRange.add(MaxBECountRange.multiply(StepRange));
3343 // Check for overflow. This must be done with ConstantRange arithmetic
3344 // because we could be called from within the ScalarEvolution overflow
3346 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3347 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3348 ConstantRange ExtMaxBECountRange =
3349 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3350 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3351 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3353 return setSignedRange(AddRec, ConservativeResult);
3355 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3356 EndRange.getSignedMin());
3357 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3358 EndRange.getSignedMax());
3359 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3360 return setSignedRange(AddRec, ConservativeResult);
3361 return setSignedRange(AddRec,
3362 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3366 return setSignedRange(AddRec, ConservativeResult);
3369 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3370 // For a SCEVUnknown, ask ValueTracking.
3371 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3372 return setSignedRange(U, ConservativeResult);
3373 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3375 return setSignedRange(U, ConservativeResult);
3376 return setSignedRange(U, ConservativeResult.intersectWith(
3377 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3378 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3381 return setSignedRange(S, ConservativeResult);
3384 /// createSCEV - We know that there is no SCEV for the specified value.
3385 /// Analyze the expression.
3387 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3388 if (!isSCEVable(V->getType()))
3389 return getUnknown(V);
3391 unsigned Opcode = Instruction::UserOp1;
3392 if (Instruction *I = dyn_cast<Instruction>(V)) {
3393 Opcode = I->getOpcode();
3395 // Don't attempt to analyze instructions in blocks that aren't
3396 // reachable. Such instructions don't matter, and they aren't required
3397 // to obey basic rules for definitions dominating uses which this
3398 // analysis depends on.
3399 if (!DT->isReachableFromEntry(I->getParent()))
3400 return getUnknown(V);
3401 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3402 Opcode = CE->getOpcode();
3403 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3404 return getConstant(CI);
3405 else if (isa<ConstantPointerNull>(V))
3406 return getConstant(V->getType(), 0);
3407 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3408 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3410 return getUnknown(V);
3412 Operator *U = cast<Operator>(V);
3414 case Instruction::Add: {
3415 // The simple thing to do would be to just call getSCEV on both operands
3416 // and call getAddExpr with the result. However if we're looking at a
3417 // bunch of things all added together, this can be quite inefficient,
3418 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3419 // Instead, gather up all the operands and make a single getAddExpr call.
3420 // LLVM IR canonical form means we need only traverse the left operands.
3421 SmallVector<const SCEV *, 4> AddOps;
3422 AddOps.push_back(getSCEV(U->getOperand(1)));
3423 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3424 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3425 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3427 U = cast<Operator>(Op);
3428 const SCEV *Op1 = getSCEV(U->getOperand(1));
3429 if (Opcode == Instruction::Sub)
3430 AddOps.push_back(getNegativeSCEV(Op1));
3432 AddOps.push_back(Op1);
3434 AddOps.push_back(getSCEV(U->getOperand(0)));
3435 return getAddExpr(AddOps);
3437 case Instruction::Mul: {
3438 // See the Add code above.
3439 SmallVector<const SCEV *, 4> MulOps;
3440 MulOps.push_back(getSCEV(U->getOperand(1)));
3441 for (Value *Op = U->getOperand(0);
3442 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3443 Op = U->getOperand(0)) {
3444 U = cast<Operator>(Op);
3445 MulOps.push_back(getSCEV(U->getOperand(1)));
3447 MulOps.push_back(getSCEV(U->getOperand(0)));
3448 return getMulExpr(MulOps);
3450 case Instruction::UDiv:
3451 return getUDivExpr(getSCEV(U->getOperand(0)),
3452 getSCEV(U->getOperand(1)));
3453 case Instruction::Sub:
3454 return getMinusSCEV(getSCEV(U->getOperand(0)),
3455 getSCEV(U->getOperand(1)));
3456 case Instruction::And:
3457 // For an expression like x&255 that merely masks off the high bits,
3458 // use zext(trunc(x)) as the SCEV expression.
3459 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3460 if (CI->isNullValue())
3461 return getSCEV(U->getOperand(1));
3462 if (CI->isAllOnesValue())
3463 return getSCEV(U->getOperand(0));
3464 const APInt &A = CI->getValue();
3466 // Instcombine's ShrinkDemandedConstant may strip bits out of
3467 // constants, obscuring what would otherwise be a low-bits mask.
3468 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3469 // knew about to reconstruct a low-bits mask value.
3470 unsigned LZ = A.countLeadingZeros();
3471 unsigned BitWidth = A.getBitWidth();
3472 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3473 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3474 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3476 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3478 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3480 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3481 IntegerType::get(getContext(), BitWidth - LZ)),
3486 case Instruction::Or:
3487 // If the RHS of the Or is a constant, we may have something like:
3488 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3489 // optimizations will transparently handle this case.
3491 // In order for this transformation to be safe, the LHS must be of the
3492 // form X*(2^n) and the Or constant must be less than 2^n.
3493 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3494 const SCEV *LHS = getSCEV(U->getOperand(0));
3495 const APInt &CIVal = CI->getValue();
3496 if (GetMinTrailingZeros(LHS) >=
3497 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3498 // Build a plain add SCEV.
3499 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3500 // If the LHS of the add was an addrec and it has no-wrap flags,
3501 // transfer the no-wrap flags, since an or won't introduce a wrap.
3502 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3503 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3504 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3505 OldAR->getNoWrapFlags());
3511 case Instruction::Xor:
3512 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3513 // If the RHS of the xor is a signbit, then this is just an add.
3514 // Instcombine turns add of signbit into xor as a strength reduction step.
3515 if (CI->getValue().isSignBit())
3516 return getAddExpr(getSCEV(U->getOperand(0)),
3517 getSCEV(U->getOperand(1)));
3519 // If the RHS of xor is -1, then this is a not operation.
3520 if (CI->isAllOnesValue())
3521 return getNotSCEV(getSCEV(U->getOperand(0)));
3523 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3524 // This is a variant of the check for xor with -1, and it handles
3525 // the case where instcombine has trimmed non-demanded bits out
3526 // of an xor with -1.
3527 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3528 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3529 if (BO->getOpcode() == Instruction::And &&
3530 LCI->getValue() == CI->getValue())
3531 if (const SCEVZeroExtendExpr *Z =
3532 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3533 const Type *UTy = U->getType();
3534 const SCEV *Z0 = Z->getOperand();
3535 const Type *Z0Ty = Z0->getType();
3536 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3538 // If C is a low-bits mask, the zero extend is serving to
3539 // mask off the high bits. Complement the operand and
3540 // re-apply the zext.
3541 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3542 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3544 // If C is a single bit, it may be in the sign-bit position
3545 // before the zero-extend. In this case, represent the xor
3546 // using an add, which is equivalent, and re-apply the zext.
3547 APInt Trunc = CI->getValue().trunc(Z0TySize);
3548 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3550 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3556 case Instruction::Shl:
3557 // Turn shift left of a constant amount into a multiply.
3558 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3559 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3561 // If the shift count is not less than the bitwidth, the result of
3562 // the shift is undefined. Don't try to analyze it, because the
3563 // resolution chosen here may differ from the resolution chosen in
3564 // other parts of the compiler.
3565 if (SA->getValue().uge(BitWidth))
3568 Constant *X = ConstantInt::get(getContext(),
3569 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3570 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3574 case Instruction::LShr:
3575 // Turn logical shift right of a constant into a unsigned divide.
3576 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3577 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3579 // If the shift count is not less than the bitwidth, the result of
3580 // the shift is undefined. Don't try to analyze it, because the
3581 // resolution chosen here may differ from the resolution chosen in
3582 // other parts of the compiler.
3583 if (SA->getValue().uge(BitWidth))
3586 Constant *X = ConstantInt::get(getContext(),
3587 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3588 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3592 case Instruction::AShr:
3593 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3594 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3595 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3596 if (L->getOpcode() == Instruction::Shl &&
3597 L->getOperand(1) == U->getOperand(1)) {
3598 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3600 // If the shift count is not less than the bitwidth, the result of
3601 // the shift is undefined. Don't try to analyze it, because the
3602 // resolution chosen here may differ from the resolution chosen in
3603 // other parts of the compiler.
3604 if (CI->getValue().uge(BitWidth))
3607 uint64_t Amt = BitWidth - CI->getZExtValue();
3608 if (Amt == BitWidth)
3609 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3611 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3612 IntegerType::get(getContext(),
3618 case Instruction::Trunc:
3619 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3621 case Instruction::ZExt:
3622 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3624 case Instruction::SExt:
3625 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3627 case Instruction::BitCast:
3628 // BitCasts are no-op casts so we just eliminate the cast.
3629 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3630 return getSCEV(U->getOperand(0));
3633 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3634 // lead to pointer expressions which cannot safely be expanded to GEPs,
3635 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3636 // simplifying integer expressions.
3638 case Instruction::GetElementPtr:
3639 return createNodeForGEP(cast<GEPOperator>(U));
3641 case Instruction::PHI:
3642 return createNodeForPHI(cast<PHINode>(U));
3644 case Instruction::Select:
3645 // This could be a smax or umax that was lowered earlier.
3646 // Try to recover it.
3647 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3648 Value *LHS = ICI->getOperand(0);
3649 Value *RHS = ICI->getOperand(1);
3650 switch (ICI->getPredicate()) {
3651 case ICmpInst::ICMP_SLT:
3652 case ICmpInst::ICMP_SLE:
3653 std::swap(LHS, RHS);
3655 case ICmpInst::ICMP_SGT:
3656 case ICmpInst::ICMP_SGE:
3657 // a >s b ? a+x : b+x -> smax(a, b)+x
3658 // a >s b ? b+x : a+x -> smin(a, b)+x
3659 if (LHS->getType() == U->getType()) {
3660 const SCEV *LS = getSCEV(LHS);
3661 const SCEV *RS = getSCEV(RHS);
3662 const SCEV *LA = getSCEV(U->getOperand(1));
3663 const SCEV *RA = getSCEV(U->getOperand(2));
3664 const SCEV *LDiff = getMinusSCEV(LA, LS);
3665 const SCEV *RDiff = getMinusSCEV(RA, RS);
3667 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3668 LDiff = getMinusSCEV(LA, RS);
3669 RDiff = getMinusSCEV(RA, LS);
3671 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3674 case ICmpInst::ICMP_ULT:
3675 case ICmpInst::ICMP_ULE:
3676 std::swap(LHS, RHS);
3678 case ICmpInst::ICMP_UGT:
3679 case ICmpInst::ICMP_UGE:
3680 // a >u b ? a+x : b+x -> umax(a, b)+x
3681 // a >u b ? b+x : a+x -> umin(a, b)+x
3682 if (LHS->getType() == U->getType()) {
3683 const SCEV *LS = getSCEV(LHS);
3684 const SCEV *RS = getSCEV(RHS);
3685 const SCEV *LA = getSCEV(U->getOperand(1));
3686 const SCEV *RA = getSCEV(U->getOperand(2));
3687 const SCEV *LDiff = getMinusSCEV(LA, LS);
3688 const SCEV *RDiff = getMinusSCEV(RA, RS);
3690 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3691 LDiff = getMinusSCEV(LA, RS);
3692 RDiff = getMinusSCEV(RA, LS);
3694 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3697 case ICmpInst::ICMP_NE:
3698 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3699 if (LHS->getType() == U->getType() &&
3700 isa<ConstantInt>(RHS) &&
3701 cast<ConstantInt>(RHS)->isZero()) {
3702 const SCEV *One = getConstant(LHS->getType(), 1);
3703 const SCEV *LS = getSCEV(LHS);
3704 const SCEV *LA = getSCEV(U->getOperand(1));
3705 const SCEV *RA = getSCEV(U->getOperand(2));
3706 const SCEV *LDiff = getMinusSCEV(LA, LS);
3707 const SCEV *RDiff = getMinusSCEV(RA, One);
3709 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3712 case ICmpInst::ICMP_EQ:
3713 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3714 if (LHS->getType() == U->getType() &&
3715 isa<ConstantInt>(RHS) &&
3716 cast<ConstantInt>(RHS)->isZero()) {
3717 const SCEV *One = getConstant(LHS->getType(), 1);
3718 const SCEV *LS = getSCEV(LHS);
3719 const SCEV *LA = getSCEV(U->getOperand(1));
3720 const SCEV *RA = getSCEV(U->getOperand(2));
3721 const SCEV *LDiff = getMinusSCEV(LA, One);
3722 const SCEV *RDiff = getMinusSCEV(RA, LS);
3724 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3732 default: // We cannot analyze this expression.
3736 return getUnknown(V);
3741 //===----------------------------------------------------------------------===//
3742 // Iteration Count Computation Code
3745 /// getBackedgeTakenCount - If the specified loop has a predictable
3746 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3747 /// object. The backedge-taken count is the number of times the loop header
3748 /// will be branched to from within the loop. This is one less than the
3749 /// trip count of the loop, since it doesn't count the first iteration,
3750 /// when the header is branched to from outside the loop.
3752 /// Note that it is not valid to call this method on a loop without a
3753 /// loop-invariant backedge-taken count (see
3754 /// hasLoopInvariantBackedgeTakenCount).
3756 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3757 return getBackedgeTakenInfo(L).Exact;
3760 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3761 /// return the least SCEV value that is known never to be less than the
3762 /// actual backedge taken count.
3763 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3764 return getBackedgeTakenInfo(L).Max;
3767 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3768 /// onto the given Worklist.
3770 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3771 BasicBlock *Header = L->getHeader();
3773 // Push all Loop-header PHIs onto the Worklist stack.
3774 for (BasicBlock::iterator I = Header->begin();
3775 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3776 Worklist.push_back(PN);
3779 const ScalarEvolution::BackedgeTakenInfo &
3780 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3781 // Initially insert a CouldNotCompute for this loop. If the insertion
3782 // succeeds, proceed to actually compute a backedge-taken count and
3783 // update the value. The temporary CouldNotCompute value tells SCEV
3784 // code elsewhere that it shouldn't attempt to request a new
3785 // backedge-taken count, which could result in infinite recursion.
3786 std::pair<std::map<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3787 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3789 return Pair.first->second;
3791 BackedgeTakenInfo Result = getCouldNotCompute();
3792 BackedgeTakenInfo Computed = ComputeBackedgeTakenCount(L);
3793 if (Computed.Exact != getCouldNotCompute()) {
3794 assert(isLoopInvariant(Computed.Exact, L) &&
3795 isLoopInvariant(Computed.Max, L) &&
3796 "Computed backedge-taken count isn't loop invariant for loop!");
3797 ++NumTripCountsComputed;
3799 // Update the value in the map.
3802 if (Computed.Max != getCouldNotCompute())
3803 // Update the value in the map.
3805 if (isa<PHINode>(L->getHeader()->begin()))
3806 // Only count loops that have phi nodes as not being computable.
3807 ++NumTripCountsNotComputed;
3810 // Now that we know more about the trip count for this loop, forget any
3811 // existing SCEV values for PHI nodes in this loop since they are only
3812 // conservative estimates made without the benefit of trip count
3813 // information. This is similar to the code in forgetLoop, except that
3814 // it handles SCEVUnknown PHI nodes specially.
3815 if (Computed.hasAnyInfo()) {
3816 SmallVector<Instruction *, 16> Worklist;
3817 PushLoopPHIs(L, Worklist);
3819 SmallPtrSet<Instruction *, 8> Visited;
3820 while (!Worklist.empty()) {
3821 Instruction *I = Worklist.pop_back_val();
3822 if (!Visited.insert(I)) continue;
3824 ValueExprMapType::iterator It =
3825 ValueExprMap.find(static_cast<Value *>(I));
3826 if (It != ValueExprMap.end()) {
3827 const SCEV *Old = It->second;
3829 // SCEVUnknown for a PHI either means that it has an unrecognized
3830 // structure, or it's a PHI that's in the progress of being computed
3831 // by createNodeForPHI. In the former case, additional loop trip
3832 // count information isn't going to change anything. In the later
3833 // case, createNodeForPHI will perform the necessary updates on its
3834 // own when it gets to that point.
3835 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
3836 forgetMemoizedResults(Old);
3837 ValueExprMap.erase(It);
3839 if (PHINode *PN = dyn_cast<PHINode>(I))
3840 ConstantEvolutionLoopExitValue.erase(PN);
3843 PushDefUseChildren(I, Worklist);
3847 // Re-lookup the insert position, since the call to
3848 // ComputeBackedgeTakenCount above could result in a
3849 // recusive call to getBackedgeTakenInfo (on a different
3850 // loop), which would invalidate the iterator computed
3852 return BackedgeTakenCounts.find(L)->second = Result;
3855 /// forgetLoop - This method should be called by the client when it has
3856 /// changed a loop in a way that may effect ScalarEvolution's ability to
3857 /// compute a trip count, or if the loop is deleted.
3858 void ScalarEvolution::forgetLoop(const Loop *L) {
3859 // Drop any stored trip count value.
3860 BackedgeTakenCounts.erase(L);
3862 // Drop information about expressions based on loop-header PHIs.
3863 SmallVector<Instruction *, 16> Worklist;
3864 PushLoopPHIs(L, Worklist);
3866 SmallPtrSet<Instruction *, 8> Visited;
3867 while (!Worklist.empty()) {
3868 Instruction *I = Worklist.pop_back_val();
3869 if (!Visited.insert(I)) continue;
3871 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3872 if (It != ValueExprMap.end()) {
3873 forgetMemoizedResults(It->second);
3874 ValueExprMap.erase(It);
3875 if (PHINode *PN = dyn_cast<PHINode>(I))
3876 ConstantEvolutionLoopExitValue.erase(PN);
3879 PushDefUseChildren(I, Worklist);
3882 // Forget all contained loops too, to avoid dangling entries in the
3883 // ValuesAtScopes map.
3884 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3888 /// forgetValue - This method should be called by the client when it has
3889 /// changed a value in a way that may effect its value, or which may
3890 /// disconnect it from a def-use chain linking it to a loop.
3891 void ScalarEvolution::forgetValue(Value *V) {
3892 Instruction *I = dyn_cast<Instruction>(V);
3895 // Drop information about expressions based on loop-header PHIs.
3896 SmallVector<Instruction *, 16> Worklist;
3897 Worklist.push_back(I);
3899 SmallPtrSet<Instruction *, 8> Visited;
3900 while (!Worklist.empty()) {
3901 I = Worklist.pop_back_val();
3902 if (!Visited.insert(I)) continue;
3904 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
3905 if (It != ValueExprMap.end()) {
3906 forgetMemoizedResults(It->second);
3907 ValueExprMap.erase(It);
3908 if (PHINode *PN = dyn_cast<PHINode>(I))
3909 ConstantEvolutionLoopExitValue.erase(PN);
3912 PushDefUseChildren(I, Worklist);
3916 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3917 /// of the specified loop will execute.
3918 ScalarEvolution::BackedgeTakenInfo
3919 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3920 SmallVector<BasicBlock *, 8> ExitingBlocks;
3921 L->getExitingBlocks(ExitingBlocks);
3923 // Examine all exits and pick the most conservative values.
3924 const SCEV *BECount = getCouldNotCompute();
3925 const SCEV *MaxBECount = getCouldNotCompute();
3926 bool CouldNotComputeBECount = false;
3927 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3928 BackedgeTakenInfo NewBTI =
3929 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3931 if (NewBTI.Exact == getCouldNotCompute()) {
3932 // We couldn't compute an exact value for this exit, so
3933 // we won't be able to compute an exact value for the loop.
3934 CouldNotComputeBECount = true;
3935 BECount = getCouldNotCompute();
3936 } else if (!CouldNotComputeBECount) {
3937 if (BECount == getCouldNotCompute())
3938 BECount = NewBTI.Exact;
3940 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3942 if (MaxBECount == getCouldNotCompute())
3943 MaxBECount = NewBTI.Max;
3944 else if (NewBTI.Max != getCouldNotCompute())
3945 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3948 return BackedgeTakenInfo(BECount, MaxBECount);
3951 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3952 /// of the specified loop will execute if it exits via the specified block.
3953 ScalarEvolution::BackedgeTakenInfo
3954 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3955 BasicBlock *ExitingBlock) {
3957 // Okay, we've chosen an exiting block. See what condition causes us to
3958 // exit at this block.
3960 // FIXME: we should be able to handle switch instructions (with a single exit)
3961 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3962 if (ExitBr == 0) return getCouldNotCompute();
3963 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3965 // At this point, we know we have a conditional branch that determines whether
3966 // the loop is exited. However, we don't know if the branch is executed each
3967 // time through the loop. If not, then the execution count of the branch will
3968 // not be equal to the trip count of the loop.
3970 // Currently we check for this by checking to see if the Exit branch goes to
3971 // the loop header. If so, we know it will always execute the same number of
3972 // times as the loop. We also handle the case where the exit block *is* the
3973 // loop header. This is common for un-rotated loops.
3975 // If both of those tests fail, walk up the unique predecessor chain to the
3976 // header, stopping if there is an edge that doesn't exit the loop. If the
3977 // header is reached, the execution count of the branch will be equal to the
3978 // trip count of the loop.
3980 // More extensive analysis could be done to handle more cases here.
3982 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3983 ExitBr->getSuccessor(1) != L->getHeader() &&
3984 ExitBr->getParent() != L->getHeader()) {
3985 // The simple checks failed, try climbing the unique predecessor chain
3986 // up to the header.
3988 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3989 BasicBlock *Pred = BB->getUniquePredecessor();
3991 return getCouldNotCompute();
3992 TerminatorInst *PredTerm = Pred->getTerminator();
3993 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3994 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3997 // If the predecessor has a successor that isn't BB and isn't
3998 // outside the loop, assume the worst.
3999 if (L->contains(PredSucc))
4000 return getCouldNotCompute();
4002 if (Pred == L->getHeader()) {
4009 return getCouldNotCompute();
4012 // Proceed to the next level to examine the exit condition expression.
4013 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
4014 ExitBr->getSuccessor(0),
4015 ExitBr->getSuccessor(1));
4018 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
4019 /// backedge of the specified loop will execute if its exit condition
4020 /// were a conditional branch of ExitCond, TBB, and FBB.
4021 ScalarEvolution::BackedgeTakenInfo
4022 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
4026 // Check if the controlling expression for this loop is an And or Or.
4027 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4028 if (BO->getOpcode() == Instruction::And) {
4029 // Recurse on the operands of the and.
4030 BackedgeTakenInfo BTI0 =
4031 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
4032 BackedgeTakenInfo BTI1 =
4033 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
4034 const SCEV *BECount = getCouldNotCompute();
4035 const SCEV *MaxBECount = getCouldNotCompute();
4036 if (L->contains(TBB)) {
4037 // Both conditions must be true for the loop to continue executing.
4038 // Choose the less conservative count.
4039 if (BTI0.Exact == getCouldNotCompute() ||
4040 BTI1.Exact == getCouldNotCompute())
4041 BECount = getCouldNotCompute();
4043 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
4044 if (BTI0.Max == getCouldNotCompute())
4045 MaxBECount = BTI1.Max;
4046 else if (BTI1.Max == getCouldNotCompute())
4047 MaxBECount = BTI0.Max;
4049 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
4051 // Both conditions must be true at the same time for the loop to exit.
4052 // For now, be conservative.
4053 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4054 if (BTI0.Max == BTI1.Max)
4055 MaxBECount = BTI0.Max;
4056 if (BTI0.Exact == BTI1.Exact)
4057 BECount = BTI0.Exact;
4060 return BackedgeTakenInfo(BECount, MaxBECount);
4062 if (BO->getOpcode() == Instruction::Or) {
4063 // Recurse on the operands of the or.
4064 BackedgeTakenInfo BTI0 =
4065 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
4066 BackedgeTakenInfo BTI1 =
4067 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
4068 const SCEV *BECount = getCouldNotCompute();
4069 const SCEV *MaxBECount = getCouldNotCompute();
4070 if (L->contains(FBB)) {
4071 // Both conditions must be false for the loop to continue executing.
4072 // Choose the less conservative count.
4073 if (BTI0.Exact == getCouldNotCompute() ||
4074 BTI1.Exact == getCouldNotCompute())
4075 BECount = getCouldNotCompute();
4077 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
4078 if (BTI0.Max == getCouldNotCompute())
4079 MaxBECount = BTI1.Max;
4080 else if (BTI1.Max == getCouldNotCompute())
4081 MaxBECount = BTI0.Max;
4083 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
4085 // Both conditions must be false at the same time for the loop to exit.
4086 // For now, be conservative.
4087 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4088 if (BTI0.Max == BTI1.Max)
4089 MaxBECount = BTI0.Max;
4090 if (BTI0.Exact == BTI1.Exact)
4091 BECount = BTI0.Exact;
4094 return BackedgeTakenInfo(BECount, MaxBECount);
4098 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4099 // Proceed to the next level to examine the icmp.
4100 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4101 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
4103 // Check for a constant condition. These are normally stripped out by
4104 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4105 // preserve the CFG and is temporarily leaving constant conditions
4107 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4108 if (L->contains(FBB) == !CI->getZExtValue())
4109 // The backedge is always taken.
4110 return getCouldNotCompute();
4112 // The backedge is never taken.
4113 return getConstant(CI->getType(), 0);
4116 // If it's not an integer or pointer comparison then compute it the hard way.
4117 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4120 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
4121 /// backedge of the specified loop will execute if its exit condition
4122 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4123 ScalarEvolution::BackedgeTakenInfo
4124 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
4129 // If the condition was exit on true, convert the condition to exit on false
4130 ICmpInst::Predicate Cond;
4131 if (!L->contains(FBB))
4132 Cond = ExitCond->getPredicate();
4134 Cond = ExitCond->getInversePredicate();
4136 // Handle common loops like: for (X = "string"; *X; ++X)
4137 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4138 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4139 BackedgeTakenInfo ItCnt =
4140 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
4141 if (ItCnt.hasAnyInfo())
4145 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4146 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4148 // Try to evaluate any dependencies out of the loop.
4149 LHS = getSCEVAtScope(LHS, L);
4150 RHS = getSCEVAtScope(RHS, L);
4152 // At this point, we would like to compute how many iterations of the
4153 // loop the predicate will return true for these inputs.
4154 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4155 // If there is a loop-invariant, force it into the RHS.
4156 std::swap(LHS, RHS);
4157 Cond = ICmpInst::getSwappedPredicate(Cond);
4160 // Simplify the operands before analyzing them.
4161 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4163 // If we have a comparison of a chrec against a constant, try to use value
4164 // ranges to answer this query.
4165 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4166 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4167 if (AddRec->getLoop() == L) {
4168 // Form the constant range.
4169 ConstantRange CompRange(
4170 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4172 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4173 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4177 case ICmpInst::ICMP_NE: { // while (X != Y)
4178 // Convert to: while (X-Y != 0)
4179 BackedgeTakenInfo BTI = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4180 if (BTI.hasAnyInfo()) return BTI;
4183 case ICmpInst::ICMP_EQ: { // while (X == Y)
4184 // Convert to: while (X-Y == 0)
4185 BackedgeTakenInfo BTI = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4186 if (BTI.hasAnyInfo()) return BTI;
4189 case ICmpInst::ICMP_SLT: {
4190 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
4191 if (BTI.hasAnyInfo()) return BTI;
4194 case ICmpInst::ICMP_SGT: {
4195 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4196 getNotSCEV(RHS), L, true);
4197 if (BTI.hasAnyInfo()) return BTI;
4200 case ICmpInst::ICMP_ULT: {
4201 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
4202 if (BTI.hasAnyInfo()) return BTI;
4205 case ICmpInst::ICMP_UGT: {
4206 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
4207 getNotSCEV(RHS), L, false);
4208 if (BTI.hasAnyInfo()) return BTI;
4213 dbgs() << "ComputeBackedgeTakenCount ";
4214 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4215 dbgs() << "[unsigned] ";
4216 dbgs() << *LHS << " "
4217 << Instruction::getOpcodeName(Instruction::ICmp)
4218 << " " << *RHS << "\n";
4223 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
4226 static ConstantInt *
4227 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4228 ScalarEvolution &SE) {
4229 const SCEV *InVal = SE.getConstant(C);
4230 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4231 assert(isa<SCEVConstant>(Val) &&
4232 "Evaluation of SCEV at constant didn't fold correctly?");
4233 return cast<SCEVConstant>(Val)->getValue();
4236 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4237 /// and a GEP expression (missing the pointer index) indexing into it, return
4238 /// the addressed element of the initializer or null if the index expression is
4241 GetAddressedElementFromGlobal(GlobalVariable *GV,
4242 const std::vector<ConstantInt*> &Indices) {
4243 Constant *Init = GV->getInitializer();
4244 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4245 uint64_t Idx = Indices[i]->getZExtValue();
4246 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4247 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4248 Init = cast<Constant>(CS->getOperand(Idx));
4249 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4250 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4251 Init = cast<Constant>(CA->getOperand(Idx));
4252 } else if (isa<ConstantAggregateZero>(Init)) {
4253 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
4254 assert(Idx < STy->getNumElements() && "Bad struct index!");
4255 Init = Constant::getNullValue(STy->getElementType(Idx));
4256 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4257 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4258 Init = Constant::getNullValue(ATy->getElementType());
4260 llvm_unreachable("Unknown constant aggregate type!");
4264 return 0; // Unknown initializer type
4270 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
4271 /// 'icmp op load X, cst', try to see if we can compute the backedge
4272 /// execution count.
4273 ScalarEvolution::BackedgeTakenInfo
4274 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
4278 ICmpInst::Predicate predicate) {
4279 if (LI->isVolatile()) return getCouldNotCompute();
4281 // Check to see if the loaded pointer is a getelementptr of a global.
4282 // TODO: Use SCEV instead of manually grubbing with GEPs.
4283 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4284 if (!GEP) return getCouldNotCompute();
4286 // Make sure that it is really a constant global we are gepping, with an
4287 // initializer, and make sure the first IDX is really 0.
4288 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4289 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4290 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4291 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4292 return getCouldNotCompute();
4294 // Okay, we allow one non-constant index into the GEP instruction.
4296 std::vector<ConstantInt*> Indexes;
4297 unsigned VarIdxNum = 0;
4298 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4299 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4300 Indexes.push_back(CI);
4301 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4302 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4303 VarIdx = GEP->getOperand(i);
4305 Indexes.push_back(0);
4308 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4309 // Check to see if X is a loop variant variable value now.
4310 const SCEV *Idx = getSCEV(VarIdx);
4311 Idx = getSCEVAtScope(Idx, L);
4313 // We can only recognize very limited forms of loop index expressions, in
4314 // particular, only affine AddRec's like {C1,+,C2}.
4315 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4316 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4317 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4318 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4319 return getCouldNotCompute();
4321 unsigned MaxSteps = MaxBruteForceIterations;
4322 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4323 ConstantInt *ItCst = ConstantInt::get(
4324 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4325 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4327 // Form the GEP offset.
4328 Indexes[VarIdxNum] = Val;
4330 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4331 if (Result == 0) break; // Cannot compute!
4333 // Evaluate the condition for this iteration.
4334 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4335 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4336 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4338 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4339 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4342 ++NumArrayLenItCounts;
4343 return getConstant(ItCst); // Found terminating iteration!
4346 return getCouldNotCompute();
4350 /// CanConstantFold - Return true if we can constant fold an instruction of the
4351 /// specified type, assuming that all operands were constants.
4352 static bool CanConstantFold(const Instruction *I) {
4353 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4354 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4357 if (const CallInst *CI = dyn_cast<CallInst>(I))
4358 if (const Function *F = CI->getCalledFunction())
4359 return canConstantFoldCallTo(F);
4363 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4364 /// in the loop that V is derived from. We allow arbitrary operations along the
4365 /// way, but the operands of an operation must either be constants or a value
4366 /// derived from a constant PHI. If this expression does not fit with these
4367 /// constraints, return null.
4368 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4369 // If this is not an instruction, or if this is an instruction outside of the
4370 // loop, it can't be derived from a loop PHI.
4371 Instruction *I = dyn_cast<Instruction>(V);
4372 if (I == 0 || !L->contains(I)) return 0;
4374 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4375 if (L->getHeader() == I->getParent())
4378 // We don't currently keep track of the control flow needed to evaluate
4379 // PHIs, so we cannot handle PHIs inside of loops.
4383 // If we won't be able to constant fold this expression even if the operands
4384 // are constants, return early.
4385 if (!CanConstantFold(I)) return 0;
4387 // Otherwise, we can evaluate this instruction if all of its operands are
4388 // constant or derived from a PHI node themselves.
4390 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4391 if (!isa<Constant>(I->getOperand(Op))) {
4392 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4393 if (P == 0) return 0; // Not evolving from PHI
4397 return 0; // Evolving from multiple different PHIs.
4400 // This is a expression evolving from a constant PHI!
4404 /// EvaluateExpression - Given an expression that passes the
4405 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4406 /// in the loop has the value PHIVal. If we can't fold this expression for some
4407 /// reason, return null.
4408 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4409 const TargetData *TD) {
4410 if (isa<PHINode>(V)) return PHIVal;
4411 if (Constant *C = dyn_cast<Constant>(V)) return C;
4412 Instruction *I = cast<Instruction>(V);
4414 std::vector<Constant*> Operands(I->getNumOperands());
4416 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4417 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4418 if (Operands[i] == 0) return 0;
4421 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4422 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4424 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4425 &Operands[0], Operands.size(), TD);
4428 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4429 /// in the header of its containing loop, we know the loop executes a
4430 /// constant number of times, and the PHI node is just a recurrence
4431 /// involving constants, fold it.
4433 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4436 std::map<PHINode*, Constant*>::const_iterator I =
4437 ConstantEvolutionLoopExitValue.find(PN);
4438 if (I != ConstantEvolutionLoopExitValue.end())
4441 if (BEs.ugt(MaxBruteForceIterations))
4442 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4444 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4446 // Since the loop is canonicalized, the PHI node must have two entries. One
4447 // entry must be a constant (coming in from outside of the loop), and the
4448 // second must be derived from the same PHI.
4449 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4450 Constant *StartCST =
4451 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4453 return RetVal = 0; // Must be a constant.
4455 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4456 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4457 !isa<Constant>(BEValue))
4458 return RetVal = 0; // Not derived from same PHI.
4460 // Execute the loop symbolically to determine the exit value.
4461 if (BEs.getActiveBits() >= 32)
4462 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4464 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4465 unsigned IterationNum = 0;
4466 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4467 if (IterationNum == NumIterations)
4468 return RetVal = PHIVal; // Got exit value!
4470 // Compute the value of the PHI node for the next iteration.
4471 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4472 if (NextPHI == PHIVal)
4473 return RetVal = NextPHI; // Stopped evolving!
4475 return 0; // Couldn't evaluate!
4480 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
4481 /// constant number of times (the condition evolves only from constants),
4482 /// try to evaluate a few iterations of the loop until we get the exit
4483 /// condition gets a value of ExitWhen (true or false). If we cannot
4484 /// evaluate the trip count of the loop, return getCouldNotCompute().
4486 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
4489 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4490 if (PN == 0) return getCouldNotCompute();
4492 // If the loop is canonicalized, the PHI will have exactly two entries.
4493 // That's the only form we support here.
4494 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4496 // One entry must be a constant (coming in from outside of the loop), and the
4497 // second must be derived from the same PHI.
4498 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4499 Constant *StartCST =
4500 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4501 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4503 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4504 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4505 !isa<Constant>(BEValue))
4506 return getCouldNotCompute(); // Not derived from same PHI.
4508 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4509 // the loop symbolically to determine when the condition gets a value of
4511 unsigned IterationNum = 0;
4512 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4513 for (Constant *PHIVal = StartCST;
4514 IterationNum != MaxIterations; ++IterationNum) {
4515 ConstantInt *CondVal =
4516 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4518 // Couldn't symbolically evaluate.
4519 if (!CondVal) return getCouldNotCompute();
4521 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4522 ++NumBruteForceTripCountsComputed;
4523 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4526 // Compute the value of the PHI node for the next iteration.
4527 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4528 if (NextPHI == 0 || NextPHI == PHIVal)
4529 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4533 // Too many iterations were needed to evaluate.
4534 return getCouldNotCompute();
4537 /// getSCEVAtScope - Return a SCEV expression for the specified value
4538 /// at the specified scope in the program. The L value specifies a loop
4539 /// nest to evaluate the expression at, where null is the top-level or a
4540 /// specified loop is immediately inside of the loop.
4542 /// This method can be used to compute the exit value for a variable defined
4543 /// in a loop by querying what the value will hold in the parent loop.
4545 /// In the case that a relevant loop exit value cannot be computed, the
4546 /// original value V is returned.
4547 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4548 // Check to see if we've folded this expression at this loop before.
4549 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4550 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4551 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4553 return Pair.first->second ? Pair.first->second : V;
4555 // Otherwise compute it.
4556 const SCEV *C = computeSCEVAtScope(V, L);
4557 ValuesAtScopes[V][L] = C;
4561 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4562 if (isa<SCEVConstant>(V)) return V;
4564 // If this instruction is evolved from a constant-evolving PHI, compute the
4565 // exit value from the loop without using SCEVs.
4566 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4567 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4568 const Loop *LI = (*this->LI)[I->getParent()];
4569 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4570 if (PHINode *PN = dyn_cast<PHINode>(I))
4571 if (PN->getParent() == LI->getHeader()) {
4572 // Okay, there is no closed form solution for the PHI node. Check
4573 // to see if the loop that contains it has a known backedge-taken
4574 // count. If so, we may be able to force computation of the exit
4576 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4577 if (const SCEVConstant *BTCC =
4578 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4579 // Okay, we know how many times the containing loop executes. If
4580 // this is a constant evolving PHI node, get the final value at
4581 // the specified iteration number.
4582 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4583 BTCC->getValue()->getValue(),
4585 if (RV) return getSCEV(RV);
4589 // Okay, this is an expression that we cannot symbolically evaluate
4590 // into a SCEV. Check to see if it's possible to symbolically evaluate
4591 // the arguments into constants, and if so, try to constant propagate the
4592 // result. This is particularly useful for computing loop exit values.
4593 if (CanConstantFold(I)) {
4594 SmallVector<Constant *, 4> Operands;
4595 bool MadeImprovement = false;
4596 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4597 Value *Op = I->getOperand(i);
4598 if (Constant *C = dyn_cast<Constant>(Op)) {
4599 Operands.push_back(C);
4603 // If any of the operands is non-constant and if they are
4604 // non-integer and non-pointer, don't even try to analyze them
4605 // with scev techniques.
4606 if (!isSCEVable(Op->getType()))
4609 const SCEV *OrigV = getSCEV(Op);
4610 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4611 MadeImprovement |= OrigV != OpV;
4614 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4616 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4617 C = dyn_cast<Constant>(SU->getValue());
4619 if (C->getType() != Op->getType())
4620 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4624 Operands.push_back(C);
4627 // Check to see if getSCEVAtScope actually made an improvement.
4628 if (MadeImprovement) {
4630 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4631 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4632 Operands[0], Operands[1], TD);
4634 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4635 &Operands[0], Operands.size(), TD);
4642 // This is some other type of SCEVUnknown, just return it.
4646 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4647 // Avoid performing the look-up in the common case where the specified
4648 // expression has no loop-variant portions.
4649 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4650 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4651 if (OpAtScope != Comm->getOperand(i)) {
4652 // Okay, at least one of these operands is loop variant but might be
4653 // foldable. Build a new instance of the folded commutative expression.
4654 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4655 Comm->op_begin()+i);
4656 NewOps.push_back(OpAtScope);
4658 for (++i; i != e; ++i) {
4659 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4660 NewOps.push_back(OpAtScope);
4662 if (isa<SCEVAddExpr>(Comm))
4663 return getAddExpr(NewOps);
4664 if (isa<SCEVMulExpr>(Comm))
4665 return getMulExpr(NewOps);
4666 if (isa<SCEVSMaxExpr>(Comm))
4667 return getSMaxExpr(NewOps);
4668 if (isa<SCEVUMaxExpr>(Comm))
4669 return getUMaxExpr(NewOps);
4670 llvm_unreachable("Unknown commutative SCEV type!");
4673 // If we got here, all operands are loop invariant.
4677 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4678 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4679 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4680 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4681 return Div; // must be loop invariant
4682 return getUDivExpr(LHS, RHS);
4685 // If this is a loop recurrence for a loop that does not contain L, then we
4686 // are dealing with the final value computed by the loop.
4687 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4688 // First, attempt to evaluate each operand.
4689 // Avoid performing the look-up in the common case where the specified
4690 // expression has no loop-variant portions.
4691 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4692 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4693 if (OpAtScope == AddRec->getOperand(i))
4696 // Okay, at least one of these operands is loop variant but might be
4697 // foldable. Build a new instance of the folded commutative expression.
4698 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4699 AddRec->op_begin()+i);
4700 NewOps.push_back(OpAtScope);
4701 for (++i; i != e; ++i)
4702 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4704 const SCEV *FoldedRec =
4705 getAddRecExpr(NewOps, AddRec->getLoop(),
4706 AddRec->getNoWrapFlags(SCEV::FlagNW));
4707 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
4708 // In cases with "undef" values, a loop's own recurrence may
4709 // fold into a constant. Go ahead and return the optimistic value.
4715 // If the scope is outside the addrec's loop, evaluate it by using the
4716 // loop exit value of the addrec.
4717 if (!AddRec->getLoop()->contains(L)) {
4718 // To evaluate this recurrence, we need to know how many times the AddRec
4719 // loop iterates. Compute this now.
4720 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4721 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4723 // Then, evaluate the AddRec.
4724 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4730 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4731 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4732 if (Op == Cast->getOperand())
4733 return Cast; // must be loop invariant
4734 return getZeroExtendExpr(Op, Cast->getType());
4737 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4738 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4739 if (Op == Cast->getOperand())
4740 return Cast; // must be loop invariant
4741 return getSignExtendExpr(Op, Cast->getType());
4744 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4745 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4746 if (Op == Cast->getOperand())
4747 return Cast; // must be loop invariant
4748 return getTruncateExpr(Op, Cast->getType());
4751 llvm_unreachable("Unknown SCEV type!");
4755 /// getSCEVAtScope - This is a convenience function which does
4756 /// getSCEVAtScope(getSCEV(V), L).
4757 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4758 return getSCEVAtScope(getSCEV(V), L);
4761 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4762 /// following equation:
4764 /// A * X = B (mod N)
4766 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4767 /// A and B isn't important.
4769 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4770 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
4771 ScalarEvolution &SE) {
4772 uint32_t BW = A.getBitWidth();
4773 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
4774 assert(A != 0 && "A must be non-zero.");
4778 // The gcd of A and N may have only one prime factor: 2. The number of
4779 // trailing zeros in A is its multiplicity
4780 uint32_t Mult2 = A.countTrailingZeros();
4783 // 2. Check if B is divisible by D.
4785 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
4786 // is not less than multiplicity of this prime factor for D.
4787 if (B.countTrailingZeros() < Mult2)
4788 return SE.getCouldNotCompute();
4790 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
4793 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
4794 // bit width during computations.
4795 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
4796 APInt Mod(BW + 1, 0);
4797 Mod.setBit(BW - Mult2); // Mod = N / D
4798 APInt I = AD.multiplicativeInverse(Mod);
4800 // 4. Compute the minimum unsigned root of the equation:
4801 // I * (B / D) mod (N / D)
4802 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4804 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4806 return SE.getConstant(Result.trunc(BW));
4809 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4810 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4811 /// might be the same) or two SCEVCouldNotCompute objects.
4813 static std::pair<const SCEV *,const SCEV *>
4814 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4815 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4816 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4817 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4818 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4820 // We currently can only solve this if the coefficients are constants.
4821 if (!LC || !MC || !NC) {
4822 const SCEV *CNC = SE.getCouldNotCompute();
4823 return std::make_pair(CNC, CNC);
4826 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4827 const APInt &L = LC->getValue()->getValue();
4828 const APInt &M = MC->getValue()->getValue();
4829 const APInt &N = NC->getValue()->getValue();
4830 APInt Two(BitWidth, 2);
4831 APInt Four(BitWidth, 4);
4834 using namespace APIntOps;
4836 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4837 // The B coefficient is M-N/2
4841 // The A coefficient is N/2
4842 APInt A(N.sdiv(Two));
4844 // Compute the B^2-4ac term.
4847 SqrtTerm -= Four * (A * C);
4849 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4850 // integer value or else APInt::sqrt() will assert.
4851 APInt SqrtVal(SqrtTerm.sqrt());
4853 // Compute the two solutions for the quadratic formula.
4854 // The divisions must be performed as signed divisions.
4856 APInt TwoA( A << 1 );
4857 if (TwoA.isMinValue()) {
4858 const SCEV *CNC = SE.getCouldNotCompute();
4859 return std::make_pair(CNC, CNC);
4862 LLVMContext &Context = SE.getContext();
4864 ConstantInt *Solution1 =
4865 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4866 ConstantInt *Solution2 =
4867 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4869 return std::make_pair(SE.getConstant(Solution1),
4870 SE.getConstant(Solution2));
4871 } // end APIntOps namespace
4874 /// HowFarToZero - Return the number of times a backedge comparing the specified
4875 /// value to zero will execute. If not computable, return CouldNotCompute.
4877 /// This is only used for loops with a "x != y" exit test. The exit condition is
4878 /// now expressed as a single expression, V = x-y. So the exit test is
4879 /// effectively V != 0. We know and take advantage of the fact that this
4880 /// expression only being used in a comparison by zero context.
4881 ScalarEvolution::BackedgeTakenInfo
4882 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4883 // If the value is a constant
4884 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4885 // If the value is already zero, the branch will execute zero times.
4886 if (C->getValue()->isZero()) return C;
4887 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4890 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4891 if (!AddRec || AddRec->getLoop() != L)
4892 return getCouldNotCompute();
4894 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4895 // the quadratic equation to solve it.
4896 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
4897 std::pair<const SCEV *,const SCEV *> Roots =
4898 SolveQuadraticEquation(AddRec, *this);
4899 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4900 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4903 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
4904 << " sol#2: " << *R2 << "\n";
4906 // Pick the smallest positive root value.
4907 if (ConstantInt *CB =
4908 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
4911 if (CB->getZExtValue() == false)
4912 std::swap(R1, R2); // R1 is the minimum root now.
4914 // We can only use this value if the chrec ends up with an exact zero
4915 // value at this index. When solving for "X*X != 5", for example, we
4916 // should not accept a root of 2.
4917 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4919 return R1; // We found a quadratic root!
4922 return getCouldNotCompute();
4925 // Otherwise we can only handle this if it is affine.
4926 if (!AddRec->isAffine())
4927 return getCouldNotCompute();
4929 // If this is an affine expression, the execution count of this branch is
4930 // the minimum unsigned root of the following equation:
4932 // Start + Step*N = 0 (mod 2^BW)
4936 // Step*N = -Start (mod 2^BW)
4938 // where BW is the common bit width of Start and Step.
4940 // Get the initial value for the loop.
4941 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
4942 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
4944 // For now we handle only constant steps.
4946 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
4947 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
4948 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
4949 // We have not yet seen any such cases.
4950 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
4952 return getCouldNotCompute();
4954 // For positive steps (counting up until unsigned overflow):
4955 // N = -Start/Step (as unsigned)
4956 // For negative steps (counting down to zero):
4958 // First compute the unsigned distance from zero in the direction of Step.
4959 bool CountDown = StepC->getValue()->getValue().isNegative();
4960 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
4962 // Handle unitary steps, which cannot wraparound.
4963 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
4964 // N = Distance (as unsigned)
4965 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue())
4968 // If the recurrence is known not to wraparound, unsigned divide computes the
4969 // back edge count. We know that the value will either become zero (and thus
4970 // the loop terminates), that the loop will terminate through some other exit
4971 // condition first, or that the loop has undefined behavior. This means
4972 // we can't "miss" the exit value, even with nonunit stride.
4974 // FIXME: Prove that loops always exhibits *acceptable* undefined
4975 // behavior. Loops must exhibit defined behavior until a wrapped value is
4976 // actually used. So the trip count computed by udiv could be smaller than the
4977 // number of well-defined iterations.
4978 if (AddRec->getNoWrapFlags(SCEV::FlagNW))
4979 // FIXME: We really want an "isexact" bit for udiv.
4980 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
4982 // Then, try to solve the above equation provided that Start is constant.
4983 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4984 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4985 -StartC->getValue()->getValue(),
4987 return getCouldNotCompute();
4990 /// HowFarToNonZero - Return the number of times a backedge checking the
4991 /// specified value for nonzero will execute. If not computable, return
4993 ScalarEvolution::BackedgeTakenInfo
4994 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4995 // Loops that look like: while (X == 0) are very strange indeed. We don't
4996 // handle them yet except for the trivial case. This could be expanded in the
4997 // future as needed.
4999 // If the value is a constant, check to see if it is known to be non-zero
5000 // already. If so, the backedge will execute zero times.
5001 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5002 if (!C->getValue()->isNullValue())
5003 return getConstant(C->getType(), 0);
5004 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5007 // We could implement others, but I really doubt anyone writes loops like
5008 // this, and if they did, they would already be constant folded.
5009 return getCouldNotCompute();
5012 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5013 /// (which may not be an immediate predecessor) which has exactly one
5014 /// successor from which BB is reachable, or null if no such block is
5017 std::pair<BasicBlock *, BasicBlock *>
5018 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5019 // If the block has a unique predecessor, then there is no path from the
5020 // predecessor to the block that does not go through the direct edge
5021 // from the predecessor to the block.
5022 if (BasicBlock *Pred = BB->getSinglePredecessor())
5023 return std::make_pair(Pred, BB);
5025 // A loop's header is defined to be a block that dominates the loop.
5026 // If the header has a unique predecessor outside the loop, it must be
5027 // a block that has exactly one successor that can reach the loop.
5028 if (Loop *L = LI->getLoopFor(BB))
5029 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5031 return std::pair<BasicBlock *, BasicBlock *>();
5034 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5035 /// testing whether two expressions are equal, however for the purposes of
5036 /// looking for a condition guarding a loop, it can be useful to be a little
5037 /// more general, since a front-end may have replicated the controlling
5040 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5041 // Quick check to see if they are the same SCEV.
5042 if (A == B) return true;
5044 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5045 // two different instructions with the same value. Check for this case.
5046 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5047 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5048 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5049 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5050 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5053 // Otherwise assume they may have a different value.
5057 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5058 /// predicate Pred. Return true iff any changes were made.
5060 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5061 const SCEV *&LHS, const SCEV *&RHS) {
5062 bool Changed = false;
5064 // Canonicalize a constant to the right side.
5065 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5066 // Check for both operands constant.
5067 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5068 if (ConstantExpr::getICmp(Pred,
5070 RHSC->getValue())->isNullValue())
5071 goto trivially_false;
5073 goto trivially_true;
5075 // Otherwise swap the operands to put the constant on the right.
5076 std::swap(LHS, RHS);
5077 Pred = ICmpInst::getSwappedPredicate(Pred);
5081 // If we're comparing an addrec with a value which is loop-invariant in the
5082 // addrec's loop, put the addrec on the left. Also make a dominance check,
5083 // as both operands could be addrecs loop-invariant in each other's loop.
5084 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5085 const Loop *L = AR->getLoop();
5086 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5087 std::swap(LHS, RHS);
5088 Pred = ICmpInst::getSwappedPredicate(Pred);
5093 // If there's a constant operand, canonicalize comparisons with boundary
5094 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5095 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5096 const APInt &RA = RC->getValue()->getValue();
5098 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5099 case ICmpInst::ICMP_EQ:
5100 case ICmpInst::ICMP_NE:
5102 case ICmpInst::ICMP_UGE:
5103 if ((RA - 1).isMinValue()) {
5104 Pred = ICmpInst::ICMP_NE;
5105 RHS = getConstant(RA - 1);
5109 if (RA.isMaxValue()) {
5110 Pred = ICmpInst::ICMP_EQ;
5114 if (RA.isMinValue()) goto trivially_true;
5116 Pred = ICmpInst::ICMP_UGT;
5117 RHS = getConstant(RA - 1);
5120 case ICmpInst::ICMP_ULE:
5121 if ((RA + 1).isMaxValue()) {
5122 Pred = ICmpInst::ICMP_NE;
5123 RHS = getConstant(RA + 1);
5127 if (RA.isMinValue()) {
5128 Pred = ICmpInst::ICMP_EQ;
5132 if (RA.isMaxValue()) goto trivially_true;
5134 Pred = ICmpInst::ICMP_ULT;
5135 RHS = getConstant(RA + 1);
5138 case ICmpInst::ICMP_SGE:
5139 if ((RA - 1).isMinSignedValue()) {
5140 Pred = ICmpInst::ICMP_NE;
5141 RHS = getConstant(RA - 1);
5145 if (RA.isMaxSignedValue()) {
5146 Pred = ICmpInst::ICMP_EQ;
5150 if (RA.isMinSignedValue()) goto trivially_true;
5152 Pred = ICmpInst::ICMP_SGT;
5153 RHS = getConstant(RA - 1);
5156 case ICmpInst::ICMP_SLE:
5157 if ((RA + 1).isMaxSignedValue()) {
5158 Pred = ICmpInst::ICMP_NE;
5159 RHS = getConstant(RA + 1);
5163 if (RA.isMinSignedValue()) {
5164 Pred = ICmpInst::ICMP_EQ;
5168 if (RA.isMaxSignedValue()) goto trivially_true;
5170 Pred = ICmpInst::ICMP_SLT;
5171 RHS = getConstant(RA + 1);
5174 case ICmpInst::ICMP_UGT:
5175 if (RA.isMinValue()) {
5176 Pred = ICmpInst::ICMP_NE;
5180 if ((RA + 1).isMaxValue()) {
5181 Pred = ICmpInst::ICMP_EQ;
5182 RHS = getConstant(RA + 1);
5186 if (RA.isMaxValue()) goto trivially_false;
5188 case ICmpInst::ICMP_ULT:
5189 if (RA.isMaxValue()) {
5190 Pred = ICmpInst::ICMP_NE;
5194 if ((RA - 1).isMinValue()) {
5195 Pred = ICmpInst::ICMP_EQ;
5196 RHS = getConstant(RA - 1);
5200 if (RA.isMinValue()) goto trivially_false;
5202 case ICmpInst::ICMP_SGT:
5203 if (RA.isMinSignedValue()) {
5204 Pred = ICmpInst::ICMP_NE;
5208 if ((RA + 1).isMaxSignedValue()) {
5209 Pred = ICmpInst::ICMP_EQ;
5210 RHS = getConstant(RA + 1);
5214 if (RA.isMaxSignedValue()) goto trivially_false;
5216 case ICmpInst::ICMP_SLT:
5217 if (RA.isMaxSignedValue()) {
5218 Pred = ICmpInst::ICMP_NE;
5222 if ((RA - 1).isMinSignedValue()) {
5223 Pred = ICmpInst::ICMP_EQ;
5224 RHS = getConstant(RA - 1);
5228 if (RA.isMinSignedValue()) goto trivially_false;
5233 // Check for obvious equality.
5234 if (HasSameValue(LHS, RHS)) {
5235 if (ICmpInst::isTrueWhenEqual(Pred))
5236 goto trivially_true;
5237 if (ICmpInst::isFalseWhenEqual(Pred))
5238 goto trivially_false;
5241 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5242 // adding or subtracting 1 from one of the operands.
5244 case ICmpInst::ICMP_SLE:
5245 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5246 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5248 Pred = ICmpInst::ICMP_SLT;
5250 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5251 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5253 Pred = ICmpInst::ICMP_SLT;
5257 case ICmpInst::ICMP_SGE:
5258 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5259 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5261 Pred = ICmpInst::ICMP_SGT;
5263 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5264 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5266 Pred = ICmpInst::ICMP_SGT;
5270 case ICmpInst::ICMP_ULE:
5271 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5272 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5274 Pred = ICmpInst::ICMP_ULT;
5276 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5277 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5279 Pred = ICmpInst::ICMP_ULT;
5283 case ICmpInst::ICMP_UGE:
5284 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5285 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5287 Pred = ICmpInst::ICMP_UGT;
5289 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5290 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5292 Pred = ICmpInst::ICMP_UGT;
5300 // TODO: More simplifications are possible here.
5306 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5307 Pred = ICmpInst::ICMP_EQ;
5312 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5313 Pred = ICmpInst::ICMP_NE;
5317 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5318 return getSignedRange(S).getSignedMax().isNegative();
5321 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5322 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5325 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5326 return !getSignedRange(S).getSignedMin().isNegative();
5329 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5330 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5333 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5334 return isKnownNegative(S) || isKnownPositive(S);
5337 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5338 const SCEV *LHS, const SCEV *RHS) {
5339 // Canonicalize the inputs first.
5340 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5342 // If LHS or RHS is an addrec, check to see if the condition is true in
5343 // every iteration of the loop.
5344 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5345 if (isLoopEntryGuardedByCond(
5346 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5347 isLoopBackedgeGuardedByCond(
5348 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5350 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5351 if (isLoopEntryGuardedByCond(
5352 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5353 isLoopBackedgeGuardedByCond(
5354 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5357 // Otherwise see what can be done with known constant ranges.
5358 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5362 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5363 const SCEV *LHS, const SCEV *RHS) {
5364 if (HasSameValue(LHS, RHS))
5365 return ICmpInst::isTrueWhenEqual(Pred);
5367 // This code is split out from isKnownPredicate because it is called from
5368 // within isLoopEntryGuardedByCond.
5371 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5373 case ICmpInst::ICMP_SGT:
5374 Pred = ICmpInst::ICMP_SLT;
5375 std::swap(LHS, RHS);
5376 case ICmpInst::ICMP_SLT: {
5377 ConstantRange LHSRange = getSignedRange(LHS);
5378 ConstantRange RHSRange = getSignedRange(RHS);
5379 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5381 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5385 case ICmpInst::ICMP_SGE:
5386 Pred = ICmpInst::ICMP_SLE;
5387 std::swap(LHS, RHS);
5388 case ICmpInst::ICMP_SLE: {
5389 ConstantRange LHSRange = getSignedRange(LHS);
5390 ConstantRange RHSRange = getSignedRange(RHS);
5391 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5393 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5397 case ICmpInst::ICMP_UGT:
5398 Pred = ICmpInst::ICMP_ULT;
5399 std::swap(LHS, RHS);
5400 case ICmpInst::ICMP_ULT: {
5401 ConstantRange LHSRange = getUnsignedRange(LHS);
5402 ConstantRange RHSRange = getUnsignedRange(RHS);
5403 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5405 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5409 case ICmpInst::ICMP_UGE:
5410 Pred = ICmpInst::ICMP_ULE;
5411 std::swap(LHS, RHS);
5412 case ICmpInst::ICMP_ULE: {
5413 ConstantRange LHSRange = getUnsignedRange(LHS);
5414 ConstantRange RHSRange = getUnsignedRange(RHS);
5415 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5417 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5421 case ICmpInst::ICMP_NE: {
5422 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5424 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5427 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5428 if (isKnownNonZero(Diff))
5432 case ICmpInst::ICMP_EQ:
5433 // The check at the top of the function catches the case where
5434 // the values are known to be equal.
5440 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5441 /// protected by a conditional between LHS and RHS. This is used to
5442 /// to eliminate casts.
5444 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5445 ICmpInst::Predicate Pred,
5446 const SCEV *LHS, const SCEV *RHS) {
5447 // Interpret a null as meaning no loop, where there is obviously no guard
5448 // (interprocedural conditions notwithstanding).
5449 if (!L) return true;
5451 BasicBlock *Latch = L->getLoopLatch();
5455 BranchInst *LoopContinuePredicate =
5456 dyn_cast<BranchInst>(Latch->getTerminator());
5457 if (!LoopContinuePredicate ||
5458 LoopContinuePredicate->isUnconditional())
5461 return isImpliedCond(Pred, LHS, RHS,
5462 LoopContinuePredicate->getCondition(),
5463 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5466 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5467 /// by a conditional between LHS and RHS. This is used to help avoid max
5468 /// expressions in loop trip counts, and to eliminate casts.
5470 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5471 ICmpInst::Predicate Pred,
5472 const SCEV *LHS, const SCEV *RHS) {
5473 // Interpret a null as meaning no loop, where there is obviously no guard
5474 // (interprocedural conditions notwithstanding).
5475 if (!L) return false;
5477 // Starting at the loop predecessor, climb up the predecessor chain, as long
5478 // as there are predecessors that can be found that have unique successors
5479 // leading to the original header.
5480 for (std::pair<BasicBlock *, BasicBlock *>
5481 Pair(L->getLoopPredecessor(), L->getHeader());
5483 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5485 BranchInst *LoopEntryPredicate =
5486 dyn_cast<BranchInst>(Pair.first->getTerminator());
5487 if (!LoopEntryPredicate ||
5488 LoopEntryPredicate->isUnconditional())
5491 if (isImpliedCond(Pred, LHS, RHS,
5492 LoopEntryPredicate->getCondition(),
5493 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5500 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5501 /// and RHS is true whenever the given Cond value evaluates to true.
5502 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
5503 const SCEV *LHS, const SCEV *RHS,
5504 Value *FoundCondValue,
5506 // Recursively handle And and Or conditions.
5507 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
5508 if (BO->getOpcode() == Instruction::And) {
5510 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5511 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5512 } else if (BO->getOpcode() == Instruction::Or) {
5514 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5515 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5519 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
5520 if (!ICI) return false;
5522 // Bail if the ICmp's operands' types are wider than the needed type
5523 // before attempting to call getSCEV on them. This avoids infinite
5524 // recursion, since the analysis of widening casts can require loop
5525 // exit condition information for overflow checking, which would
5527 if (getTypeSizeInBits(LHS->getType()) <
5528 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5531 // Now that we found a conditional branch that dominates the loop, check to
5532 // see if it is the comparison we are looking for.
5533 ICmpInst::Predicate FoundPred;
5535 FoundPred = ICI->getInversePredicate();
5537 FoundPred = ICI->getPredicate();
5539 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5540 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5542 // Balance the types. The case where FoundLHS' type is wider than
5543 // LHS' type is checked for above.
5544 if (getTypeSizeInBits(LHS->getType()) >
5545 getTypeSizeInBits(FoundLHS->getType())) {
5546 if (CmpInst::isSigned(Pred)) {
5547 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5548 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5550 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5551 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5555 // Canonicalize the query to match the way instcombine will have
5556 // canonicalized the comparison.
5557 if (SimplifyICmpOperands(Pred, LHS, RHS))
5559 return CmpInst::isTrueWhenEqual(Pred);
5560 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5561 if (FoundLHS == FoundRHS)
5562 return CmpInst::isFalseWhenEqual(Pred);
5564 // Check to see if we can make the LHS or RHS match.
5565 if (LHS == FoundRHS || RHS == FoundLHS) {
5566 if (isa<SCEVConstant>(RHS)) {
5567 std::swap(FoundLHS, FoundRHS);
5568 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5570 std::swap(LHS, RHS);
5571 Pred = ICmpInst::getSwappedPredicate(Pred);
5575 // Check whether the found predicate is the same as the desired predicate.
5576 if (FoundPred == Pred)
5577 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5579 // Check whether swapping the found predicate makes it the same as the
5580 // desired predicate.
5581 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5582 if (isa<SCEVConstant>(RHS))
5583 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5585 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5586 RHS, LHS, FoundLHS, FoundRHS);
5589 // Check whether the actual condition is beyond sufficient.
5590 if (FoundPred == ICmpInst::ICMP_EQ)
5591 if (ICmpInst::isTrueWhenEqual(Pred))
5592 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5594 if (Pred == ICmpInst::ICMP_NE)
5595 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5596 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5599 // Otherwise assume the worst.
5603 /// isImpliedCondOperands - Test whether the condition described by Pred,
5604 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5605 /// and FoundRHS is true.
5606 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5607 const SCEV *LHS, const SCEV *RHS,
5608 const SCEV *FoundLHS,
5609 const SCEV *FoundRHS) {
5610 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5611 FoundLHS, FoundRHS) ||
5612 // ~x < ~y --> x > y
5613 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5614 getNotSCEV(FoundRHS),
5615 getNotSCEV(FoundLHS));
5618 /// isImpliedCondOperandsHelper - Test whether the condition described by
5619 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5620 /// FoundLHS, and FoundRHS is true.
5622 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5623 const SCEV *LHS, const SCEV *RHS,
5624 const SCEV *FoundLHS,
5625 const SCEV *FoundRHS) {
5627 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5628 case ICmpInst::ICMP_EQ:
5629 case ICmpInst::ICMP_NE:
5630 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5633 case ICmpInst::ICMP_SLT:
5634 case ICmpInst::ICMP_SLE:
5635 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5636 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5639 case ICmpInst::ICMP_SGT:
5640 case ICmpInst::ICMP_SGE:
5641 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5642 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5645 case ICmpInst::ICMP_ULT:
5646 case ICmpInst::ICMP_ULE:
5647 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5648 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5651 case ICmpInst::ICMP_UGT:
5652 case ICmpInst::ICMP_UGE:
5653 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5654 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5662 /// getBECount - Subtract the end and start values and divide by the step,
5663 /// rounding up, to get the number of times the backedge is executed. Return
5664 /// CouldNotCompute if an intermediate computation overflows.
5665 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5669 assert(!isKnownNegative(Step) &&
5670 "This code doesn't handle negative strides yet!");
5672 const Type *Ty = Start->getType();
5674 // When Start == End, we have an exact BECount == 0. Short-circuit this case
5675 // here because SCEV may not be able to determine that the unsigned division
5676 // after rounding is zero.
5678 return getConstant(Ty, 0);
5680 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5681 const SCEV *Diff = getMinusSCEV(End, Start);
5682 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5684 // Add an adjustment to the difference between End and Start so that
5685 // the division will effectively round up.
5686 const SCEV *Add = getAddExpr(Diff, RoundUp);
5689 // Check Add for unsigned overflow.
5690 // TODO: More sophisticated things could be done here.
5691 const Type *WideTy = IntegerType::get(getContext(),
5692 getTypeSizeInBits(Ty) + 1);
5693 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5694 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5695 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5696 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5697 return getCouldNotCompute();
5700 return getUDivExpr(Add, Step);
5703 /// HowManyLessThans - Return the number of times a backedge containing the
5704 /// specified less-than comparison will execute. If not computable, return
5705 /// CouldNotCompute.
5706 ScalarEvolution::BackedgeTakenInfo
5707 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5708 const Loop *L, bool isSigned) {
5709 // Only handle: "ADDREC < LoopInvariant".
5710 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
5712 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5713 if (!AddRec || AddRec->getLoop() != L)
5714 return getCouldNotCompute();
5716 // Check to see if we have a flag which makes analysis easy.
5717 bool NoWrap = isSigned ? AddRec->getNoWrapFlags(SCEV::FlagNSW) :
5718 AddRec->getNoWrapFlags(SCEV::FlagNUW);
5720 if (AddRec->isAffine()) {
5721 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5722 const SCEV *Step = AddRec->getStepRecurrence(*this);
5725 return getCouldNotCompute();
5726 if (Step->isOne()) {
5727 // With unit stride, the iteration never steps past the limit value.
5728 } else if (isKnownPositive(Step)) {
5729 // Test whether a positive iteration can step past the limit
5730 // value and past the maximum value for its type in a single step.
5731 // Note that it's not sufficient to check NoWrap here, because even
5732 // though the value after a wrap is undefined, it's not undefined
5733 // behavior, so if wrap does occur, the loop could either terminate or
5734 // loop infinitely, but in either case, the loop is guaranteed to
5735 // iterate at least until the iteration where the wrapping occurs.
5736 const SCEV *One = getConstant(Step->getType(), 1);
5738 APInt Max = APInt::getSignedMaxValue(BitWidth);
5739 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5740 .slt(getSignedRange(RHS).getSignedMax()))
5741 return getCouldNotCompute();
5743 APInt Max = APInt::getMaxValue(BitWidth);
5744 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5745 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5746 return getCouldNotCompute();
5749 // TODO: Handle negative strides here and below.
5750 return getCouldNotCompute();
5752 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5753 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5754 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5755 // treat m-n as signed nor unsigned due to overflow possibility.
5757 // First, we get the value of the LHS in the first iteration: n
5758 const SCEV *Start = AddRec->getOperand(0);
5760 // Determine the minimum constant start value.
5761 const SCEV *MinStart = getConstant(isSigned ?
5762 getSignedRange(Start).getSignedMin() :
5763 getUnsignedRange(Start).getUnsignedMin());
5765 // If we know that the condition is true in order to enter the loop,
5766 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5767 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5768 // the division must round up.
5769 const SCEV *End = RHS;
5770 if (!isLoopEntryGuardedByCond(L,
5771 isSigned ? ICmpInst::ICMP_SLT :
5773 getMinusSCEV(Start, Step), RHS))
5774 End = isSigned ? getSMaxExpr(RHS, Start)
5775 : getUMaxExpr(RHS, Start);
5777 // Determine the maximum constant end value.
5778 const SCEV *MaxEnd = getConstant(isSigned ?
5779 getSignedRange(End).getSignedMax() :
5780 getUnsignedRange(End).getUnsignedMax());
5782 // If MaxEnd is within a step of the maximum integer value in its type,
5783 // adjust it down to the minimum value which would produce the same effect.
5784 // This allows the subsequent ceiling division of (N+(step-1))/step to
5785 // compute the correct value.
5786 const SCEV *StepMinusOne = getMinusSCEV(Step,
5787 getConstant(Step->getType(), 1));
5790 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
5793 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
5796 // Finally, we subtract these two values and divide, rounding up, to get
5797 // the number of times the backedge is executed.
5798 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
5800 // The maximum backedge count is similar, except using the minimum start
5801 // value and the maximum end value.
5802 // If we already have an exact constant BECount, use it instead.
5803 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
5804 : getBECount(MinStart, MaxEnd, Step, NoWrap);
5806 // If the stride is nonconstant, and NoWrap == true, then
5807 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
5808 // exact BECount and invalid MaxBECount, which should be avoided to catch
5809 // more optimization opportunities.
5810 if (isa<SCEVCouldNotCompute>(MaxBECount))
5811 MaxBECount = BECount;
5813 return BackedgeTakenInfo(BECount, MaxBECount);
5816 return getCouldNotCompute();
5819 /// getNumIterationsInRange - Return the number of iterations of this loop that
5820 /// produce values in the specified constant range. Another way of looking at
5821 /// this is that it returns the first iteration number where the value is not in
5822 /// the condition, thus computing the exit count. If the iteration count can't
5823 /// be computed, an instance of SCEVCouldNotCompute is returned.
5824 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
5825 ScalarEvolution &SE) const {
5826 if (Range.isFullSet()) // Infinite loop.
5827 return SE.getCouldNotCompute();
5829 // If the start is a non-zero constant, shift the range to simplify things.
5830 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
5831 if (!SC->getValue()->isZero()) {
5832 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
5833 Operands[0] = SE.getConstant(SC->getType(), 0);
5834 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
5835 getNoWrapFlags(FlagNW));
5836 if (const SCEVAddRecExpr *ShiftedAddRec =
5837 dyn_cast<SCEVAddRecExpr>(Shifted))
5838 return ShiftedAddRec->getNumIterationsInRange(
5839 Range.subtract(SC->getValue()->getValue()), SE);
5840 // This is strange and shouldn't happen.
5841 return SE.getCouldNotCompute();
5844 // The only time we can solve this is when we have all constant indices.
5845 // Otherwise, we cannot determine the overflow conditions.
5846 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
5847 if (!isa<SCEVConstant>(getOperand(i)))
5848 return SE.getCouldNotCompute();
5851 // Okay at this point we know that all elements of the chrec are constants and
5852 // that the start element is zero.
5854 // First check to see if the range contains zero. If not, the first
5856 unsigned BitWidth = SE.getTypeSizeInBits(getType());
5857 if (!Range.contains(APInt(BitWidth, 0)))
5858 return SE.getConstant(getType(), 0);
5861 // If this is an affine expression then we have this situation:
5862 // Solve {0,+,A} in Range === Ax in Range
5864 // We know that zero is in the range. If A is positive then we know that
5865 // the upper value of the range must be the first possible exit value.
5866 // If A is negative then the lower of the range is the last possible loop
5867 // value. Also note that we already checked for a full range.
5868 APInt One(BitWidth,1);
5869 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
5870 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
5872 // The exit value should be (End+A)/A.
5873 APInt ExitVal = (End + A).udiv(A);
5874 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
5876 // Evaluate at the exit value. If we really did fall out of the valid
5877 // range, then we computed our trip count, otherwise wrap around or other
5878 // things must have happened.
5879 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
5880 if (Range.contains(Val->getValue()))
5881 return SE.getCouldNotCompute(); // Something strange happened
5883 // Ensure that the previous value is in the range. This is a sanity check.
5884 assert(Range.contains(
5885 EvaluateConstantChrecAtConstant(this,
5886 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
5887 "Linear scev computation is off in a bad way!");
5888 return SE.getConstant(ExitValue);
5889 } else if (isQuadratic()) {
5890 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
5891 // quadratic equation to solve it. To do this, we must frame our problem in
5892 // terms of figuring out when zero is crossed, instead of when
5893 // Range.getUpper() is crossed.
5894 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
5895 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
5896 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
5897 // getNoWrapFlags(FlagNW)
5900 // Next, solve the constructed addrec
5901 std::pair<const SCEV *,const SCEV *> Roots =
5902 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
5903 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5904 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5906 // Pick the smallest positive root value.
5907 if (ConstantInt *CB =
5908 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
5909 R1->getValue(), R2->getValue()))) {
5910 if (CB->getZExtValue() == false)
5911 std::swap(R1, R2); // R1 is the minimum root now.
5913 // Make sure the root is not off by one. The returned iteration should
5914 // not be in the range, but the previous one should be. When solving
5915 // for "X*X < 5", for example, we should not return a root of 2.
5916 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
5919 if (Range.contains(R1Val->getValue())) {
5920 // The next iteration must be out of the range...
5921 ConstantInt *NextVal =
5922 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
5924 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5925 if (!Range.contains(R1Val->getValue()))
5926 return SE.getConstant(NextVal);
5927 return SE.getCouldNotCompute(); // Something strange happened
5930 // If R1 was not in the range, then it is a good return value. Make
5931 // sure that R1-1 WAS in the range though, just in case.
5932 ConstantInt *NextVal =
5933 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
5934 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
5935 if (Range.contains(R1Val->getValue()))
5937 return SE.getCouldNotCompute(); // Something strange happened
5942 return SE.getCouldNotCompute();
5947 //===----------------------------------------------------------------------===//
5948 // SCEVCallbackVH Class Implementation
5949 //===----------------------------------------------------------------------===//
5951 void ScalarEvolution::SCEVCallbackVH::deleted() {
5952 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5953 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
5954 SE->ConstantEvolutionLoopExitValue.erase(PN);
5955 SE->ValueExprMap.erase(getValPtr());
5956 // this now dangles!
5959 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
5960 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
5962 // Forget all the expressions associated with users of the old value,
5963 // so that future queries will recompute the expressions using the new
5965 Value *Old = getValPtr();
5966 SmallVector<User *, 16> Worklist;
5967 SmallPtrSet<User *, 8> Visited;
5968 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
5970 Worklist.push_back(*UI);
5971 while (!Worklist.empty()) {
5972 User *U = Worklist.pop_back_val();
5973 // Deleting the Old value will cause this to dangle. Postpone
5974 // that until everything else is done.
5977 if (!Visited.insert(U))
5979 if (PHINode *PN = dyn_cast<PHINode>(U))
5980 SE->ConstantEvolutionLoopExitValue.erase(PN);
5981 SE->ValueExprMap.erase(U);
5982 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
5984 Worklist.push_back(*UI);
5986 // Delete the Old value.
5987 if (PHINode *PN = dyn_cast<PHINode>(Old))
5988 SE->ConstantEvolutionLoopExitValue.erase(PN);
5989 SE->ValueExprMap.erase(Old);
5990 // this now dangles!
5993 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
5994 : CallbackVH(V), SE(se) {}
5996 //===----------------------------------------------------------------------===//
5997 // ScalarEvolution Class Implementation
5998 //===----------------------------------------------------------------------===//
6000 ScalarEvolution::ScalarEvolution()
6001 : FunctionPass(ID), FirstUnknown(0) {
6002 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6005 bool ScalarEvolution::runOnFunction(Function &F) {
6007 LI = &getAnalysis<LoopInfo>();
6008 TD = getAnalysisIfAvailable<TargetData>();
6009 DT = &getAnalysis<DominatorTree>();
6013 void ScalarEvolution::releaseMemory() {
6014 // Iterate through all the SCEVUnknown instances and call their
6015 // destructors, so that they release their references to their values.
6016 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6020 ValueExprMap.clear();
6021 BackedgeTakenCounts.clear();
6022 ConstantEvolutionLoopExitValue.clear();
6023 ValuesAtScopes.clear();
6024 LoopDispositions.clear();
6025 BlockDispositions.clear();
6026 UnsignedRanges.clear();
6027 SignedRanges.clear();
6028 UniqueSCEVs.clear();
6029 SCEVAllocator.Reset();
6032 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6033 AU.setPreservesAll();
6034 AU.addRequiredTransitive<LoopInfo>();
6035 AU.addRequiredTransitive<DominatorTree>();
6038 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6039 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6042 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6044 // Print all inner loops first
6045 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6046 PrintLoopInfo(OS, SE, *I);
6049 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6052 SmallVector<BasicBlock *, 8> ExitBlocks;
6053 L->getExitBlocks(ExitBlocks);
6054 if (ExitBlocks.size() != 1)
6055 OS << "<multiple exits> ";
6057 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6058 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6060 OS << "Unpredictable backedge-taken count. ";
6065 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6068 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6069 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6071 OS << "Unpredictable max backedge-taken count. ";
6077 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6078 // ScalarEvolution's implementation of the print method is to print
6079 // out SCEV values of all instructions that are interesting. Doing
6080 // this potentially causes it to create new SCEV objects though,
6081 // which technically conflicts with the const qualifier. This isn't
6082 // observable from outside the class though, so casting away the
6083 // const isn't dangerous.
6084 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6086 OS << "Classifying expressions for: ";
6087 WriteAsOperand(OS, F, /*PrintType=*/false);
6089 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6090 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6093 const SCEV *SV = SE.getSCEV(&*I);
6096 const Loop *L = LI->getLoopFor((*I).getParent());
6098 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6105 OS << "\t\t" "Exits: ";
6106 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6107 if (!SE.isLoopInvariant(ExitValue, L)) {
6108 OS << "<<Unknown>>";
6117 OS << "Determining loop execution counts for: ";
6118 WriteAsOperand(OS, F, /*PrintType=*/false);
6120 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6121 PrintLoopInfo(OS, &SE, *I);
6124 ScalarEvolution::LoopDisposition
6125 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6126 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6127 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6128 Values.insert(std::make_pair(L, LoopVariant));
6130 return Pair.first->second;
6132 LoopDisposition D = computeLoopDisposition(S, L);
6133 return LoopDispositions[S][L] = D;
6136 ScalarEvolution::LoopDisposition
6137 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6138 switch (S->getSCEVType()) {
6140 return LoopInvariant;
6144 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6145 case scAddRecExpr: {
6146 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6148 // If L is the addrec's loop, it's computable.
6149 if (AR->getLoop() == L)
6150 return LoopComputable;
6152 // Add recurrences are never invariant in the function-body (null loop).
6156 // This recurrence is variant w.r.t. L if L contains AR's loop.
6157 if (L->contains(AR->getLoop()))
6160 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6161 if (AR->getLoop()->contains(L))
6162 return LoopInvariant;
6164 // This recurrence is variant w.r.t. L if any of its operands
6166 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6168 if (!isLoopInvariant(*I, L))
6171 // Otherwise it's loop-invariant.
6172 return LoopInvariant;
6178 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6179 bool HasVarying = false;
6180 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6182 LoopDisposition D = getLoopDisposition(*I, L);
6183 if (D == LoopVariant)
6185 if (D == LoopComputable)
6188 return HasVarying ? LoopComputable : LoopInvariant;
6191 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6192 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6193 if (LD == LoopVariant)
6195 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6196 if (RD == LoopVariant)
6198 return (LD == LoopInvariant && RD == LoopInvariant) ?
6199 LoopInvariant : LoopComputable;
6202 // All non-instruction values are loop invariant. All instructions are loop
6203 // invariant if they are not contained in the specified loop.
6204 // Instructions are never considered invariant in the function body
6205 // (null loop) because they are defined within the "loop".
6206 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6207 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6208 return LoopInvariant;
6209 case scCouldNotCompute:
6210 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6214 llvm_unreachable("Unknown SCEV kind!");
6218 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6219 return getLoopDisposition(S, L) == LoopInvariant;
6222 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6223 return getLoopDisposition(S, L) == LoopComputable;
6226 ScalarEvolution::BlockDisposition
6227 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6228 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6229 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6230 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6232 return Pair.first->second;
6234 BlockDisposition D = computeBlockDisposition(S, BB);
6235 return BlockDispositions[S][BB] = D;
6238 ScalarEvolution::BlockDisposition
6239 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6240 switch (S->getSCEVType()) {
6242 return ProperlyDominatesBlock;
6246 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6247 case scAddRecExpr: {
6248 // This uses a "dominates" query instead of "properly dominates" query
6249 // to test for proper dominance too, because the instruction which
6250 // produces the addrec's value is a PHI, and a PHI effectively properly
6251 // dominates its entire containing block.
6252 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6253 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6254 return DoesNotDominateBlock;
6256 // FALL THROUGH into SCEVNAryExpr handling.
6261 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6263 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6265 BlockDisposition D = getBlockDisposition(*I, BB);
6266 if (D == DoesNotDominateBlock)
6267 return DoesNotDominateBlock;
6268 if (D == DominatesBlock)
6271 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6274 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6275 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6276 BlockDisposition LD = getBlockDisposition(LHS, BB);
6277 if (LD == DoesNotDominateBlock)
6278 return DoesNotDominateBlock;
6279 BlockDisposition RD = getBlockDisposition(RHS, BB);
6280 if (RD == DoesNotDominateBlock)
6281 return DoesNotDominateBlock;
6282 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6283 ProperlyDominatesBlock : DominatesBlock;
6286 if (Instruction *I =
6287 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6288 if (I->getParent() == BB)
6289 return DominatesBlock;
6290 if (DT->properlyDominates(I->getParent(), BB))
6291 return ProperlyDominatesBlock;
6292 return DoesNotDominateBlock;
6294 return ProperlyDominatesBlock;
6295 case scCouldNotCompute:
6296 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6297 return DoesNotDominateBlock;
6300 llvm_unreachable("Unknown SCEV kind!");
6301 return DoesNotDominateBlock;
6304 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6305 return getBlockDisposition(S, BB) >= DominatesBlock;
6308 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6309 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6312 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6313 switch (S->getSCEVType()) {
6318 case scSignExtend: {
6319 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
6320 const SCEV *CastOp = Cast->getOperand();
6321 return Op == CastOp || hasOperand(CastOp, Op);
6328 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6329 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6331 const SCEV *NAryOp = *I;
6332 if (NAryOp == Op || hasOperand(NAryOp, Op))
6338 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6339 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6340 return LHS == Op || hasOperand(LHS, Op) ||
6341 RHS == Op || hasOperand(RHS, Op);
6345 case scCouldNotCompute:
6346 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6350 llvm_unreachable("Unknown SCEV kind!");
6354 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6355 ValuesAtScopes.erase(S);
6356 LoopDispositions.erase(S);
6357 BlockDispositions.erase(S);
6358 UnsignedRanges.erase(S);
6359 SignedRanges.erase(S);