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/ScalarEvolution.h"
63 #include "llvm/ADT/STLExtras.h"
64 #include "llvm/ADT/SmallPtrSet.h"
65 #include "llvm/ADT/Statistic.h"
66 #include "llvm/Analysis/ConstantFolding.h"
67 #include "llvm/Analysis/InstructionSimplify.h"
68 #include "llvm/Analysis/LoopInfo.h"
69 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
70 #include "llvm/Analysis/ValueTracking.h"
71 #include "llvm/IR/Constants.h"
72 #include "llvm/IR/DataLayout.h"
73 #include "llvm/IR/DerivedTypes.h"
74 #include "llvm/IR/Dominators.h"
75 #include "llvm/IR/GlobalAlias.h"
76 #include "llvm/IR/GlobalVariable.h"
77 #include "llvm/IR/Instructions.h"
78 #include "llvm/IR/LLVMContext.h"
79 #include "llvm/IR/Operator.h"
80 #include "llvm/Support/CommandLine.h"
81 #include "llvm/Support/ConstantRange.h"
82 #include "llvm/Support/Debug.h"
83 #include "llvm/Support/ErrorHandling.h"
84 #include "llvm/Support/GetElementPtrTypeIterator.h"
85 #include "llvm/Support/InstIterator.h"
86 #include "llvm/Support/MathExtras.h"
87 #include "llvm/Support/raw_ostream.h"
88 #include "llvm/Target/TargetLibraryInfo.h"
92 STATISTIC(NumArrayLenItCounts,
93 "Number of trip counts computed with array length");
94 STATISTIC(NumTripCountsComputed,
95 "Number of loops with predictable loop counts");
96 STATISTIC(NumTripCountsNotComputed,
97 "Number of loops without predictable loop counts");
98 STATISTIC(NumBruteForceTripCountsComputed,
99 "Number of loops with trip counts computed by force");
101 static cl::opt<unsigned>
102 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
103 cl::desc("Maximum number of iterations SCEV will "
104 "symbolically execute a constant "
108 // FIXME: Enable this with XDEBUG when the test suite is clean.
110 VerifySCEV("verify-scev",
111 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
113 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
114 "Scalar Evolution Analysis", false, true)
115 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
116 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
117 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
118 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
119 "Scalar Evolution Analysis", false, true)
120 char ScalarEvolution::ID = 0;
122 //===----------------------------------------------------------------------===//
123 // SCEV class definitions
124 //===----------------------------------------------------------------------===//
126 //===----------------------------------------------------------------------===//
127 // Implementation of the SCEV class.
130 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
131 void SCEV::dump() const {
137 void SCEV::print(raw_ostream &OS) const {
138 switch (getSCEVType()) {
140 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
143 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
144 const SCEV *Op = Trunc->getOperand();
145 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
146 << *Trunc->getType() << ")";
150 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
151 const SCEV *Op = ZExt->getOperand();
152 OS << "(zext " << *Op->getType() << " " << *Op << " to "
153 << *ZExt->getType() << ")";
157 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
158 const SCEV *Op = SExt->getOperand();
159 OS << "(sext " << *Op->getType() << " " << *Op << " to "
160 << *SExt->getType() << ")";
164 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
165 OS << "{" << *AR->getOperand(0);
166 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
167 OS << ",+," << *AR->getOperand(i);
169 if (AR->getNoWrapFlags(FlagNUW))
171 if (AR->getNoWrapFlags(FlagNSW))
173 if (AR->getNoWrapFlags(FlagNW) &&
174 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
176 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
184 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
185 const char *OpStr = 0;
186 switch (NAry->getSCEVType()) {
187 case scAddExpr: OpStr = " + "; break;
188 case scMulExpr: OpStr = " * "; break;
189 case scUMaxExpr: OpStr = " umax "; break;
190 case scSMaxExpr: OpStr = " smax "; break;
193 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
196 if (llvm::next(I) != E)
200 switch (NAry->getSCEVType()) {
203 if (NAry->getNoWrapFlags(FlagNUW))
205 if (NAry->getNoWrapFlags(FlagNSW))
211 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
212 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
216 const SCEVUnknown *U = cast<SCEVUnknown>(this);
218 if (U->isSizeOf(AllocTy)) {
219 OS << "sizeof(" << *AllocTy << ")";
222 if (U->isAlignOf(AllocTy)) {
223 OS << "alignof(" << *AllocTy << ")";
229 if (U->isOffsetOf(CTy, FieldNo)) {
230 OS << "offsetof(" << *CTy << ", ";
231 FieldNo->printAsOperand(OS, false);
236 // Otherwise just print it normally.
237 U->getValue()->printAsOperand(OS, false);
240 case scCouldNotCompute:
241 OS << "***COULDNOTCOMPUTE***";
245 llvm_unreachable("Unknown SCEV kind!");
248 Type *SCEV::getType() const {
249 switch (getSCEVType()) {
251 return cast<SCEVConstant>(this)->getType();
255 return cast<SCEVCastExpr>(this)->getType();
260 return cast<SCEVNAryExpr>(this)->getType();
262 return cast<SCEVAddExpr>(this)->getType();
264 return cast<SCEVUDivExpr>(this)->getType();
266 return cast<SCEVUnknown>(this)->getType();
267 case scCouldNotCompute:
268 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
270 llvm_unreachable("Unknown SCEV kind!");
274 bool SCEV::isZero() const {
275 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
276 return SC->getValue()->isZero();
280 bool SCEV::isOne() const {
281 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
282 return SC->getValue()->isOne();
286 bool SCEV::isAllOnesValue() const {
287 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
288 return SC->getValue()->isAllOnesValue();
292 /// isNonConstantNegative - Return true if the specified scev is negated, but
294 bool SCEV::isNonConstantNegative() const {
295 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
296 if (!Mul) return false;
298 // If there is a constant factor, it will be first.
299 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
300 if (!SC) return false;
302 // Return true if the value is negative, this matches things like (-42 * V).
303 return SC->getValue()->getValue().isNegative();
306 SCEVCouldNotCompute::SCEVCouldNotCompute() :
307 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
309 bool SCEVCouldNotCompute::classof(const SCEV *S) {
310 return S->getSCEVType() == scCouldNotCompute;
313 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
315 ID.AddInteger(scConstant);
318 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
319 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
320 UniqueSCEVs.InsertNode(S, IP);
324 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
325 return getConstant(ConstantInt::get(getContext(), Val));
329 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
330 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
331 return getConstant(ConstantInt::get(ITy, V, isSigned));
334 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
335 unsigned SCEVTy, const SCEV *op, Type *ty)
336 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
338 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
339 const SCEV *op, Type *ty)
340 : SCEVCastExpr(ID, scTruncate, op, ty) {
341 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
342 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
343 "Cannot truncate non-integer value!");
346 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
347 const SCEV *op, Type *ty)
348 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
349 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
350 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
351 "Cannot zero extend non-integer value!");
354 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
355 const SCEV *op, Type *ty)
356 : SCEVCastExpr(ID, scSignExtend, op, ty) {
357 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
358 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
359 "Cannot sign extend non-integer value!");
362 void SCEVUnknown::deleted() {
363 // Clear this SCEVUnknown from various maps.
364 SE->forgetMemoizedResults(this);
366 // Remove this SCEVUnknown from the uniquing map.
367 SE->UniqueSCEVs.RemoveNode(this);
369 // Release the value.
373 void SCEVUnknown::allUsesReplacedWith(Value *New) {
374 // Clear this SCEVUnknown from various maps.
375 SE->forgetMemoizedResults(this);
377 // Remove this SCEVUnknown from the uniquing map.
378 SE->UniqueSCEVs.RemoveNode(this);
380 // Update this SCEVUnknown to point to the new value. This is needed
381 // because there may still be outstanding SCEVs which still point to
386 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
387 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
388 if (VCE->getOpcode() == Instruction::PtrToInt)
389 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
390 if (CE->getOpcode() == Instruction::GetElementPtr &&
391 CE->getOperand(0)->isNullValue() &&
392 CE->getNumOperands() == 2)
393 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
395 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
403 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
404 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
405 if (VCE->getOpcode() == Instruction::PtrToInt)
406 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
407 if (CE->getOpcode() == Instruction::GetElementPtr &&
408 CE->getOperand(0)->isNullValue()) {
410 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
411 if (StructType *STy = dyn_cast<StructType>(Ty))
412 if (!STy->isPacked() &&
413 CE->getNumOperands() == 3 &&
414 CE->getOperand(1)->isNullValue()) {
415 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
417 STy->getNumElements() == 2 &&
418 STy->getElementType(0)->isIntegerTy(1)) {
419 AllocTy = STy->getElementType(1);
428 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
429 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
430 if (VCE->getOpcode() == Instruction::PtrToInt)
431 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
432 if (CE->getOpcode() == Instruction::GetElementPtr &&
433 CE->getNumOperands() == 3 &&
434 CE->getOperand(0)->isNullValue() &&
435 CE->getOperand(1)->isNullValue()) {
437 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
438 // Ignore vector types here so that ScalarEvolutionExpander doesn't
439 // emit getelementptrs that index into vectors.
440 if (Ty->isStructTy() || Ty->isArrayTy()) {
442 FieldNo = CE->getOperand(2);
450 //===----------------------------------------------------------------------===//
452 //===----------------------------------------------------------------------===//
455 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
456 /// than the complexity of the RHS. This comparator is used to canonicalize
458 class SCEVComplexityCompare {
459 const LoopInfo *const LI;
461 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
463 // Return true or false if LHS is less than, or at least RHS, respectively.
464 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
465 return compare(LHS, RHS) < 0;
468 // Return negative, zero, or positive, if LHS is less than, equal to, or
469 // greater than RHS, respectively. A three-way result allows recursive
470 // comparisons to be more efficient.
471 int compare(const SCEV *LHS, const SCEV *RHS) const {
472 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
476 // Primarily, sort the SCEVs by their getSCEVType().
477 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
479 return (int)LType - (int)RType;
481 // Aside from the getSCEVType() ordering, the particular ordering
482 // isn't very important except that it's beneficial to be consistent,
483 // so that (a + b) and (b + a) don't end up as different expressions.
486 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
487 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
489 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
490 // not as complete as it could be.
491 const Value *LV = LU->getValue(), *RV = RU->getValue();
493 // Order pointer values after integer values. This helps SCEVExpander
495 bool LIsPointer = LV->getType()->isPointerTy(),
496 RIsPointer = RV->getType()->isPointerTy();
497 if (LIsPointer != RIsPointer)
498 return (int)LIsPointer - (int)RIsPointer;
500 // Compare getValueID values.
501 unsigned LID = LV->getValueID(),
502 RID = RV->getValueID();
504 return (int)LID - (int)RID;
506 // Sort arguments by their position.
507 if (const Argument *LA = dyn_cast<Argument>(LV)) {
508 const Argument *RA = cast<Argument>(RV);
509 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
510 return (int)LArgNo - (int)RArgNo;
513 // For instructions, compare their loop depth, and their operand
514 // count. This is pretty loose.
515 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
516 const Instruction *RInst = cast<Instruction>(RV);
518 // Compare loop depths.
519 const BasicBlock *LParent = LInst->getParent(),
520 *RParent = RInst->getParent();
521 if (LParent != RParent) {
522 unsigned LDepth = LI->getLoopDepth(LParent),
523 RDepth = LI->getLoopDepth(RParent);
524 if (LDepth != RDepth)
525 return (int)LDepth - (int)RDepth;
528 // Compare the number of operands.
529 unsigned LNumOps = LInst->getNumOperands(),
530 RNumOps = RInst->getNumOperands();
531 return (int)LNumOps - (int)RNumOps;
538 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
539 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
541 // Compare constant values.
542 const APInt &LA = LC->getValue()->getValue();
543 const APInt &RA = RC->getValue()->getValue();
544 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
545 if (LBitWidth != RBitWidth)
546 return (int)LBitWidth - (int)RBitWidth;
547 return LA.ult(RA) ? -1 : 1;
551 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
552 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
554 // Compare addrec loop depths.
555 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
556 if (LLoop != RLoop) {
557 unsigned LDepth = LLoop->getLoopDepth(),
558 RDepth = RLoop->getLoopDepth();
559 if (LDepth != RDepth)
560 return (int)LDepth - (int)RDepth;
563 // Addrec complexity grows with operand count.
564 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
565 if (LNumOps != RNumOps)
566 return (int)LNumOps - (int)RNumOps;
568 // Lexicographically compare.
569 for (unsigned i = 0; i != LNumOps; ++i) {
570 long X = compare(LA->getOperand(i), RA->getOperand(i));
582 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
583 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
585 // Lexicographically compare n-ary expressions.
586 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
587 if (LNumOps != RNumOps)
588 return (int)LNumOps - (int)RNumOps;
590 for (unsigned i = 0; i != LNumOps; ++i) {
593 long X = compare(LC->getOperand(i), RC->getOperand(i));
597 return (int)LNumOps - (int)RNumOps;
601 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
602 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
604 // Lexicographically compare udiv expressions.
605 long X = compare(LC->getLHS(), RC->getLHS());
608 return compare(LC->getRHS(), RC->getRHS());
614 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
615 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
617 // Compare cast expressions by operand.
618 return compare(LC->getOperand(), RC->getOperand());
622 llvm_unreachable("Unknown SCEV kind!");
628 /// GroupByComplexity - Given a list of SCEV objects, order them by their
629 /// complexity, and group objects of the same complexity together by value.
630 /// When this routine is finished, we know that any duplicates in the vector are
631 /// consecutive and that complexity is monotonically increasing.
633 /// Note that we go take special precautions to ensure that we get deterministic
634 /// results from this routine. In other words, we don't want the results of
635 /// this to depend on where the addresses of various SCEV objects happened to
638 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
640 if (Ops.size() < 2) return; // Noop
641 if (Ops.size() == 2) {
642 // This is the common case, which also happens to be trivially simple.
644 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
645 if (SCEVComplexityCompare(LI)(RHS, LHS))
650 // Do the rough sort by complexity.
651 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
653 // Now that we are sorted by complexity, group elements of the same
654 // complexity. Note that this is, at worst, N^2, but the vector is likely to
655 // be extremely short in practice. Note that we take this approach because we
656 // do not want to depend on the addresses of the objects we are grouping.
657 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
658 const SCEV *S = Ops[i];
659 unsigned Complexity = S->getSCEVType();
661 // If there are any objects of the same complexity and same value as this
663 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
664 if (Ops[j] == S) { // Found a duplicate.
665 // Move it to immediately after i'th element.
666 std::swap(Ops[i+1], Ops[j]);
667 ++i; // no need to rescan it.
668 if (i == e-2) return; // Done!
676 //===----------------------------------------------------------------------===//
677 // Simple SCEV method implementations
678 //===----------------------------------------------------------------------===//
680 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
682 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
685 // Handle the simplest case efficiently.
687 return SE.getTruncateOrZeroExtend(It, ResultTy);
689 // We are using the following formula for BC(It, K):
691 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
693 // Suppose, W is the bitwidth of the return value. We must be prepared for
694 // overflow. Hence, we must assure that the result of our computation is
695 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
696 // safe in modular arithmetic.
698 // However, this code doesn't use exactly that formula; the formula it uses
699 // is something like the following, where T is the number of factors of 2 in
700 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
703 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
705 // This formula is trivially equivalent to the previous formula. However,
706 // this formula can be implemented much more efficiently. The trick is that
707 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
708 // arithmetic. To do exact division in modular arithmetic, all we have
709 // to do is multiply by the inverse. Therefore, this step can be done at
712 // The next issue is how to safely do the division by 2^T. The way this
713 // is done is by doing the multiplication step at a width of at least W + T
714 // bits. This way, the bottom W+T bits of the product are accurate. Then,
715 // when we perform the division by 2^T (which is equivalent to a right shift
716 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
717 // truncated out after the division by 2^T.
719 // In comparison to just directly using the first formula, this technique
720 // is much more efficient; using the first formula requires W * K bits,
721 // but this formula less than W + K bits. Also, the first formula requires
722 // a division step, whereas this formula only requires multiplies and shifts.
724 // It doesn't matter whether the subtraction step is done in the calculation
725 // width or the input iteration count's width; if the subtraction overflows,
726 // the result must be zero anyway. We prefer here to do it in the width of
727 // the induction variable because it helps a lot for certain cases; CodeGen
728 // isn't smart enough to ignore the overflow, which leads to much less
729 // efficient code if the width of the subtraction is wider than the native
732 // (It's possible to not widen at all by pulling out factors of 2 before
733 // the multiplication; for example, K=2 can be calculated as
734 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
735 // extra arithmetic, so it's not an obvious win, and it gets
736 // much more complicated for K > 3.)
738 // Protection from insane SCEVs; this bound is conservative,
739 // but it probably doesn't matter.
741 return SE.getCouldNotCompute();
743 unsigned W = SE.getTypeSizeInBits(ResultTy);
745 // Calculate K! / 2^T and T; we divide out the factors of two before
746 // multiplying for calculating K! / 2^T to avoid overflow.
747 // Other overflow doesn't matter because we only care about the bottom
748 // W bits of the result.
749 APInt OddFactorial(W, 1);
751 for (unsigned i = 3; i <= K; ++i) {
753 unsigned TwoFactors = Mult.countTrailingZeros();
755 Mult = Mult.lshr(TwoFactors);
756 OddFactorial *= Mult;
759 // We need at least W + T bits for the multiplication step
760 unsigned CalculationBits = W + T;
762 // Calculate 2^T, at width T+W.
763 APInt DivFactor = APInt::getOneBitSet(CalculationBits, T);
765 // Calculate the multiplicative inverse of K! / 2^T;
766 // this multiplication factor will perform the exact division by
768 APInt Mod = APInt::getSignedMinValue(W+1);
769 APInt MultiplyFactor = OddFactorial.zext(W+1);
770 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
771 MultiplyFactor = MultiplyFactor.trunc(W);
773 // Calculate the product, at width T+W
774 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
776 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
777 for (unsigned i = 1; i != K; ++i) {
778 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
779 Dividend = SE.getMulExpr(Dividend,
780 SE.getTruncateOrZeroExtend(S, CalculationTy));
784 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
786 // Truncate the result, and divide by K! / 2^T.
788 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
789 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
792 /// evaluateAtIteration - Return the value of this chain of recurrences at
793 /// the specified iteration number. We can evaluate this recurrence by
794 /// multiplying each element in the chain by the binomial coefficient
795 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
797 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
799 /// where BC(It, k) stands for binomial coefficient.
801 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
802 ScalarEvolution &SE) const {
803 const SCEV *Result = getStart();
804 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
805 // The computation is correct in the face of overflow provided that the
806 // multiplication is performed _after_ the evaluation of the binomial
808 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
809 if (isa<SCEVCouldNotCompute>(Coeff))
812 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
817 //===----------------------------------------------------------------------===//
818 // SCEV Expression folder implementations
819 //===----------------------------------------------------------------------===//
821 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
823 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
824 "This is not a truncating conversion!");
825 assert(isSCEVable(Ty) &&
826 "This is not a conversion to a SCEVable type!");
827 Ty = getEffectiveSCEVType(Ty);
830 ID.AddInteger(scTruncate);
834 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
836 // Fold if the operand is constant.
837 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
839 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
841 // trunc(trunc(x)) --> trunc(x)
842 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
843 return getTruncateExpr(ST->getOperand(), Ty);
845 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
846 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
847 return getTruncateOrSignExtend(SS->getOperand(), Ty);
849 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
850 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
851 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
853 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
854 // eliminate all the truncates.
855 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
856 SmallVector<const SCEV *, 4> Operands;
857 bool hasTrunc = false;
858 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
859 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
860 hasTrunc = isa<SCEVTruncateExpr>(S);
861 Operands.push_back(S);
864 return getAddExpr(Operands);
865 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
868 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
869 // eliminate all the truncates.
870 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
871 SmallVector<const SCEV *, 4> Operands;
872 bool hasTrunc = false;
873 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
874 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
875 hasTrunc = isa<SCEVTruncateExpr>(S);
876 Operands.push_back(S);
879 return getMulExpr(Operands);
880 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
883 // If the input value is a chrec scev, truncate the chrec's operands.
884 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
885 SmallVector<const SCEV *, 4> Operands;
886 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
887 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
888 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
891 // The cast wasn't folded; create an explicit cast node. We can reuse
892 // the existing insert position since if we get here, we won't have
893 // made any changes which would invalidate it.
894 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
896 UniqueSCEVs.InsertNode(S, IP);
900 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
902 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
903 "This is not an extending conversion!");
904 assert(isSCEVable(Ty) &&
905 "This is not a conversion to a SCEVable type!");
906 Ty = getEffectiveSCEVType(Ty);
908 // Fold if the operand is constant.
909 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
911 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(), Ty)));
913 // zext(zext(x)) --> zext(x)
914 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
915 return getZeroExtendExpr(SZ->getOperand(), Ty);
917 // Before doing any expensive analysis, check to see if we've already
918 // computed a SCEV for this Op and Ty.
920 ID.AddInteger(scZeroExtend);
924 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
926 // zext(trunc(x)) --> zext(x) or x or trunc(x)
927 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
928 // It's possible the bits taken off by the truncate were all zero bits. If
929 // so, we should be able to simplify this further.
930 const SCEV *X = ST->getOperand();
931 ConstantRange CR = getUnsignedRange(X);
932 unsigned TruncBits = getTypeSizeInBits(ST->getType());
933 unsigned NewBits = getTypeSizeInBits(Ty);
934 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
935 CR.zextOrTrunc(NewBits)))
936 return getTruncateOrZeroExtend(X, Ty);
939 // If the input value is a chrec scev, and we can prove that the value
940 // did not overflow the old, smaller, value, we can zero extend all of the
941 // operands (often constants). This allows analysis of something like
942 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
943 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
944 if (AR->isAffine()) {
945 const SCEV *Start = AR->getStart();
946 const SCEV *Step = AR->getStepRecurrence(*this);
947 unsigned BitWidth = getTypeSizeInBits(AR->getType());
948 const Loop *L = AR->getLoop();
950 // If we have special knowledge that this addrec won't overflow,
951 // we don't need to do any further analysis.
952 if (AR->getNoWrapFlags(SCEV::FlagNUW))
953 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
954 getZeroExtendExpr(Step, Ty),
955 L, AR->getNoWrapFlags());
957 // Check whether the backedge-taken count is SCEVCouldNotCompute.
958 // Note that this serves two purposes: It filters out loops that are
959 // simply not analyzable, and it covers the case where this code is
960 // being called from within backedge-taken count analysis, such that
961 // attempting to ask for the backedge-taken count would likely result
962 // in infinite recursion. In the later case, the analysis code will
963 // cope with a conservative value, and it will take care to purge
964 // that value once it has finished.
965 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
966 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
967 // Manually compute the final value for AR, checking for
970 // Check whether the backedge-taken count can be losslessly casted to
971 // the addrec's type. The count is always unsigned.
972 const SCEV *CastedMaxBECount =
973 getTruncateOrZeroExtend(MaxBECount, Start->getType());
974 const SCEV *RecastedMaxBECount =
975 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
976 if (MaxBECount == RecastedMaxBECount) {
977 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
978 // Check whether Start+Step*MaxBECount has no unsigned overflow.
979 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
980 const SCEV *ZAdd = getZeroExtendExpr(getAddExpr(Start, ZMul), WideTy);
981 const SCEV *WideStart = getZeroExtendExpr(Start, WideTy);
982 const SCEV *WideMaxBECount =
983 getZeroExtendExpr(CastedMaxBECount, WideTy);
984 const SCEV *OperandExtendedAdd =
985 getAddExpr(WideStart,
986 getMulExpr(WideMaxBECount,
987 getZeroExtendExpr(Step, WideTy)));
988 if (ZAdd == OperandExtendedAdd) {
989 // Cache knowledge of AR NUW, which is propagated to this AddRec.
990 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
991 // Return the expression with the addrec on the outside.
992 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
993 getZeroExtendExpr(Step, Ty),
994 L, AR->getNoWrapFlags());
996 // Similar to above, only this time treat the step value as signed.
997 // This covers loops that count down.
999 getAddExpr(WideStart,
1000 getMulExpr(WideMaxBECount,
1001 getSignExtendExpr(Step, WideTy)));
1002 if (ZAdd == OperandExtendedAdd) {
1003 // Cache knowledge of AR NW, which is propagated to this AddRec.
1004 // Negative step causes unsigned wrap, but it still can't self-wrap.
1005 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1006 // Return the expression with the addrec on the outside.
1007 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1008 getSignExtendExpr(Step, Ty),
1009 L, AR->getNoWrapFlags());
1013 // If the backedge is guarded by a comparison with the pre-inc value
1014 // the addrec is safe. Also, if the entry is guarded by a comparison
1015 // with the start value and the backedge is guarded by a comparison
1016 // with the post-inc value, the addrec is safe.
1017 if (isKnownPositive(Step)) {
1018 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
1019 getUnsignedRange(Step).getUnsignedMax());
1020 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1021 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1022 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1023 AR->getPostIncExpr(*this), N))) {
1024 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1025 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1026 // Return the expression with the addrec on the outside.
1027 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1028 getZeroExtendExpr(Step, Ty),
1029 L, AR->getNoWrapFlags());
1031 } else if (isKnownNegative(Step)) {
1032 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1033 getSignedRange(Step).getSignedMin());
1034 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1035 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1036 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1037 AR->getPostIncExpr(*this), N))) {
1038 // Cache knowledge of AR NW, which is propagated to this AddRec.
1039 // Negative step causes unsigned wrap, but it still can't self-wrap.
1040 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1041 // Return the expression with the addrec on the outside.
1042 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1043 getSignExtendExpr(Step, Ty),
1044 L, AR->getNoWrapFlags());
1050 // The cast wasn't folded; create an explicit cast node.
1051 // Recompute the insert position, as it may have been invalidated.
1052 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1053 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1055 UniqueSCEVs.InsertNode(S, IP);
1059 // Get the limit of a recurrence such that incrementing by Step cannot cause
1060 // signed overflow as long as the value of the recurrence within the loop does
1061 // not exceed this limit before incrementing.
1062 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1063 ICmpInst::Predicate *Pred,
1064 ScalarEvolution *SE) {
1065 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1066 if (SE->isKnownPositive(Step)) {
1067 *Pred = ICmpInst::ICMP_SLT;
1068 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1069 SE->getSignedRange(Step).getSignedMax());
1071 if (SE->isKnownNegative(Step)) {
1072 *Pred = ICmpInst::ICMP_SGT;
1073 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1074 SE->getSignedRange(Step).getSignedMin());
1079 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1080 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1081 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1082 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1083 // result, the expression "Step + sext(PreIncAR)" is congruent with
1084 // "sext(PostIncAR)"
1085 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1087 ScalarEvolution *SE) {
1088 const Loop *L = AR->getLoop();
1089 const SCEV *Start = AR->getStart();
1090 const SCEV *Step = AR->getStepRecurrence(*SE);
1092 // Check for a simple looking step prior to loop entry.
1093 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1097 // Create an AddExpr for "PreStart" after subtracting Step. Full SCEV
1098 // subtraction is expensive. For this purpose, perform a quick and dirty
1099 // difference, by checking for Step in the operand list.
1100 SmallVector<const SCEV *, 4> DiffOps;
1101 for (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end();
1104 DiffOps.push_back(*I);
1106 if (DiffOps.size() == SA->getNumOperands())
1109 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1110 // same three conditions that getSignExtendedExpr checks.
1112 // 1. NSW flags on the step increment.
1113 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1114 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1115 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1117 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1120 // 2. Direct overflow check on the step operation's expression.
1121 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1122 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1123 const SCEV *OperandExtendedStart =
1124 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1125 SE->getSignExtendExpr(Step, WideTy));
1126 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1127 // Cache knowledge of PreAR NSW.
1129 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1130 // FIXME: this optimization needs a unit test
1131 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1135 // 3. Loop precondition.
1136 ICmpInst::Predicate Pred;
1137 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1139 if (OverflowLimit &&
1140 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1146 // Get the normalized sign-extended expression for this AddRec's Start.
1147 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1149 ScalarEvolution *SE) {
1150 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1152 return SE->getSignExtendExpr(AR->getStart(), Ty);
1154 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1155 SE->getSignExtendExpr(PreStart, Ty));
1158 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1160 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1161 "This is not an extending conversion!");
1162 assert(isSCEVable(Ty) &&
1163 "This is not a conversion to a SCEVable type!");
1164 Ty = getEffectiveSCEVType(Ty);
1166 // Fold if the operand is constant.
1167 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1169 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1171 // sext(sext(x)) --> sext(x)
1172 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1173 return getSignExtendExpr(SS->getOperand(), Ty);
1175 // sext(zext(x)) --> zext(x)
1176 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1177 return getZeroExtendExpr(SZ->getOperand(), Ty);
1179 // Before doing any expensive analysis, check to see if we've already
1180 // computed a SCEV for this Op and Ty.
1181 FoldingSetNodeID ID;
1182 ID.AddInteger(scSignExtend);
1186 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1188 // If the input value is provably positive, build a zext instead.
1189 if (isKnownNonNegative(Op))
1190 return getZeroExtendExpr(Op, Ty);
1192 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1193 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1194 // It's possible the bits taken off by the truncate were all sign bits. If
1195 // so, we should be able to simplify this further.
1196 const SCEV *X = ST->getOperand();
1197 ConstantRange CR = getSignedRange(X);
1198 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1199 unsigned NewBits = getTypeSizeInBits(Ty);
1200 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1201 CR.sextOrTrunc(NewBits)))
1202 return getTruncateOrSignExtend(X, Ty);
1205 // If the input value is a chrec scev, and we can prove that the value
1206 // did not overflow the old, smaller, value, we can sign extend all of the
1207 // operands (often constants). This allows analysis of something like
1208 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1209 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1210 if (AR->isAffine()) {
1211 const SCEV *Start = AR->getStart();
1212 const SCEV *Step = AR->getStepRecurrence(*this);
1213 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1214 const Loop *L = AR->getLoop();
1216 // If we have special knowledge that this addrec won't overflow,
1217 // we don't need to do any further analysis.
1218 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1219 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1220 getSignExtendExpr(Step, Ty),
1223 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1224 // Note that this serves two purposes: It filters out loops that are
1225 // simply not analyzable, and it covers the case where this code is
1226 // being called from within backedge-taken count analysis, such that
1227 // attempting to ask for the backedge-taken count would likely result
1228 // in infinite recursion. In the later case, the analysis code will
1229 // cope with a conservative value, and it will take care to purge
1230 // that value once it has finished.
1231 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1232 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1233 // Manually compute the final value for AR, checking for
1236 // Check whether the backedge-taken count can be losslessly casted to
1237 // the addrec's type. The count is always unsigned.
1238 const SCEV *CastedMaxBECount =
1239 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1240 const SCEV *RecastedMaxBECount =
1241 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1242 if (MaxBECount == RecastedMaxBECount) {
1243 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1244 // Check whether Start+Step*MaxBECount has no signed overflow.
1245 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1246 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1247 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1248 const SCEV *WideMaxBECount =
1249 getZeroExtendExpr(CastedMaxBECount, WideTy);
1250 const SCEV *OperandExtendedAdd =
1251 getAddExpr(WideStart,
1252 getMulExpr(WideMaxBECount,
1253 getSignExtendExpr(Step, WideTy)));
1254 if (SAdd == OperandExtendedAdd) {
1255 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1256 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1257 // Return the expression with the addrec on the outside.
1258 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1259 getSignExtendExpr(Step, Ty),
1260 L, AR->getNoWrapFlags());
1262 // Similar to above, only this time treat the step value as unsigned.
1263 // This covers loops that count up with an unsigned step.
1264 OperandExtendedAdd =
1265 getAddExpr(WideStart,
1266 getMulExpr(WideMaxBECount,
1267 getZeroExtendExpr(Step, WideTy)));
1268 if (SAdd == OperandExtendedAdd) {
1269 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1270 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1271 // Return the expression with the addrec on the outside.
1272 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1273 getZeroExtendExpr(Step, Ty),
1274 L, AR->getNoWrapFlags());
1278 // If the backedge is guarded by a comparison with the pre-inc value
1279 // the addrec is safe. Also, if the entry is guarded by a comparison
1280 // with the start value and the backedge is guarded by a comparison
1281 // with the post-inc value, the addrec is safe.
1282 ICmpInst::Predicate Pred;
1283 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1284 if (OverflowLimit &&
1285 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1286 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1287 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1289 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1290 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1291 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1292 getSignExtendExpr(Step, Ty),
1293 L, AR->getNoWrapFlags());
1298 // The cast wasn't folded; create an explicit cast node.
1299 // Recompute the insert position, as it may have been invalidated.
1300 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1301 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1303 UniqueSCEVs.InsertNode(S, IP);
1307 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1308 /// unspecified bits out to the given type.
1310 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1312 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1313 "This is not an extending conversion!");
1314 assert(isSCEVable(Ty) &&
1315 "This is not a conversion to a SCEVable type!");
1316 Ty = getEffectiveSCEVType(Ty);
1318 // Sign-extend negative constants.
1319 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1320 if (SC->getValue()->getValue().isNegative())
1321 return getSignExtendExpr(Op, Ty);
1323 // Peel off a truncate cast.
1324 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1325 const SCEV *NewOp = T->getOperand();
1326 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1327 return getAnyExtendExpr(NewOp, Ty);
1328 return getTruncateOrNoop(NewOp, Ty);
1331 // Next try a zext cast. If the cast is folded, use it.
1332 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1333 if (!isa<SCEVZeroExtendExpr>(ZExt))
1336 // Next try a sext cast. If the cast is folded, use it.
1337 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1338 if (!isa<SCEVSignExtendExpr>(SExt))
1341 // Force the cast to be folded into the operands of an addrec.
1342 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1343 SmallVector<const SCEV *, 4> Ops;
1344 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1346 Ops.push_back(getAnyExtendExpr(*I, Ty));
1347 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1350 // If the expression is obviously signed, use the sext cast value.
1351 if (isa<SCEVSMaxExpr>(Op))
1354 // Absent any other information, use the zext cast value.
1358 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1359 /// a list of operands to be added under the given scale, update the given
1360 /// map. This is a helper function for getAddRecExpr. As an example of
1361 /// what it does, given a sequence of operands that would form an add
1362 /// expression like this:
1364 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1366 /// where A and B are constants, update the map with these values:
1368 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1370 /// and add 13 + A*B*29 to AccumulatedConstant.
1371 /// This will allow getAddRecExpr to produce this:
1373 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1375 /// This form often exposes folding opportunities that are hidden in
1376 /// the original operand list.
1378 /// Return true iff it appears that any interesting folding opportunities
1379 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1380 /// the common case where no interesting opportunities are present, and
1381 /// is also used as a check to avoid infinite recursion.
1384 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1385 SmallVectorImpl<const SCEV *> &NewOps,
1386 APInt &AccumulatedConstant,
1387 const SCEV *const *Ops, size_t NumOperands,
1389 ScalarEvolution &SE) {
1390 bool Interesting = false;
1392 // Iterate over the add operands. They are sorted, with constants first.
1394 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1396 // Pull a buried constant out to the outside.
1397 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1399 AccumulatedConstant += Scale * C->getValue()->getValue();
1402 // Next comes everything else. We're especially interested in multiplies
1403 // here, but they're in the middle, so just visit the rest with one loop.
1404 for (; i != NumOperands; ++i) {
1405 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1406 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1408 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1409 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1410 // A multiplication of a constant with another add; recurse.
1411 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1413 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1414 Add->op_begin(), Add->getNumOperands(),
1417 // A multiplication of a constant with some other value. Update
1419 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1420 const SCEV *Key = SE.getMulExpr(MulOps);
1421 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1422 M.insert(std::make_pair(Key, NewScale));
1424 NewOps.push_back(Pair.first->first);
1426 Pair.first->second += NewScale;
1427 // The map already had an entry for this value, which may indicate
1428 // a folding opportunity.
1433 // An ordinary operand. Update the map.
1434 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1435 M.insert(std::make_pair(Ops[i], Scale));
1437 NewOps.push_back(Pair.first->first);
1439 Pair.first->second += Scale;
1440 // The map already had an entry for this value, which may indicate
1441 // a folding opportunity.
1451 struct APIntCompare {
1452 bool operator()(const APInt &LHS, const APInt &RHS) const {
1453 return LHS.ult(RHS);
1458 /// getAddExpr - Get a canonical add expression, or something simpler if
1460 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1461 SCEV::NoWrapFlags Flags) {
1462 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1463 "only nuw or nsw allowed");
1464 assert(!Ops.empty() && "Cannot get empty add!");
1465 if (Ops.size() == 1) return Ops[0];
1467 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1468 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1469 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1470 "SCEVAddExpr operand types don't match!");
1473 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1475 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1476 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1477 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1479 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1480 E = Ops.end(); I != E; ++I)
1481 if (!isKnownNonNegative(*I)) {
1485 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1488 // Sort by complexity, this groups all similar expression types together.
1489 GroupByComplexity(Ops, LI);
1491 // If there are any constants, fold them together.
1493 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1495 assert(Idx < Ops.size());
1496 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1497 // We found two constants, fold them together!
1498 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1499 RHSC->getValue()->getValue());
1500 if (Ops.size() == 2) return Ops[0];
1501 Ops.erase(Ops.begin()+1); // Erase the folded element
1502 LHSC = cast<SCEVConstant>(Ops[0]);
1505 // If we are left with a constant zero being added, strip it off.
1506 if (LHSC->getValue()->isZero()) {
1507 Ops.erase(Ops.begin());
1511 if (Ops.size() == 1) return Ops[0];
1514 // Okay, check to see if the same value occurs in the operand list more than
1515 // once. If so, merge them together into an multiply expression. Since we
1516 // sorted the list, these values are required to be adjacent.
1517 Type *Ty = Ops[0]->getType();
1518 bool FoundMatch = false;
1519 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1520 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1521 // Scan ahead to count how many equal operands there are.
1523 while (i+Count != e && Ops[i+Count] == Ops[i])
1525 // Merge the values into a multiply.
1526 const SCEV *Scale = getConstant(Ty, Count);
1527 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1528 if (Ops.size() == Count)
1531 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1532 --i; e -= Count - 1;
1536 return getAddExpr(Ops, Flags);
1538 // Check for truncates. If all the operands are truncated from the same
1539 // type, see if factoring out the truncate would permit the result to be
1540 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1541 // if the contents of the resulting outer trunc fold to something simple.
1542 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1543 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1544 Type *DstType = Trunc->getType();
1545 Type *SrcType = Trunc->getOperand()->getType();
1546 SmallVector<const SCEV *, 8> LargeOps;
1548 // Check all the operands to see if they can be represented in the
1549 // source type of the truncate.
1550 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1551 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1552 if (T->getOperand()->getType() != SrcType) {
1556 LargeOps.push_back(T->getOperand());
1557 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1558 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1559 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1560 SmallVector<const SCEV *, 8> LargeMulOps;
1561 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1562 if (const SCEVTruncateExpr *T =
1563 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1564 if (T->getOperand()->getType() != SrcType) {
1568 LargeMulOps.push_back(T->getOperand());
1569 } else if (const SCEVConstant *C =
1570 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1571 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1578 LargeOps.push_back(getMulExpr(LargeMulOps));
1585 // Evaluate the expression in the larger type.
1586 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1587 // If it folds to something simple, use it. Otherwise, don't.
1588 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1589 return getTruncateExpr(Fold, DstType);
1593 // Skip past any other cast SCEVs.
1594 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1597 // If there are add operands they would be next.
1598 if (Idx < Ops.size()) {
1599 bool DeletedAdd = false;
1600 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1601 // If we have an add, expand the add operands onto the end of the operands
1603 Ops.erase(Ops.begin()+Idx);
1604 Ops.append(Add->op_begin(), Add->op_end());
1608 // If we deleted at least one add, we added operands to the end of the list,
1609 // and they are not necessarily sorted. Recurse to resort and resimplify
1610 // any operands we just acquired.
1612 return getAddExpr(Ops);
1615 // Skip over the add expression until we get to a multiply.
1616 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1619 // Check to see if there are any folding opportunities present with
1620 // operands multiplied by constant values.
1621 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1622 uint64_t BitWidth = getTypeSizeInBits(Ty);
1623 DenseMap<const SCEV *, APInt> M;
1624 SmallVector<const SCEV *, 8> NewOps;
1625 APInt AccumulatedConstant(BitWidth, 0);
1626 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1627 Ops.data(), Ops.size(),
1628 APInt(BitWidth, 1), *this)) {
1629 // Some interesting folding opportunity is present, so its worthwhile to
1630 // re-generate the operands list. Group the operands by constant scale,
1631 // to avoid multiplying by the same constant scale multiple times.
1632 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1633 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1634 E = NewOps.end(); I != E; ++I)
1635 MulOpLists[M.find(*I)->second].push_back(*I);
1636 // Re-generate the operands list.
1638 if (AccumulatedConstant != 0)
1639 Ops.push_back(getConstant(AccumulatedConstant));
1640 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1641 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1643 Ops.push_back(getMulExpr(getConstant(I->first),
1644 getAddExpr(I->second)));
1646 return getConstant(Ty, 0);
1647 if (Ops.size() == 1)
1649 return getAddExpr(Ops);
1653 // If we are adding something to a multiply expression, make sure the
1654 // something is not already an operand of the multiply. If so, merge it into
1656 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1657 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1658 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1659 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1660 if (isa<SCEVConstant>(MulOpSCEV))
1662 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1663 if (MulOpSCEV == Ops[AddOp]) {
1664 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1665 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1666 if (Mul->getNumOperands() != 2) {
1667 // If the multiply has more than two operands, we must get the
1669 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1670 Mul->op_begin()+MulOp);
1671 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1672 InnerMul = getMulExpr(MulOps);
1674 const SCEV *One = getConstant(Ty, 1);
1675 const SCEV *AddOne = getAddExpr(One, InnerMul);
1676 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1677 if (Ops.size() == 2) return OuterMul;
1679 Ops.erase(Ops.begin()+AddOp);
1680 Ops.erase(Ops.begin()+Idx-1);
1682 Ops.erase(Ops.begin()+Idx);
1683 Ops.erase(Ops.begin()+AddOp-1);
1685 Ops.push_back(OuterMul);
1686 return getAddExpr(Ops);
1689 // Check this multiply against other multiplies being added together.
1690 for (unsigned OtherMulIdx = Idx+1;
1691 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1693 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1694 // If MulOp occurs in OtherMul, we can fold the two multiplies
1696 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1697 OMulOp != e; ++OMulOp)
1698 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1699 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1700 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1701 if (Mul->getNumOperands() != 2) {
1702 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1703 Mul->op_begin()+MulOp);
1704 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1705 InnerMul1 = getMulExpr(MulOps);
1707 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1708 if (OtherMul->getNumOperands() != 2) {
1709 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1710 OtherMul->op_begin()+OMulOp);
1711 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1712 InnerMul2 = getMulExpr(MulOps);
1714 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1715 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1716 if (Ops.size() == 2) return OuterMul;
1717 Ops.erase(Ops.begin()+Idx);
1718 Ops.erase(Ops.begin()+OtherMulIdx-1);
1719 Ops.push_back(OuterMul);
1720 return getAddExpr(Ops);
1726 // If there are any add recurrences in the operands list, see if any other
1727 // added values are loop invariant. If so, we can fold them into the
1729 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1732 // Scan over all recurrences, trying to fold loop invariants into them.
1733 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1734 // Scan all of the other operands to this add and add them to the vector if
1735 // they are loop invariant w.r.t. the recurrence.
1736 SmallVector<const SCEV *, 8> LIOps;
1737 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1738 const Loop *AddRecLoop = AddRec->getLoop();
1739 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1740 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1741 LIOps.push_back(Ops[i]);
1742 Ops.erase(Ops.begin()+i);
1746 // If we found some loop invariants, fold them into the recurrence.
1747 if (!LIOps.empty()) {
1748 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1749 LIOps.push_back(AddRec->getStart());
1751 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1753 AddRecOps[0] = getAddExpr(LIOps);
1755 // Build the new addrec. Propagate the NUW and NSW flags if both the
1756 // outer add and the inner addrec are guaranteed to have no overflow.
1757 // Always propagate NW.
1758 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1759 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1761 // If all of the other operands were loop invariant, we are done.
1762 if (Ops.size() == 1) return NewRec;
1764 // Otherwise, add the folded AddRec by the non-invariant parts.
1765 for (unsigned i = 0;; ++i)
1766 if (Ops[i] == AddRec) {
1770 return getAddExpr(Ops);
1773 // Okay, if there weren't any loop invariants to be folded, check to see if
1774 // there are multiple AddRec's with the same loop induction variable being
1775 // added together. If so, we can fold them.
1776 for (unsigned OtherIdx = Idx+1;
1777 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1779 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1780 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1781 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1783 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1785 if (const SCEVAddRecExpr *OtherAddRec =
1786 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1787 if (OtherAddRec->getLoop() == AddRecLoop) {
1788 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1790 if (i >= AddRecOps.size()) {
1791 AddRecOps.append(OtherAddRec->op_begin()+i,
1792 OtherAddRec->op_end());
1795 AddRecOps[i] = getAddExpr(AddRecOps[i],
1796 OtherAddRec->getOperand(i));
1798 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1800 // Step size has changed, so we cannot guarantee no self-wraparound.
1801 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1802 return getAddExpr(Ops);
1805 // Otherwise couldn't fold anything into this recurrence. Move onto the
1809 // Okay, it looks like we really DO need an add expr. Check to see if we
1810 // already have one, otherwise create a new one.
1811 FoldingSetNodeID ID;
1812 ID.AddInteger(scAddExpr);
1813 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1814 ID.AddPointer(Ops[i]);
1817 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1819 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1820 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1821 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1823 UniqueSCEVs.InsertNode(S, IP);
1825 S->setNoWrapFlags(Flags);
1829 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1831 if (j > 1 && k / j != i) Overflow = true;
1835 /// Compute the result of "n choose k", the binomial coefficient. If an
1836 /// intermediate computation overflows, Overflow will be set and the return will
1837 /// be garbage. Overflow is not cleared on absence of overflow.
1838 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1839 // We use the multiplicative formula:
1840 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1841 // At each iteration, we take the n-th term of the numeral and divide by the
1842 // (k-n)th term of the denominator. This division will always produce an
1843 // integral result, and helps reduce the chance of overflow in the
1844 // intermediate computations. However, we can still overflow even when the
1845 // final result would fit.
1847 if (n == 0 || n == k) return 1;
1848 if (k > n) return 0;
1854 for (uint64_t i = 1; i <= k; ++i) {
1855 r = umul_ov(r, n-(i-1), Overflow);
1861 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1863 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1864 SCEV::NoWrapFlags Flags) {
1865 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1866 "only nuw or nsw allowed");
1867 assert(!Ops.empty() && "Cannot get empty mul!");
1868 if (Ops.size() == 1) return Ops[0];
1870 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1871 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1872 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1873 "SCEVMulExpr operand types don't match!");
1876 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1878 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1879 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1880 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1882 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1883 E = Ops.end(); I != E; ++I)
1884 if (!isKnownNonNegative(*I)) {
1888 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1891 // Sort by complexity, this groups all similar expression types together.
1892 GroupByComplexity(Ops, LI);
1894 // If there are any constants, fold them together.
1896 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1898 // C1*(C2+V) -> C1*C2 + C1*V
1899 if (Ops.size() == 2)
1900 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1901 if (Add->getNumOperands() == 2 &&
1902 isa<SCEVConstant>(Add->getOperand(0)))
1903 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1904 getMulExpr(LHSC, Add->getOperand(1)));
1907 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1908 // We found two constants, fold them together!
1909 ConstantInt *Fold = ConstantInt::get(getContext(),
1910 LHSC->getValue()->getValue() *
1911 RHSC->getValue()->getValue());
1912 Ops[0] = getConstant(Fold);
1913 Ops.erase(Ops.begin()+1); // Erase the folded element
1914 if (Ops.size() == 1) return Ops[0];
1915 LHSC = cast<SCEVConstant>(Ops[0]);
1918 // If we are left with a constant one being multiplied, strip it off.
1919 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1920 Ops.erase(Ops.begin());
1922 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1923 // If we have a multiply of zero, it will always be zero.
1925 } else if (Ops[0]->isAllOnesValue()) {
1926 // If we have a mul by -1 of an add, try distributing the -1 among the
1928 if (Ops.size() == 2) {
1929 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1930 SmallVector<const SCEV *, 4> NewOps;
1931 bool AnyFolded = false;
1932 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1933 E = Add->op_end(); I != E; ++I) {
1934 const SCEV *Mul = getMulExpr(Ops[0], *I);
1935 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1936 NewOps.push_back(Mul);
1939 return getAddExpr(NewOps);
1941 else if (const SCEVAddRecExpr *
1942 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1943 // Negation preserves a recurrence's no self-wrap property.
1944 SmallVector<const SCEV *, 4> Operands;
1945 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1946 E = AddRec->op_end(); I != E; ++I) {
1947 Operands.push_back(getMulExpr(Ops[0], *I));
1949 return getAddRecExpr(Operands, AddRec->getLoop(),
1950 AddRec->getNoWrapFlags(SCEV::FlagNW));
1955 if (Ops.size() == 1)
1959 // Skip over the add expression until we get to a multiply.
1960 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1963 // If there are mul operands inline them all into this expression.
1964 if (Idx < Ops.size()) {
1965 bool DeletedMul = false;
1966 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1967 // If we have an mul, expand the mul operands onto the end of the operands
1969 Ops.erase(Ops.begin()+Idx);
1970 Ops.append(Mul->op_begin(), Mul->op_end());
1974 // If we deleted at least one mul, we added operands to the end of the list,
1975 // and they are not necessarily sorted. Recurse to resort and resimplify
1976 // any operands we just acquired.
1978 return getMulExpr(Ops);
1981 // If there are any add recurrences in the operands list, see if any other
1982 // added values are loop invariant. If so, we can fold them into the
1984 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1987 // Scan over all recurrences, trying to fold loop invariants into them.
1988 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1989 // Scan all of the other operands to this mul and add them to the vector if
1990 // they are loop invariant w.r.t. the recurrence.
1991 SmallVector<const SCEV *, 8> LIOps;
1992 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1993 const Loop *AddRecLoop = AddRec->getLoop();
1994 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1995 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1996 LIOps.push_back(Ops[i]);
1997 Ops.erase(Ops.begin()+i);
2001 // If we found some loop invariants, fold them into the recurrence.
2002 if (!LIOps.empty()) {
2003 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2004 SmallVector<const SCEV *, 4> NewOps;
2005 NewOps.reserve(AddRec->getNumOperands());
2006 const SCEV *Scale = getMulExpr(LIOps);
2007 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2008 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2010 // Build the new addrec. Propagate the NUW and NSW flags if both the
2011 // outer mul and the inner addrec are guaranteed to have no overflow.
2013 // No self-wrap cannot be guaranteed after changing the step size, but
2014 // will be inferred if either NUW or NSW is true.
2015 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2016 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2018 // If all of the other operands were loop invariant, we are done.
2019 if (Ops.size() == 1) return NewRec;
2021 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2022 for (unsigned i = 0;; ++i)
2023 if (Ops[i] == AddRec) {
2027 return getMulExpr(Ops);
2030 // Okay, if there weren't any loop invariants to be folded, check to see if
2031 // there are multiple AddRec's with the same loop induction variable being
2032 // multiplied together. If so, we can fold them.
2033 for (unsigned OtherIdx = Idx+1;
2034 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2036 if (AddRecLoop != cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop())
2039 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2040 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2041 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2042 // ]]],+,...up to x=2n}.
2043 // Note that the arguments to choose() are always integers with values
2044 // known at compile time, never SCEV objects.
2046 // The implementation avoids pointless extra computations when the two
2047 // addrec's are of different length (mathematically, it's equivalent to
2048 // an infinite stream of zeros on the right).
2049 bool OpsModified = false;
2050 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2052 const SCEVAddRecExpr *OtherAddRec =
2053 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2054 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2057 bool Overflow = false;
2058 Type *Ty = AddRec->getType();
2059 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2060 SmallVector<const SCEV*, 7> AddRecOps;
2061 for (int x = 0, xe = AddRec->getNumOperands() +
2062 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2063 const SCEV *Term = getConstant(Ty, 0);
2064 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2065 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2066 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2067 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2068 z < ze && !Overflow; ++z) {
2069 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2071 if (LargerThan64Bits)
2072 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2074 Coeff = Coeff1*Coeff2;
2075 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2076 const SCEV *Term1 = AddRec->getOperand(y-z);
2077 const SCEV *Term2 = OtherAddRec->getOperand(z);
2078 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2081 AddRecOps.push_back(Term);
2084 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2086 if (Ops.size() == 2) return NewAddRec;
2087 Ops[Idx] = NewAddRec;
2088 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2090 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2096 return getMulExpr(Ops);
2099 // Otherwise couldn't fold anything into this recurrence. Move onto the
2103 // Okay, it looks like we really DO need an mul expr. Check to see if we
2104 // already have one, otherwise create a new one.
2105 FoldingSetNodeID ID;
2106 ID.AddInteger(scMulExpr);
2107 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2108 ID.AddPointer(Ops[i]);
2111 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2113 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2114 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2115 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2117 UniqueSCEVs.InsertNode(S, IP);
2119 S->setNoWrapFlags(Flags);
2123 /// getUDivExpr - Get a canonical unsigned division expression, or something
2124 /// simpler if possible.
2125 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2127 assert(getEffectiveSCEVType(LHS->getType()) ==
2128 getEffectiveSCEVType(RHS->getType()) &&
2129 "SCEVUDivExpr operand types don't match!");
2131 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2132 if (RHSC->getValue()->equalsInt(1))
2133 return LHS; // X udiv 1 --> x
2134 // If the denominator is zero, the result of the udiv is undefined. Don't
2135 // try to analyze it, because the resolution chosen here may differ from
2136 // the resolution chosen in other parts of the compiler.
2137 if (!RHSC->getValue()->isZero()) {
2138 // Determine if the division can be folded into the operands of
2140 // TODO: Generalize this to non-constants by using known-bits information.
2141 Type *Ty = LHS->getType();
2142 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2143 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2144 // For non-power-of-two values, effectively round the value up to the
2145 // nearest power of two.
2146 if (!RHSC->getValue()->getValue().isPowerOf2())
2148 IntegerType *ExtTy =
2149 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2150 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2151 if (const SCEVConstant *Step =
2152 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2153 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2154 const APInt &StepInt = Step->getValue()->getValue();
2155 const APInt &DivInt = RHSC->getValue()->getValue();
2156 if (!StepInt.urem(DivInt) &&
2157 getZeroExtendExpr(AR, ExtTy) ==
2158 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2159 getZeroExtendExpr(Step, ExtTy),
2160 AR->getLoop(), SCEV::FlagAnyWrap)) {
2161 SmallVector<const SCEV *, 4> Operands;
2162 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2163 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2164 return getAddRecExpr(Operands, AR->getLoop(),
2167 /// Get a canonical UDivExpr for a recurrence.
2168 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2169 // We can currently only fold X%N if X is constant.
2170 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2171 if (StartC && !DivInt.urem(StepInt) &&
2172 getZeroExtendExpr(AR, ExtTy) ==
2173 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2174 getZeroExtendExpr(Step, ExtTy),
2175 AR->getLoop(), SCEV::FlagAnyWrap)) {
2176 const APInt &StartInt = StartC->getValue()->getValue();
2177 const APInt &StartRem = StartInt.urem(StepInt);
2179 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2180 AR->getLoop(), SCEV::FlagNW);
2183 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2184 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2185 SmallVector<const SCEV *, 4> Operands;
2186 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2187 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2188 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2189 // Find an operand that's safely divisible.
2190 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2191 const SCEV *Op = M->getOperand(i);
2192 const SCEV *Div = getUDivExpr(Op, RHSC);
2193 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2194 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2197 return getMulExpr(Operands);
2201 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2202 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2203 SmallVector<const SCEV *, 4> Operands;
2204 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2205 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2206 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2208 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2209 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2210 if (isa<SCEVUDivExpr>(Op) ||
2211 getMulExpr(Op, RHS) != A->getOperand(i))
2213 Operands.push_back(Op);
2215 if (Operands.size() == A->getNumOperands())
2216 return getAddExpr(Operands);
2220 // Fold if both operands are constant.
2221 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2222 Constant *LHSCV = LHSC->getValue();
2223 Constant *RHSCV = RHSC->getValue();
2224 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2230 FoldingSetNodeID ID;
2231 ID.AddInteger(scUDivExpr);
2235 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2236 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2238 UniqueSCEVs.InsertNode(S, IP);
2242 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2243 APInt A = C1->getValue()->getValue().abs();
2244 APInt B = C2->getValue()->getValue().abs();
2245 uint32_t ABW = A.getBitWidth();
2246 uint32_t BBW = B.getBitWidth();
2253 return APIntOps::GreatestCommonDivisor(A, B);
2256 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2257 /// something simpler if possible. There is no representation for an exact udiv
2258 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2259 /// We can't do this when it's not exact because the udiv may be clearing bits.
2260 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2262 // TODO: we could try to find factors in all sorts of things, but for now we
2263 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2264 // end of this file for inspiration.
2266 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2268 return getUDivExpr(LHS, RHS);
2270 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2271 // If the mulexpr multiplies by a constant, then that constant must be the
2272 // first element of the mulexpr.
2273 if (const SCEVConstant *LHSCst =
2274 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2275 if (LHSCst == RHSCst) {
2276 SmallVector<const SCEV *, 2> Operands;
2277 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2278 return getMulExpr(Operands);
2281 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2282 // that there's a factor provided by one of the other terms. We need to
2284 APInt Factor = gcd(LHSCst, RHSCst);
2285 if (!Factor.isIntN(1)) {
2286 LHSCst = cast<SCEVConstant>(
2287 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2288 RHSCst = cast<SCEVConstant>(
2289 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2290 SmallVector<const SCEV *, 2> Operands;
2291 Operands.push_back(LHSCst);
2292 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2293 LHS = getMulExpr(Operands);
2295 Mul = dyn_cast<SCEVMulExpr>(LHS);
2297 return getUDivExactExpr(LHS, RHS);
2302 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2303 if (Mul->getOperand(i) == RHS) {
2304 SmallVector<const SCEV *, 2> Operands;
2305 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2306 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2307 return getMulExpr(Operands);
2311 return getUDivExpr(LHS, RHS);
2314 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2315 /// Simplify the expression as much as possible.
2316 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2318 SCEV::NoWrapFlags Flags) {
2319 SmallVector<const SCEV *, 4> Operands;
2320 Operands.push_back(Start);
2321 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2322 if (StepChrec->getLoop() == L) {
2323 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2324 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2327 Operands.push_back(Step);
2328 return getAddRecExpr(Operands, L, Flags);
2331 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2332 /// Simplify the expression as much as possible.
2334 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2335 const Loop *L, SCEV::NoWrapFlags Flags) {
2336 if (Operands.size() == 1) return Operands[0];
2338 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2339 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2340 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2341 "SCEVAddRecExpr operand types don't match!");
2342 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2343 assert(isLoopInvariant(Operands[i], L) &&
2344 "SCEVAddRecExpr operand is not loop-invariant!");
2347 if (Operands.back()->isZero()) {
2348 Operands.pop_back();
2349 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2352 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2353 // use that information to infer NUW and NSW flags. However, computing a
2354 // BE count requires calling getAddRecExpr, so we may not yet have a
2355 // meaningful BE count at this point (and if we don't, we'd be stuck
2356 // with a SCEVCouldNotCompute as the cached BE count).
2358 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2360 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2361 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2362 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2364 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2365 E = Operands.end(); I != E; ++I)
2366 if (!isKnownNonNegative(*I)) {
2370 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2373 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2374 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2375 const Loop *NestedLoop = NestedAR->getLoop();
2376 if (L->contains(NestedLoop) ?
2377 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2378 (!NestedLoop->contains(L) &&
2379 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2380 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2381 NestedAR->op_end());
2382 Operands[0] = NestedAR->getStart();
2383 // AddRecs require their operands be loop-invariant with respect to their
2384 // loops. Don't perform this transformation if it would break this
2386 bool AllInvariant = true;
2387 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2388 if (!isLoopInvariant(Operands[i], L)) {
2389 AllInvariant = false;
2393 // Create a recurrence for the outer loop with the same step size.
2395 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2396 // inner recurrence has the same property.
2397 SCEV::NoWrapFlags OuterFlags =
2398 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2400 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2401 AllInvariant = true;
2402 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2403 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2404 AllInvariant = false;
2408 // Ok, both add recurrences are valid after the transformation.
2410 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2411 // the outer recurrence has the same property.
2412 SCEV::NoWrapFlags InnerFlags =
2413 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2414 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2417 // Reset Operands to its original state.
2418 Operands[0] = NestedAR;
2422 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2423 // already have one, otherwise create a new one.
2424 FoldingSetNodeID ID;
2425 ID.AddInteger(scAddRecExpr);
2426 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2427 ID.AddPointer(Operands[i]);
2431 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2433 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2434 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2435 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2436 O, Operands.size(), L);
2437 UniqueSCEVs.InsertNode(S, IP);
2439 S->setNoWrapFlags(Flags);
2443 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2445 SmallVector<const SCEV *, 2> Ops;
2448 return getSMaxExpr(Ops);
2452 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2453 assert(!Ops.empty() && "Cannot get empty smax!");
2454 if (Ops.size() == 1) return Ops[0];
2456 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2457 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2458 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2459 "SCEVSMaxExpr operand types don't match!");
2462 // Sort by complexity, this groups all similar expression types together.
2463 GroupByComplexity(Ops, LI);
2465 // If there are any constants, fold them together.
2467 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2469 assert(Idx < Ops.size());
2470 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2471 // We found two constants, fold them together!
2472 ConstantInt *Fold = ConstantInt::get(getContext(),
2473 APIntOps::smax(LHSC->getValue()->getValue(),
2474 RHSC->getValue()->getValue()));
2475 Ops[0] = getConstant(Fold);
2476 Ops.erase(Ops.begin()+1); // Erase the folded element
2477 if (Ops.size() == 1) return Ops[0];
2478 LHSC = cast<SCEVConstant>(Ops[0]);
2481 // If we are left with a constant minimum-int, strip it off.
2482 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2483 Ops.erase(Ops.begin());
2485 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2486 // If we have an smax with a constant maximum-int, it will always be
2491 if (Ops.size() == 1) return Ops[0];
2494 // Find the first SMax
2495 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2498 // Check to see if one of the operands is an SMax. If so, expand its operands
2499 // onto our operand list, and recurse to simplify.
2500 if (Idx < Ops.size()) {
2501 bool DeletedSMax = false;
2502 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2503 Ops.erase(Ops.begin()+Idx);
2504 Ops.append(SMax->op_begin(), SMax->op_end());
2509 return getSMaxExpr(Ops);
2512 // Okay, check to see if the same value occurs in the operand list twice. If
2513 // so, delete one. Since we sorted the list, these values are required to
2515 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2516 // X smax Y smax Y --> X smax Y
2517 // X smax Y --> X, if X is always greater than Y
2518 if (Ops[i] == Ops[i+1] ||
2519 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2520 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2522 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2523 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2527 if (Ops.size() == 1) return Ops[0];
2529 assert(!Ops.empty() && "Reduced smax down to nothing!");
2531 // Okay, it looks like we really DO need an smax expr. Check to see if we
2532 // already have one, otherwise create a new one.
2533 FoldingSetNodeID ID;
2534 ID.AddInteger(scSMaxExpr);
2535 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2536 ID.AddPointer(Ops[i]);
2538 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2539 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2540 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2541 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2543 UniqueSCEVs.InsertNode(S, IP);
2547 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2549 SmallVector<const SCEV *, 2> Ops;
2552 return getUMaxExpr(Ops);
2556 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2557 assert(!Ops.empty() && "Cannot get empty umax!");
2558 if (Ops.size() == 1) return Ops[0];
2560 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2561 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2562 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2563 "SCEVUMaxExpr operand types don't match!");
2566 // Sort by complexity, this groups all similar expression types together.
2567 GroupByComplexity(Ops, LI);
2569 // If there are any constants, fold them together.
2571 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2573 assert(Idx < Ops.size());
2574 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2575 // We found two constants, fold them together!
2576 ConstantInt *Fold = ConstantInt::get(getContext(),
2577 APIntOps::umax(LHSC->getValue()->getValue(),
2578 RHSC->getValue()->getValue()));
2579 Ops[0] = getConstant(Fold);
2580 Ops.erase(Ops.begin()+1); // Erase the folded element
2581 if (Ops.size() == 1) return Ops[0];
2582 LHSC = cast<SCEVConstant>(Ops[0]);
2585 // If we are left with a constant minimum-int, strip it off.
2586 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2587 Ops.erase(Ops.begin());
2589 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2590 // If we have an umax with a constant maximum-int, it will always be
2595 if (Ops.size() == 1) return Ops[0];
2598 // Find the first UMax
2599 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2602 // Check to see if one of the operands is a UMax. If so, expand its operands
2603 // onto our operand list, and recurse to simplify.
2604 if (Idx < Ops.size()) {
2605 bool DeletedUMax = false;
2606 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2607 Ops.erase(Ops.begin()+Idx);
2608 Ops.append(UMax->op_begin(), UMax->op_end());
2613 return getUMaxExpr(Ops);
2616 // Okay, check to see if the same value occurs in the operand list twice. If
2617 // so, delete one. Since we sorted the list, these values are required to
2619 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2620 // X umax Y umax Y --> X umax Y
2621 // X umax Y --> X, if X is always greater than Y
2622 if (Ops[i] == Ops[i+1] ||
2623 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2624 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2626 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2627 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2631 if (Ops.size() == 1) return Ops[0];
2633 assert(!Ops.empty() && "Reduced umax down to nothing!");
2635 // Okay, it looks like we really DO need a umax expr. Check to see if we
2636 // already have one, otherwise create a new one.
2637 FoldingSetNodeID ID;
2638 ID.AddInteger(scUMaxExpr);
2639 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2640 ID.AddPointer(Ops[i]);
2642 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2643 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2644 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2645 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2647 UniqueSCEVs.InsertNode(S, IP);
2651 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2653 // ~smax(~x, ~y) == smin(x, y).
2654 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2657 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2659 // ~umax(~x, ~y) == umin(x, y)
2660 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2663 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2664 // If we have DataLayout, we can bypass creating a target-independent
2665 // constant expression and then folding it back into a ConstantInt.
2666 // This is just a compile-time optimization.
2668 return getConstant(IntTy, TD->getTypeAllocSize(AllocTy));
2670 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2671 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2672 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2674 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2675 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2676 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2679 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2682 // If we have DataLayout, we can bypass creating a target-independent
2683 // constant expression and then folding it back into a ConstantInt.
2684 // This is just a compile-time optimization.
2686 return getConstant(IntTy,
2687 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2690 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2691 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2692 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD, TLI))
2695 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2696 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2699 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2700 // Don't attempt to do anything other than create a SCEVUnknown object
2701 // here. createSCEV only calls getUnknown after checking for all other
2702 // interesting possibilities, and any other code that calls getUnknown
2703 // is doing so in order to hide a value from SCEV canonicalization.
2705 FoldingSetNodeID ID;
2706 ID.AddInteger(scUnknown);
2709 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2710 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2711 "Stale SCEVUnknown in uniquing map!");
2714 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2716 FirstUnknown = cast<SCEVUnknown>(S);
2717 UniqueSCEVs.InsertNode(S, IP);
2721 //===----------------------------------------------------------------------===//
2722 // Basic SCEV Analysis and PHI Idiom Recognition Code
2725 /// isSCEVable - Test if values of the given type are analyzable within
2726 /// the SCEV framework. This primarily includes integer types, and it
2727 /// can optionally include pointer types if the ScalarEvolution class
2728 /// has access to target-specific information.
2729 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2730 // Integers and pointers are always SCEVable.
2731 return Ty->isIntegerTy() || Ty->isPointerTy();
2734 /// getTypeSizeInBits - Return the size in bits of the specified type,
2735 /// for which isSCEVable must return true.
2736 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2737 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2739 // If we have a DataLayout, use it!
2741 return TD->getTypeSizeInBits(Ty);
2743 // Integer types have fixed sizes.
2744 if (Ty->isIntegerTy())
2745 return Ty->getPrimitiveSizeInBits();
2747 // The only other support type is pointer. Without DataLayout, conservatively
2748 // assume pointers are 64-bit.
2749 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2753 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2754 /// the given type and which represents how SCEV will treat the given
2755 /// type, for which isSCEVable must return true. For pointer types,
2756 /// this is the pointer-sized integer type.
2757 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2758 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2760 if (Ty->isIntegerTy()) {
2764 // The only other support type is pointer.
2765 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2768 return TD->getIntPtrType(Ty);
2770 // Without DataLayout, conservatively assume pointers are 64-bit.
2771 return Type::getInt64Ty(getContext());
2774 const SCEV *ScalarEvolution::getCouldNotCompute() {
2775 return &CouldNotCompute;
2779 // Helper class working with SCEVTraversal to figure out if a SCEV contains
2780 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
2781 // is set iff if find such SCEVUnknown.
2783 struct FindInvalidSCEVUnknown {
2785 FindInvalidSCEVUnknown() { FindOne = false; }
2786 bool follow(const SCEV *S) {
2787 switch (S->getSCEVType()) {
2791 if (!cast<SCEVUnknown>(S)->getValue())
2798 bool isDone() const { return FindOne; }
2802 bool ScalarEvolution::checkValidity(const SCEV *S) const {
2803 FindInvalidSCEVUnknown F;
2804 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
2810 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2811 /// expression and create a new one.
2812 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2813 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2815 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
2816 if (I != ValueExprMap.end()) {
2817 const SCEV *S = I->second;
2818 if (checkValidity(S))
2821 ValueExprMap.erase(I);
2823 const SCEV *S = createSCEV(V);
2825 // The process of creating a SCEV for V may have caused other SCEVs
2826 // to have been created, so it's necessary to insert the new entry
2827 // from scratch, rather than trying to remember the insert position
2829 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2833 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2835 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2836 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2838 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2840 Type *Ty = V->getType();
2841 Ty = getEffectiveSCEVType(Ty);
2842 return getMulExpr(V,
2843 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2846 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2847 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2848 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2850 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2852 Type *Ty = V->getType();
2853 Ty = getEffectiveSCEVType(Ty);
2854 const SCEV *AllOnes =
2855 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2856 return getMinusSCEV(AllOnes, V);
2859 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2860 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2861 SCEV::NoWrapFlags Flags) {
2862 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2864 // Fast path: X - X --> 0.
2866 return getConstant(LHS->getType(), 0);
2869 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2872 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2873 /// input value to the specified type. If the type must be extended, it is zero
2876 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2877 Type *SrcTy = V->getType();
2878 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2879 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2880 "Cannot truncate or zero extend with non-integer arguments!");
2881 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2882 return V; // No conversion
2883 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2884 return getTruncateExpr(V, Ty);
2885 return getZeroExtendExpr(V, Ty);
2888 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2889 /// input value to the specified type. If the type must be extended, it is sign
2892 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2894 Type *SrcTy = V->getType();
2895 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2896 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2897 "Cannot truncate or zero extend with non-integer arguments!");
2898 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2899 return V; // No conversion
2900 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2901 return getTruncateExpr(V, Ty);
2902 return getSignExtendExpr(V, Ty);
2905 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2906 /// input value to the specified type. If the type must be extended, it is zero
2907 /// extended. The conversion must not be narrowing.
2909 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2910 Type *SrcTy = V->getType();
2911 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2912 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2913 "Cannot noop or zero extend with non-integer arguments!");
2914 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2915 "getNoopOrZeroExtend cannot truncate!");
2916 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2917 return V; // No conversion
2918 return getZeroExtendExpr(V, Ty);
2921 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2922 /// input value to the specified type. If the type must be extended, it is sign
2923 /// extended. The conversion must not be narrowing.
2925 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2926 Type *SrcTy = V->getType();
2927 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2928 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2929 "Cannot noop or sign extend with non-integer arguments!");
2930 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2931 "getNoopOrSignExtend cannot truncate!");
2932 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2933 return V; // No conversion
2934 return getSignExtendExpr(V, Ty);
2937 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2938 /// the input value to the specified type. If the type must be extended,
2939 /// it is extended with unspecified bits. The conversion must not be
2942 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2943 Type *SrcTy = V->getType();
2944 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2945 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2946 "Cannot noop or any extend with non-integer arguments!");
2947 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2948 "getNoopOrAnyExtend cannot truncate!");
2949 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2950 return V; // No conversion
2951 return getAnyExtendExpr(V, Ty);
2954 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2955 /// input value to the specified type. The conversion must not be widening.
2957 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2958 Type *SrcTy = V->getType();
2959 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2960 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2961 "Cannot truncate or noop with non-integer arguments!");
2962 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2963 "getTruncateOrNoop cannot extend!");
2964 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2965 return V; // No conversion
2966 return getTruncateExpr(V, Ty);
2969 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2970 /// the types using zero-extension, and then perform a umax operation
2972 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2974 const SCEV *PromotedLHS = LHS;
2975 const SCEV *PromotedRHS = RHS;
2977 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2978 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2980 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2982 return getUMaxExpr(PromotedLHS, PromotedRHS);
2985 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2986 /// the types using zero-extension, and then perform a umin operation
2988 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2990 const SCEV *PromotedLHS = LHS;
2991 const SCEV *PromotedRHS = RHS;
2993 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2994 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2996 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2998 return getUMinExpr(PromotedLHS, PromotedRHS);
3001 /// getPointerBase - Transitively follow the chain of pointer-type operands
3002 /// until reaching a SCEV that does not have a single pointer operand. This
3003 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3004 /// but corner cases do exist.
3005 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3006 // A pointer operand may evaluate to a nonpointer expression, such as null.
3007 if (!V->getType()->isPointerTy())
3010 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3011 return getPointerBase(Cast->getOperand());
3013 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3014 const SCEV *PtrOp = 0;
3015 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3017 if ((*I)->getType()->isPointerTy()) {
3018 // Cannot find the base of an expression with multiple pointer operands.
3026 return getPointerBase(PtrOp);
3031 /// PushDefUseChildren - Push users of the given Instruction
3032 /// onto the given Worklist.
3034 PushDefUseChildren(Instruction *I,
3035 SmallVectorImpl<Instruction *> &Worklist) {
3036 // Push the def-use children onto the Worklist stack.
3037 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
3039 Worklist.push_back(cast<Instruction>(*UI));
3042 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3043 /// instructions that depend on the given instruction and removes them from
3044 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3047 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3048 SmallVector<Instruction *, 16> Worklist;
3049 PushDefUseChildren(PN, Worklist);
3051 SmallPtrSet<Instruction *, 8> Visited;
3053 while (!Worklist.empty()) {
3054 Instruction *I = Worklist.pop_back_val();
3055 if (!Visited.insert(I)) continue;
3057 ValueExprMapType::iterator It =
3058 ValueExprMap.find_as(static_cast<Value *>(I));
3059 if (It != ValueExprMap.end()) {
3060 const SCEV *Old = It->second;
3062 // Short-circuit the def-use traversal if the symbolic name
3063 // ceases to appear in expressions.
3064 if (Old != SymName && !hasOperand(Old, SymName))
3067 // SCEVUnknown for a PHI either means that it has an unrecognized
3068 // structure, it's a PHI that's in the progress of being computed
3069 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3070 // additional loop trip count information isn't going to change anything.
3071 // In the second case, createNodeForPHI will perform the necessary
3072 // updates on its own when it gets to that point. In the third, we do
3073 // want to forget the SCEVUnknown.
3074 if (!isa<PHINode>(I) ||
3075 !isa<SCEVUnknown>(Old) ||
3076 (I != PN && Old == SymName)) {
3077 forgetMemoizedResults(Old);
3078 ValueExprMap.erase(It);
3082 PushDefUseChildren(I, Worklist);
3086 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3087 /// a loop header, making it a potential recurrence, or it doesn't.
3089 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3090 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3091 if (L->getHeader() == PN->getParent()) {
3092 // The loop may have multiple entrances or multiple exits; we can analyze
3093 // this phi as an addrec if it has a unique entry value and a unique
3095 Value *BEValueV = 0, *StartValueV = 0;
3096 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3097 Value *V = PN->getIncomingValue(i);
3098 if (L->contains(PN->getIncomingBlock(i))) {
3101 } else if (BEValueV != V) {
3105 } else if (!StartValueV) {
3107 } else if (StartValueV != V) {
3112 if (BEValueV && StartValueV) {
3113 // While we are analyzing this PHI node, handle its value symbolically.
3114 const SCEV *SymbolicName = getUnknown(PN);
3115 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3116 "PHI node already processed?");
3117 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3119 // Using this symbolic name for the PHI, analyze the value coming around
3121 const SCEV *BEValue = getSCEV(BEValueV);
3123 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3124 // has a special value for the first iteration of the loop.
3126 // If the value coming around the backedge is an add with the symbolic
3127 // value we just inserted, then we found a simple induction variable!
3128 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3129 // If there is a single occurrence of the symbolic value, replace it
3130 // with a recurrence.
3131 unsigned FoundIndex = Add->getNumOperands();
3132 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3133 if (Add->getOperand(i) == SymbolicName)
3134 if (FoundIndex == e) {
3139 if (FoundIndex != Add->getNumOperands()) {
3140 // Create an add with everything but the specified operand.
3141 SmallVector<const SCEV *, 8> Ops;
3142 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3143 if (i != FoundIndex)
3144 Ops.push_back(Add->getOperand(i));
3145 const SCEV *Accum = getAddExpr(Ops);
3147 // This is not a valid addrec if the step amount is varying each
3148 // loop iteration, but is not itself an addrec in this loop.
3149 if (isLoopInvariant(Accum, L) ||
3150 (isa<SCEVAddRecExpr>(Accum) &&
3151 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3152 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3154 // If the increment doesn't overflow, then neither the addrec nor
3155 // the post-increment will overflow.
3156 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3157 if (OBO->hasNoUnsignedWrap())
3158 Flags = setFlags(Flags, SCEV::FlagNUW);
3159 if (OBO->hasNoSignedWrap())
3160 Flags = setFlags(Flags, SCEV::FlagNSW);
3161 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3162 // If the increment is an inbounds GEP, then we know the address
3163 // space cannot be wrapped around. We cannot make any guarantee
3164 // about signed or unsigned overflow because pointers are
3165 // unsigned but we may have a negative index from the base
3166 // pointer. We can guarantee that no unsigned wrap occurs if the
3167 // indices form a positive value.
3168 if (GEP->isInBounds()) {
3169 Flags = setFlags(Flags, SCEV::FlagNW);
3171 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3172 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3173 Flags = setFlags(Flags, SCEV::FlagNUW);
3175 } else if (const SubOperator *OBO =
3176 dyn_cast<SubOperator>(BEValueV)) {
3177 if (OBO->hasNoUnsignedWrap())
3178 Flags = setFlags(Flags, SCEV::FlagNUW);
3179 if (OBO->hasNoSignedWrap())
3180 Flags = setFlags(Flags, SCEV::FlagNSW);
3183 const SCEV *StartVal = getSCEV(StartValueV);
3184 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3186 // Since the no-wrap flags are on the increment, they apply to the
3187 // post-incremented value as well.
3188 if (isLoopInvariant(Accum, L))
3189 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3192 // Okay, for the entire analysis of this edge we assumed the PHI
3193 // to be symbolic. We now need to go back and purge all of the
3194 // entries for the scalars that use the symbolic expression.
3195 ForgetSymbolicName(PN, SymbolicName);
3196 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3200 } else if (const SCEVAddRecExpr *AddRec =
3201 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3202 // Otherwise, this could be a loop like this:
3203 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3204 // In this case, j = {1,+,1} and BEValue is j.
3205 // Because the other in-value of i (0) fits the evolution of BEValue
3206 // i really is an addrec evolution.
3207 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3208 const SCEV *StartVal = getSCEV(StartValueV);
3210 // If StartVal = j.start - j.stride, we can use StartVal as the
3211 // initial step of the addrec evolution.
3212 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3213 AddRec->getOperand(1))) {
3214 // FIXME: For constant StartVal, we should be able to infer
3216 const SCEV *PHISCEV =
3217 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3220 // Okay, for the entire analysis of this edge we assumed the PHI
3221 // to be symbolic. We now need to go back and purge all of the
3222 // entries for the scalars that use the symbolic expression.
3223 ForgetSymbolicName(PN, SymbolicName);
3224 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3232 // If the PHI has a single incoming value, follow that value, unless the
3233 // PHI's incoming blocks are in a different loop, in which case doing so
3234 // risks breaking LCSSA form. Instcombine would normally zap these, but
3235 // it doesn't have DominatorTree information, so it may miss cases.
3236 if (Value *V = SimplifyInstruction(PN, TD, TLI, DT))
3237 if (LI->replacementPreservesLCSSAForm(PN, V))
3240 // If it's not a loop phi, we can't handle it yet.
3241 return getUnknown(PN);
3244 /// createNodeForGEP - Expand GEP instructions into add and multiply
3245 /// operations. This allows them to be analyzed by regular SCEV code.
3247 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3248 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3249 Value *Base = GEP->getOperand(0);
3250 // Don't attempt to analyze GEPs over unsized objects.
3251 if (!Base->getType()->getPointerElementType()->isSized())
3252 return getUnknown(GEP);
3254 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3255 // Add expression, because the Instruction may be guarded by control flow
3256 // and the no-overflow bits may not be valid for the expression in any
3258 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3260 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3261 gep_type_iterator GTI = gep_type_begin(GEP);
3262 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3266 // Compute the (potentially symbolic) offset in bytes for this index.
3267 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3268 // For a struct, add the member offset.
3269 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3270 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3272 // Add the field offset to the running total offset.
3273 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3275 // For an array, add the element offset, explicitly scaled.
3276 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3277 const SCEV *IndexS = getSCEV(Index);
3278 // Getelementptr indices are signed.
3279 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3281 // Multiply the index by the element size to compute the element offset.
3282 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3284 // Add the element offset to the running total offset.
3285 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3289 // Get the SCEV for the GEP base.
3290 const SCEV *BaseS = getSCEV(Base);
3292 // Add the total offset from all the GEP indices to the base.
3293 return getAddExpr(BaseS, TotalOffset, Wrap);
3296 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3297 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3298 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3299 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3301 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3302 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3303 return C->getValue()->getValue().countTrailingZeros();
3305 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3306 return std::min(GetMinTrailingZeros(T->getOperand()),
3307 (uint32_t)getTypeSizeInBits(T->getType()));
3309 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3310 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3311 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3312 getTypeSizeInBits(E->getType()) : OpRes;
3315 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3316 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3317 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3318 getTypeSizeInBits(E->getType()) : OpRes;
3321 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3322 // The result is the min of all operands results.
3323 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3324 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3325 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3329 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3330 // The result is the sum of all operands results.
3331 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3332 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3333 for (unsigned i = 1, e = M->getNumOperands();
3334 SumOpRes != BitWidth && i != e; ++i)
3335 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3340 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3341 // The result is the min of all operands results.
3342 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3343 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3344 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3348 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3349 // The result is the min of all operands results.
3350 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3351 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3352 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3356 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3357 // The result is the min of all operands results.
3358 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3359 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3360 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3364 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3365 // For a SCEVUnknown, ask ValueTracking.
3366 unsigned BitWidth = getTypeSizeInBits(U->getType());
3367 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3368 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3369 return Zeros.countTrailingOnes();
3376 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3379 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3380 // See if we've computed this range already.
3381 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3382 if (I != UnsignedRanges.end())
3385 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3386 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3388 unsigned BitWidth = getTypeSizeInBits(S->getType());
3389 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3391 // If the value has known zeros, the maximum unsigned value will have those
3392 // known zeros as well.
3393 uint32_t TZ = GetMinTrailingZeros(S);
3395 ConservativeResult =
3396 ConstantRange(APInt::getMinValue(BitWidth),
3397 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3399 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3400 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3401 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3402 X = X.add(getUnsignedRange(Add->getOperand(i)));
3403 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3406 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3407 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3408 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3409 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3410 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3413 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3414 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3415 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3416 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3417 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3420 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3421 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3422 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3423 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3424 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3427 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3428 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3429 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3430 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3433 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3434 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3435 return setUnsignedRange(ZExt,
3436 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3439 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3440 ConstantRange X = getUnsignedRange(SExt->getOperand());
3441 return setUnsignedRange(SExt,
3442 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3445 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3446 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3447 return setUnsignedRange(Trunc,
3448 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3451 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3452 // If there's no unsigned wrap, the value will never be less than its
3454 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3455 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3456 if (!C->getValue()->isZero())
3457 ConservativeResult =
3458 ConservativeResult.intersectWith(
3459 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3461 // TODO: non-affine addrec
3462 if (AddRec->isAffine()) {
3463 Type *Ty = AddRec->getType();
3464 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3465 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3466 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3467 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3469 const SCEV *Start = AddRec->getStart();
3470 const SCEV *Step = AddRec->getStepRecurrence(*this);
3472 ConstantRange StartRange = getUnsignedRange(Start);
3473 ConstantRange StepRange = getSignedRange(Step);
3474 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3475 ConstantRange EndRange =
3476 StartRange.add(MaxBECountRange.multiply(StepRange));
3478 // Check for overflow. This must be done with ConstantRange arithmetic
3479 // because we could be called from within the ScalarEvolution overflow
3481 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3482 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3483 ConstantRange ExtMaxBECountRange =
3484 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3485 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3486 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3488 return setUnsignedRange(AddRec, ConservativeResult);
3490 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3491 EndRange.getUnsignedMin());
3492 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3493 EndRange.getUnsignedMax());
3494 if (Min.isMinValue() && Max.isMaxValue())
3495 return setUnsignedRange(AddRec, ConservativeResult);
3496 return setUnsignedRange(AddRec,
3497 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3501 return setUnsignedRange(AddRec, ConservativeResult);
3504 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3505 // For a SCEVUnknown, ask ValueTracking.
3506 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3507 ComputeMaskedBits(U->getValue(), Zeros, Ones, TD);
3508 if (Ones == ~Zeros + 1)
3509 return setUnsignedRange(U, ConservativeResult);
3510 return setUnsignedRange(U,
3511 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3514 return setUnsignedRange(S, ConservativeResult);
3517 /// getSignedRange - Determine the signed range for a particular SCEV.
3520 ScalarEvolution::getSignedRange(const SCEV *S) {
3521 // See if we've computed this range already.
3522 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3523 if (I != SignedRanges.end())
3526 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3527 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3529 unsigned BitWidth = getTypeSizeInBits(S->getType());
3530 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3532 // If the value has known zeros, the maximum signed value will have those
3533 // known zeros as well.
3534 uint32_t TZ = GetMinTrailingZeros(S);
3536 ConservativeResult =
3537 ConstantRange(APInt::getSignedMinValue(BitWidth),
3538 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3540 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3541 ConstantRange X = getSignedRange(Add->getOperand(0));
3542 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3543 X = X.add(getSignedRange(Add->getOperand(i)));
3544 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3547 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3548 ConstantRange X = getSignedRange(Mul->getOperand(0));
3549 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3550 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3551 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3554 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3555 ConstantRange X = getSignedRange(SMax->getOperand(0));
3556 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3557 X = X.smax(getSignedRange(SMax->getOperand(i)));
3558 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3561 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3562 ConstantRange X = getSignedRange(UMax->getOperand(0));
3563 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3564 X = X.umax(getSignedRange(UMax->getOperand(i)));
3565 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3568 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3569 ConstantRange X = getSignedRange(UDiv->getLHS());
3570 ConstantRange Y = getSignedRange(UDiv->getRHS());
3571 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3574 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3575 ConstantRange X = getSignedRange(ZExt->getOperand());
3576 return setSignedRange(ZExt,
3577 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3580 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3581 ConstantRange X = getSignedRange(SExt->getOperand());
3582 return setSignedRange(SExt,
3583 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3586 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3587 ConstantRange X = getSignedRange(Trunc->getOperand());
3588 return setSignedRange(Trunc,
3589 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3592 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3593 // If there's no signed wrap, and all the operands have the same sign or
3594 // zero, the value won't ever change sign.
3595 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3596 bool AllNonNeg = true;
3597 bool AllNonPos = true;
3598 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3599 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3600 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3603 ConservativeResult = ConservativeResult.intersectWith(
3604 ConstantRange(APInt(BitWidth, 0),
3605 APInt::getSignedMinValue(BitWidth)));
3607 ConservativeResult = ConservativeResult.intersectWith(
3608 ConstantRange(APInt::getSignedMinValue(BitWidth),
3609 APInt(BitWidth, 1)));
3612 // TODO: non-affine addrec
3613 if (AddRec->isAffine()) {
3614 Type *Ty = AddRec->getType();
3615 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3616 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3617 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3618 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3620 const SCEV *Start = AddRec->getStart();
3621 const SCEV *Step = AddRec->getStepRecurrence(*this);
3623 ConstantRange StartRange = getSignedRange(Start);
3624 ConstantRange StepRange = getSignedRange(Step);
3625 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3626 ConstantRange EndRange =
3627 StartRange.add(MaxBECountRange.multiply(StepRange));
3629 // Check for overflow. This must be done with ConstantRange arithmetic
3630 // because we could be called from within the ScalarEvolution overflow
3632 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3633 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3634 ConstantRange ExtMaxBECountRange =
3635 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3636 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3637 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3639 return setSignedRange(AddRec, ConservativeResult);
3641 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3642 EndRange.getSignedMin());
3643 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3644 EndRange.getSignedMax());
3645 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3646 return setSignedRange(AddRec, ConservativeResult);
3647 return setSignedRange(AddRec,
3648 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3652 return setSignedRange(AddRec, ConservativeResult);
3655 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3656 // For a SCEVUnknown, ask ValueTracking.
3657 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3658 return setSignedRange(U, ConservativeResult);
3659 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3661 return setSignedRange(U, ConservativeResult);
3662 return setSignedRange(U, ConservativeResult.intersectWith(
3663 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3664 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3667 return setSignedRange(S, ConservativeResult);
3670 /// createSCEV - We know that there is no SCEV for the specified value.
3671 /// Analyze the expression.
3673 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3674 if (!isSCEVable(V->getType()))
3675 return getUnknown(V);
3677 unsigned Opcode = Instruction::UserOp1;
3678 if (Instruction *I = dyn_cast<Instruction>(V)) {
3679 Opcode = I->getOpcode();
3681 // Don't attempt to analyze instructions in blocks that aren't
3682 // reachable. Such instructions don't matter, and they aren't required
3683 // to obey basic rules for definitions dominating uses which this
3684 // analysis depends on.
3685 if (!DT->isReachableFromEntry(I->getParent()))
3686 return getUnknown(V);
3687 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3688 Opcode = CE->getOpcode();
3689 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3690 return getConstant(CI);
3691 else if (isa<ConstantPointerNull>(V))
3692 return getConstant(V->getType(), 0);
3693 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3694 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3696 return getUnknown(V);
3698 Operator *U = cast<Operator>(V);
3700 case Instruction::Add: {
3701 // The simple thing to do would be to just call getSCEV on both operands
3702 // and call getAddExpr with the result. However if we're looking at a
3703 // bunch of things all added together, this can be quite inefficient,
3704 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3705 // Instead, gather up all the operands and make a single getAddExpr call.
3706 // LLVM IR canonical form means we need only traverse the left operands.
3708 // Don't apply this instruction's NSW or NUW flags to the new
3709 // expression. The instruction may be guarded by control flow that the
3710 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3711 // mapped to the same SCEV expression, and it would be incorrect to transfer
3712 // NSW/NUW semantics to those operations.
3713 SmallVector<const SCEV *, 4> AddOps;
3714 AddOps.push_back(getSCEV(U->getOperand(1)));
3715 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3716 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3717 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3719 U = cast<Operator>(Op);
3720 const SCEV *Op1 = getSCEV(U->getOperand(1));
3721 if (Opcode == Instruction::Sub)
3722 AddOps.push_back(getNegativeSCEV(Op1));
3724 AddOps.push_back(Op1);
3726 AddOps.push_back(getSCEV(U->getOperand(0)));
3727 return getAddExpr(AddOps);
3729 case Instruction::Mul: {
3730 // Don't transfer NSW/NUW for the same reason as AddExpr.
3731 SmallVector<const SCEV *, 4> MulOps;
3732 MulOps.push_back(getSCEV(U->getOperand(1)));
3733 for (Value *Op = U->getOperand(0);
3734 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3735 Op = U->getOperand(0)) {
3736 U = cast<Operator>(Op);
3737 MulOps.push_back(getSCEV(U->getOperand(1)));
3739 MulOps.push_back(getSCEV(U->getOperand(0)));
3740 return getMulExpr(MulOps);
3742 case Instruction::UDiv:
3743 return getUDivExpr(getSCEV(U->getOperand(0)),
3744 getSCEV(U->getOperand(1)));
3745 case Instruction::Sub:
3746 return getMinusSCEV(getSCEV(U->getOperand(0)),
3747 getSCEV(U->getOperand(1)));
3748 case Instruction::And:
3749 // For an expression like x&255 that merely masks off the high bits,
3750 // use zext(trunc(x)) as the SCEV expression.
3751 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3752 if (CI->isNullValue())
3753 return getSCEV(U->getOperand(1));
3754 if (CI->isAllOnesValue())
3755 return getSCEV(U->getOperand(0));
3756 const APInt &A = CI->getValue();
3758 // Instcombine's ShrinkDemandedConstant may strip bits out of
3759 // constants, obscuring what would otherwise be a low-bits mask.
3760 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3761 // knew about to reconstruct a low-bits mask value.
3762 unsigned LZ = A.countLeadingZeros();
3763 unsigned TZ = A.countTrailingZeros();
3764 unsigned BitWidth = A.getBitWidth();
3765 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3766 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, TD);
3768 APInt EffectiveMask =
3769 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
3770 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
3771 const SCEV *MulCount = getConstant(
3772 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
3776 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
3777 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
3784 case Instruction::Or:
3785 // If the RHS of the Or is a constant, we may have something like:
3786 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3787 // optimizations will transparently handle this case.
3789 // In order for this transformation to be safe, the LHS must be of the
3790 // form X*(2^n) and the Or constant must be less than 2^n.
3791 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3792 const SCEV *LHS = getSCEV(U->getOperand(0));
3793 const APInt &CIVal = CI->getValue();
3794 if (GetMinTrailingZeros(LHS) >=
3795 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3796 // Build a plain add SCEV.
3797 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3798 // If the LHS of the add was an addrec and it has no-wrap flags,
3799 // transfer the no-wrap flags, since an or won't introduce a wrap.
3800 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3801 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3802 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3803 OldAR->getNoWrapFlags());
3809 case Instruction::Xor:
3810 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3811 // If the RHS of the xor is a signbit, then this is just an add.
3812 // Instcombine turns add of signbit into xor as a strength reduction step.
3813 if (CI->getValue().isSignBit())
3814 return getAddExpr(getSCEV(U->getOperand(0)),
3815 getSCEV(U->getOperand(1)));
3817 // If the RHS of xor is -1, then this is a not operation.
3818 if (CI->isAllOnesValue())
3819 return getNotSCEV(getSCEV(U->getOperand(0)));
3821 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3822 // This is a variant of the check for xor with -1, and it handles
3823 // the case where instcombine has trimmed non-demanded bits out
3824 // of an xor with -1.
3825 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3826 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3827 if (BO->getOpcode() == Instruction::And &&
3828 LCI->getValue() == CI->getValue())
3829 if (const SCEVZeroExtendExpr *Z =
3830 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3831 Type *UTy = U->getType();
3832 const SCEV *Z0 = Z->getOperand();
3833 Type *Z0Ty = Z0->getType();
3834 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3836 // If C is a low-bits mask, the zero extend is serving to
3837 // mask off the high bits. Complement the operand and
3838 // re-apply the zext.
3839 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3840 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3842 // If C is a single bit, it may be in the sign-bit position
3843 // before the zero-extend. In this case, represent the xor
3844 // using an add, which is equivalent, and re-apply the zext.
3845 APInt Trunc = CI->getValue().trunc(Z0TySize);
3846 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3848 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3854 case Instruction::Shl:
3855 // Turn shift left of a constant amount into a multiply.
3856 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3857 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3859 // If the shift count is not less than the bitwidth, the result of
3860 // the shift is undefined. Don't try to analyze it, because the
3861 // resolution chosen here may differ from the resolution chosen in
3862 // other parts of the compiler.
3863 if (SA->getValue().uge(BitWidth))
3866 Constant *X = ConstantInt::get(getContext(),
3867 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3868 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3872 case Instruction::LShr:
3873 // Turn logical shift right of a constant into a unsigned divide.
3874 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3875 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3877 // If the shift count is not less than the bitwidth, the result of
3878 // the shift is undefined. Don't try to analyze it, because the
3879 // resolution chosen here may differ from the resolution chosen in
3880 // other parts of the compiler.
3881 if (SA->getValue().uge(BitWidth))
3884 Constant *X = ConstantInt::get(getContext(),
3885 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3886 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3890 case Instruction::AShr:
3891 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3892 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3893 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3894 if (L->getOpcode() == Instruction::Shl &&
3895 L->getOperand(1) == U->getOperand(1)) {
3896 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3898 // If the shift count is not less than the bitwidth, the result of
3899 // the shift is undefined. Don't try to analyze it, because the
3900 // resolution chosen here may differ from the resolution chosen in
3901 // other parts of the compiler.
3902 if (CI->getValue().uge(BitWidth))
3905 uint64_t Amt = BitWidth - CI->getZExtValue();
3906 if (Amt == BitWidth)
3907 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3909 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3910 IntegerType::get(getContext(),
3916 case Instruction::Trunc:
3917 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3919 case Instruction::ZExt:
3920 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3922 case Instruction::SExt:
3923 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3925 case Instruction::BitCast:
3926 // BitCasts are no-op casts so we just eliminate the cast.
3927 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3928 return getSCEV(U->getOperand(0));
3931 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3932 // lead to pointer expressions which cannot safely be expanded to GEPs,
3933 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3934 // simplifying integer expressions.
3936 case Instruction::GetElementPtr:
3937 return createNodeForGEP(cast<GEPOperator>(U));
3939 case Instruction::PHI:
3940 return createNodeForPHI(cast<PHINode>(U));
3942 case Instruction::Select:
3943 // This could be a smax or umax that was lowered earlier.
3944 // Try to recover it.
3945 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3946 Value *LHS = ICI->getOperand(0);
3947 Value *RHS = ICI->getOperand(1);
3948 switch (ICI->getPredicate()) {
3949 case ICmpInst::ICMP_SLT:
3950 case ICmpInst::ICMP_SLE:
3951 std::swap(LHS, RHS);
3953 case ICmpInst::ICMP_SGT:
3954 case ICmpInst::ICMP_SGE:
3955 // a >s b ? a+x : b+x -> smax(a, b)+x
3956 // a >s b ? b+x : a+x -> smin(a, b)+x
3957 if (LHS->getType() == U->getType()) {
3958 const SCEV *LS = getSCEV(LHS);
3959 const SCEV *RS = getSCEV(RHS);
3960 const SCEV *LA = getSCEV(U->getOperand(1));
3961 const SCEV *RA = getSCEV(U->getOperand(2));
3962 const SCEV *LDiff = getMinusSCEV(LA, LS);
3963 const SCEV *RDiff = getMinusSCEV(RA, RS);
3965 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3966 LDiff = getMinusSCEV(LA, RS);
3967 RDiff = getMinusSCEV(RA, LS);
3969 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3972 case ICmpInst::ICMP_ULT:
3973 case ICmpInst::ICMP_ULE:
3974 std::swap(LHS, RHS);
3976 case ICmpInst::ICMP_UGT:
3977 case ICmpInst::ICMP_UGE:
3978 // a >u b ? a+x : b+x -> umax(a, b)+x
3979 // a >u b ? b+x : a+x -> umin(a, b)+x
3980 if (LHS->getType() == U->getType()) {
3981 const SCEV *LS = getSCEV(LHS);
3982 const SCEV *RS = getSCEV(RHS);
3983 const SCEV *LA = getSCEV(U->getOperand(1));
3984 const SCEV *RA = getSCEV(U->getOperand(2));
3985 const SCEV *LDiff = getMinusSCEV(LA, LS);
3986 const SCEV *RDiff = getMinusSCEV(RA, RS);
3988 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3989 LDiff = getMinusSCEV(LA, RS);
3990 RDiff = getMinusSCEV(RA, LS);
3992 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3995 case ICmpInst::ICMP_NE:
3996 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3997 if (LHS->getType() == U->getType() &&
3998 isa<ConstantInt>(RHS) &&
3999 cast<ConstantInt>(RHS)->isZero()) {
4000 const SCEV *One = getConstant(LHS->getType(), 1);
4001 const SCEV *LS = getSCEV(LHS);
4002 const SCEV *LA = getSCEV(U->getOperand(1));
4003 const SCEV *RA = getSCEV(U->getOperand(2));
4004 const SCEV *LDiff = getMinusSCEV(LA, LS);
4005 const SCEV *RDiff = getMinusSCEV(RA, One);
4007 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4010 case ICmpInst::ICMP_EQ:
4011 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4012 if (LHS->getType() == U->getType() &&
4013 isa<ConstantInt>(RHS) &&
4014 cast<ConstantInt>(RHS)->isZero()) {
4015 const SCEV *One = getConstant(LHS->getType(), 1);
4016 const SCEV *LS = getSCEV(LHS);
4017 const SCEV *LA = getSCEV(U->getOperand(1));
4018 const SCEV *RA = getSCEV(U->getOperand(2));
4019 const SCEV *LDiff = getMinusSCEV(LA, One);
4020 const SCEV *RDiff = getMinusSCEV(RA, LS);
4022 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4030 default: // We cannot analyze this expression.
4034 return getUnknown(V);
4039 //===----------------------------------------------------------------------===//
4040 // Iteration Count Computation Code
4043 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4044 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4045 /// constant. Will also return 0 if the maximum trip count is very large (>=
4048 /// This "trip count" assumes that control exits via ExitingBlock. More
4049 /// precisely, it is the number of times that control may reach ExitingBlock
4050 /// before taking the branch. For loops with multiple exits, it may not be the
4051 /// number times that the loop header executes because the loop may exit
4052 /// prematurely via another branch.
4054 /// FIXME: We conservatively call getBackedgeTakenCount(L) instead of
4055 /// getExitCount(L, ExitingBlock) to compute a safe trip count considering all
4056 /// loop exits. getExitCount() may return an exact count for this branch
4057 /// assuming no-signed-wrap. The number of well-defined iterations may actually
4058 /// be higher than this trip count if this exit test is skipped and the loop
4059 /// exits via a different branch. Ideally, getExitCount() would know whether it
4060 /// depends on a NSW assumption, and we would only fall back to a conservative
4061 /// trip count in that case.
4062 unsigned ScalarEvolution::
4063 getSmallConstantTripCount(Loop *L, BasicBlock * /*ExitingBlock*/) {
4064 const SCEVConstant *ExitCount =
4065 dyn_cast<SCEVConstant>(getBackedgeTakenCount(L));
4069 ConstantInt *ExitConst = ExitCount->getValue();
4071 // Guard against huge trip counts.
4072 if (ExitConst->getValue().getActiveBits() > 32)
4075 // In case of integer overflow, this returns 0, which is correct.
4076 return ((unsigned)ExitConst->getZExtValue()) + 1;
4079 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4080 /// trip count of this loop as a normal unsigned value, if possible. This
4081 /// means that the actual trip count is always a multiple of the returned
4082 /// value (don't forget the trip count could very well be zero as well!).
4084 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4085 /// multiple of a constant (which is also the case if the trip count is simply
4086 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4087 /// if the trip count is very large (>= 2^32).
4089 /// As explained in the comments for getSmallConstantTripCount, this assumes
4090 /// that control exits the loop via ExitingBlock.
4091 unsigned ScalarEvolution::
4092 getSmallConstantTripMultiple(Loop *L, BasicBlock * /*ExitingBlock*/) {
4093 const SCEV *ExitCount = getBackedgeTakenCount(L);
4094 if (ExitCount == getCouldNotCompute())
4097 // Get the trip count from the BE count by adding 1.
4098 const SCEV *TCMul = getAddExpr(ExitCount,
4099 getConstant(ExitCount->getType(), 1));
4100 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4101 // to factor simple cases.
4102 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4103 TCMul = Mul->getOperand(0);
4105 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4109 ConstantInt *Result = MulC->getValue();
4111 // Guard against huge trip counts (this requires checking
4112 // for zero to handle the case where the trip count == -1 and the
4114 if (!Result || Result->getValue().getActiveBits() > 32 ||
4115 Result->getValue().getActiveBits() == 0)
4118 return (unsigned)Result->getZExtValue();
4121 // getExitCount - Get the expression for the number of loop iterations for which
4122 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4123 // SCEVCouldNotCompute.
4124 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4125 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4128 /// getBackedgeTakenCount - If the specified loop has a predictable
4129 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4130 /// object. The backedge-taken count is the number of times the loop header
4131 /// will be branched to from within the loop. This is one less than the
4132 /// trip count of the loop, since it doesn't count the first iteration,
4133 /// when the header is branched to from outside the loop.
4135 /// Note that it is not valid to call this method on a loop without a
4136 /// loop-invariant backedge-taken count (see
4137 /// hasLoopInvariantBackedgeTakenCount).
4139 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4140 return getBackedgeTakenInfo(L).getExact(this);
4143 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4144 /// return the least SCEV value that is known never to be less than the
4145 /// actual backedge taken count.
4146 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4147 return getBackedgeTakenInfo(L).getMax(this);
4150 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4151 /// onto the given Worklist.
4153 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4154 BasicBlock *Header = L->getHeader();
4156 // Push all Loop-header PHIs onto the Worklist stack.
4157 for (BasicBlock::iterator I = Header->begin();
4158 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4159 Worklist.push_back(PN);
4162 const ScalarEvolution::BackedgeTakenInfo &
4163 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4164 // Initially insert an invalid entry for this loop. If the insertion
4165 // succeeds, proceed to actually compute a backedge-taken count and
4166 // update the value. The temporary CouldNotCompute value tells SCEV
4167 // code elsewhere that it shouldn't attempt to request a new
4168 // backedge-taken count, which could result in infinite recursion.
4169 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4170 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4172 return Pair.first->second;
4174 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4175 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4176 // must be cleared in this scope.
4177 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4179 if (Result.getExact(this) != getCouldNotCompute()) {
4180 assert(isLoopInvariant(Result.getExact(this), L) &&
4181 isLoopInvariant(Result.getMax(this), L) &&
4182 "Computed backedge-taken count isn't loop invariant for loop!");
4183 ++NumTripCountsComputed;
4185 else if (Result.getMax(this) == getCouldNotCompute() &&
4186 isa<PHINode>(L->getHeader()->begin())) {
4187 // Only count loops that have phi nodes as not being computable.
4188 ++NumTripCountsNotComputed;
4191 // Now that we know more about the trip count for this loop, forget any
4192 // existing SCEV values for PHI nodes in this loop since they are only
4193 // conservative estimates made without the benefit of trip count
4194 // information. This is similar to the code in forgetLoop, except that
4195 // it handles SCEVUnknown PHI nodes specially.
4196 if (Result.hasAnyInfo()) {
4197 SmallVector<Instruction *, 16> Worklist;
4198 PushLoopPHIs(L, Worklist);
4200 SmallPtrSet<Instruction *, 8> Visited;
4201 while (!Worklist.empty()) {
4202 Instruction *I = Worklist.pop_back_val();
4203 if (!Visited.insert(I)) continue;
4205 ValueExprMapType::iterator It =
4206 ValueExprMap.find_as(static_cast<Value *>(I));
4207 if (It != ValueExprMap.end()) {
4208 const SCEV *Old = It->second;
4210 // SCEVUnknown for a PHI either means that it has an unrecognized
4211 // structure, or it's a PHI that's in the progress of being computed
4212 // by createNodeForPHI. In the former case, additional loop trip
4213 // count information isn't going to change anything. In the later
4214 // case, createNodeForPHI will perform the necessary updates on its
4215 // own when it gets to that point.
4216 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4217 forgetMemoizedResults(Old);
4218 ValueExprMap.erase(It);
4220 if (PHINode *PN = dyn_cast<PHINode>(I))
4221 ConstantEvolutionLoopExitValue.erase(PN);
4224 PushDefUseChildren(I, Worklist);
4228 // Re-lookup the insert position, since the call to
4229 // ComputeBackedgeTakenCount above could result in a
4230 // recusive call to getBackedgeTakenInfo (on a different
4231 // loop), which would invalidate the iterator computed
4233 return BackedgeTakenCounts.find(L)->second = Result;
4236 /// forgetLoop - This method should be called by the client when it has
4237 /// changed a loop in a way that may effect ScalarEvolution's ability to
4238 /// compute a trip count, or if the loop is deleted.
4239 void ScalarEvolution::forgetLoop(const Loop *L) {
4240 // Drop any stored trip count value.
4241 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4242 BackedgeTakenCounts.find(L);
4243 if (BTCPos != BackedgeTakenCounts.end()) {
4244 BTCPos->second.clear();
4245 BackedgeTakenCounts.erase(BTCPos);
4248 // Drop information about expressions based on loop-header PHIs.
4249 SmallVector<Instruction *, 16> Worklist;
4250 PushLoopPHIs(L, Worklist);
4252 SmallPtrSet<Instruction *, 8> Visited;
4253 while (!Worklist.empty()) {
4254 Instruction *I = Worklist.pop_back_val();
4255 if (!Visited.insert(I)) continue;
4257 ValueExprMapType::iterator It =
4258 ValueExprMap.find_as(static_cast<Value *>(I));
4259 if (It != ValueExprMap.end()) {
4260 forgetMemoizedResults(It->second);
4261 ValueExprMap.erase(It);
4262 if (PHINode *PN = dyn_cast<PHINode>(I))
4263 ConstantEvolutionLoopExitValue.erase(PN);
4266 PushDefUseChildren(I, Worklist);
4269 // Forget all contained loops too, to avoid dangling entries in the
4270 // ValuesAtScopes map.
4271 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4275 /// forgetValue - This method should be called by the client when it has
4276 /// changed a value in a way that may effect its value, or which may
4277 /// disconnect it from a def-use chain linking it to a loop.
4278 void ScalarEvolution::forgetValue(Value *V) {
4279 Instruction *I = dyn_cast<Instruction>(V);
4282 // Drop information about expressions based on loop-header PHIs.
4283 SmallVector<Instruction *, 16> Worklist;
4284 Worklist.push_back(I);
4286 SmallPtrSet<Instruction *, 8> Visited;
4287 while (!Worklist.empty()) {
4288 I = Worklist.pop_back_val();
4289 if (!Visited.insert(I)) continue;
4291 ValueExprMapType::iterator It =
4292 ValueExprMap.find_as(static_cast<Value *>(I));
4293 if (It != ValueExprMap.end()) {
4294 forgetMemoizedResults(It->second);
4295 ValueExprMap.erase(It);
4296 if (PHINode *PN = dyn_cast<PHINode>(I))
4297 ConstantEvolutionLoopExitValue.erase(PN);
4300 PushDefUseChildren(I, Worklist);
4304 /// getExact - Get the exact loop backedge taken count considering all loop
4305 /// exits. A computable result can only be return for loops with a single exit.
4306 /// Returning the minimum taken count among all exits is incorrect because one
4307 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4308 /// the limit of each loop test is never skipped. This is a valid assumption as
4309 /// long as the loop exits via that test. For precise results, it is the
4310 /// caller's responsibility to specify the relevant loop exit using
4311 /// getExact(ExitingBlock, SE).
4313 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4314 // If any exits were not computable, the loop is not computable.
4315 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4317 // We need exactly one computable exit.
4318 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4319 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4321 const SCEV *BECount = 0;
4322 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4323 ENT != 0; ENT = ENT->getNextExit()) {
4325 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4328 BECount = ENT->ExactNotTaken;
4329 else if (BECount != ENT->ExactNotTaken)
4330 return SE->getCouldNotCompute();
4332 assert(BECount && "Invalid not taken count for loop exit");
4336 /// getExact - Get the exact not taken count for this loop exit.
4338 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4339 ScalarEvolution *SE) const {
4340 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4341 ENT != 0; ENT = ENT->getNextExit()) {
4343 if (ENT->ExitingBlock == ExitingBlock)
4344 return ENT->ExactNotTaken;
4346 return SE->getCouldNotCompute();
4349 /// getMax - Get the max backedge taken count for the loop.
4351 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4352 return Max ? Max : SE->getCouldNotCompute();
4355 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4356 ScalarEvolution *SE) const {
4357 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4360 if (!ExitNotTaken.ExitingBlock)
4363 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4364 ENT != 0; ENT = ENT->getNextExit()) {
4366 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4367 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4374 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4375 /// computable exit into a persistent ExitNotTakenInfo array.
4376 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4377 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4378 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4381 ExitNotTaken.setIncomplete();
4383 unsigned NumExits = ExitCounts.size();
4384 if (NumExits == 0) return;
4386 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4387 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4388 if (NumExits == 1) return;
4390 // Handle the rare case of multiple computable exits.
4391 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4393 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4394 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4395 PrevENT->setNextExit(ENT);
4396 ENT->ExitingBlock = ExitCounts[i].first;
4397 ENT->ExactNotTaken = ExitCounts[i].second;
4401 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4402 void ScalarEvolution::BackedgeTakenInfo::clear() {
4403 ExitNotTaken.ExitingBlock = 0;
4404 ExitNotTaken.ExactNotTaken = 0;
4405 delete[] ExitNotTaken.getNextExit();
4408 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4409 /// of the specified loop will execute.
4410 ScalarEvolution::BackedgeTakenInfo
4411 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4412 SmallVector<BasicBlock *, 8> ExitingBlocks;
4413 L->getExitingBlocks(ExitingBlocks);
4415 // Examine all exits and pick the most conservative values.
4416 const SCEV *MaxBECount = getCouldNotCompute();
4417 bool CouldComputeBECount = true;
4418 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4419 const SCEV *LatchMaxCount = 0;
4420 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4421 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4422 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4423 if (EL.Exact == getCouldNotCompute())
4424 // We couldn't compute an exact value for this exit, so
4425 // we won't be able to compute an exact value for the loop.
4426 CouldComputeBECount = false;
4428 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4430 if (MaxBECount == getCouldNotCompute())
4431 MaxBECount = EL.Max;
4432 else if (EL.Max != getCouldNotCompute()) {
4433 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4434 // skip some loop tests. Taking the max over the exits is sufficiently
4435 // conservative. TODO: We could do better taking into consideration
4436 // non-latch exits that dominate the latch.
4437 if (EL.MustExit && ExitingBlocks[i] == Latch)
4438 LatchMaxCount = EL.Max;
4440 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4443 // Be more precise in the easy case of a loop latch that must exit.
4444 if (LatchMaxCount) {
4445 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, LatchMaxCount);
4447 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4450 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4451 /// loop will execute if it exits via the specified block.
4452 ScalarEvolution::ExitLimit
4453 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4455 // Okay, we've chosen an exiting block. See what condition causes us to
4456 // exit at this block and remember the exit block and whether all other targets
4457 // lead to the loop header.
4458 bool MustExecuteLoopHeader = true;
4459 BasicBlock *Exit = 0;
4460 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4462 if (!L->contains(*SI)) {
4463 if (Exit) // Multiple exit successors.
4464 return getCouldNotCompute();
4466 } else if (*SI != L->getHeader()) {
4467 MustExecuteLoopHeader = false;
4470 // At this point, we know we have a conditional branch that determines whether
4471 // the loop is exited. However, we don't know if the branch is executed each
4472 // time through the loop. If not, then the execution count of the branch will
4473 // not be equal to the trip count of the loop.
4475 // Currently we check for this by checking to see if the Exit branch goes to
4476 // the loop header. If so, we know it will always execute the same number of
4477 // times as the loop. We also handle the case where the exit block *is* the
4478 // loop header. This is common for un-rotated loops.
4480 // If both of those tests fail, walk up the unique predecessor chain to the
4481 // header, stopping if there is an edge that doesn't exit the loop. If the
4482 // header is reached, the execution count of the branch will be equal to the
4483 // trip count of the loop.
4485 // More extensive analysis could be done to handle more cases here.
4487 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4488 // The simple checks failed, try climbing the unique predecessor chain
4489 // up to the header.
4491 for (BasicBlock *BB = ExitingBlock; BB; ) {
4492 BasicBlock *Pred = BB->getUniquePredecessor();
4494 return getCouldNotCompute();
4495 TerminatorInst *PredTerm = Pred->getTerminator();
4496 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4497 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4500 // If the predecessor has a successor that isn't BB and isn't
4501 // outside the loop, assume the worst.
4502 if (L->contains(PredSucc))
4503 return getCouldNotCompute();
4505 if (Pred == L->getHeader()) {
4512 return getCouldNotCompute();
4515 TerminatorInst *Term = ExitingBlock->getTerminator();
4516 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4517 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4518 // Proceed to the next level to examine the exit condition expression.
4519 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4520 BI->getSuccessor(1),
4521 /*IsSubExpr=*/false);
4524 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4525 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4526 /*IsSubExpr=*/false);
4528 return getCouldNotCompute();
4531 /// ComputeExitLimitFromCond - Compute the number of times the
4532 /// backedge of the specified loop will execute if its exit condition
4533 /// were a conditional branch of ExitCond, TBB, and FBB.
4535 /// @param IsSubExpr is true if ExitCond does not directly control the exit
4536 /// branch. In this case, we cannot assume that the loop only exits when the
4537 /// condition is true and cannot infer that failing to meet the condition prior
4538 /// to integer wraparound results in undefined behavior.
4539 ScalarEvolution::ExitLimit
4540 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4545 // Check if the controlling expression for this loop is an And or Or.
4546 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4547 if (BO->getOpcode() == Instruction::And) {
4548 // Recurse on the operands of the and.
4549 bool EitherMayExit = L->contains(TBB);
4550 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4551 IsSubExpr || EitherMayExit);
4552 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4553 IsSubExpr || EitherMayExit);
4554 const SCEV *BECount = getCouldNotCompute();
4555 const SCEV *MaxBECount = getCouldNotCompute();
4556 bool MustExit = false;
4557 if (EitherMayExit) {
4558 // Both conditions must be true for the loop to continue executing.
4559 // Choose the less conservative count.
4560 if (EL0.Exact == getCouldNotCompute() ||
4561 EL1.Exact == getCouldNotCompute())
4562 BECount = getCouldNotCompute();
4564 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4565 if (EL0.Max == getCouldNotCompute())
4566 MaxBECount = EL1.Max;
4567 else if (EL1.Max == getCouldNotCompute())
4568 MaxBECount = EL0.Max;
4570 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4571 MustExit = EL0.MustExit || EL1.MustExit;
4573 // Both conditions must be true at the same time for the loop to exit.
4574 // For now, be conservative.
4575 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4576 if (EL0.Max == EL1.Max)
4577 MaxBECount = EL0.Max;
4578 if (EL0.Exact == EL1.Exact)
4579 BECount = EL0.Exact;
4580 MustExit = EL0.MustExit && EL1.MustExit;
4583 return ExitLimit(BECount, MaxBECount, MustExit);
4585 if (BO->getOpcode() == Instruction::Or) {
4586 // Recurse on the operands of the or.
4587 bool EitherMayExit = L->contains(FBB);
4588 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4589 IsSubExpr || EitherMayExit);
4590 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4591 IsSubExpr || EitherMayExit);
4592 const SCEV *BECount = getCouldNotCompute();
4593 const SCEV *MaxBECount = getCouldNotCompute();
4594 bool MustExit = false;
4595 if (EitherMayExit) {
4596 // Both conditions must be false for the loop to continue executing.
4597 // Choose the less conservative count.
4598 if (EL0.Exact == getCouldNotCompute() ||
4599 EL1.Exact == getCouldNotCompute())
4600 BECount = getCouldNotCompute();
4602 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4603 if (EL0.Max == getCouldNotCompute())
4604 MaxBECount = EL1.Max;
4605 else if (EL1.Max == getCouldNotCompute())
4606 MaxBECount = EL0.Max;
4608 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4609 MustExit = EL0.MustExit || EL1.MustExit;
4611 // Both conditions must be false at the same time for the loop to exit.
4612 // For now, be conservative.
4613 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4614 if (EL0.Max == EL1.Max)
4615 MaxBECount = EL0.Max;
4616 if (EL0.Exact == EL1.Exact)
4617 BECount = EL0.Exact;
4618 MustExit = EL0.MustExit && EL1.MustExit;
4621 return ExitLimit(BECount, MaxBECount, MustExit);
4625 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4626 // Proceed to the next level to examine the icmp.
4627 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4628 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, IsSubExpr);
4630 // Check for a constant condition. These are normally stripped out by
4631 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4632 // preserve the CFG and is temporarily leaving constant conditions
4634 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4635 if (L->contains(FBB) == !CI->getZExtValue())
4636 // The backedge is always taken.
4637 return getCouldNotCompute();
4639 // The backedge is never taken.
4640 return getConstant(CI->getType(), 0);
4643 // If it's not an integer or pointer comparison then compute it the hard way.
4644 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4647 /// ComputeExitLimitFromICmp - Compute the number of times the
4648 /// backedge of the specified loop will execute if its exit condition
4649 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4650 ScalarEvolution::ExitLimit
4651 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4657 // If the condition was exit on true, convert the condition to exit on false
4658 ICmpInst::Predicate Cond;
4659 if (!L->contains(FBB))
4660 Cond = ExitCond->getPredicate();
4662 Cond = ExitCond->getInversePredicate();
4664 // Handle common loops like: for (X = "string"; *X; ++X)
4665 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4666 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4668 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4669 if (ItCnt.hasAnyInfo())
4673 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4674 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4676 // Try to evaluate any dependencies out of the loop.
4677 LHS = getSCEVAtScope(LHS, L);
4678 RHS = getSCEVAtScope(RHS, L);
4680 // At this point, we would like to compute how many iterations of the
4681 // loop the predicate will return true for these inputs.
4682 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4683 // If there is a loop-invariant, force it into the RHS.
4684 std::swap(LHS, RHS);
4685 Cond = ICmpInst::getSwappedPredicate(Cond);
4688 // Simplify the operands before analyzing them.
4689 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4691 // If we have a comparison of a chrec against a constant, try to use value
4692 // ranges to answer this query.
4693 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4694 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4695 if (AddRec->getLoop() == L) {
4696 // Form the constant range.
4697 ConstantRange CompRange(
4698 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4700 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4701 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4705 case ICmpInst::ICMP_NE: { // while (X != Y)
4706 // Convert to: while (X-Y != 0)
4707 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4708 if (EL.hasAnyInfo()) return EL;
4711 case ICmpInst::ICMP_EQ: { // while (X == Y)
4712 // Convert to: while (X-Y == 0)
4713 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4714 if (EL.hasAnyInfo()) return EL;
4717 case ICmpInst::ICMP_SLT:
4718 case ICmpInst::ICMP_ULT: { // while (X < Y)
4719 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
4720 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, IsSubExpr);
4721 if (EL.hasAnyInfo()) return EL;
4724 case ICmpInst::ICMP_SGT:
4725 case ICmpInst::ICMP_UGT: { // while (X > Y)
4726 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
4727 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, IsSubExpr);
4728 if (EL.hasAnyInfo()) return EL;
4733 dbgs() << "ComputeBackedgeTakenCount ";
4734 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4735 dbgs() << "[unsigned] ";
4736 dbgs() << *LHS << " "
4737 << Instruction::getOpcodeName(Instruction::ICmp)
4738 << " " << *RHS << "\n";
4742 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4745 ScalarEvolution::ExitLimit
4746 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
4748 BasicBlock *ExitingBlock,
4750 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
4752 // Give up if the exit is the default dest of a switch.
4753 if (Switch->getDefaultDest() == ExitingBlock)
4754 return getCouldNotCompute();
4756 assert(L->contains(Switch->getDefaultDest()) &&
4757 "Default case must not exit the loop!");
4758 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
4759 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
4761 // while (X != Y) --> while (X-Y != 0)
4762 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4763 if (EL.hasAnyInfo())
4766 return getCouldNotCompute();
4769 static ConstantInt *
4770 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4771 ScalarEvolution &SE) {
4772 const SCEV *InVal = SE.getConstant(C);
4773 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4774 assert(isa<SCEVConstant>(Val) &&
4775 "Evaluation of SCEV at constant didn't fold correctly?");
4776 return cast<SCEVConstant>(Val)->getValue();
4779 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4780 /// 'icmp op load X, cst', try to see if we can compute the backedge
4781 /// execution count.
4782 ScalarEvolution::ExitLimit
4783 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4787 ICmpInst::Predicate predicate) {
4789 if (LI->isVolatile()) return getCouldNotCompute();
4791 // Check to see if the loaded pointer is a getelementptr of a global.
4792 // TODO: Use SCEV instead of manually grubbing with GEPs.
4793 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4794 if (!GEP) return getCouldNotCompute();
4796 // Make sure that it is really a constant global we are gepping, with an
4797 // initializer, and make sure the first IDX is really 0.
4798 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4799 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4800 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4801 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4802 return getCouldNotCompute();
4804 // Okay, we allow one non-constant index into the GEP instruction.
4806 std::vector<Constant*> Indexes;
4807 unsigned VarIdxNum = 0;
4808 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4809 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4810 Indexes.push_back(CI);
4811 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4812 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4813 VarIdx = GEP->getOperand(i);
4815 Indexes.push_back(0);
4818 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4820 return getCouldNotCompute();
4822 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4823 // Check to see if X is a loop variant variable value now.
4824 const SCEV *Idx = getSCEV(VarIdx);
4825 Idx = getSCEVAtScope(Idx, L);
4827 // We can only recognize very limited forms of loop index expressions, in
4828 // particular, only affine AddRec's like {C1,+,C2}.
4829 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4830 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4831 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4832 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4833 return getCouldNotCompute();
4835 unsigned MaxSteps = MaxBruteForceIterations;
4836 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4837 ConstantInt *ItCst = ConstantInt::get(
4838 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4839 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4841 // Form the GEP offset.
4842 Indexes[VarIdxNum] = Val;
4844 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4846 if (Result == 0) break; // Cannot compute!
4848 // Evaluate the condition for this iteration.
4849 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4850 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4851 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4853 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4854 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4857 ++NumArrayLenItCounts;
4858 return getConstant(ItCst); // Found terminating iteration!
4861 return getCouldNotCompute();
4865 /// CanConstantFold - Return true if we can constant fold an instruction of the
4866 /// specified type, assuming that all operands were constants.
4867 static bool CanConstantFold(const Instruction *I) {
4868 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4869 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4873 if (const CallInst *CI = dyn_cast<CallInst>(I))
4874 if (const Function *F = CI->getCalledFunction())
4875 return canConstantFoldCallTo(F);
4879 /// Determine whether this instruction can constant evolve within this loop
4880 /// assuming its operands can all constant evolve.
4881 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4882 // An instruction outside of the loop can't be derived from a loop PHI.
4883 if (!L->contains(I)) return false;
4885 if (isa<PHINode>(I)) {
4886 if (L->getHeader() == I->getParent())
4889 // We don't currently keep track of the control flow needed to evaluate
4890 // PHIs, so we cannot handle PHIs inside of loops.
4894 // If we won't be able to constant fold this expression even if the operands
4895 // are constants, bail early.
4896 return CanConstantFold(I);
4899 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4900 /// recursing through each instruction operand until reaching a loop header phi.
4902 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4903 DenseMap<Instruction *, PHINode *> &PHIMap) {
4905 // Otherwise, we can evaluate this instruction if all of its operands are
4906 // constant or derived from a PHI node themselves.
4908 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4909 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4911 if (isa<Constant>(*OpI)) continue;
4913 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4914 if (!OpInst || !canConstantEvolve(OpInst, L)) return 0;
4916 PHINode *P = dyn_cast<PHINode>(OpInst);
4918 // If this operand is already visited, reuse the prior result.
4919 // We may have P != PHI if this is the deepest point at which the
4920 // inconsistent paths meet.
4921 P = PHIMap.lookup(OpInst);
4923 // Recurse and memoize the results, whether a phi is found or not.
4924 // This recursive call invalidates pointers into PHIMap.
4925 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4928 if (P == 0) return 0; // Not evolving from PHI
4929 if (PHI && PHI != P) return 0; // Evolving from multiple different PHIs.
4932 // This is a expression evolving from a constant PHI!
4936 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4937 /// in the loop that V is derived from. We allow arbitrary operations along the
4938 /// way, but the operands of an operation must either be constants or a value
4939 /// derived from a constant PHI. If this expression does not fit with these
4940 /// constraints, return null.
4941 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4942 Instruction *I = dyn_cast<Instruction>(V);
4943 if (I == 0 || !canConstantEvolve(I, L)) return 0;
4945 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4949 // Record non-constant instructions contained by the loop.
4950 DenseMap<Instruction *, PHINode *> PHIMap;
4951 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4954 /// EvaluateExpression - Given an expression that passes the
4955 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4956 /// in the loop has the value PHIVal. If we can't fold this expression for some
4957 /// reason, return null.
4958 static Constant *EvaluateExpression(Value *V, const Loop *L,
4959 DenseMap<Instruction *, Constant *> &Vals,
4960 const DataLayout *TD,
4961 const TargetLibraryInfo *TLI) {
4962 // Convenient constant check, but redundant for recursive calls.
4963 if (Constant *C = dyn_cast<Constant>(V)) return C;
4964 Instruction *I = dyn_cast<Instruction>(V);
4967 if (Constant *C = Vals.lookup(I)) return C;
4969 // An instruction inside the loop depends on a value outside the loop that we
4970 // weren't given a mapping for, or a value such as a call inside the loop.
4971 if (!canConstantEvolve(I, L)) return 0;
4973 // An unmapped PHI can be due to a branch or another loop inside this loop,
4974 // or due to this not being the initial iteration through a loop where we
4975 // couldn't compute the evolution of this particular PHI last time.
4976 if (isa<PHINode>(I)) return 0;
4978 std::vector<Constant*> Operands(I->getNumOperands());
4980 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4981 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4983 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4984 if (!Operands[i]) return 0;
4987 Constant *C = EvaluateExpression(Operand, L, Vals, TD, TLI);
4993 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4994 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4995 Operands[1], TD, TLI);
4996 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4997 if (!LI->isVolatile())
4998 return ConstantFoldLoadFromConstPtr(Operands[0], TD);
5000 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD,
5004 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5005 /// in the header of its containing loop, we know the loop executes a
5006 /// constant number of times, and the PHI node is just a recurrence
5007 /// involving constants, fold it.
5009 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5012 DenseMap<PHINode*, Constant*>::const_iterator I =
5013 ConstantEvolutionLoopExitValue.find(PN);
5014 if (I != ConstantEvolutionLoopExitValue.end())
5017 if (BEs.ugt(MaxBruteForceIterations))
5018 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
5020 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5022 DenseMap<Instruction *, Constant *> CurrentIterVals;
5023 BasicBlock *Header = L->getHeader();
5024 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5026 // Since the loop is canonicalized, the PHI node must have two entries. One
5027 // entry must be a constant (coming in from outside of the loop), and the
5028 // second must be derived from the same PHI.
5029 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5031 for (BasicBlock::iterator I = Header->begin();
5032 (PHI = dyn_cast<PHINode>(I)); ++I) {
5033 Constant *StartCST =
5034 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5035 if (StartCST == 0) continue;
5036 CurrentIterVals[PHI] = StartCST;
5038 if (!CurrentIterVals.count(PN))
5041 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5043 // Execute the loop symbolically to determine the exit value.
5044 if (BEs.getActiveBits() >= 32)
5045 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
5047 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5048 unsigned IterationNum = 0;
5049 for (; ; ++IterationNum) {
5050 if (IterationNum == NumIterations)
5051 return RetVal = CurrentIterVals[PN]; // Got exit value!
5053 // Compute the value of the PHIs for the next iteration.
5054 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5055 DenseMap<Instruction *, Constant *> NextIterVals;
5056 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD,
5059 return 0; // Couldn't evaluate!
5060 NextIterVals[PN] = NextPHI;
5062 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5064 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5065 // cease to be able to evaluate one of them or if they stop evolving,
5066 // because that doesn't necessarily prevent us from computing PN.
5067 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5068 for (DenseMap<Instruction *, Constant *>::const_iterator
5069 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5070 PHINode *PHI = dyn_cast<PHINode>(I->first);
5071 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5072 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5074 // We use two distinct loops because EvaluateExpression may invalidate any
5075 // iterators into CurrentIterVals.
5076 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5077 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5078 PHINode *PHI = I->first;
5079 Constant *&NextPHI = NextIterVals[PHI];
5080 if (!NextPHI) { // Not already computed.
5081 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5082 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
5084 if (NextPHI != I->second)
5085 StoppedEvolving = false;
5088 // If all entries in CurrentIterVals == NextIterVals then we can stop
5089 // iterating, the loop can't continue to change.
5090 if (StoppedEvolving)
5091 return RetVal = CurrentIterVals[PN];
5093 CurrentIterVals.swap(NextIterVals);
5097 /// ComputeExitCountExhaustively - If the loop is known to execute a
5098 /// constant number of times (the condition evolves only from constants),
5099 /// try to evaluate a few iterations of the loop until we get the exit
5100 /// condition gets a value of ExitWhen (true or false). If we cannot
5101 /// evaluate the trip count of the loop, return getCouldNotCompute().
5102 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5105 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5106 if (PN == 0) return getCouldNotCompute();
5108 // If the loop is canonicalized, the PHI will have exactly two entries.
5109 // That's the only form we support here.
5110 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5112 DenseMap<Instruction *, Constant *> CurrentIterVals;
5113 BasicBlock *Header = L->getHeader();
5114 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5116 // One entry must be a constant (coming in from outside of the loop), and the
5117 // second must be derived from the same PHI.
5118 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5120 for (BasicBlock::iterator I = Header->begin();
5121 (PHI = dyn_cast<PHINode>(I)); ++I) {
5122 Constant *StartCST =
5123 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5124 if (StartCST == 0) continue;
5125 CurrentIterVals[PHI] = StartCST;
5127 if (!CurrentIterVals.count(PN))
5128 return getCouldNotCompute();
5130 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5131 // the loop symbolically to determine when the condition gets a value of
5134 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5135 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5136 ConstantInt *CondVal =
5137 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5140 // Couldn't symbolically evaluate.
5141 if (!CondVal) return getCouldNotCompute();
5143 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5144 ++NumBruteForceTripCountsComputed;
5145 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5148 // Update all the PHI nodes for the next iteration.
5149 DenseMap<Instruction *, Constant *> NextIterVals;
5151 // Create a list of which PHIs we need to compute. We want to do this before
5152 // calling EvaluateExpression on them because that may invalidate iterators
5153 // into CurrentIterVals.
5154 SmallVector<PHINode *, 8> PHIsToCompute;
5155 for (DenseMap<Instruction *, Constant *>::const_iterator
5156 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5157 PHINode *PHI = dyn_cast<PHINode>(I->first);
5158 if (!PHI || PHI->getParent() != Header) continue;
5159 PHIsToCompute.push_back(PHI);
5161 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5162 E = PHIsToCompute.end(); I != E; ++I) {
5164 Constant *&NextPHI = NextIterVals[PHI];
5165 if (NextPHI) continue; // Already computed!
5167 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5168 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, TD, TLI);
5170 CurrentIterVals.swap(NextIterVals);
5173 // Too many iterations were needed to evaluate.
5174 return getCouldNotCompute();
5177 /// getSCEVAtScope - Return a SCEV expression for the specified value
5178 /// at the specified scope in the program. The L value specifies a loop
5179 /// nest to evaluate the expression at, where null is the top-level or a
5180 /// specified loop is immediately inside of the loop.
5182 /// This method can be used to compute the exit value for a variable defined
5183 /// in a loop by querying what the value will hold in the parent loop.
5185 /// In the case that a relevant loop exit value cannot be computed, the
5186 /// original value V is returned.
5187 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5188 // Check to see if we've folded this expression at this loop before.
5189 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5190 for (unsigned u = 0; u < Values.size(); u++) {
5191 if (Values[u].first == L)
5192 return Values[u].second ? Values[u].second : V;
5194 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(0)));
5195 // Otherwise compute it.
5196 const SCEV *C = computeSCEVAtScope(V, L);
5197 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5198 for (unsigned u = Values2.size(); u > 0; u--) {
5199 if (Values2[u - 1].first == L) {
5200 Values2[u - 1].second = C;
5207 /// This builds up a Constant using the ConstantExpr interface. That way, we
5208 /// will return Constants for objects which aren't represented by a
5209 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5210 /// Returns NULL if the SCEV isn't representable as a Constant.
5211 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5212 switch (V->getSCEVType()) {
5213 default: // TODO: smax, umax.
5214 case scCouldNotCompute:
5218 return cast<SCEVConstant>(V)->getValue();
5220 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5221 case scSignExtend: {
5222 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5223 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5224 return ConstantExpr::getSExt(CastOp, SS->getType());
5227 case scZeroExtend: {
5228 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5229 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5230 return ConstantExpr::getZExt(CastOp, SZ->getType());
5234 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5235 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5236 return ConstantExpr::getTrunc(CastOp, ST->getType());
5240 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5241 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5242 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5243 unsigned AS = PTy->getAddressSpace();
5244 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5245 C = ConstantExpr::getBitCast(C, DestPtrTy);
5247 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5248 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5252 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5253 unsigned AS = C2->getType()->getPointerAddressSpace();
5255 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5256 // The offsets have been converted to bytes. We can add bytes to an
5257 // i8* by GEP with the byte count in the first index.
5258 C = ConstantExpr::getBitCast(C, DestPtrTy);
5261 // Don't bother trying to sum two pointers. We probably can't
5262 // statically compute a load that results from it anyway.
5263 if (C2->getType()->isPointerTy())
5266 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5267 if (PTy->getElementType()->isStructTy())
5268 C2 = ConstantExpr::getIntegerCast(
5269 C2, Type::getInt32Ty(C->getContext()), true);
5270 C = ConstantExpr::getGetElementPtr(C, C2);
5272 C = ConstantExpr::getAdd(C, C2);
5279 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5280 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5281 // Don't bother with pointers at all.
5282 if (C->getType()->isPointerTy()) return 0;
5283 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5284 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5285 if (!C2 || C2->getType()->isPointerTy()) return 0;
5286 C = ConstantExpr::getMul(C, C2);
5293 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5294 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5295 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5296 if (LHS->getType() == RHS->getType())
5297 return ConstantExpr::getUDiv(LHS, RHS);
5304 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5305 if (isa<SCEVConstant>(V)) return V;
5307 // If this instruction is evolved from a constant-evolving PHI, compute the
5308 // exit value from the loop without using SCEVs.
5309 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5310 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5311 const Loop *LI = (*this->LI)[I->getParent()];
5312 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5313 if (PHINode *PN = dyn_cast<PHINode>(I))
5314 if (PN->getParent() == LI->getHeader()) {
5315 // Okay, there is no closed form solution for the PHI node. Check
5316 // to see if the loop that contains it has a known backedge-taken
5317 // count. If so, we may be able to force computation of the exit
5319 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5320 if (const SCEVConstant *BTCC =
5321 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5322 // Okay, we know how many times the containing loop executes. If
5323 // this is a constant evolving PHI node, get the final value at
5324 // the specified iteration number.
5325 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5326 BTCC->getValue()->getValue(),
5328 if (RV) return getSCEV(RV);
5332 // Okay, this is an expression that we cannot symbolically evaluate
5333 // into a SCEV. Check to see if it's possible to symbolically evaluate
5334 // the arguments into constants, and if so, try to constant propagate the
5335 // result. This is particularly useful for computing loop exit values.
5336 if (CanConstantFold(I)) {
5337 SmallVector<Constant *, 4> Operands;
5338 bool MadeImprovement = false;
5339 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5340 Value *Op = I->getOperand(i);
5341 if (Constant *C = dyn_cast<Constant>(Op)) {
5342 Operands.push_back(C);
5346 // If any of the operands is non-constant and if they are
5347 // non-integer and non-pointer, don't even try to analyze them
5348 // with scev techniques.
5349 if (!isSCEVable(Op->getType()))
5352 const SCEV *OrigV = getSCEV(Op);
5353 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5354 MadeImprovement |= OrigV != OpV;
5356 Constant *C = BuildConstantFromSCEV(OpV);
5358 if (C->getType() != Op->getType())
5359 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5363 Operands.push_back(C);
5366 // Check to see if getSCEVAtScope actually made an improvement.
5367 if (MadeImprovement) {
5369 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5370 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5371 Operands[0], Operands[1], TD,
5373 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5374 if (!LI->isVolatile())
5375 C = ConstantFoldLoadFromConstPtr(Operands[0], TD);
5377 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5385 // This is some other type of SCEVUnknown, just return it.
5389 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5390 // Avoid performing the look-up in the common case where the specified
5391 // expression has no loop-variant portions.
5392 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5393 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5394 if (OpAtScope != Comm->getOperand(i)) {
5395 // Okay, at least one of these operands is loop variant but might be
5396 // foldable. Build a new instance of the folded commutative expression.
5397 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5398 Comm->op_begin()+i);
5399 NewOps.push_back(OpAtScope);
5401 for (++i; i != e; ++i) {
5402 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5403 NewOps.push_back(OpAtScope);
5405 if (isa<SCEVAddExpr>(Comm))
5406 return getAddExpr(NewOps);
5407 if (isa<SCEVMulExpr>(Comm))
5408 return getMulExpr(NewOps);
5409 if (isa<SCEVSMaxExpr>(Comm))
5410 return getSMaxExpr(NewOps);
5411 if (isa<SCEVUMaxExpr>(Comm))
5412 return getUMaxExpr(NewOps);
5413 llvm_unreachable("Unknown commutative SCEV type!");
5416 // If we got here, all operands are loop invariant.
5420 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5421 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5422 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5423 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5424 return Div; // must be loop invariant
5425 return getUDivExpr(LHS, RHS);
5428 // If this is a loop recurrence for a loop that does not contain L, then we
5429 // are dealing with the final value computed by the loop.
5430 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5431 // First, attempt to evaluate each operand.
5432 // Avoid performing the look-up in the common case where the specified
5433 // expression has no loop-variant portions.
5434 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5435 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5436 if (OpAtScope == AddRec->getOperand(i))
5439 // Okay, at least one of these operands is loop variant but might be
5440 // foldable. Build a new instance of the folded commutative expression.
5441 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5442 AddRec->op_begin()+i);
5443 NewOps.push_back(OpAtScope);
5444 for (++i; i != e; ++i)
5445 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5447 const SCEV *FoldedRec =
5448 getAddRecExpr(NewOps, AddRec->getLoop(),
5449 AddRec->getNoWrapFlags(SCEV::FlagNW));
5450 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5451 // The addrec may be folded to a nonrecurrence, for example, if the
5452 // induction variable is multiplied by zero after constant folding. Go
5453 // ahead and return the folded value.
5459 // If the scope is outside the addrec's loop, evaluate it by using the
5460 // loop exit value of the addrec.
5461 if (!AddRec->getLoop()->contains(L)) {
5462 // To evaluate this recurrence, we need to know how many times the AddRec
5463 // loop iterates. Compute this now.
5464 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5465 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5467 // Then, evaluate the AddRec.
5468 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5474 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5475 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5476 if (Op == Cast->getOperand())
5477 return Cast; // must be loop invariant
5478 return getZeroExtendExpr(Op, Cast->getType());
5481 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5482 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5483 if (Op == Cast->getOperand())
5484 return Cast; // must be loop invariant
5485 return getSignExtendExpr(Op, Cast->getType());
5488 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5489 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5490 if (Op == Cast->getOperand())
5491 return Cast; // must be loop invariant
5492 return getTruncateExpr(Op, Cast->getType());
5495 llvm_unreachable("Unknown SCEV type!");
5498 /// getSCEVAtScope - This is a convenience function which does
5499 /// getSCEVAtScope(getSCEV(V), L).
5500 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5501 return getSCEVAtScope(getSCEV(V), L);
5504 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5505 /// following equation:
5507 /// A * X = B (mod N)
5509 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5510 /// A and B isn't important.
5512 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5513 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5514 ScalarEvolution &SE) {
5515 uint32_t BW = A.getBitWidth();
5516 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5517 assert(A != 0 && "A must be non-zero.");
5521 // The gcd of A and N may have only one prime factor: 2. The number of
5522 // trailing zeros in A is its multiplicity
5523 uint32_t Mult2 = A.countTrailingZeros();
5526 // 2. Check if B is divisible by D.
5528 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5529 // is not less than multiplicity of this prime factor for D.
5530 if (B.countTrailingZeros() < Mult2)
5531 return SE.getCouldNotCompute();
5533 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5536 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5537 // bit width during computations.
5538 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5539 APInt Mod(BW + 1, 0);
5540 Mod.setBit(BW - Mult2); // Mod = N / D
5541 APInt I = AD.multiplicativeInverse(Mod);
5543 // 4. Compute the minimum unsigned root of the equation:
5544 // I * (B / D) mod (N / D)
5545 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5547 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5549 return SE.getConstant(Result.trunc(BW));
5552 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5553 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5554 /// might be the same) or two SCEVCouldNotCompute objects.
5556 static std::pair<const SCEV *,const SCEV *>
5557 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5558 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5559 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5560 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5561 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5563 // We currently can only solve this if the coefficients are constants.
5564 if (!LC || !MC || !NC) {
5565 const SCEV *CNC = SE.getCouldNotCompute();
5566 return std::make_pair(CNC, CNC);
5569 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5570 const APInt &L = LC->getValue()->getValue();
5571 const APInt &M = MC->getValue()->getValue();
5572 const APInt &N = NC->getValue()->getValue();
5573 APInt Two(BitWidth, 2);
5574 APInt Four(BitWidth, 4);
5577 using namespace APIntOps;
5579 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5580 // The B coefficient is M-N/2
5584 // The A coefficient is N/2
5585 APInt A(N.sdiv(Two));
5587 // Compute the B^2-4ac term.
5590 SqrtTerm -= Four * (A * C);
5592 if (SqrtTerm.isNegative()) {
5593 // The loop is provably infinite.
5594 const SCEV *CNC = SE.getCouldNotCompute();
5595 return std::make_pair(CNC, CNC);
5598 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5599 // integer value or else APInt::sqrt() will assert.
5600 APInt SqrtVal(SqrtTerm.sqrt());
5602 // Compute the two solutions for the quadratic formula.
5603 // The divisions must be performed as signed divisions.
5606 if (TwoA.isMinValue()) {
5607 const SCEV *CNC = SE.getCouldNotCompute();
5608 return std::make_pair(CNC, CNC);
5611 LLVMContext &Context = SE.getContext();
5613 ConstantInt *Solution1 =
5614 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5615 ConstantInt *Solution2 =
5616 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5618 return std::make_pair(SE.getConstant(Solution1),
5619 SE.getConstant(Solution2));
5620 } // end APIntOps namespace
5623 /// HowFarToZero - Return the number of times a backedge comparing the specified
5624 /// value to zero will execute. If not computable, return CouldNotCompute.
5626 /// This is only used for loops with a "x != y" exit test. The exit condition is
5627 /// now expressed as a single expression, V = x-y. So the exit test is
5628 /// effectively V != 0. We know and take advantage of the fact that this
5629 /// expression only being used in a comparison by zero context.
5630 ScalarEvolution::ExitLimit
5631 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
5632 // If the value is a constant
5633 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5634 // If the value is already zero, the branch will execute zero times.
5635 if (C->getValue()->isZero()) return C;
5636 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5639 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5640 if (!AddRec || AddRec->getLoop() != L)
5641 return getCouldNotCompute();
5643 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5644 // the quadratic equation to solve it.
5645 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5646 std::pair<const SCEV *,const SCEV *> Roots =
5647 SolveQuadraticEquation(AddRec, *this);
5648 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5649 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5652 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5653 << " sol#2: " << *R2 << "\n";
5655 // Pick the smallest positive root value.
5656 if (ConstantInt *CB =
5657 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5660 if (CB->getZExtValue() == false)
5661 std::swap(R1, R2); // R1 is the minimum root now.
5663 // We can only use this value if the chrec ends up with an exact zero
5664 // value at this index. When solving for "X*X != 5", for example, we
5665 // should not accept a root of 2.
5666 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5668 return R1; // We found a quadratic root!
5671 return getCouldNotCompute();
5674 // Otherwise we can only handle this if it is affine.
5675 if (!AddRec->isAffine())
5676 return getCouldNotCompute();
5678 // If this is an affine expression, the execution count of this branch is
5679 // the minimum unsigned root of the following equation:
5681 // Start + Step*N = 0 (mod 2^BW)
5685 // Step*N = -Start (mod 2^BW)
5687 // where BW is the common bit width of Start and Step.
5689 // Get the initial value for the loop.
5690 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5691 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5693 // For now we handle only constant steps.
5695 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5696 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5697 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5698 // We have not yet seen any such cases.
5699 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5700 if (StepC == 0 || StepC->getValue()->equalsInt(0))
5701 return getCouldNotCompute();
5703 // For positive steps (counting up until unsigned overflow):
5704 // N = -Start/Step (as unsigned)
5705 // For negative steps (counting down to zero):
5707 // First compute the unsigned distance from zero in the direction of Step.
5708 bool CountDown = StepC->getValue()->getValue().isNegative();
5709 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5711 // Handle unitary steps, which cannot wraparound.
5712 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5713 // N = Distance (as unsigned)
5714 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5715 ConstantRange CR = getUnsignedRange(Start);
5716 const SCEV *MaxBECount;
5717 if (!CountDown && CR.getUnsignedMin().isMinValue())
5718 // When counting up, the worst starting value is 1, not 0.
5719 MaxBECount = CR.getUnsignedMax().isMinValue()
5720 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5721 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5723 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5724 : -CR.getUnsignedMin());
5725 return ExitLimit(Distance, MaxBECount, /*MustExit=*/true);
5728 // If the recurrence is known not to wraparound, unsigned divide computes the
5729 // back edge count. (Ideally we would have an "isexact" bit for udiv). We know
5730 // that the value will either become zero (and thus the loop terminates), that
5731 // the loop will terminate through some other exit condition first, or that
5732 // the loop has undefined behavior. This means we can't "miss" the exit
5733 // value, even with nonunit stride, and exit later via the same branch. Note
5734 // that we can skip this exit if loop later exits via a different
5735 // branch. Hence MustExit=false.
5737 // This is only valid for expressions that directly compute the loop exit. It
5738 // is invalid for subexpressions in which the loop may exit through this
5739 // branch even if this subexpression is false. In that case, the trip count
5740 // computed by this udiv could be smaller than the number of well-defined
5742 if (!IsSubExpr && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5744 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5745 return ExitLimit(Exact, Exact, /*MustExit=*/false);
5747 // Then, try to solve the above equation provided that Start is constant.
5748 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5749 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5750 -StartC->getValue()->getValue(),
5752 return getCouldNotCompute();
5755 /// HowFarToNonZero - Return the number of times a backedge checking the
5756 /// specified value for nonzero will execute. If not computable, return
5758 ScalarEvolution::ExitLimit
5759 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5760 // Loops that look like: while (X == 0) are very strange indeed. We don't
5761 // handle them yet except for the trivial case. This could be expanded in the
5762 // future as needed.
5764 // If the value is a constant, check to see if it is known to be non-zero
5765 // already. If so, the backedge will execute zero times.
5766 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5767 if (!C->getValue()->isNullValue())
5768 return getConstant(C->getType(), 0);
5769 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5772 // We could implement others, but I really doubt anyone writes loops like
5773 // this, and if they did, they would already be constant folded.
5774 return getCouldNotCompute();
5777 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5778 /// (which may not be an immediate predecessor) which has exactly one
5779 /// successor from which BB is reachable, or null if no such block is
5782 std::pair<BasicBlock *, BasicBlock *>
5783 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5784 // If the block has a unique predecessor, then there is no path from the
5785 // predecessor to the block that does not go through the direct edge
5786 // from the predecessor to the block.
5787 if (BasicBlock *Pred = BB->getSinglePredecessor())
5788 return std::make_pair(Pred, BB);
5790 // A loop's header is defined to be a block that dominates the loop.
5791 // If the header has a unique predecessor outside the loop, it must be
5792 // a block that has exactly one successor that can reach the loop.
5793 if (Loop *L = LI->getLoopFor(BB))
5794 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5796 return std::pair<BasicBlock *, BasicBlock *>();
5799 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5800 /// testing whether two expressions are equal, however for the purposes of
5801 /// looking for a condition guarding a loop, it can be useful to be a little
5802 /// more general, since a front-end may have replicated the controlling
5805 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5806 // Quick check to see if they are the same SCEV.
5807 if (A == B) return true;
5809 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5810 // two different instructions with the same value. Check for this case.
5811 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5812 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5813 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5814 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5815 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5818 // Otherwise assume they may have a different value.
5822 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5823 /// predicate Pred. Return true iff any changes were made.
5825 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5826 const SCEV *&LHS, const SCEV *&RHS,
5828 bool Changed = false;
5830 // If we hit the max recursion limit bail out.
5834 // Canonicalize a constant to the right side.
5835 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5836 // Check for both operands constant.
5837 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5838 if (ConstantExpr::getICmp(Pred,
5840 RHSC->getValue())->isNullValue())
5841 goto trivially_false;
5843 goto trivially_true;
5845 // Otherwise swap the operands to put the constant on the right.
5846 std::swap(LHS, RHS);
5847 Pred = ICmpInst::getSwappedPredicate(Pred);
5851 // If we're comparing an addrec with a value which is loop-invariant in the
5852 // addrec's loop, put the addrec on the left. Also make a dominance check,
5853 // as both operands could be addrecs loop-invariant in each other's loop.
5854 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5855 const Loop *L = AR->getLoop();
5856 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5857 std::swap(LHS, RHS);
5858 Pred = ICmpInst::getSwappedPredicate(Pred);
5863 // If there's a constant operand, canonicalize comparisons with boundary
5864 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5865 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5866 const APInt &RA = RC->getValue()->getValue();
5868 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5869 case ICmpInst::ICMP_EQ:
5870 case ICmpInst::ICMP_NE:
5871 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5873 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5874 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5875 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5876 ME->getOperand(0)->isAllOnesValue()) {
5877 RHS = AE->getOperand(1);
5878 LHS = ME->getOperand(1);
5882 case ICmpInst::ICMP_UGE:
5883 if ((RA - 1).isMinValue()) {
5884 Pred = ICmpInst::ICMP_NE;
5885 RHS = getConstant(RA - 1);
5889 if (RA.isMaxValue()) {
5890 Pred = ICmpInst::ICMP_EQ;
5894 if (RA.isMinValue()) goto trivially_true;
5896 Pred = ICmpInst::ICMP_UGT;
5897 RHS = getConstant(RA - 1);
5900 case ICmpInst::ICMP_ULE:
5901 if ((RA + 1).isMaxValue()) {
5902 Pred = ICmpInst::ICMP_NE;
5903 RHS = getConstant(RA + 1);
5907 if (RA.isMinValue()) {
5908 Pred = ICmpInst::ICMP_EQ;
5912 if (RA.isMaxValue()) goto trivially_true;
5914 Pred = ICmpInst::ICMP_ULT;
5915 RHS = getConstant(RA + 1);
5918 case ICmpInst::ICMP_SGE:
5919 if ((RA - 1).isMinSignedValue()) {
5920 Pred = ICmpInst::ICMP_NE;
5921 RHS = getConstant(RA - 1);
5925 if (RA.isMaxSignedValue()) {
5926 Pred = ICmpInst::ICMP_EQ;
5930 if (RA.isMinSignedValue()) goto trivially_true;
5932 Pred = ICmpInst::ICMP_SGT;
5933 RHS = getConstant(RA - 1);
5936 case ICmpInst::ICMP_SLE:
5937 if ((RA + 1).isMaxSignedValue()) {
5938 Pred = ICmpInst::ICMP_NE;
5939 RHS = getConstant(RA + 1);
5943 if (RA.isMinSignedValue()) {
5944 Pred = ICmpInst::ICMP_EQ;
5948 if (RA.isMaxSignedValue()) goto trivially_true;
5950 Pred = ICmpInst::ICMP_SLT;
5951 RHS = getConstant(RA + 1);
5954 case ICmpInst::ICMP_UGT:
5955 if (RA.isMinValue()) {
5956 Pred = ICmpInst::ICMP_NE;
5960 if ((RA + 1).isMaxValue()) {
5961 Pred = ICmpInst::ICMP_EQ;
5962 RHS = getConstant(RA + 1);
5966 if (RA.isMaxValue()) goto trivially_false;
5968 case ICmpInst::ICMP_ULT:
5969 if (RA.isMaxValue()) {
5970 Pred = ICmpInst::ICMP_NE;
5974 if ((RA - 1).isMinValue()) {
5975 Pred = ICmpInst::ICMP_EQ;
5976 RHS = getConstant(RA - 1);
5980 if (RA.isMinValue()) goto trivially_false;
5982 case ICmpInst::ICMP_SGT:
5983 if (RA.isMinSignedValue()) {
5984 Pred = ICmpInst::ICMP_NE;
5988 if ((RA + 1).isMaxSignedValue()) {
5989 Pred = ICmpInst::ICMP_EQ;
5990 RHS = getConstant(RA + 1);
5994 if (RA.isMaxSignedValue()) goto trivially_false;
5996 case ICmpInst::ICMP_SLT:
5997 if (RA.isMaxSignedValue()) {
5998 Pred = ICmpInst::ICMP_NE;
6002 if ((RA - 1).isMinSignedValue()) {
6003 Pred = ICmpInst::ICMP_EQ;
6004 RHS = getConstant(RA - 1);
6008 if (RA.isMinSignedValue()) goto trivially_false;
6013 // Check for obvious equality.
6014 if (HasSameValue(LHS, RHS)) {
6015 if (ICmpInst::isTrueWhenEqual(Pred))
6016 goto trivially_true;
6017 if (ICmpInst::isFalseWhenEqual(Pred))
6018 goto trivially_false;
6021 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6022 // adding or subtracting 1 from one of the operands.
6024 case ICmpInst::ICMP_SLE:
6025 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6026 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6028 Pred = ICmpInst::ICMP_SLT;
6030 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6031 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6033 Pred = ICmpInst::ICMP_SLT;
6037 case ICmpInst::ICMP_SGE:
6038 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6039 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6041 Pred = ICmpInst::ICMP_SGT;
6043 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6044 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6046 Pred = ICmpInst::ICMP_SGT;
6050 case ICmpInst::ICMP_ULE:
6051 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6052 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6054 Pred = ICmpInst::ICMP_ULT;
6056 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6057 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6059 Pred = ICmpInst::ICMP_ULT;
6063 case ICmpInst::ICMP_UGE:
6064 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6065 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6067 Pred = ICmpInst::ICMP_UGT;
6069 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6070 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6072 Pred = ICmpInst::ICMP_UGT;
6080 // TODO: More simplifications are possible here.
6082 // Recursively simplify until we either hit a recursion limit or nothing
6085 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6091 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6092 Pred = ICmpInst::ICMP_EQ;
6097 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6098 Pred = ICmpInst::ICMP_NE;
6102 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6103 return getSignedRange(S).getSignedMax().isNegative();
6106 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6107 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6110 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6111 return !getSignedRange(S).getSignedMin().isNegative();
6114 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6115 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6118 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6119 return isKnownNegative(S) || isKnownPositive(S);
6122 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6123 const SCEV *LHS, const SCEV *RHS) {
6124 // Canonicalize the inputs first.
6125 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6127 // If LHS or RHS is an addrec, check to see if the condition is true in
6128 // every iteration of the loop.
6129 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
6130 if (isLoopEntryGuardedByCond(
6131 AR->getLoop(), Pred, AR->getStart(), RHS) &&
6132 isLoopBackedgeGuardedByCond(
6133 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
6135 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
6136 if (isLoopEntryGuardedByCond(
6137 AR->getLoop(), Pred, LHS, AR->getStart()) &&
6138 isLoopBackedgeGuardedByCond(
6139 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
6142 // Otherwise see what can be done with known constant ranges.
6143 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6147 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6148 const SCEV *LHS, const SCEV *RHS) {
6149 if (HasSameValue(LHS, RHS))
6150 return ICmpInst::isTrueWhenEqual(Pred);
6152 // This code is split out from isKnownPredicate because it is called from
6153 // within isLoopEntryGuardedByCond.
6156 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6157 case ICmpInst::ICMP_SGT:
6158 Pred = ICmpInst::ICMP_SLT;
6159 std::swap(LHS, RHS);
6160 case ICmpInst::ICMP_SLT: {
6161 ConstantRange LHSRange = getSignedRange(LHS);
6162 ConstantRange RHSRange = getSignedRange(RHS);
6163 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6165 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6169 case ICmpInst::ICMP_SGE:
6170 Pred = ICmpInst::ICMP_SLE;
6171 std::swap(LHS, RHS);
6172 case ICmpInst::ICMP_SLE: {
6173 ConstantRange LHSRange = getSignedRange(LHS);
6174 ConstantRange RHSRange = getSignedRange(RHS);
6175 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6177 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6181 case ICmpInst::ICMP_UGT:
6182 Pred = ICmpInst::ICMP_ULT;
6183 std::swap(LHS, RHS);
6184 case ICmpInst::ICMP_ULT: {
6185 ConstantRange LHSRange = getUnsignedRange(LHS);
6186 ConstantRange RHSRange = getUnsignedRange(RHS);
6187 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6189 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6193 case ICmpInst::ICMP_UGE:
6194 Pred = ICmpInst::ICMP_ULE;
6195 std::swap(LHS, RHS);
6196 case ICmpInst::ICMP_ULE: {
6197 ConstantRange LHSRange = getUnsignedRange(LHS);
6198 ConstantRange RHSRange = getUnsignedRange(RHS);
6199 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6201 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6205 case ICmpInst::ICMP_NE: {
6206 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6208 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6211 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6212 if (isKnownNonZero(Diff))
6216 case ICmpInst::ICMP_EQ:
6217 // The check at the top of the function catches the case where
6218 // the values are known to be equal.
6224 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6225 /// protected by a conditional between LHS and RHS. This is used to
6226 /// to eliminate casts.
6228 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6229 ICmpInst::Predicate Pred,
6230 const SCEV *LHS, const SCEV *RHS) {
6231 // Interpret a null as meaning no loop, where there is obviously no guard
6232 // (interprocedural conditions notwithstanding).
6233 if (!L) return true;
6235 BasicBlock *Latch = L->getLoopLatch();
6239 BranchInst *LoopContinuePredicate =
6240 dyn_cast<BranchInst>(Latch->getTerminator());
6241 if (!LoopContinuePredicate ||
6242 LoopContinuePredicate->isUnconditional())
6245 return isImpliedCond(Pred, LHS, RHS,
6246 LoopContinuePredicate->getCondition(),
6247 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6250 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6251 /// by a conditional between LHS and RHS. This is used to help avoid max
6252 /// expressions in loop trip counts, and to eliminate casts.
6254 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6255 ICmpInst::Predicate Pred,
6256 const SCEV *LHS, const SCEV *RHS) {
6257 // Interpret a null as meaning no loop, where there is obviously no guard
6258 // (interprocedural conditions notwithstanding).
6259 if (!L) return false;
6261 // Starting at the loop predecessor, climb up the predecessor chain, as long
6262 // as there are predecessors that can be found that have unique successors
6263 // leading to the original header.
6264 for (std::pair<BasicBlock *, BasicBlock *>
6265 Pair(L->getLoopPredecessor(), L->getHeader());
6267 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6269 BranchInst *LoopEntryPredicate =
6270 dyn_cast<BranchInst>(Pair.first->getTerminator());
6271 if (!LoopEntryPredicate ||
6272 LoopEntryPredicate->isUnconditional())
6275 if (isImpliedCond(Pred, LHS, RHS,
6276 LoopEntryPredicate->getCondition(),
6277 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6284 /// RAII wrapper to prevent recursive application of isImpliedCond.
6285 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6286 /// currently evaluating isImpliedCond.
6287 struct MarkPendingLoopPredicate {
6289 DenseSet<Value*> &LoopPreds;
6292 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6293 : Cond(C), LoopPreds(LP) {
6294 Pending = !LoopPreds.insert(Cond).second;
6296 ~MarkPendingLoopPredicate() {
6298 LoopPreds.erase(Cond);
6302 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6303 /// and RHS is true whenever the given Cond value evaluates to true.
6304 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6305 const SCEV *LHS, const SCEV *RHS,
6306 Value *FoundCondValue,
6308 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6312 // Recursively handle And and Or conditions.
6313 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6314 if (BO->getOpcode() == Instruction::And) {
6316 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6317 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6318 } else if (BO->getOpcode() == Instruction::Or) {
6320 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6321 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6325 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6326 if (!ICI) return false;
6328 // Bail if the ICmp's operands' types are wider than the needed type
6329 // before attempting to call getSCEV on them. This avoids infinite
6330 // recursion, since the analysis of widening casts can require loop
6331 // exit condition information for overflow checking, which would
6333 if (getTypeSizeInBits(LHS->getType()) <
6334 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6337 // Now that we found a conditional branch that dominates the loop or controls
6338 // the loop latch. Check to see if it is the comparison we are looking for.
6339 ICmpInst::Predicate FoundPred;
6341 FoundPred = ICI->getInversePredicate();
6343 FoundPred = ICI->getPredicate();
6345 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6346 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6348 // Balance the types. The case where FoundLHS' type is wider than
6349 // LHS' type is checked for above.
6350 if (getTypeSizeInBits(LHS->getType()) >
6351 getTypeSizeInBits(FoundLHS->getType())) {
6352 if (CmpInst::isSigned(FoundPred)) {
6353 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6354 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6356 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6357 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6361 // Canonicalize the query to match the way instcombine will have
6362 // canonicalized the comparison.
6363 if (SimplifyICmpOperands(Pred, LHS, RHS))
6365 return CmpInst::isTrueWhenEqual(Pred);
6366 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6367 if (FoundLHS == FoundRHS)
6368 return CmpInst::isFalseWhenEqual(FoundPred);
6370 // Check to see if we can make the LHS or RHS match.
6371 if (LHS == FoundRHS || RHS == FoundLHS) {
6372 if (isa<SCEVConstant>(RHS)) {
6373 std::swap(FoundLHS, FoundRHS);
6374 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6376 std::swap(LHS, RHS);
6377 Pred = ICmpInst::getSwappedPredicate(Pred);
6381 // Check whether the found predicate is the same as the desired predicate.
6382 if (FoundPred == Pred)
6383 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6385 // Check whether swapping the found predicate makes it the same as the
6386 // desired predicate.
6387 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6388 if (isa<SCEVConstant>(RHS))
6389 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6391 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6392 RHS, LHS, FoundLHS, FoundRHS);
6395 // Check whether the actual condition is beyond sufficient.
6396 if (FoundPred == ICmpInst::ICMP_EQ)
6397 if (ICmpInst::isTrueWhenEqual(Pred))
6398 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6400 if (Pred == ICmpInst::ICMP_NE)
6401 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6402 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6405 // Otherwise assume the worst.
6409 /// isImpliedCondOperands - Test whether the condition described by Pred,
6410 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6411 /// and FoundRHS is true.
6412 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6413 const SCEV *LHS, const SCEV *RHS,
6414 const SCEV *FoundLHS,
6415 const SCEV *FoundRHS) {
6416 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6417 FoundLHS, FoundRHS) ||
6418 // ~x < ~y --> x > y
6419 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6420 getNotSCEV(FoundRHS),
6421 getNotSCEV(FoundLHS));
6424 /// isImpliedCondOperandsHelper - Test whether the condition described by
6425 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6426 /// FoundLHS, and FoundRHS is true.
6428 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6429 const SCEV *LHS, const SCEV *RHS,
6430 const SCEV *FoundLHS,
6431 const SCEV *FoundRHS) {
6433 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6434 case ICmpInst::ICMP_EQ:
6435 case ICmpInst::ICMP_NE:
6436 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6439 case ICmpInst::ICMP_SLT:
6440 case ICmpInst::ICMP_SLE:
6441 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6442 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6445 case ICmpInst::ICMP_SGT:
6446 case ICmpInst::ICMP_SGE:
6447 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6448 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6451 case ICmpInst::ICMP_ULT:
6452 case ICmpInst::ICMP_ULE:
6453 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6454 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6457 case ICmpInst::ICMP_UGT:
6458 case ICmpInst::ICMP_UGE:
6459 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6460 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6468 // Verify if an linear IV with positive stride can overflow when in a
6469 // less-than comparison, knowing the invariant term of the comparison, the
6470 // stride and the knowledge of NSW/NUW flags on the recurrence.
6471 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
6472 bool IsSigned, bool NoWrap) {
6473 if (NoWrap) return false;
6475 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6476 const SCEV *One = getConstant(Stride->getType(), 1);
6479 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
6480 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
6481 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6484 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
6485 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
6488 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
6489 APInt MaxValue = APInt::getMaxValue(BitWidth);
6490 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6493 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
6494 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
6497 // Verify if an linear IV with negative stride can overflow when in a
6498 // greater-than comparison, knowing the invariant term of the comparison,
6499 // the stride and the knowledge of NSW/NUW flags on the recurrence.
6500 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
6501 bool IsSigned, bool NoWrap) {
6502 if (NoWrap) return false;
6504 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6505 const SCEV *One = getConstant(Stride->getType(), 1);
6508 APInt MinRHS = getSignedRange(RHS).getSignedMin();
6509 APInt MinValue = APInt::getSignedMinValue(BitWidth);
6510 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6513 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
6514 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
6517 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
6518 APInt MinValue = APInt::getMinValue(BitWidth);
6519 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6522 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
6523 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
6526 // Compute the backedge taken count knowing the interval difference, the
6527 // stride and presence of the equality in the comparison.
6528 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
6530 const SCEV *One = getConstant(Step->getType(), 1);
6531 Delta = Equality ? getAddExpr(Delta, Step)
6532 : getAddExpr(Delta, getMinusSCEV(Step, One));
6533 return getUDivExpr(Delta, Step);
6536 /// HowManyLessThans - Return the number of times a backedge containing the
6537 /// specified less-than comparison will execute. If not computable, return
6538 /// CouldNotCompute.
6540 /// @param IsSubExpr is true when the LHS < RHS condition does not directly
6541 /// control the branch. In this case, we can only compute an iteration count for
6542 /// a subexpression that cannot overflow before evaluating true.
6543 ScalarEvolution::ExitLimit
6544 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6545 const Loop *L, bool IsSigned,
6547 // We handle only IV < Invariant
6548 if (!isLoopInvariant(RHS, L))
6549 return getCouldNotCompute();
6551 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6553 // Avoid weird loops
6554 if (!IV || IV->getLoop() != L || !IV->isAffine())
6555 return getCouldNotCompute();
6557 bool NoWrap = !IsSubExpr &&
6558 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6560 const SCEV *Stride = IV->getStepRecurrence(*this);
6562 // Avoid negative or zero stride values
6563 if (!isKnownPositive(Stride))
6564 return getCouldNotCompute();
6566 // Avoid proven overflow cases: this will ensure that the backedge taken count
6567 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6568 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6569 // behaviors like the case of C language.
6570 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
6571 return getCouldNotCompute();
6573 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
6574 : ICmpInst::ICMP_ULT;
6575 const SCEV *Start = IV->getStart();
6576 const SCEV *End = RHS;
6577 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
6578 End = IsSigned ? getSMaxExpr(RHS, Start)
6579 : getUMaxExpr(RHS, Start);
6581 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
6583 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
6584 : getUnsignedRange(Start).getUnsignedMin();
6586 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6587 : getUnsignedRange(Stride).getUnsignedMin();
6589 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6590 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
6591 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
6593 // Although End can be a MAX expression we estimate MaxEnd considering only
6594 // the case End = RHS. This is safe because in the other case (End - Start)
6595 // is zero, leading to a zero maximum backedge taken count.
6597 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
6598 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
6600 const SCEV *MaxBECount = getCouldNotCompute();
6601 if (isa<SCEVConstant>(BECount))
6602 MaxBECount = BECount;
6604 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
6605 getConstant(MinStride), false);
6607 if (isa<SCEVCouldNotCompute>(MaxBECount))
6608 MaxBECount = BECount;
6610 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6613 ScalarEvolution::ExitLimit
6614 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
6615 const Loop *L, bool IsSigned,
6617 // We handle only IV > Invariant
6618 if (!isLoopInvariant(RHS, L))
6619 return getCouldNotCompute();
6621 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6623 // Avoid weird loops
6624 if (!IV || IV->getLoop() != L || !IV->isAffine())
6625 return getCouldNotCompute();
6627 bool NoWrap = !IsSubExpr &&
6628 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6630 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
6632 // Avoid negative or zero stride values
6633 if (!isKnownPositive(Stride))
6634 return getCouldNotCompute();
6636 // Avoid proven overflow cases: this will ensure that the backedge taken count
6637 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6638 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6639 // behaviors like the case of C language.
6640 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
6641 return getCouldNotCompute();
6643 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
6644 : ICmpInst::ICMP_UGT;
6646 const SCEV *Start = IV->getStart();
6647 const SCEV *End = RHS;
6648 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
6649 End = IsSigned ? getSMinExpr(RHS, Start)
6650 : getUMinExpr(RHS, Start);
6652 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
6654 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
6655 : getUnsignedRange(Start).getUnsignedMax();
6657 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6658 : getUnsignedRange(Stride).getUnsignedMin();
6660 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6661 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
6662 : APInt::getMinValue(BitWidth) + (MinStride - 1);
6664 // Although End can be a MIN expression we estimate MinEnd considering only
6665 // the case End = RHS. This is safe because in the other case (Start - End)
6666 // is zero, leading to a zero maximum backedge taken count.
6668 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
6669 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
6672 const SCEV *MaxBECount = getCouldNotCompute();
6673 if (isa<SCEVConstant>(BECount))
6674 MaxBECount = BECount;
6676 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
6677 getConstant(MinStride), false);
6679 if (isa<SCEVCouldNotCompute>(MaxBECount))
6680 MaxBECount = BECount;
6682 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6685 /// getNumIterationsInRange - Return the number of iterations of this loop that
6686 /// produce values in the specified constant range. Another way of looking at
6687 /// this is that it returns the first iteration number where the value is not in
6688 /// the condition, thus computing the exit count. If the iteration count can't
6689 /// be computed, an instance of SCEVCouldNotCompute is returned.
6690 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6691 ScalarEvolution &SE) const {
6692 if (Range.isFullSet()) // Infinite loop.
6693 return SE.getCouldNotCompute();
6695 // If the start is a non-zero constant, shift the range to simplify things.
6696 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6697 if (!SC->getValue()->isZero()) {
6698 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6699 Operands[0] = SE.getConstant(SC->getType(), 0);
6700 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6701 getNoWrapFlags(FlagNW));
6702 if (const SCEVAddRecExpr *ShiftedAddRec =
6703 dyn_cast<SCEVAddRecExpr>(Shifted))
6704 return ShiftedAddRec->getNumIterationsInRange(
6705 Range.subtract(SC->getValue()->getValue()), SE);
6706 // This is strange and shouldn't happen.
6707 return SE.getCouldNotCompute();
6710 // The only time we can solve this is when we have all constant indices.
6711 // Otherwise, we cannot determine the overflow conditions.
6712 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6713 if (!isa<SCEVConstant>(getOperand(i)))
6714 return SE.getCouldNotCompute();
6717 // Okay at this point we know that all elements of the chrec are constants and
6718 // that the start element is zero.
6720 // First check to see if the range contains zero. If not, the first
6722 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6723 if (!Range.contains(APInt(BitWidth, 0)))
6724 return SE.getConstant(getType(), 0);
6727 // If this is an affine expression then we have this situation:
6728 // Solve {0,+,A} in Range === Ax in Range
6730 // We know that zero is in the range. If A is positive then we know that
6731 // the upper value of the range must be the first possible exit value.
6732 // If A is negative then the lower of the range is the last possible loop
6733 // value. Also note that we already checked for a full range.
6734 APInt One(BitWidth,1);
6735 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6736 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6738 // The exit value should be (End+A)/A.
6739 APInt ExitVal = (End + A).udiv(A);
6740 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6742 // Evaluate at the exit value. If we really did fall out of the valid
6743 // range, then we computed our trip count, otherwise wrap around or other
6744 // things must have happened.
6745 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6746 if (Range.contains(Val->getValue()))
6747 return SE.getCouldNotCompute(); // Something strange happened
6749 // Ensure that the previous value is in the range. This is a sanity check.
6750 assert(Range.contains(
6751 EvaluateConstantChrecAtConstant(this,
6752 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6753 "Linear scev computation is off in a bad way!");
6754 return SE.getConstant(ExitValue);
6755 } else if (isQuadratic()) {
6756 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6757 // quadratic equation to solve it. To do this, we must frame our problem in
6758 // terms of figuring out when zero is crossed, instead of when
6759 // Range.getUpper() is crossed.
6760 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6761 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6762 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6763 // getNoWrapFlags(FlagNW)
6766 // Next, solve the constructed addrec
6767 std::pair<const SCEV *,const SCEV *> Roots =
6768 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6769 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6770 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6772 // Pick the smallest positive root value.
6773 if (ConstantInt *CB =
6774 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6775 R1->getValue(), R2->getValue()))) {
6776 if (CB->getZExtValue() == false)
6777 std::swap(R1, R2); // R1 is the minimum root now.
6779 // Make sure the root is not off by one. The returned iteration should
6780 // not be in the range, but the previous one should be. When solving
6781 // for "X*X < 5", for example, we should not return a root of 2.
6782 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6785 if (Range.contains(R1Val->getValue())) {
6786 // The next iteration must be out of the range...
6787 ConstantInt *NextVal =
6788 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6790 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6791 if (!Range.contains(R1Val->getValue()))
6792 return SE.getConstant(NextVal);
6793 return SE.getCouldNotCompute(); // Something strange happened
6796 // If R1 was not in the range, then it is a good return value. Make
6797 // sure that R1-1 WAS in the range though, just in case.
6798 ConstantInt *NextVal =
6799 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6800 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6801 if (Range.contains(R1Val->getValue()))
6803 return SE.getCouldNotCompute(); // Something strange happened
6808 return SE.getCouldNotCompute();
6811 static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
6812 APInt A = C1->getValue()->getValue();
6813 APInt B = C2->getValue()->getValue();
6814 uint32_t ABW = A.getBitWidth();
6815 uint32_t BBW = B.getBitWidth();
6822 return APIntOps::srem(A, B);
6825 static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
6826 APInt A = C1->getValue()->getValue();
6827 APInt B = C2->getValue()->getValue();
6828 uint32_t ABW = A.getBitWidth();
6829 uint32_t BBW = B.getBitWidth();
6836 return APIntOps::sdiv(A, B);
6840 struct SCEVGCD : public SCEVVisitor<SCEVGCD, const SCEV *> {
6842 // Pattern match Step into Start. When Step is a multiply expression, find
6843 // the largest subexpression of Step that appears in Start. When Start is an
6844 // add expression, try to match Step in the subexpressions of Start, non
6845 // matching subexpressions are returned under Remainder.
6846 static const SCEV *findGCD(ScalarEvolution &SE, const SCEV *Start,
6847 const SCEV *Step, const SCEV **Remainder) {
6848 assert(Remainder && "Remainder should not be NULL");
6849 SCEVGCD R(SE, Step, SE.getConstant(Step->getType(), 0));
6850 const SCEV *Res = R.visit(Start);
6851 *Remainder = R.Remainder;
6855 SCEVGCD(ScalarEvolution &S, const SCEV *G, const SCEV *R)
6856 : SE(S), GCD(G), Remainder(R) {
6857 Zero = SE.getConstant(GCD->getType(), 0);
6858 One = SE.getConstant(GCD->getType(), 1);
6861 const SCEV *visitConstant(const SCEVConstant *Constant) {
6862 if (GCD == Constant || Constant == Zero)
6865 if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD)) {
6866 const SCEV *Res = SE.getConstant(gcd(Constant, CGCD));
6870 Remainder = SE.getConstant(srem(Constant, CGCD));
6871 Constant = cast<SCEVConstant>(SE.getMinusSCEV(Constant, Remainder));
6872 Res = SE.getConstant(gcd(Constant, CGCD));
6876 // When GCD is not a constant, it could be that the GCD is an Add, Mul,
6877 // AddRec, etc., in which case we want to find out how many times the
6878 // Constant divides the GCD: we then return that as the new GCD.
6879 const SCEV *Rem = Zero;
6880 const SCEV *Res = findGCD(SE, GCD, Constant, &Rem);
6882 if (Res == One || Rem != Zero) {
6883 Remainder = Constant;
6887 assert(isa<SCEVConstant>(Res) && "Res should be a constant");
6888 Remainder = SE.getConstant(srem(Constant, cast<SCEVConstant>(Res)));
6892 const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
6898 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
6904 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
6910 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
6914 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6915 const SCEV *Rem = Zero;
6916 const SCEV *Res = findGCD(SE, Expr->getOperand(e - 1 - i), GCD, &Rem);
6918 // FIXME: There may be ambiguous situations: for instance,
6919 // GCD(-4 + (3 * %m), 2 * %m) where 2 divides -4 and %m divides (3 * %m).
6920 // The order in which the AddExpr is traversed computes a different GCD
6925 Remainder = SE.getAddExpr(Remainder, Rem);
6931 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
6935 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6936 if (Expr->getOperand(i) == GCD)
6940 // If we have not returned yet, it means that GCD is not part of Expr.
6941 const SCEV *PartialGCD = One;
6942 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6943 const SCEV *Rem = Zero;
6944 const SCEV *Res = findGCD(SE, Expr->getOperand(i), GCD, &Rem);
6946 // GCD does not divide Expr->getOperand(i).
6951 PartialGCD = SE.getMulExpr(PartialGCD, Res);
6952 if (PartialGCD == GCD)
6956 if (PartialGCD != One)
6960 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(GCD);
6964 // When the GCD is a multiply expression, try to decompose it:
6965 // this occurs when Step does not divide the Start expression
6966 // as in: {(-4 + (3 * %m)),+,(2 * %m)}
6967 for (int i = 0, e = Mul->getNumOperands(); i < e; ++i) {
6968 const SCEV *Rem = Zero;
6969 const SCEV *Res = findGCD(SE, Expr, Mul->getOperand(i), &Rem);
6979 const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
6985 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
6989 if (!Expr->isAffine()) {
6994 const SCEV *Rem = Zero;
6995 const SCEV *Res = findGCD(SE, Expr->getOperand(0), GCD, &Rem);
6997 Remainder = SE.getAddExpr(Remainder, Rem);
7000 Res = findGCD(SE, Expr->getOperand(1), Res, &Rem);
7009 const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
7015 const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
7021 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
7027 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
7032 ScalarEvolution &SE;
7033 const SCEV *GCD, *Remainder, *Zero, *One;
7036 struct SCEVDivision : public SCEVVisitor<SCEVDivision, const SCEV *> {
7038 // Remove from Start all multiples of Step.
7039 static const SCEV *divide(ScalarEvolution &SE, const SCEV *Start,
7041 SCEVDivision D(SE, Step);
7042 const SCEV *Rem = D.Zero;
7044 // The division is guaranteed to succeed: Step should divide Start with no
7046 assert(Step == SCEVGCD::findGCD(SE, Start, Step, &Rem) && Rem == D.Zero &&
7047 "Step should divide Start with no remainder.");
7048 return D.visit(Start);
7051 SCEVDivision(ScalarEvolution &S, const SCEV *G) : SE(S), GCD(G) {
7052 Zero = SE.getConstant(GCD->getType(), 0);
7053 One = SE.getConstant(GCD->getType(), 1);
7056 const SCEV *visitConstant(const SCEVConstant *Constant) {
7057 if (GCD == Constant)
7060 if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD))
7061 return SE.getConstant(sdiv(Constant, CGCD));
7065 const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
7071 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
7077 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
7083 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
7087 SmallVector<const SCEV *, 2> Operands;
7088 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
7089 Operands.push_back(divide(SE, Expr->getOperand(i), GCD));
7091 if (Operands.size() == 1)
7093 return SE.getAddExpr(Operands);
7096 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
7100 bool FoundGCDTerm = false;
7101 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
7102 if (Expr->getOperand(i) == GCD)
7103 FoundGCDTerm = true;
7105 SmallVector<const SCEV *, 2> Operands;
7107 FoundGCDTerm = false;
7108 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
7110 Operands.push_back(Expr->getOperand(i));
7111 else if (Expr->getOperand(i) == GCD)
7112 FoundGCDTerm = true;
7114 Operands.push_back(Expr->getOperand(i));
7117 FoundGCDTerm = false;
7118 const SCEV *PartialGCD = One;
7119 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
7120 if (PartialGCD == GCD) {
7121 Operands.push_back(Expr->getOperand(i));
7125 const SCEV *Rem = Zero;
7126 const SCEV *Res = SCEVGCD::findGCD(SE, Expr->getOperand(i), GCD, &Rem);
7128 PartialGCD = SE.getMulExpr(PartialGCD, Res);
7129 Operands.push_back(divide(SE, Expr->getOperand(i), GCD));
7131 Operands.push_back(Expr->getOperand(i));
7136 if (Operands.size() == 1)
7138 return SE.getMulExpr(Operands);
7141 const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
7147 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
7151 assert(Expr->isAffine() && "Expr should be affine");
7153 const SCEV *Start = divide(SE, Expr->getStart(), GCD);
7154 const SCEV *Step = divide(SE, Expr->getStepRecurrence(SE), GCD);
7156 return SE.getAddRecExpr(Start, Step, Expr->getLoop(),
7157 Expr->getNoWrapFlags());
7160 const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
7166 const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
7172 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
7178 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
7183 ScalarEvolution &SE;
7184 const SCEV *GCD, *Zero, *One;
7188 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7189 /// sizes of an array access. Returns the remainder of the delinearization that
7190 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7191 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7192 /// expressions in the stride and base of a SCEV corresponding to the
7193 /// computation of a GCD (greatest common divisor) of base and stride. When
7194 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7196 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7198 /// void foo(long n, long m, long o, double A[n][m][o]) {
7200 /// for (long i = 0; i < n; i++)
7201 /// for (long j = 0; j < m; j++)
7202 /// for (long k = 0; k < o; k++)
7203 /// A[i][j][k] = 1.0;
7206 /// the delinearization input is the following AddRec SCEV:
7208 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7210 /// From this SCEV, we are able to say that the base offset of the access is %A
7211 /// because it appears as an offset that does not divide any of the strides in
7214 /// CHECK: Base offset: %A
7216 /// and then SCEV->delinearize determines the size of some of the dimensions of
7217 /// the array as these are the multiples by which the strides are happening:
7219 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7221 /// Note that the outermost dimension remains of UnknownSize because there are
7222 /// no strides that would help identifying the size of the last dimension: when
7223 /// the array has been statically allocated, one could compute the size of that
7224 /// dimension by dividing the overall size of the array by the size of the known
7225 /// dimensions: %m * %o * 8.
7227 /// Finally delinearize provides the access functions for the array reference
7228 /// that does correspond to A[i][j][k] of the above C testcase:
7230 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7232 /// The testcases are checking the output of a function pass:
7233 /// DelinearizationPass that walks through all loads and stores of a function
7234 /// asking for the SCEV of the memory access with respect to all enclosing
7235 /// loops, calling SCEV->delinearize on that and printing the results.
7238 SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7239 SmallVectorImpl<const SCEV *> &Subscripts,
7240 SmallVectorImpl<const SCEV *> &Sizes) const {
7241 // Early exit in case this SCEV is not an affine multivariate function.
7242 if (!this->isAffine())
7245 const SCEV *Start = this->getStart();
7246 const SCEV *Step = this->getStepRecurrence(SE);
7248 // Build the SCEV representation of the canonical induction variable in the
7249 // loop of this SCEV.
7250 const SCEV *Zero = SE.getConstant(this->getType(), 0);
7251 const SCEV *One = SE.getConstant(this->getType(), 1);
7253 SE.getAddRecExpr(Zero, One, this->getLoop(), this->getNoWrapFlags());
7255 DEBUG(dbgs() << "(delinearize: " << *this << "\n");
7257 // Currently we fail to delinearize when the stride of this SCEV is 1. We
7258 // could decide to not fail in this case: we could just return 1 for the size
7259 // of the subscript, and this same SCEV for the access function.
7261 DEBUG(dbgs() << "failed to delinearize " << *this << "\n)\n");
7265 // Find the GCD and Remainder of the Start and Step coefficients of this SCEV.
7266 const SCEV *Remainder = NULL;
7267 const SCEV *GCD = SCEVGCD::findGCD(SE, Start, Step, &Remainder);
7269 DEBUG(dbgs() << "GCD: " << *GCD << "\n");
7270 DEBUG(dbgs() << "Remainder: " << *Remainder << "\n");
7272 // Same remark as above: we currently fail the delinearization, although we
7273 // can very well handle this special case.
7275 DEBUG(dbgs() << "failed to delinearize " << *this << "\n)\n");
7279 // As findGCD computed Remainder, GCD divides "Start - Remainder." The
7280 // Quotient is then this SCEV without Remainder, scaled down by the GCD. The
7281 // Quotient is what will be used in the next subscript delinearization.
7282 const SCEV *Quotient =
7283 SCEVDivision::divide(SE, SE.getMinusSCEV(Start, Remainder), GCD);
7284 DEBUG(dbgs() << "Quotient: " << *Quotient << "\n");
7287 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Quotient))
7288 // Recursively call delinearize on the Quotient until there are no more
7289 // multiples that can be recognized.
7290 Rem = AR->delinearize(SE, Subscripts, Sizes);
7294 // Scale up the canonical induction variable IV by whatever remains from the
7295 // Step after division by the GCD: the GCD is the size of all the sub-array.
7297 Step = SCEVDivision::divide(SE, Step, GCD);
7298 IV = SE.getMulExpr(IV, Step);
7300 // The access function in the current subscript is computed as the canonical
7301 // induction variable IV (potentially scaled up by the step) and offset by
7302 // Rem, the offset of delinearization in the sub-array.
7303 const SCEV *Index = SE.getAddExpr(IV, Rem);
7305 // Record the access function and the size of the current subscript.
7306 Subscripts.push_back(Index);
7307 Sizes.push_back(GCD);
7310 int Size = Sizes.size();
7311 DEBUG(dbgs() << "succeeded to delinearize " << *this << "\n");
7312 DEBUG(dbgs() << "ArrayDecl[UnknownSize]");
7313 for (int i = 0; i < Size - 1; i++)
7314 DEBUG(dbgs() << "[" << *Sizes[i] << "]");
7315 DEBUG(dbgs() << " with elements of " << *Sizes[Size - 1] << " bytes.\n");
7317 DEBUG(dbgs() << "ArrayRef");
7318 for (int i = 0; i < Size; i++)
7319 DEBUG(dbgs() << "[" << *Subscripts[i] << "]");
7320 DEBUG(dbgs() << "\n)\n");
7326 //===----------------------------------------------------------------------===//
7327 // SCEVCallbackVH Class Implementation
7328 //===----------------------------------------------------------------------===//
7330 void ScalarEvolution::SCEVCallbackVH::deleted() {
7331 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7332 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7333 SE->ConstantEvolutionLoopExitValue.erase(PN);
7334 SE->ValueExprMap.erase(getValPtr());
7335 // this now dangles!
7338 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7339 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7341 // Forget all the expressions associated with users of the old value,
7342 // so that future queries will recompute the expressions using the new
7344 Value *Old = getValPtr();
7345 SmallVector<User *, 16> Worklist;
7346 SmallPtrSet<User *, 8> Visited;
7347 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
7349 Worklist.push_back(*UI);
7350 while (!Worklist.empty()) {
7351 User *U = Worklist.pop_back_val();
7352 // Deleting the Old value will cause this to dangle. Postpone
7353 // that until everything else is done.
7356 if (!Visited.insert(U))
7358 if (PHINode *PN = dyn_cast<PHINode>(U))
7359 SE->ConstantEvolutionLoopExitValue.erase(PN);
7360 SE->ValueExprMap.erase(U);
7361 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
7363 Worklist.push_back(*UI);
7365 // Delete the Old value.
7366 if (PHINode *PN = dyn_cast<PHINode>(Old))
7367 SE->ConstantEvolutionLoopExitValue.erase(PN);
7368 SE->ValueExprMap.erase(Old);
7369 // this now dangles!
7372 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7373 : CallbackVH(V), SE(se) {}
7375 //===----------------------------------------------------------------------===//
7376 // ScalarEvolution Class Implementation
7377 //===----------------------------------------------------------------------===//
7379 ScalarEvolution::ScalarEvolution()
7380 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64), BlockDispositions(64), FirstUnknown(0) {
7381 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7384 bool ScalarEvolution::runOnFunction(Function &F) {
7386 LI = &getAnalysis<LoopInfo>();
7387 TD = getAnalysisIfAvailable<DataLayout>();
7388 TLI = &getAnalysis<TargetLibraryInfo>();
7389 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7393 void ScalarEvolution::releaseMemory() {
7394 // Iterate through all the SCEVUnknown instances and call their
7395 // destructors, so that they release their references to their values.
7396 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7400 ValueExprMap.clear();
7402 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7403 // that a loop had multiple computable exits.
7404 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7405 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7410 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7412 BackedgeTakenCounts.clear();
7413 ConstantEvolutionLoopExitValue.clear();
7414 ValuesAtScopes.clear();
7415 LoopDispositions.clear();
7416 BlockDispositions.clear();
7417 UnsignedRanges.clear();
7418 SignedRanges.clear();
7419 UniqueSCEVs.clear();
7420 SCEVAllocator.Reset();
7423 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7424 AU.setPreservesAll();
7425 AU.addRequiredTransitive<LoopInfo>();
7426 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7427 AU.addRequired<TargetLibraryInfo>();
7430 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7431 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7434 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7436 // Print all inner loops first
7437 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7438 PrintLoopInfo(OS, SE, *I);
7441 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7444 SmallVector<BasicBlock *, 8> ExitBlocks;
7445 L->getExitBlocks(ExitBlocks);
7446 if (ExitBlocks.size() != 1)
7447 OS << "<multiple exits> ";
7449 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7450 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7452 OS << "Unpredictable backedge-taken count. ";
7457 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7460 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7461 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7463 OS << "Unpredictable max backedge-taken count. ";
7469 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7470 // ScalarEvolution's implementation of the print method is to print
7471 // out SCEV values of all instructions that are interesting. Doing
7472 // this potentially causes it to create new SCEV objects though,
7473 // which technically conflicts with the const qualifier. This isn't
7474 // observable from outside the class though, so casting away the
7475 // const isn't dangerous.
7476 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7478 OS << "Classifying expressions for: ";
7479 F->printAsOperand(OS, /*PrintType=*/false);
7481 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7482 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7485 const SCEV *SV = SE.getSCEV(&*I);
7488 const Loop *L = LI->getLoopFor((*I).getParent());
7490 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
7497 OS << "\t\t" "Exits: ";
7498 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
7499 if (!SE.isLoopInvariant(ExitValue, L)) {
7500 OS << "<<Unknown>>";
7509 OS << "Determining loop execution counts for: ";
7510 F->printAsOperand(OS, /*PrintType=*/false);
7512 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
7513 PrintLoopInfo(OS, &SE, *I);
7516 ScalarEvolution::LoopDisposition
7517 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
7518 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
7519 for (unsigned u = 0; u < Values.size(); u++) {
7520 if (Values[u].first == L)
7521 return Values[u].second;
7523 Values.push_back(std::make_pair(L, LoopVariant));
7524 LoopDisposition D = computeLoopDisposition(S, L);
7525 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
7526 for (unsigned u = Values2.size(); u > 0; u--) {
7527 if (Values2[u - 1].first == L) {
7528 Values2[u - 1].second = D;
7535 ScalarEvolution::LoopDisposition
7536 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
7537 switch (S->getSCEVType()) {
7539 return LoopInvariant;
7543 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
7544 case scAddRecExpr: {
7545 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7547 // If L is the addrec's loop, it's computable.
7548 if (AR->getLoop() == L)
7549 return LoopComputable;
7551 // Add recurrences are never invariant in the function-body (null loop).
7555 // This recurrence is variant w.r.t. L if L contains AR's loop.
7556 if (L->contains(AR->getLoop()))
7559 // This recurrence is invariant w.r.t. L if AR's loop contains L.
7560 if (AR->getLoop()->contains(L))
7561 return LoopInvariant;
7563 // This recurrence is variant w.r.t. L if any of its operands
7565 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
7567 if (!isLoopInvariant(*I, L))
7570 // Otherwise it's loop-invariant.
7571 return LoopInvariant;
7577 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7578 bool HasVarying = false;
7579 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7581 LoopDisposition D = getLoopDisposition(*I, L);
7582 if (D == LoopVariant)
7584 if (D == LoopComputable)
7587 return HasVarying ? LoopComputable : LoopInvariant;
7590 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7591 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
7592 if (LD == LoopVariant)
7594 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
7595 if (RD == LoopVariant)
7597 return (LD == LoopInvariant && RD == LoopInvariant) ?
7598 LoopInvariant : LoopComputable;
7601 // All non-instruction values are loop invariant. All instructions are loop
7602 // invariant if they are not contained in the specified loop.
7603 // Instructions are never considered invariant in the function body
7604 // (null loop) because they are defined within the "loop".
7605 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
7606 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
7607 return LoopInvariant;
7608 case scCouldNotCompute:
7609 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7610 default: llvm_unreachable("Unknown SCEV kind!");
7614 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
7615 return getLoopDisposition(S, L) == LoopInvariant;
7618 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
7619 return getLoopDisposition(S, L) == LoopComputable;
7622 ScalarEvolution::BlockDisposition
7623 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7624 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
7625 for (unsigned u = 0; u < Values.size(); u++) {
7626 if (Values[u].first == BB)
7627 return Values[u].second;
7629 Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
7630 BlockDisposition D = computeBlockDisposition(S, BB);
7631 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
7632 for (unsigned u = Values2.size(); u > 0; u--) {
7633 if (Values2[u - 1].first == BB) {
7634 Values2[u - 1].second = D;
7641 ScalarEvolution::BlockDisposition
7642 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7643 switch (S->getSCEVType()) {
7645 return ProperlyDominatesBlock;
7649 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
7650 case scAddRecExpr: {
7651 // This uses a "dominates" query instead of "properly dominates" query
7652 // to test for proper dominance too, because the instruction which
7653 // produces the addrec's value is a PHI, and a PHI effectively properly
7654 // dominates its entire containing block.
7655 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7656 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
7657 return DoesNotDominateBlock;
7659 // FALL THROUGH into SCEVNAryExpr handling.
7664 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7666 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7668 BlockDisposition D = getBlockDisposition(*I, BB);
7669 if (D == DoesNotDominateBlock)
7670 return DoesNotDominateBlock;
7671 if (D == DominatesBlock)
7674 return Proper ? ProperlyDominatesBlock : DominatesBlock;
7677 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7678 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
7679 BlockDisposition LD = getBlockDisposition(LHS, BB);
7680 if (LD == DoesNotDominateBlock)
7681 return DoesNotDominateBlock;
7682 BlockDisposition RD = getBlockDisposition(RHS, BB);
7683 if (RD == DoesNotDominateBlock)
7684 return DoesNotDominateBlock;
7685 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
7686 ProperlyDominatesBlock : DominatesBlock;
7689 if (Instruction *I =
7690 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
7691 if (I->getParent() == BB)
7692 return DominatesBlock;
7693 if (DT->properlyDominates(I->getParent(), BB))
7694 return ProperlyDominatesBlock;
7695 return DoesNotDominateBlock;
7697 return ProperlyDominatesBlock;
7698 case scCouldNotCompute:
7699 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7701 llvm_unreachable("Unknown SCEV kind!");
7705 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
7706 return getBlockDisposition(S, BB) >= DominatesBlock;
7709 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
7710 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
7714 // Search for a SCEV expression node within an expression tree.
7715 // Implements SCEVTraversal::Visitor.
7720 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
7722 bool follow(const SCEV *S) {
7723 IsFound |= (S == Node);
7726 bool isDone() const { return IsFound; }
7730 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
7731 SCEVSearch Search(Op);
7732 visitAll(S, Search);
7733 return Search.IsFound;
7736 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
7737 ValuesAtScopes.erase(S);
7738 LoopDispositions.erase(S);
7739 BlockDispositions.erase(S);
7740 UnsignedRanges.erase(S);
7741 SignedRanges.erase(S);
7743 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7744 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
7745 BackedgeTakenInfo &BEInfo = I->second;
7746 if (BEInfo.hasOperand(S, this)) {
7748 BackedgeTakenCounts.erase(I++);
7755 typedef DenseMap<const Loop *, std::string> VerifyMap;
7757 /// replaceSubString - Replaces all occurrences of From in Str with To.
7758 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
7760 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
7761 Str.replace(Pos, From.size(), To.data(), To.size());
7766 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
7768 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
7769 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
7770 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
7772 std::string &S = Map[L];
7774 raw_string_ostream OS(S);
7775 SE.getBackedgeTakenCount(L)->print(OS);
7777 // false and 0 are semantically equivalent. This can happen in dead loops.
7778 replaceSubString(OS.str(), "false", "0");
7779 // Remove wrap flags, their use in SCEV is highly fragile.
7780 // FIXME: Remove this when SCEV gets smarter about them.
7781 replaceSubString(OS.str(), "<nw>", "");
7782 replaceSubString(OS.str(), "<nsw>", "");
7783 replaceSubString(OS.str(), "<nuw>", "");
7788 void ScalarEvolution::verifyAnalysis() const {
7792 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7794 // Gather stringified backedge taken counts for all loops using SCEV's caches.
7795 // FIXME: It would be much better to store actual values instead of strings,
7796 // but SCEV pointers will change if we drop the caches.
7797 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
7798 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7799 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
7801 // Gather stringified backedge taken counts for all loops without using
7804 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7805 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
7807 // Now compare whether they're the same with and without caches. This allows
7808 // verifying that no pass changed the cache.
7809 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
7810 "New loops suddenly appeared!");
7812 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
7813 OldE = BackedgeDumpsOld.end(),
7814 NewI = BackedgeDumpsNew.begin();
7815 OldI != OldE; ++OldI, ++NewI) {
7816 assert(OldI->first == NewI->first && "Loop order changed!");
7818 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
7820 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
7821 // means that a pass is buggy or SCEV has to learn a new pattern but is
7822 // usually not harmful.
7823 if (OldI->second != NewI->second &&
7824 OldI->second.find("undef") == std::string::npos &&
7825 NewI->second.find("undef") == std::string::npos &&
7826 OldI->second != "***COULDNOTCOMPUTE***" &&
7827 NewI->second != "***COULDNOTCOMPUTE***") {
7828 dbgs() << "SCEVValidator: SCEV for loop '"
7829 << OldI->first->getHeader()->getName()
7830 << "' changed from '" << OldI->second
7831 << "' to '" << NewI->second << "'!\n";
7836 // TODO: Verify more things.