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 #include "llvm/Analysis/ScalarEvolution.h"
62 #include "llvm/ADT/STLExtras.h"
63 #include "llvm/ADT/SmallPtrSet.h"
64 #include "llvm/ADT/Statistic.h"
65 #include "llvm/Analysis/ConstantFolding.h"
66 #include "llvm/Analysis/InstructionSimplify.h"
67 #include "llvm/Analysis/LoopInfo.h"
68 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
69 #include "llvm/Analysis/ValueTracking.h"
70 #include "llvm/IR/ConstantRange.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/GetElementPtrTypeIterator.h"
76 #include "llvm/IR/GlobalAlias.h"
77 #include "llvm/IR/GlobalVariable.h"
78 #include "llvm/IR/InstIterator.h"
79 #include "llvm/IR/Instructions.h"
80 #include "llvm/IR/LLVMContext.h"
81 #include "llvm/IR/Operator.h"
82 #include "llvm/Support/CommandLine.h"
83 #include "llvm/Support/Debug.h"
84 #include "llvm/Support/ErrorHandling.h"
85 #include "llvm/Support/MathExtras.h"
86 #include "llvm/Support/raw_ostream.h"
87 #include "llvm/Target/TargetLibraryInfo.h"
91 #define DEBUG_TYPE "scalar-evolution"
93 STATISTIC(NumArrayLenItCounts,
94 "Number of trip counts computed with array length");
95 STATISTIC(NumTripCountsComputed,
96 "Number of loops with predictable loop counts");
97 STATISTIC(NumTripCountsNotComputed,
98 "Number of loops without predictable loop counts");
99 STATISTIC(NumBruteForceTripCountsComputed,
100 "Number of loops with trip counts computed by force");
102 static cl::opt<unsigned>
103 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
104 cl::desc("Maximum number of iterations SCEV will "
105 "symbolically execute a constant "
109 // FIXME: Enable this with XDEBUG when the test suite is clean.
111 VerifySCEV("verify-scev",
112 cl::desc("Verify ScalarEvolution's backedge taken counts (slow)"));
114 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
115 "Scalar Evolution Analysis", false, true)
116 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
117 INITIALIZE_PASS_DEPENDENCY(DominatorTreeWrapperPass)
118 INITIALIZE_PASS_DEPENDENCY(TargetLibraryInfo)
119 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
120 "Scalar Evolution Analysis", false, true)
121 char ScalarEvolution::ID = 0;
123 //===----------------------------------------------------------------------===//
124 // SCEV class definitions
125 //===----------------------------------------------------------------------===//
127 //===----------------------------------------------------------------------===//
128 // Implementation of the SCEV class.
131 #if !defined(NDEBUG) || defined(LLVM_ENABLE_DUMP)
132 void SCEV::dump() const {
138 void SCEV::print(raw_ostream &OS) const {
139 switch (static_cast<SCEVTypes>(getSCEVType())) {
141 cast<SCEVConstant>(this)->getValue()->printAsOperand(OS, false);
144 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
145 const SCEV *Op = Trunc->getOperand();
146 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
147 << *Trunc->getType() << ")";
151 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
152 const SCEV *Op = ZExt->getOperand();
153 OS << "(zext " << *Op->getType() << " " << *Op << " to "
154 << *ZExt->getType() << ")";
158 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
159 const SCEV *Op = SExt->getOperand();
160 OS << "(sext " << *Op->getType() << " " << *Op << " to "
161 << *SExt->getType() << ")";
165 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
166 OS << "{" << *AR->getOperand(0);
167 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
168 OS << ",+," << *AR->getOperand(i);
170 if (AR->getNoWrapFlags(FlagNUW))
172 if (AR->getNoWrapFlags(FlagNSW))
174 if (AR->getNoWrapFlags(FlagNW) &&
175 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
177 AR->getLoop()->getHeader()->printAsOperand(OS, /*PrintType=*/false);
185 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
186 const char *OpStr = nullptr;
187 switch (NAry->getSCEVType()) {
188 case scAddExpr: OpStr = " + "; break;
189 case scMulExpr: OpStr = " * "; break;
190 case scUMaxExpr: OpStr = " umax "; break;
191 case scSMaxExpr: OpStr = " smax "; break;
194 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
197 if (std::next(I) != E)
201 switch (NAry->getSCEVType()) {
204 if (NAry->getNoWrapFlags(FlagNUW))
206 if (NAry->getNoWrapFlags(FlagNSW))
212 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
213 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
217 const SCEVUnknown *U = cast<SCEVUnknown>(this);
219 if (U->isSizeOf(AllocTy)) {
220 OS << "sizeof(" << *AllocTy << ")";
223 if (U->isAlignOf(AllocTy)) {
224 OS << "alignof(" << *AllocTy << ")";
230 if (U->isOffsetOf(CTy, FieldNo)) {
231 OS << "offsetof(" << *CTy << ", ";
232 FieldNo->printAsOperand(OS, false);
237 // Otherwise just print it normally.
238 U->getValue()->printAsOperand(OS, false);
241 case scCouldNotCompute:
242 OS << "***COULDNOTCOMPUTE***";
245 llvm_unreachable("Unknown SCEV kind!");
248 Type *SCEV::getType() const {
249 switch (static_cast<SCEVTypes>(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!");
273 bool SCEV::isZero() const {
274 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
275 return SC->getValue()->isZero();
279 bool SCEV::isOne() const {
280 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
281 return SC->getValue()->isOne();
285 bool SCEV::isAllOnesValue() const {
286 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
287 return SC->getValue()->isAllOnesValue();
291 /// isNonConstantNegative - Return true if the specified scev is negated, but
293 bool SCEV::isNonConstantNegative() const {
294 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(this);
295 if (!Mul) return false;
297 // If there is a constant factor, it will be first.
298 const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
299 if (!SC) return false;
301 // Return true if the value is negative, this matches things like (-42 * V).
302 return SC->getValue()->getValue().isNegative();
305 SCEVCouldNotCompute::SCEVCouldNotCompute() :
306 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
308 bool SCEVCouldNotCompute::classof(const SCEV *S) {
309 return S->getSCEVType() == scCouldNotCompute;
312 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
314 ID.AddInteger(scConstant);
317 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
318 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
319 UniqueSCEVs.InsertNode(S, IP);
323 const SCEV *ScalarEvolution::getConstant(const APInt &Val) {
324 return getConstant(ConstantInt::get(getContext(), Val));
328 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
329 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
330 return getConstant(ConstantInt::get(ITy, V, isSigned));
333 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
334 unsigned SCEVTy, const SCEV *op, Type *ty)
335 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
337 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
338 const SCEV *op, Type *ty)
339 : SCEVCastExpr(ID, scTruncate, op, ty) {
340 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
341 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
342 "Cannot truncate non-integer value!");
345 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
346 const SCEV *op, Type *ty)
347 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
348 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
349 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
350 "Cannot zero extend non-integer value!");
353 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
354 const SCEV *op, Type *ty)
355 : SCEVCastExpr(ID, scSignExtend, op, ty) {
356 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
357 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
358 "Cannot sign extend non-integer value!");
361 void SCEVUnknown::deleted() {
362 // Clear this SCEVUnknown from various maps.
363 SE->forgetMemoizedResults(this);
365 // Remove this SCEVUnknown from the uniquing map.
366 SE->UniqueSCEVs.RemoveNode(this);
368 // Release the value.
372 void SCEVUnknown::allUsesReplacedWith(Value *New) {
373 // Clear this SCEVUnknown from various maps.
374 SE->forgetMemoizedResults(this);
376 // Remove this SCEVUnknown from the uniquing map.
377 SE->UniqueSCEVs.RemoveNode(this);
379 // Update this SCEVUnknown to point to the new value. This is needed
380 // because there may still be outstanding SCEVs which still point to
385 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
386 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
387 if (VCE->getOpcode() == Instruction::PtrToInt)
388 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
389 if (CE->getOpcode() == Instruction::GetElementPtr &&
390 CE->getOperand(0)->isNullValue() &&
391 CE->getNumOperands() == 2)
392 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
394 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
402 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
403 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
404 if (VCE->getOpcode() == Instruction::PtrToInt)
405 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
406 if (CE->getOpcode() == Instruction::GetElementPtr &&
407 CE->getOperand(0)->isNullValue()) {
409 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
410 if (StructType *STy = dyn_cast<StructType>(Ty))
411 if (!STy->isPacked() &&
412 CE->getNumOperands() == 3 &&
413 CE->getOperand(1)->isNullValue()) {
414 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
416 STy->getNumElements() == 2 &&
417 STy->getElementType(0)->isIntegerTy(1)) {
418 AllocTy = STy->getElementType(1);
427 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
428 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
429 if (VCE->getOpcode() == Instruction::PtrToInt)
430 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
431 if (CE->getOpcode() == Instruction::GetElementPtr &&
432 CE->getNumOperands() == 3 &&
433 CE->getOperand(0)->isNullValue() &&
434 CE->getOperand(1)->isNullValue()) {
436 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
437 // Ignore vector types here so that ScalarEvolutionExpander doesn't
438 // emit getelementptrs that index into vectors.
439 if (Ty->isStructTy() || Ty->isArrayTy()) {
441 FieldNo = CE->getOperand(2);
449 //===----------------------------------------------------------------------===//
451 //===----------------------------------------------------------------------===//
454 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
455 /// than the complexity of the RHS. This comparator is used to canonicalize
457 class SCEVComplexityCompare {
458 const LoopInfo *const LI;
460 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
462 // Return true or false if LHS is less than, or at least RHS, respectively.
463 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
464 return compare(LHS, RHS) < 0;
467 // Return negative, zero, or positive, if LHS is less than, equal to, or
468 // greater than RHS, respectively. A three-way result allows recursive
469 // comparisons to be more efficient.
470 int compare(const SCEV *LHS, const SCEV *RHS) const {
471 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
475 // Primarily, sort the SCEVs by their getSCEVType().
476 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
478 return (int)LType - (int)RType;
480 // Aside from the getSCEVType() ordering, the particular ordering
481 // isn't very important except that it's beneficial to be consistent,
482 // so that (a + b) and (b + a) don't end up as different expressions.
483 switch (static_cast<SCEVTypes>(LType)) {
485 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
486 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
488 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
489 // not as complete as it could be.
490 const Value *LV = LU->getValue(), *RV = RU->getValue();
492 // Order pointer values after integer values. This helps SCEVExpander
494 bool LIsPointer = LV->getType()->isPointerTy(),
495 RIsPointer = RV->getType()->isPointerTy();
496 if (LIsPointer != RIsPointer)
497 return (int)LIsPointer - (int)RIsPointer;
499 // Compare getValueID values.
500 unsigned LID = LV->getValueID(),
501 RID = RV->getValueID();
503 return (int)LID - (int)RID;
505 // Sort arguments by their position.
506 if (const Argument *LA = dyn_cast<Argument>(LV)) {
507 const Argument *RA = cast<Argument>(RV);
508 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
509 return (int)LArgNo - (int)RArgNo;
512 // For instructions, compare their loop depth, and their operand
513 // count. This is pretty loose.
514 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
515 const Instruction *RInst = cast<Instruction>(RV);
517 // Compare loop depths.
518 const BasicBlock *LParent = LInst->getParent(),
519 *RParent = RInst->getParent();
520 if (LParent != RParent) {
521 unsigned LDepth = LI->getLoopDepth(LParent),
522 RDepth = LI->getLoopDepth(RParent);
523 if (LDepth != RDepth)
524 return (int)LDepth - (int)RDepth;
527 // Compare the number of operands.
528 unsigned LNumOps = LInst->getNumOperands(),
529 RNumOps = RInst->getNumOperands();
530 return (int)LNumOps - (int)RNumOps;
537 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
538 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
540 // Compare constant values.
541 const APInt &LA = LC->getValue()->getValue();
542 const APInt &RA = RC->getValue()->getValue();
543 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
544 if (LBitWidth != RBitWidth)
545 return (int)LBitWidth - (int)RBitWidth;
546 return LA.ult(RA) ? -1 : 1;
550 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
551 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
553 // Compare addrec loop depths.
554 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
555 if (LLoop != RLoop) {
556 unsigned LDepth = LLoop->getLoopDepth(),
557 RDepth = RLoop->getLoopDepth();
558 if (LDepth != RDepth)
559 return (int)LDepth - (int)RDepth;
562 // Addrec complexity grows with operand count.
563 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
564 if (LNumOps != RNumOps)
565 return (int)LNumOps - (int)RNumOps;
567 // Lexicographically compare.
568 for (unsigned i = 0; i != LNumOps; ++i) {
569 long X = compare(LA->getOperand(i), RA->getOperand(i));
581 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
582 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
584 // Lexicographically compare n-ary expressions.
585 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
586 if (LNumOps != RNumOps)
587 return (int)LNumOps - (int)RNumOps;
589 for (unsigned i = 0; i != LNumOps; ++i) {
592 long X = compare(LC->getOperand(i), RC->getOperand(i));
596 return (int)LNumOps - (int)RNumOps;
600 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
601 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
603 // Lexicographically compare udiv expressions.
604 long X = compare(LC->getLHS(), RC->getLHS());
607 return compare(LC->getRHS(), RC->getRHS());
613 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
614 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
616 // Compare cast expressions by operand.
617 return compare(LC->getOperand(), RC->getOperand());
620 case scCouldNotCompute:
621 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
623 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 (const SCEV *Op : SA->operands())
1103 DiffOps.push_back(Op);
1105 if (DiffOps.size() == SA->getNumOperands())
1108 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1109 // same three conditions that getSignExtendedExpr checks.
1111 // 1. NSW flags on the step increment.
1112 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1113 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1114 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1116 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1119 // 2. Direct overflow check on the step operation's expression.
1120 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1121 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1122 const SCEV *OperandExtendedStart =
1123 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1124 SE->getSignExtendExpr(Step, WideTy));
1125 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1126 // Cache knowledge of PreAR NSW.
1128 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1129 // FIXME: this optimization needs a unit test
1130 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1134 // 3. Loop precondition.
1135 ICmpInst::Predicate Pred;
1136 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1138 if (OverflowLimit &&
1139 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1145 // Get the normalized sign-extended expression for this AddRec's Start.
1146 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1148 ScalarEvolution *SE) {
1149 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1151 return SE->getSignExtendExpr(AR->getStart(), Ty);
1153 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1154 SE->getSignExtendExpr(PreStart, Ty));
1157 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1159 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1160 "This is not an extending conversion!");
1161 assert(isSCEVable(Ty) &&
1162 "This is not a conversion to a SCEVable type!");
1163 Ty = getEffectiveSCEVType(Ty);
1165 // Fold if the operand is constant.
1166 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1168 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1170 // sext(sext(x)) --> sext(x)
1171 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1172 return getSignExtendExpr(SS->getOperand(), Ty);
1174 // sext(zext(x)) --> zext(x)
1175 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1176 return getZeroExtendExpr(SZ->getOperand(), Ty);
1178 // Before doing any expensive analysis, check to see if we've already
1179 // computed a SCEV for this Op and Ty.
1180 FoldingSetNodeID ID;
1181 ID.AddInteger(scSignExtend);
1185 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1187 // If the input value is provably positive, build a zext instead.
1188 if (isKnownNonNegative(Op))
1189 return getZeroExtendExpr(Op, Ty);
1191 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1192 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1193 // It's possible the bits taken off by the truncate were all sign bits. If
1194 // so, we should be able to simplify this further.
1195 const SCEV *X = ST->getOperand();
1196 ConstantRange CR = getSignedRange(X);
1197 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1198 unsigned NewBits = getTypeSizeInBits(Ty);
1199 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1200 CR.sextOrTrunc(NewBits)))
1201 return getTruncateOrSignExtend(X, Ty);
1204 // If the input value is a chrec scev, and we can prove that the value
1205 // did not overflow the old, smaller, value, we can sign extend all of the
1206 // operands (often constants). This allows analysis of something like
1207 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1208 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1209 if (AR->isAffine()) {
1210 const SCEV *Start = AR->getStart();
1211 const SCEV *Step = AR->getStepRecurrence(*this);
1212 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1213 const Loop *L = AR->getLoop();
1215 // If we have special knowledge that this addrec won't overflow,
1216 // we don't need to do any further analysis.
1217 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1218 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1219 getSignExtendExpr(Step, Ty),
1222 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1223 // Note that this serves two purposes: It filters out loops that are
1224 // simply not analyzable, and it covers the case where this code is
1225 // being called from within backedge-taken count analysis, such that
1226 // attempting to ask for the backedge-taken count would likely result
1227 // in infinite recursion. In the later case, the analysis code will
1228 // cope with a conservative value, and it will take care to purge
1229 // that value once it has finished.
1230 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1231 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1232 // Manually compute the final value for AR, checking for
1235 // Check whether the backedge-taken count can be losslessly casted to
1236 // the addrec's type. The count is always unsigned.
1237 const SCEV *CastedMaxBECount =
1238 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1239 const SCEV *RecastedMaxBECount =
1240 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1241 if (MaxBECount == RecastedMaxBECount) {
1242 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1243 // Check whether Start+Step*MaxBECount has no signed overflow.
1244 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1245 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1246 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1247 const SCEV *WideMaxBECount =
1248 getZeroExtendExpr(CastedMaxBECount, WideTy);
1249 const SCEV *OperandExtendedAdd =
1250 getAddExpr(WideStart,
1251 getMulExpr(WideMaxBECount,
1252 getSignExtendExpr(Step, WideTy)));
1253 if (SAdd == OperandExtendedAdd) {
1254 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1255 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1256 // Return the expression with the addrec on the outside.
1257 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1258 getSignExtendExpr(Step, Ty),
1259 L, AR->getNoWrapFlags());
1261 // Similar to above, only this time treat the step value as unsigned.
1262 // This covers loops that count up with an unsigned step.
1263 OperandExtendedAdd =
1264 getAddExpr(WideStart,
1265 getMulExpr(WideMaxBECount,
1266 getZeroExtendExpr(Step, WideTy)));
1267 if (SAdd == OperandExtendedAdd) {
1268 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1269 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1270 // Return the expression with the addrec on the outside.
1271 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1272 getZeroExtendExpr(Step, Ty),
1273 L, AR->getNoWrapFlags());
1277 // If the backedge is guarded by a comparison with the pre-inc value
1278 // the addrec is safe. Also, if the entry is guarded by a comparison
1279 // with the start value and the backedge is guarded by a comparison
1280 // with the post-inc value, the addrec is safe.
1281 ICmpInst::Predicate Pred;
1282 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1283 if (OverflowLimit &&
1284 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1285 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1286 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1288 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1289 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1290 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1291 getSignExtendExpr(Step, Ty),
1292 L, AR->getNoWrapFlags());
1297 // The cast wasn't folded; create an explicit cast node.
1298 // Recompute the insert position, as it may have been invalidated.
1299 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1300 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1302 UniqueSCEVs.InsertNode(S, IP);
1306 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1307 /// unspecified bits out to the given type.
1309 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1311 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1312 "This is not an extending conversion!");
1313 assert(isSCEVable(Ty) &&
1314 "This is not a conversion to a SCEVable type!");
1315 Ty = getEffectiveSCEVType(Ty);
1317 // Sign-extend negative constants.
1318 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1319 if (SC->getValue()->getValue().isNegative())
1320 return getSignExtendExpr(Op, Ty);
1322 // Peel off a truncate cast.
1323 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1324 const SCEV *NewOp = T->getOperand();
1325 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1326 return getAnyExtendExpr(NewOp, Ty);
1327 return getTruncateOrNoop(NewOp, Ty);
1330 // Next try a zext cast. If the cast is folded, use it.
1331 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1332 if (!isa<SCEVZeroExtendExpr>(ZExt))
1335 // Next try a sext cast. If the cast is folded, use it.
1336 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1337 if (!isa<SCEVSignExtendExpr>(SExt))
1340 // Force the cast to be folded into the operands of an addrec.
1341 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1342 SmallVector<const SCEV *, 4> Ops;
1343 for (const SCEV *Op : AR->operands())
1344 Ops.push_back(getAnyExtendExpr(Op, Ty));
1345 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1348 // If the expression is obviously signed, use the sext cast value.
1349 if (isa<SCEVSMaxExpr>(Op))
1352 // Absent any other information, use the zext cast value.
1356 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1357 /// a list of operands to be added under the given scale, update the given
1358 /// map. This is a helper function for getAddRecExpr. As an example of
1359 /// what it does, given a sequence of operands that would form an add
1360 /// expression like this:
1362 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1364 /// where A and B are constants, update the map with these values:
1366 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1368 /// and add 13 + A*B*29 to AccumulatedConstant.
1369 /// This will allow getAddRecExpr to produce this:
1371 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1373 /// This form often exposes folding opportunities that are hidden in
1374 /// the original operand list.
1376 /// Return true iff it appears that any interesting folding opportunities
1377 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1378 /// the common case where no interesting opportunities are present, and
1379 /// is also used as a check to avoid infinite recursion.
1382 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1383 SmallVectorImpl<const SCEV *> &NewOps,
1384 APInt &AccumulatedConstant,
1385 const SCEV *const *Ops, size_t NumOperands,
1387 ScalarEvolution &SE) {
1388 bool Interesting = false;
1390 // Iterate over the add operands. They are sorted, with constants first.
1392 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1394 // Pull a buried constant out to the outside.
1395 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1397 AccumulatedConstant += Scale * C->getValue()->getValue();
1400 // Next comes everything else. We're especially interested in multiplies
1401 // here, but they're in the middle, so just visit the rest with one loop.
1402 for (; i != NumOperands; ++i) {
1403 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1404 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1406 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1407 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1408 // A multiplication of a constant with another add; recurse.
1409 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1411 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1412 Add->op_begin(), Add->getNumOperands(),
1415 // A multiplication of a constant with some other value. Update
1417 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1418 const SCEV *Key = SE.getMulExpr(MulOps);
1419 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1420 M.insert(std::make_pair(Key, NewScale));
1422 NewOps.push_back(Pair.first->first);
1424 Pair.first->second += NewScale;
1425 // The map already had an entry for this value, which may indicate
1426 // a folding opportunity.
1431 // An ordinary operand. Update the map.
1432 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1433 M.insert(std::make_pair(Ops[i], Scale));
1435 NewOps.push_back(Pair.first->first);
1437 Pair.first->second += Scale;
1438 // The map already had an entry for this value, which may indicate
1439 // a folding opportunity.
1449 struct APIntCompare {
1450 bool operator()(const APInt &LHS, const APInt &RHS) const {
1451 return LHS.ult(RHS);
1456 /// getAddExpr - Get a canonical add expression, or something simpler if
1458 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1459 SCEV::NoWrapFlags Flags) {
1460 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1461 "only nuw or nsw allowed");
1462 assert(!Ops.empty() && "Cannot get empty add!");
1463 if (Ops.size() == 1) return Ops[0];
1465 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1466 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1467 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1468 "SCEVAddExpr operand types don't match!");
1471 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1473 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1474 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1475 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1477 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1478 E = Ops.end(); I != E; ++I)
1479 if (!isKnownNonNegative(*I)) {
1483 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1486 // Sort by complexity, this groups all similar expression types together.
1487 GroupByComplexity(Ops, LI);
1489 // If there are any constants, fold them together.
1491 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1493 assert(Idx < Ops.size());
1494 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1495 // We found two constants, fold them together!
1496 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1497 RHSC->getValue()->getValue());
1498 if (Ops.size() == 2) return Ops[0];
1499 Ops.erase(Ops.begin()+1); // Erase the folded element
1500 LHSC = cast<SCEVConstant>(Ops[0]);
1503 // If we are left with a constant zero being added, strip it off.
1504 if (LHSC->getValue()->isZero()) {
1505 Ops.erase(Ops.begin());
1509 if (Ops.size() == 1) return Ops[0];
1512 // Okay, check to see if the same value occurs in the operand list more than
1513 // once. If so, merge them together into an multiply expression. Since we
1514 // sorted the list, these values are required to be adjacent.
1515 Type *Ty = Ops[0]->getType();
1516 bool FoundMatch = false;
1517 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1518 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1519 // Scan ahead to count how many equal operands there are.
1521 while (i+Count != e && Ops[i+Count] == Ops[i])
1523 // Merge the values into a multiply.
1524 const SCEV *Scale = getConstant(Ty, Count);
1525 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1526 if (Ops.size() == Count)
1529 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1530 --i; e -= Count - 1;
1534 return getAddExpr(Ops, Flags);
1536 // Check for truncates. If all the operands are truncated from the same
1537 // type, see if factoring out the truncate would permit the result to be
1538 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1539 // if the contents of the resulting outer trunc fold to something simple.
1540 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1541 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1542 Type *DstType = Trunc->getType();
1543 Type *SrcType = Trunc->getOperand()->getType();
1544 SmallVector<const SCEV *, 8> LargeOps;
1546 // Check all the operands to see if they can be represented in the
1547 // source type of the truncate.
1548 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1549 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1550 if (T->getOperand()->getType() != SrcType) {
1554 LargeOps.push_back(T->getOperand());
1555 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1556 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1557 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1558 SmallVector<const SCEV *, 8> LargeMulOps;
1559 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1560 if (const SCEVTruncateExpr *T =
1561 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1562 if (T->getOperand()->getType() != SrcType) {
1566 LargeMulOps.push_back(T->getOperand());
1567 } else if (const SCEVConstant *C =
1568 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1569 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1576 LargeOps.push_back(getMulExpr(LargeMulOps));
1583 // Evaluate the expression in the larger type.
1584 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1585 // If it folds to something simple, use it. Otherwise, don't.
1586 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1587 return getTruncateExpr(Fold, DstType);
1591 // Skip past any other cast SCEVs.
1592 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1595 // If there are add operands they would be next.
1596 if (Idx < Ops.size()) {
1597 bool DeletedAdd = false;
1598 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1599 // If we have an add, expand the add operands onto the end of the operands
1601 Ops.erase(Ops.begin()+Idx);
1602 Ops.append(Add->op_begin(), Add->op_end());
1606 // If we deleted at least one add, we added operands to the end of the list,
1607 // and they are not necessarily sorted. Recurse to resort and resimplify
1608 // any operands we just acquired.
1610 return getAddExpr(Ops);
1613 // Skip over the add expression until we get to a multiply.
1614 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1617 // Check to see if there are any folding opportunities present with
1618 // operands multiplied by constant values.
1619 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1620 uint64_t BitWidth = getTypeSizeInBits(Ty);
1621 DenseMap<const SCEV *, APInt> M;
1622 SmallVector<const SCEV *, 8> NewOps;
1623 APInt AccumulatedConstant(BitWidth, 0);
1624 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1625 Ops.data(), Ops.size(),
1626 APInt(BitWidth, 1), *this)) {
1627 // Some interesting folding opportunity is present, so its worthwhile to
1628 // re-generate the operands list. Group the operands by constant scale,
1629 // to avoid multiplying by the same constant scale multiple times.
1630 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1631 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1632 E = NewOps.end(); I != E; ++I)
1633 MulOpLists[M.find(*I)->second].push_back(*I);
1634 // Re-generate the operands list.
1636 if (AccumulatedConstant != 0)
1637 Ops.push_back(getConstant(AccumulatedConstant));
1638 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1639 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1641 Ops.push_back(getMulExpr(getConstant(I->first),
1642 getAddExpr(I->second)));
1644 return getConstant(Ty, 0);
1645 if (Ops.size() == 1)
1647 return getAddExpr(Ops);
1651 // If we are adding something to a multiply expression, make sure the
1652 // something is not already an operand of the multiply. If so, merge it into
1654 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1655 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1656 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1657 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1658 if (isa<SCEVConstant>(MulOpSCEV))
1660 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1661 if (MulOpSCEV == Ops[AddOp]) {
1662 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1663 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1664 if (Mul->getNumOperands() != 2) {
1665 // If the multiply has more than two operands, we must get the
1667 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1668 Mul->op_begin()+MulOp);
1669 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1670 InnerMul = getMulExpr(MulOps);
1672 const SCEV *One = getConstant(Ty, 1);
1673 const SCEV *AddOne = getAddExpr(One, InnerMul);
1674 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1675 if (Ops.size() == 2) return OuterMul;
1677 Ops.erase(Ops.begin()+AddOp);
1678 Ops.erase(Ops.begin()+Idx-1);
1680 Ops.erase(Ops.begin()+Idx);
1681 Ops.erase(Ops.begin()+AddOp-1);
1683 Ops.push_back(OuterMul);
1684 return getAddExpr(Ops);
1687 // Check this multiply against other multiplies being added together.
1688 for (unsigned OtherMulIdx = Idx+1;
1689 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1691 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1692 // If MulOp occurs in OtherMul, we can fold the two multiplies
1694 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1695 OMulOp != e; ++OMulOp)
1696 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1697 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1698 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1699 if (Mul->getNumOperands() != 2) {
1700 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1701 Mul->op_begin()+MulOp);
1702 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1703 InnerMul1 = getMulExpr(MulOps);
1705 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1706 if (OtherMul->getNumOperands() != 2) {
1707 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1708 OtherMul->op_begin()+OMulOp);
1709 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1710 InnerMul2 = getMulExpr(MulOps);
1712 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1713 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1714 if (Ops.size() == 2) return OuterMul;
1715 Ops.erase(Ops.begin()+Idx);
1716 Ops.erase(Ops.begin()+OtherMulIdx-1);
1717 Ops.push_back(OuterMul);
1718 return getAddExpr(Ops);
1724 // If there are any add recurrences in the operands list, see if any other
1725 // added values are loop invariant. If so, we can fold them into the
1727 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1730 // Scan over all recurrences, trying to fold loop invariants into them.
1731 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1732 // Scan all of the other operands to this add and add them to the vector if
1733 // they are loop invariant w.r.t. the recurrence.
1734 SmallVector<const SCEV *, 8> LIOps;
1735 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1736 const Loop *AddRecLoop = AddRec->getLoop();
1737 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1738 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1739 LIOps.push_back(Ops[i]);
1740 Ops.erase(Ops.begin()+i);
1744 // If we found some loop invariants, fold them into the recurrence.
1745 if (!LIOps.empty()) {
1746 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1747 LIOps.push_back(AddRec->getStart());
1749 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1751 AddRecOps[0] = getAddExpr(LIOps);
1753 // Build the new addrec. Propagate the NUW and NSW flags if both the
1754 // outer add and the inner addrec are guaranteed to have no overflow.
1755 // Always propagate NW.
1756 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1757 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1759 // If all of the other operands were loop invariant, we are done.
1760 if (Ops.size() == 1) return NewRec;
1762 // Otherwise, add the folded AddRec by the non-invariant parts.
1763 for (unsigned i = 0;; ++i)
1764 if (Ops[i] == AddRec) {
1768 return getAddExpr(Ops);
1771 // Okay, if there weren't any loop invariants to be folded, check to see if
1772 // there are multiple AddRec's with the same loop induction variable being
1773 // added together. If so, we can fold them.
1774 for (unsigned OtherIdx = Idx+1;
1775 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1777 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1778 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1779 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1781 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1783 if (const SCEVAddRecExpr *OtherAddRec =
1784 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1785 if (OtherAddRec->getLoop() == AddRecLoop) {
1786 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1788 if (i >= AddRecOps.size()) {
1789 AddRecOps.append(OtherAddRec->op_begin()+i,
1790 OtherAddRec->op_end());
1793 AddRecOps[i] = getAddExpr(AddRecOps[i],
1794 OtherAddRec->getOperand(i));
1796 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1798 // Step size has changed, so we cannot guarantee no self-wraparound.
1799 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1800 return getAddExpr(Ops);
1803 // Otherwise couldn't fold anything into this recurrence. Move onto the
1807 // Okay, it looks like we really DO need an add expr. Check to see if we
1808 // already have one, otherwise create a new one.
1809 FoldingSetNodeID ID;
1810 ID.AddInteger(scAddExpr);
1811 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1812 ID.AddPointer(Ops[i]);
1815 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1817 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1818 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1819 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1821 UniqueSCEVs.InsertNode(S, IP);
1823 S->setNoWrapFlags(Flags);
1827 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1829 if (j > 1 && k / j != i) Overflow = true;
1833 /// Compute the result of "n choose k", the binomial coefficient. If an
1834 /// intermediate computation overflows, Overflow will be set and the return will
1835 /// be garbage. Overflow is not cleared on absence of overflow.
1836 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1837 // We use the multiplicative formula:
1838 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1839 // At each iteration, we take the n-th term of the numeral and divide by the
1840 // (k-n)th term of the denominator. This division will always produce an
1841 // integral result, and helps reduce the chance of overflow in the
1842 // intermediate computations. However, we can still overflow even when the
1843 // final result would fit.
1845 if (n == 0 || n == k) return 1;
1846 if (k > n) return 0;
1852 for (uint64_t i = 1; i <= k; ++i) {
1853 r = umul_ov(r, n-(i-1), Overflow);
1859 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1861 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1862 SCEV::NoWrapFlags Flags) {
1863 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1864 "only nuw or nsw allowed");
1865 assert(!Ops.empty() && "Cannot get empty mul!");
1866 if (Ops.size() == 1) return Ops[0];
1868 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1869 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1870 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1871 "SCEVMulExpr operand types don't match!");
1874 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1876 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1877 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1878 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1880 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1881 E = Ops.end(); I != E; ++I)
1882 if (!isKnownNonNegative(*I)) {
1886 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1889 // Sort by complexity, this groups all similar expression types together.
1890 GroupByComplexity(Ops, LI);
1892 // If there are any constants, fold them together.
1894 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1896 // C1*(C2+V) -> C1*C2 + C1*V
1897 if (Ops.size() == 2)
1898 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1899 if (Add->getNumOperands() == 2 &&
1900 isa<SCEVConstant>(Add->getOperand(0)))
1901 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1902 getMulExpr(LHSC, Add->getOperand(1)));
1905 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1906 // We found two constants, fold them together!
1907 ConstantInt *Fold = ConstantInt::get(getContext(),
1908 LHSC->getValue()->getValue() *
1909 RHSC->getValue()->getValue());
1910 Ops[0] = getConstant(Fold);
1911 Ops.erase(Ops.begin()+1); // Erase the folded element
1912 if (Ops.size() == 1) return Ops[0];
1913 LHSC = cast<SCEVConstant>(Ops[0]);
1916 // If we are left with a constant one being multiplied, strip it off.
1917 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1918 Ops.erase(Ops.begin());
1920 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1921 // If we have a multiply of zero, it will always be zero.
1923 } else if (Ops[0]->isAllOnesValue()) {
1924 // If we have a mul by -1 of an add, try distributing the -1 among the
1926 if (Ops.size() == 2) {
1927 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1928 SmallVector<const SCEV *, 4> NewOps;
1929 bool AnyFolded = false;
1930 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1931 E = Add->op_end(); I != E; ++I) {
1932 const SCEV *Mul = getMulExpr(Ops[0], *I);
1933 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1934 NewOps.push_back(Mul);
1937 return getAddExpr(NewOps);
1939 else if (const SCEVAddRecExpr *
1940 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1941 // Negation preserves a recurrence's no self-wrap property.
1942 SmallVector<const SCEV *, 4> Operands;
1943 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1944 E = AddRec->op_end(); I != E; ++I) {
1945 Operands.push_back(getMulExpr(Ops[0], *I));
1947 return getAddRecExpr(Operands, AddRec->getLoop(),
1948 AddRec->getNoWrapFlags(SCEV::FlagNW));
1953 if (Ops.size() == 1)
1957 // Skip over the add expression until we get to a multiply.
1958 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1961 // If there are mul operands inline them all into this expression.
1962 if (Idx < Ops.size()) {
1963 bool DeletedMul = false;
1964 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1965 // If we have an mul, expand the mul operands onto the end of the operands
1967 Ops.erase(Ops.begin()+Idx);
1968 Ops.append(Mul->op_begin(), Mul->op_end());
1972 // If we deleted at least one mul, we added operands to the end of the list,
1973 // and they are not necessarily sorted. Recurse to resort and resimplify
1974 // any operands we just acquired.
1976 return getMulExpr(Ops);
1979 // If there are any add recurrences in the operands list, see if any other
1980 // added values are loop invariant. If so, we can fold them into the
1982 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1985 // Scan over all recurrences, trying to fold loop invariants into them.
1986 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1987 // Scan all of the other operands to this mul and add them to the vector if
1988 // they are loop invariant w.r.t. the recurrence.
1989 SmallVector<const SCEV *, 8> LIOps;
1990 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1991 const Loop *AddRecLoop = AddRec->getLoop();
1992 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1993 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1994 LIOps.push_back(Ops[i]);
1995 Ops.erase(Ops.begin()+i);
1999 // If we found some loop invariants, fold them into the recurrence.
2000 if (!LIOps.empty()) {
2001 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2002 SmallVector<const SCEV *, 4> NewOps;
2003 NewOps.reserve(AddRec->getNumOperands());
2004 const SCEV *Scale = getMulExpr(LIOps);
2005 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2006 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2008 // Build the new addrec. Propagate the NUW and NSW flags if both the
2009 // outer mul and the inner addrec are guaranteed to have no overflow.
2011 // No self-wrap cannot be guaranteed after changing the step size, but
2012 // will be inferred if either NUW or NSW is true.
2013 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2014 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2016 // If all of the other operands were loop invariant, we are done.
2017 if (Ops.size() == 1) return NewRec;
2019 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2020 for (unsigned i = 0;; ++i)
2021 if (Ops[i] == AddRec) {
2025 return getMulExpr(Ops);
2028 // Okay, if there weren't any loop invariants to be folded, check to see if
2029 // there are multiple AddRec's with the same loop induction variable being
2030 // multiplied together. If so, we can fold them.
2031 for (unsigned OtherIdx = Idx+1;
2032 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2034 if (AddRecLoop != cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop())
2037 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2038 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2039 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2040 // ]]],+,...up to x=2n}.
2041 // Note that the arguments to choose() are always integers with values
2042 // known at compile time, never SCEV objects.
2044 // The implementation avoids pointless extra computations when the two
2045 // addrec's are of different length (mathematically, it's equivalent to
2046 // an infinite stream of zeros on the right).
2047 bool OpsModified = false;
2048 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2050 const SCEVAddRecExpr *OtherAddRec =
2051 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2052 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2055 bool Overflow = false;
2056 Type *Ty = AddRec->getType();
2057 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2058 SmallVector<const SCEV*, 7> AddRecOps;
2059 for (int x = 0, xe = AddRec->getNumOperands() +
2060 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2061 const SCEV *Term = getConstant(Ty, 0);
2062 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2063 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2064 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2065 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2066 z < ze && !Overflow; ++z) {
2067 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2069 if (LargerThan64Bits)
2070 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2072 Coeff = Coeff1*Coeff2;
2073 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2074 const SCEV *Term1 = AddRec->getOperand(y-z);
2075 const SCEV *Term2 = OtherAddRec->getOperand(z);
2076 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2079 AddRecOps.push_back(Term);
2082 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2084 if (Ops.size() == 2) return NewAddRec;
2085 Ops[Idx] = NewAddRec;
2086 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2088 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2094 return getMulExpr(Ops);
2097 // Otherwise couldn't fold anything into this recurrence. Move onto the
2101 // Okay, it looks like we really DO need an mul expr. Check to see if we
2102 // already have one, otherwise create a new one.
2103 FoldingSetNodeID ID;
2104 ID.AddInteger(scMulExpr);
2105 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2106 ID.AddPointer(Ops[i]);
2109 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2111 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2112 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2113 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2115 UniqueSCEVs.InsertNode(S, IP);
2117 S->setNoWrapFlags(Flags);
2121 /// getUDivExpr - Get a canonical unsigned division expression, or something
2122 /// simpler if possible.
2123 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2125 assert(getEffectiveSCEVType(LHS->getType()) ==
2126 getEffectiveSCEVType(RHS->getType()) &&
2127 "SCEVUDivExpr operand types don't match!");
2129 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2130 if (RHSC->getValue()->equalsInt(1))
2131 return LHS; // X udiv 1 --> x
2132 // If the denominator is zero, the result of the udiv is undefined. Don't
2133 // try to analyze it, because the resolution chosen here may differ from
2134 // the resolution chosen in other parts of the compiler.
2135 if (!RHSC->getValue()->isZero()) {
2136 // Determine if the division can be folded into the operands of
2138 // TODO: Generalize this to non-constants by using known-bits information.
2139 Type *Ty = LHS->getType();
2140 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2141 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2142 // For non-power-of-two values, effectively round the value up to the
2143 // nearest power of two.
2144 if (!RHSC->getValue()->getValue().isPowerOf2())
2146 IntegerType *ExtTy =
2147 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2148 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2149 if (const SCEVConstant *Step =
2150 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2151 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2152 const APInt &StepInt = Step->getValue()->getValue();
2153 const APInt &DivInt = RHSC->getValue()->getValue();
2154 if (!StepInt.urem(DivInt) &&
2155 getZeroExtendExpr(AR, ExtTy) ==
2156 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2157 getZeroExtendExpr(Step, ExtTy),
2158 AR->getLoop(), SCEV::FlagAnyWrap)) {
2159 SmallVector<const SCEV *, 4> Operands;
2160 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2161 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2162 return getAddRecExpr(Operands, AR->getLoop(),
2165 /// Get a canonical UDivExpr for a recurrence.
2166 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2167 // We can currently only fold X%N if X is constant.
2168 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2169 if (StartC && !DivInt.urem(StepInt) &&
2170 getZeroExtendExpr(AR, ExtTy) ==
2171 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2172 getZeroExtendExpr(Step, ExtTy),
2173 AR->getLoop(), SCEV::FlagAnyWrap)) {
2174 const APInt &StartInt = StartC->getValue()->getValue();
2175 const APInt &StartRem = StartInt.urem(StepInt);
2177 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2178 AR->getLoop(), SCEV::FlagNW);
2181 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2182 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2183 SmallVector<const SCEV *, 4> Operands;
2184 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2185 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2186 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2187 // Find an operand that's safely divisible.
2188 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2189 const SCEV *Op = M->getOperand(i);
2190 const SCEV *Div = getUDivExpr(Op, RHSC);
2191 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2192 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2195 return getMulExpr(Operands);
2199 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2200 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2201 SmallVector<const SCEV *, 4> Operands;
2202 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2203 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2204 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2206 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2207 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2208 if (isa<SCEVUDivExpr>(Op) ||
2209 getMulExpr(Op, RHS) != A->getOperand(i))
2211 Operands.push_back(Op);
2213 if (Operands.size() == A->getNumOperands())
2214 return getAddExpr(Operands);
2218 // Fold if both operands are constant.
2219 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2220 Constant *LHSCV = LHSC->getValue();
2221 Constant *RHSCV = RHSC->getValue();
2222 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2228 FoldingSetNodeID ID;
2229 ID.AddInteger(scUDivExpr);
2233 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2234 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2236 UniqueSCEVs.InsertNode(S, IP);
2240 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2241 APInt A = C1->getValue()->getValue().abs();
2242 APInt B = C2->getValue()->getValue().abs();
2243 uint32_t ABW = A.getBitWidth();
2244 uint32_t BBW = B.getBitWidth();
2251 return APIntOps::GreatestCommonDivisor(A, B);
2254 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2255 /// something simpler if possible. There is no representation for an exact udiv
2256 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2257 /// We can't do this when it's not exact because the udiv may be clearing bits.
2258 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2260 // TODO: we could try to find factors in all sorts of things, but for now we
2261 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2262 // end of this file for inspiration.
2264 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2266 return getUDivExpr(LHS, RHS);
2268 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2269 // If the mulexpr multiplies by a constant, then that constant must be the
2270 // first element of the mulexpr.
2271 if (const SCEVConstant *LHSCst =
2272 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2273 if (LHSCst == RHSCst) {
2274 SmallVector<const SCEV *, 2> Operands;
2275 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2276 return getMulExpr(Operands);
2279 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2280 // that there's a factor provided by one of the other terms. We need to
2282 APInt Factor = gcd(LHSCst, RHSCst);
2283 if (!Factor.isIntN(1)) {
2284 LHSCst = cast<SCEVConstant>(
2285 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2286 RHSCst = cast<SCEVConstant>(
2287 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2288 SmallVector<const SCEV *, 2> Operands;
2289 Operands.push_back(LHSCst);
2290 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2291 LHS = getMulExpr(Operands);
2293 Mul = dyn_cast<SCEVMulExpr>(LHS);
2295 return getUDivExactExpr(LHS, RHS);
2300 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2301 if (Mul->getOperand(i) == RHS) {
2302 SmallVector<const SCEV *, 2> Operands;
2303 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2304 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2305 return getMulExpr(Operands);
2309 return getUDivExpr(LHS, RHS);
2312 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2313 /// Simplify the expression as much as possible.
2314 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2316 SCEV::NoWrapFlags Flags) {
2317 SmallVector<const SCEV *, 4> Operands;
2318 Operands.push_back(Start);
2319 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2320 if (StepChrec->getLoop() == L) {
2321 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2322 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2325 Operands.push_back(Step);
2326 return getAddRecExpr(Operands, L, Flags);
2329 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2330 /// Simplify the expression as much as possible.
2332 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2333 const Loop *L, SCEV::NoWrapFlags Flags) {
2334 if (Operands.size() == 1) return Operands[0];
2336 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2337 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2338 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2339 "SCEVAddRecExpr operand types don't match!");
2340 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2341 assert(isLoopInvariant(Operands[i], L) &&
2342 "SCEVAddRecExpr operand is not loop-invariant!");
2345 if (Operands.back()->isZero()) {
2346 Operands.pop_back();
2347 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2350 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2351 // use that information to infer NUW and NSW flags. However, computing a
2352 // BE count requires calling getAddRecExpr, so we may not yet have a
2353 // meaningful BE count at this point (and if we don't, we'd be stuck
2354 // with a SCEVCouldNotCompute as the cached BE count).
2356 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2358 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2359 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2360 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2362 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2363 E = Operands.end(); I != E; ++I)
2364 if (!isKnownNonNegative(*I)) {
2368 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2371 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2372 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2373 const Loop *NestedLoop = NestedAR->getLoop();
2374 if (L->contains(NestedLoop) ?
2375 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2376 (!NestedLoop->contains(L) &&
2377 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2378 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2379 NestedAR->op_end());
2380 Operands[0] = NestedAR->getStart();
2381 // AddRecs require their operands be loop-invariant with respect to their
2382 // loops. Don't perform this transformation if it would break this
2384 bool AllInvariant = true;
2385 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2386 if (!isLoopInvariant(Operands[i], L)) {
2387 AllInvariant = false;
2391 // Create a recurrence for the outer loop with the same step size.
2393 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2394 // inner recurrence has the same property.
2395 SCEV::NoWrapFlags OuterFlags =
2396 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2398 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2399 AllInvariant = true;
2400 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2401 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2402 AllInvariant = false;
2406 // Ok, both add recurrences are valid after the transformation.
2408 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2409 // the outer recurrence has the same property.
2410 SCEV::NoWrapFlags InnerFlags =
2411 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2412 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2415 // Reset Operands to its original state.
2416 Operands[0] = NestedAR;
2420 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2421 // already have one, otherwise create a new one.
2422 FoldingSetNodeID ID;
2423 ID.AddInteger(scAddRecExpr);
2424 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2425 ID.AddPointer(Operands[i]);
2429 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2431 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2432 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2433 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2434 O, Operands.size(), L);
2435 UniqueSCEVs.InsertNode(S, IP);
2437 S->setNoWrapFlags(Flags);
2441 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2443 SmallVector<const SCEV *, 2> Ops;
2446 return getSMaxExpr(Ops);
2450 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2451 assert(!Ops.empty() && "Cannot get empty smax!");
2452 if (Ops.size() == 1) return Ops[0];
2454 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2455 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2456 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2457 "SCEVSMaxExpr operand types don't match!");
2460 // Sort by complexity, this groups all similar expression types together.
2461 GroupByComplexity(Ops, LI);
2463 // If there are any constants, fold them together.
2465 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2467 assert(Idx < Ops.size());
2468 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2469 // We found two constants, fold them together!
2470 ConstantInt *Fold = ConstantInt::get(getContext(),
2471 APIntOps::smax(LHSC->getValue()->getValue(),
2472 RHSC->getValue()->getValue()));
2473 Ops[0] = getConstant(Fold);
2474 Ops.erase(Ops.begin()+1); // Erase the folded element
2475 if (Ops.size() == 1) return Ops[0];
2476 LHSC = cast<SCEVConstant>(Ops[0]);
2479 // If we are left with a constant minimum-int, strip it off.
2480 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2481 Ops.erase(Ops.begin());
2483 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2484 // If we have an smax with a constant maximum-int, it will always be
2489 if (Ops.size() == 1) return Ops[0];
2492 // Find the first SMax
2493 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2496 // Check to see if one of the operands is an SMax. If so, expand its operands
2497 // onto our operand list, and recurse to simplify.
2498 if (Idx < Ops.size()) {
2499 bool DeletedSMax = false;
2500 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2501 Ops.erase(Ops.begin()+Idx);
2502 Ops.append(SMax->op_begin(), SMax->op_end());
2507 return getSMaxExpr(Ops);
2510 // Okay, check to see if the same value occurs in the operand list twice. If
2511 // so, delete one. Since we sorted the list, these values are required to
2513 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2514 // X smax Y smax Y --> X smax Y
2515 // X smax Y --> X, if X is always greater than Y
2516 if (Ops[i] == Ops[i+1] ||
2517 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2518 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2520 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2521 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2525 if (Ops.size() == 1) return Ops[0];
2527 assert(!Ops.empty() && "Reduced smax down to nothing!");
2529 // Okay, it looks like we really DO need an smax expr. Check to see if we
2530 // already have one, otherwise create a new one.
2531 FoldingSetNodeID ID;
2532 ID.AddInteger(scSMaxExpr);
2533 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2534 ID.AddPointer(Ops[i]);
2536 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2537 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2538 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2539 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2541 UniqueSCEVs.InsertNode(S, IP);
2545 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2547 SmallVector<const SCEV *, 2> Ops;
2550 return getUMaxExpr(Ops);
2554 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2555 assert(!Ops.empty() && "Cannot get empty umax!");
2556 if (Ops.size() == 1) return Ops[0];
2558 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2559 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2560 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2561 "SCEVUMaxExpr operand types don't match!");
2564 // Sort by complexity, this groups all similar expression types together.
2565 GroupByComplexity(Ops, LI);
2567 // If there are any constants, fold them together.
2569 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2571 assert(Idx < Ops.size());
2572 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2573 // We found two constants, fold them together!
2574 ConstantInt *Fold = ConstantInt::get(getContext(),
2575 APIntOps::umax(LHSC->getValue()->getValue(),
2576 RHSC->getValue()->getValue()));
2577 Ops[0] = getConstant(Fold);
2578 Ops.erase(Ops.begin()+1); // Erase the folded element
2579 if (Ops.size() == 1) return Ops[0];
2580 LHSC = cast<SCEVConstant>(Ops[0]);
2583 // If we are left with a constant minimum-int, strip it off.
2584 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2585 Ops.erase(Ops.begin());
2587 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2588 // If we have an umax with a constant maximum-int, it will always be
2593 if (Ops.size() == 1) return Ops[0];
2596 // Find the first UMax
2597 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2600 // Check to see if one of the operands is a UMax. If so, expand its operands
2601 // onto our operand list, and recurse to simplify.
2602 if (Idx < Ops.size()) {
2603 bool DeletedUMax = false;
2604 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2605 Ops.erase(Ops.begin()+Idx);
2606 Ops.append(UMax->op_begin(), UMax->op_end());
2611 return getUMaxExpr(Ops);
2614 // Okay, check to see if the same value occurs in the operand list twice. If
2615 // so, delete one. Since we sorted the list, these values are required to
2617 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2618 // X umax Y umax Y --> X umax Y
2619 // X umax Y --> X, if X is always greater than Y
2620 if (Ops[i] == Ops[i+1] ||
2621 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2622 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2624 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2625 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2629 if (Ops.size() == 1) return Ops[0];
2631 assert(!Ops.empty() && "Reduced umax down to nothing!");
2633 // Okay, it looks like we really DO need a umax expr. Check to see if we
2634 // already have one, otherwise create a new one.
2635 FoldingSetNodeID ID;
2636 ID.AddInteger(scUMaxExpr);
2637 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2638 ID.AddPointer(Ops[i]);
2640 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2641 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2642 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2643 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2645 UniqueSCEVs.InsertNode(S, IP);
2649 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2651 // ~smax(~x, ~y) == smin(x, y).
2652 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2655 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2657 // ~umax(~x, ~y) == umin(x, y)
2658 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2661 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2662 // If we have DataLayout, we can bypass creating a target-independent
2663 // constant expression and then folding it back into a ConstantInt.
2664 // This is just a compile-time optimization.
2666 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
2668 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2669 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2670 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2672 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2673 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2674 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2677 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2680 // If we have DataLayout, we can bypass creating a target-independent
2681 // constant expression and then folding it back into a ConstantInt.
2682 // This is just a compile-time optimization.
2684 return getConstant(IntTy,
2685 DL->getStructLayout(STy)->getElementOffset(FieldNo));
2688 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2689 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2690 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2693 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2694 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2697 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2698 // Don't attempt to do anything other than create a SCEVUnknown object
2699 // here. createSCEV only calls getUnknown after checking for all other
2700 // interesting possibilities, and any other code that calls getUnknown
2701 // is doing so in order to hide a value from SCEV canonicalization.
2703 FoldingSetNodeID ID;
2704 ID.AddInteger(scUnknown);
2707 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2708 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2709 "Stale SCEVUnknown in uniquing map!");
2712 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2714 FirstUnknown = cast<SCEVUnknown>(S);
2715 UniqueSCEVs.InsertNode(S, IP);
2719 //===----------------------------------------------------------------------===//
2720 // Basic SCEV Analysis and PHI Idiom Recognition Code
2723 /// isSCEVable - Test if values of the given type are analyzable within
2724 /// the SCEV framework. This primarily includes integer types, and it
2725 /// can optionally include pointer types if the ScalarEvolution class
2726 /// has access to target-specific information.
2727 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2728 // Integers and pointers are always SCEVable.
2729 return Ty->isIntegerTy() || Ty->isPointerTy();
2732 /// getTypeSizeInBits - Return the size in bits of the specified type,
2733 /// for which isSCEVable must return true.
2734 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2735 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2737 // If we have a DataLayout, use it!
2739 return DL->getTypeSizeInBits(Ty);
2741 // Integer types have fixed sizes.
2742 if (Ty->isIntegerTy())
2743 return Ty->getPrimitiveSizeInBits();
2745 // The only other support type is pointer. Without DataLayout, conservatively
2746 // assume pointers are 64-bit.
2747 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2751 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2752 /// the given type and which represents how SCEV will treat the given
2753 /// type, for which isSCEVable must return true. For pointer types,
2754 /// this is the pointer-sized integer type.
2755 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2756 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2758 if (Ty->isIntegerTy()) {
2762 // The only other support type is pointer.
2763 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2766 return DL->getIntPtrType(Ty);
2768 // Without DataLayout, conservatively assume pointers are 64-bit.
2769 return Type::getInt64Ty(getContext());
2772 const SCEV *ScalarEvolution::getCouldNotCompute() {
2773 return &CouldNotCompute;
2777 // Helper class working with SCEVTraversal to figure out if a SCEV contains
2778 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
2779 // is set iff if find such SCEVUnknown.
2781 struct FindInvalidSCEVUnknown {
2783 FindInvalidSCEVUnknown() { FindOne = false; }
2784 bool follow(const SCEV *S) {
2785 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
2789 if (!cast<SCEVUnknown>(S)->getValue())
2796 bool isDone() const { return FindOne; }
2800 bool ScalarEvolution::checkValidity(const SCEV *S) const {
2801 FindInvalidSCEVUnknown F;
2802 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
2808 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2809 /// expression and create a new one.
2810 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2811 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2813 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
2814 if (I != ValueExprMap.end()) {
2815 const SCEV *S = I->second;
2816 if (checkValidity(S))
2819 ValueExprMap.erase(I);
2821 const SCEV *S = createSCEV(V);
2823 // The process of creating a SCEV for V may have caused other SCEVs
2824 // to have been created, so it's necessary to insert the new entry
2825 // from scratch, rather than trying to remember the insert position
2827 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2831 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2833 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2834 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2836 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2838 Type *Ty = V->getType();
2839 Ty = getEffectiveSCEVType(Ty);
2840 return getMulExpr(V,
2841 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2844 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2845 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2846 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2848 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2850 Type *Ty = V->getType();
2851 Ty = getEffectiveSCEVType(Ty);
2852 const SCEV *AllOnes =
2853 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2854 return getMinusSCEV(AllOnes, V);
2857 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2858 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2859 SCEV::NoWrapFlags Flags) {
2860 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2862 // Fast path: X - X --> 0.
2864 return getConstant(LHS->getType(), 0);
2867 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2870 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2871 /// input value to the specified type. If the type must be extended, it is zero
2874 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2875 Type *SrcTy = V->getType();
2876 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2877 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2878 "Cannot truncate or zero extend with non-integer arguments!");
2879 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2880 return V; // No conversion
2881 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2882 return getTruncateExpr(V, Ty);
2883 return getZeroExtendExpr(V, Ty);
2886 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2887 /// input value to the specified type. If the type must be extended, it is sign
2890 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2892 Type *SrcTy = V->getType();
2893 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2894 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2895 "Cannot truncate or zero extend with non-integer arguments!");
2896 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2897 return V; // No conversion
2898 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2899 return getTruncateExpr(V, Ty);
2900 return getSignExtendExpr(V, Ty);
2903 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2904 /// input value to the specified type. If the type must be extended, it is zero
2905 /// extended. The conversion must not be narrowing.
2907 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2908 Type *SrcTy = V->getType();
2909 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2910 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2911 "Cannot noop or zero extend with non-integer arguments!");
2912 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2913 "getNoopOrZeroExtend cannot truncate!");
2914 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2915 return V; // No conversion
2916 return getZeroExtendExpr(V, Ty);
2919 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2920 /// input value to the specified type. If the type must be extended, it is sign
2921 /// extended. The conversion must not be narrowing.
2923 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2924 Type *SrcTy = V->getType();
2925 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2926 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2927 "Cannot noop or sign extend with non-integer arguments!");
2928 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2929 "getNoopOrSignExtend cannot truncate!");
2930 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2931 return V; // No conversion
2932 return getSignExtendExpr(V, Ty);
2935 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2936 /// the input value to the specified type. If the type must be extended,
2937 /// it is extended with unspecified bits. The conversion must not be
2940 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2941 Type *SrcTy = V->getType();
2942 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2943 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2944 "Cannot noop or any extend with non-integer arguments!");
2945 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2946 "getNoopOrAnyExtend cannot truncate!");
2947 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2948 return V; // No conversion
2949 return getAnyExtendExpr(V, Ty);
2952 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2953 /// input value to the specified type. The conversion must not be widening.
2955 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2956 Type *SrcTy = V->getType();
2957 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2958 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2959 "Cannot truncate or noop with non-integer arguments!");
2960 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2961 "getTruncateOrNoop cannot extend!");
2962 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2963 return V; // No conversion
2964 return getTruncateExpr(V, Ty);
2967 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2968 /// the types using zero-extension, and then perform a umax operation
2970 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2972 const SCEV *PromotedLHS = LHS;
2973 const SCEV *PromotedRHS = RHS;
2975 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2976 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2978 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2980 return getUMaxExpr(PromotedLHS, PromotedRHS);
2983 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2984 /// the types using zero-extension, and then perform a umin operation
2986 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2988 const SCEV *PromotedLHS = LHS;
2989 const SCEV *PromotedRHS = RHS;
2991 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2992 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2994 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2996 return getUMinExpr(PromotedLHS, PromotedRHS);
2999 /// getPointerBase - Transitively follow the chain of pointer-type operands
3000 /// until reaching a SCEV that does not have a single pointer operand. This
3001 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3002 /// but corner cases do exist.
3003 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3004 // A pointer operand may evaluate to a nonpointer expression, such as null.
3005 if (!V->getType()->isPointerTy())
3008 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3009 return getPointerBase(Cast->getOperand());
3011 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3012 const SCEV *PtrOp = nullptr;
3013 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3015 if ((*I)->getType()->isPointerTy()) {
3016 // Cannot find the base of an expression with multiple pointer operands.
3024 return getPointerBase(PtrOp);
3029 /// PushDefUseChildren - Push users of the given Instruction
3030 /// onto the given Worklist.
3032 PushDefUseChildren(Instruction *I,
3033 SmallVectorImpl<Instruction *> &Worklist) {
3034 // Push the def-use children onto the Worklist stack.
3035 for (User *U : I->users())
3036 Worklist.push_back(cast<Instruction>(U));
3039 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3040 /// instructions that depend on the given instruction and removes them from
3041 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3044 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3045 SmallVector<Instruction *, 16> Worklist;
3046 PushDefUseChildren(PN, Worklist);
3048 SmallPtrSet<Instruction *, 8> Visited;
3050 while (!Worklist.empty()) {
3051 Instruction *I = Worklist.pop_back_val();
3052 if (!Visited.insert(I)) continue;
3054 ValueExprMapType::iterator It =
3055 ValueExprMap.find_as(static_cast<Value *>(I));
3056 if (It != ValueExprMap.end()) {
3057 const SCEV *Old = It->second;
3059 // Short-circuit the def-use traversal if the symbolic name
3060 // ceases to appear in expressions.
3061 if (Old != SymName && !hasOperand(Old, SymName))
3064 // SCEVUnknown for a PHI either means that it has an unrecognized
3065 // structure, it's a PHI that's in the progress of being computed
3066 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3067 // additional loop trip count information isn't going to change anything.
3068 // In the second case, createNodeForPHI will perform the necessary
3069 // updates on its own when it gets to that point. In the third, we do
3070 // want to forget the SCEVUnknown.
3071 if (!isa<PHINode>(I) ||
3072 !isa<SCEVUnknown>(Old) ||
3073 (I != PN && Old == SymName)) {
3074 forgetMemoizedResults(Old);
3075 ValueExprMap.erase(It);
3079 PushDefUseChildren(I, Worklist);
3083 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3084 /// a loop header, making it a potential recurrence, or it doesn't.
3086 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3087 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3088 if (L->getHeader() == PN->getParent()) {
3089 // The loop may have multiple entrances or multiple exits; we can analyze
3090 // this phi as an addrec if it has a unique entry value and a unique
3092 Value *BEValueV = nullptr, *StartValueV = nullptr;
3093 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3094 Value *V = PN->getIncomingValue(i);
3095 if (L->contains(PN->getIncomingBlock(i))) {
3098 } else if (BEValueV != V) {
3102 } else if (!StartValueV) {
3104 } else if (StartValueV != V) {
3105 StartValueV = nullptr;
3109 if (BEValueV && StartValueV) {
3110 // While we are analyzing this PHI node, handle its value symbolically.
3111 const SCEV *SymbolicName = getUnknown(PN);
3112 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3113 "PHI node already processed?");
3114 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3116 // Using this symbolic name for the PHI, analyze the value coming around
3118 const SCEV *BEValue = getSCEV(BEValueV);
3120 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3121 // has a special value for the first iteration of the loop.
3123 // If the value coming around the backedge is an add with the symbolic
3124 // value we just inserted, then we found a simple induction variable!
3125 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3126 // If there is a single occurrence of the symbolic value, replace it
3127 // with a recurrence.
3128 unsigned FoundIndex = Add->getNumOperands();
3129 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3130 if (Add->getOperand(i) == SymbolicName)
3131 if (FoundIndex == e) {
3136 if (FoundIndex != Add->getNumOperands()) {
3137 // Create an add with everything but the specified operand.
3138 SmallVector<const SCEV *, 8> Ops;
3139 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3140 if (i != FoundIndex)
3141 Ops.push_back(Add->getOperand(i));
3142 const SCEV *Accum = getAddExpr(Ops);
3144 // This is not a valid addrec if the step amount is varying each
3145 // loop iteration, but is not itself an addrec in this loop.
3146 if (isLoopInvariant(Accum, L) ||
3147 (isa<SCEVAddRecExpr>(Accum) &&
3148 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3149 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3151 // If the increment doesn't overflow, then neither the addrec nor
3152 // the post-increment will overflow.
3153 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3154 if (OBO->hasNoUnsignedWrap())
3155 Flags = setFlags(Flags, SCEV::FlagNUW);
3156 if (OBO->hasNoSignedWrap())
3157 Flags = setFlags(Flags, SCEV::FlagNSW);
3158 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3159 // If the increment is an inbounds GEP, then we know the address
3160 // space cannot be wrapped around. We cannot make any guarantee
3161 // about signed or unsigned overflow because pointers are
3162 // unsigned but we may have a negative index from the base
3163 // pointer. We can guarantee that no unsigned wrap occurs if the
3164 // indices form a positive value.
3165 if (GEP->isInBounds()) {
3166 Flags = setFlags(Flags, SCEV::FlagNW);
3168 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3169 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3170 Flags = setFlags(Flags, SCEV::FlagNUW);
3172 } else if (const SubOperator *OBO =
3173 dyn_cast<SubOperator>(BEValueV)) {
3174 if (OBO->hasNoUnsignedWrap())
3175 Flags = setFlags(Flags, SCEV::FlagNUW);
3176 if (OBO->hasNoSignedWrap())
3177 Flags = setFlags(Flags, SCEV::FlagNSW);
3180 const SCEV *StartVal = getSCEV(StartValueV);
3181 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3183 // Since the no-wrap flags are on the increment, they apply to the
3184 // post-incremented value as well.
3185 if (isLoopInvariant(Accum, L))
3186 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3189 // Okay, for the entire analysis of this edge we assumed the PHI
3190 // to be symbolic. We now need to go back and purge all of the
3191 // entries for the scalars that use the symbolic expression.
3192 ForgetSymbolicName(PN, SymbolicName);
3193 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3197 } else if (const SCEVAddRecExpr *AddRec =
3198 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3199 // Otherwise, this could be a loop like this:
3200 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3201 // In this case, j = {1,+,1} and BEValue is j.
3202 // Because the other in-value of i (0) fits the evolution of BEValue
3203 // i really is an addrec evolution.
3204 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3205 const SCEV *StartVal = getSCEV(StartValueV);
3207 // If StartVal = j.start - j.stride, we can use StartVal as the
3208 // initial step of the addrec evolution.
3209 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3210 AddRec->getOperand(1))) {
3211 // FIXME: For constant StartVal, we should be able to infer
3213 const SCEV *PHISCEV =
3214 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3217 // Okay, for the entire analysis of this edge we assumed the PHI
3218 // to be symbolic. We now need to go back and purge all of the
3219 // entries for the scalars that use the symbolic expression.
3220 ForgetSymbolicName(PN, SymbolicName);
3221 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3229 // If the PHI has a single incoming value, follow that value, unless the
3230 // PHI's incoming blocks are in a different loop, in which case doing so
3231 // risks breaking LCSSA form. Instcombine would normally zap these, but
3232 // it doesn't have DominatorTree information, so it may miss cases.
3233 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT))
3234 if (LI->replacementPreservesLCSSAForm(PN, V))
3237 // If it's not a loop phi, we can't handle it yet.
3238 return getUnknown(PN);
3241 /// createNodeForGEP - Expand GEP instructions into add and multiply
3242 /// operations. This allows them to be analyzed by regular SCEV code.
3244 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3245 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3246 Value *Base = GEP->getOperand(0);
3247 // Don't attempt to analyze GEPs over unsized objects.
3248 if (!Base->getType()->getPointerElementType()->isSized())
3249 return getUnknown(GEP);
3251 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3252 // Add expression, because the Instruction may be guarded by control flow
3253 // and the no-overflow bits may not be valid for the expression in any
3255 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3257 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3258 gep_type_iterator GTI = gep_type_begin(GEP);
3259 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3263 // Compute the (potentially symbolic) offset in bytes for this index.
3264 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3265 // For a struct, add the member offset.
3266 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3267 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3269 // Add the field offset to the running total offset.
3270 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3272 // For an array, add the element offset, explicitly scaled.
3273 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3274 const SCEV *IndexS = getSCEV(Index);
3275 // Getelementptr indices are signed.
3276 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3278 // Multiply the index by the element size to compute the element offset.
3279 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3281 // Add the element offset to the running total offset.
3282 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3286 // Get the SCEV for the GEP base.
3287 const SCEV *BaseS = getSCEV(Base);
3289 // Add the total offset from all the GEP indices to the base.
3290 return getAddExpr(BaseS, TotalOffset, Wrap);
3293 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3294 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3295 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3296 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3298 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3299 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3300 return C->getValue()->getValue().countTrailingZeros();
3302 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3303 return std::min(GetMinTrailingZeros(T->getOperand()),
3304 (uint32_t)getTypeSizeInBits(T->getType()));
3306 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3307 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3308 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3309 getTypeSizeInBits(E->getType()) : OpRes;
3312 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3313 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3314 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3315 getTypeSizeInBits(E->getType()) : OpRes;
3318 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3319 // The result is the min of all operands results.
3320 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3321 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3322 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3326 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3327 // The result is the sum of all operands results.
3328 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3329 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3330 for (unsigned i = 1, e = M->getNumOperands();
3331 SumOpRes != BitWidth && i != e; ++i)
3332 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3337 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3338 // The result is the min of all operands results.
3339 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3340 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3341 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3345 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3346 // The result is the min of all operands results.
3347 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3348 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3349 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3353 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3354 // The result is the min of all operands results.
3355 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3356 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3357 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3361 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3362 // For a SCEVUnknown, ask ValueTracking.
3363 unsigned BitWidth = getTypeSizeInBits(U->getType());
3364 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3365 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3366 return Zeros.countTrailingOnes();
3373 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3376 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3377 // See if we've computed this range already.
3378 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3379 if (I != UnsignedRanges.end())
3382 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3383 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3385 unsigned BitWidth = getTypeSizeInBits(S->getType());
3386 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3388 // If the value has known zeros, the maximum unsigned value will have those
3389 // known zeros as well.
3390 uint32_t TZ = GetMinTrailingZeros(S);
3392 ConservativeResult =
3393 ConstantRange(APInt::getMinValue(BitWidth),
3394 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3396 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3397 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3398 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3399 X = X.add(getUnsignedRange(Add->getOperand(i)));
3400 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3403 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3404 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3405 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3406 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3407 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3410 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3411 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3412 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3413 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3414 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3417 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3418 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3419 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3420 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3421 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3424 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3425 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3426 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3427 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3430 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3431 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3432 return setUnsignedRange(ZExt,
3433 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3436 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3437 ConstantRange X = getUnsignedRange(SExt->getOperand());
3438 return setUnsignedRange(SExt,
3439 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3442 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3443 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3444 return setUnsignedRange(Trunc,
3445 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3448 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3449 // If there's no unsigned wrap, the value will never be less than its
3451 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3452 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3453 if (!C->getValue()->isZero())
3454 ConservativeResult =
3455 ConservativeResult.intersectWith(
3456 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3458 // TODO: non-affine addrec
3459 if (AddRec->isAffine()) {
3460 Type *Ty = AddRec->getType();
3461 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3462 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3463 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3464 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3466 const SCEV *Start = AddRec->getStart();
3467 const SCEV *Step = AddRec->getStepRecurrence(*this);
3469 ConstantRange StartRange = getUnsignedRange(Start);
3470 ConstantRange StepRange = getSignedRange(Step);
3471 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3472 ConstantRange EndRange =
3473 StartRange.add(MaxBECountRange.multiply(StepRange));
3475 // Check for overflow. This must be done with ConstantRange arithmetic
3476 // because we could be called from within the ScalarEvolution overflow
3478 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3479 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3480 ConstantRange ExtMaxBECountRange =
3481 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3482 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3483 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3485 return setUnsignedRange(AddRec, ConservativeResult);
3487 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3488 EndRange.getUnsignedMin());
3489 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3490 EndRange.getUnsignedMax());
3491 if (Min.isMinValue() && Max.isMaxValue())
3492 return setUnsignedRange(AddRec, ConservativeResult);
3493 return setUnsignedRange(AddRec,
3494 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3498 return setUnsignedRange(AddRec, ConservativeResult);
3501 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3502 // For a SCEVUnknown, ask ValueTracking.
3503 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3504 ComputeMaskedBits(U->getValue(), Zeros, Ones, DL);
3505 if (Ones == ~Zeros + 1)
3506 return setUnsignedRange(U, ConservativeResult);
3507 return setUnsignedRange(U,
3508 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3511 return setUnsignedRange(S, ConservativeResult);
3514 /// getSignedRange - Determine the signed range for a particular SCEV.
3517 ScalarEvolution::getSignedRange(const SCEV *S) {
3518 // See if we've computed this range already.
3519 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3520 if (I != SignedRanges.end())
3523 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3524 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3526 unsigned BitWidth = getTypeSizeInBits(S->getType());
3527 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3529 // If the value has known zeros, the maximum signed value will have those
3530 // known zeros as well.
3531 uint32_t TZ = GetMinTrailingZeros(S);
3533 ConservativeResult =
3534 ConstantRange(APInt::getSignedMinValue(BitWidth),
3535 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3537 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3538 ConstantRange X = getSignedRange(Add->getOperand(0));
3539 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3540 X = X.add(getSignedRange(Add->getOperand(i)));
3541 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3544 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3545 ConstantRange X = getSignedRange(Mul->getOperand(0));
3546 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3547 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3548 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3551 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3552 ConstantRange X = getSignedRange(SMax->getOperand(0));
3553 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3554 X = X.smax(getSignedRange(SMax->getOperand(i)));
3555 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3558 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3559 ConstantRange X = getSignedRange(UMax->getOperand(0));
3560 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3561 X = X.umax(getSignedRange(UMax->getOperand(i)));
3562 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3565 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3566 ConstantRange X = getSignedRange(UDiv->getLHS());
3567 ConstantRange Y = getSignedRange(UDiv->getRHS());
3568 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3571 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3572 ConstantRange X = getSignedRange(ZExt->getOperand());
3573 return setSignedRange(ZExt,
3574 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3577 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3578 ConstantRange X = getSignedRange(SExt->getOperand());
3579 return setSignedRange(SExt,
3580 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3583 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3584 ConstantRange X = getSignedRange(Trunc->getOperand());
3585 return setSignedRange(Trunc,
3586 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3589 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3590 // If there's no signed wrap, and all the operands have the same sign or
3591 // zero, the value won't ever change sign.
3592 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3593 bool AllNonNeg = true;
3594 bool AllNonPos = true;
3595 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3596 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3597 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3600 ConservativeResult = ConservativeResult.intersectWith(
3601 ConstantRange(APInt(BitWidth, 0),
3602 APInt::getSignedMinValue(BitWidth)));
3604 ConservativeResult = ConservativeResult.intersectWith(
3605 ConstantRange(APInt::getSignedMinValue(BitWidth),
3606 APInt(BitWidth, 1)));
3609 // TODO: non-affine addrec
3610 if (AddRec->isAffine()) {
3611 Type *Ty = AddRec->getType();
3612 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3613 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3614 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3615 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3617 const SCEV *Start = AddRec->getStart();
3618 const SCEV *Step = AddRec->getStepRecurrence(*this);
3620 ConstantRange StartRange = getSignedRange(Start);
3621 ConstantRange StepRange = getSignedRange(Step);
3622 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3623 ConstantRange EndRange =
3624 StartRange.add(MaxBECountRange.multiply(StepRange));
3626 // Check for overflow. This must be done with ConstantRange arithmetic
3627 // because we could be called from within the ScalarEvolution overflow
3629 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3630 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3631 ConstantRange ExtMaxBECountRange =
3632 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3633 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3634 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3636 return setSignedRange(AddRec, ConservativeResult);
3638 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3639 EndRange.getSignedMin());
3640 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3641 EndRange.getSignedMax());
3642 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3643 return setSignedRange(AddRec, ConservativeResult);
3644 return setSignedRange(AddRec,
3645 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3649 return setSignedRange(AddRec, ConservativeResult);
3652 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3653 // For a SCEVUnknown, ask ValueTracking.
3654 if (!U->getValue()->getType()->isIntegerTy() && !DL)
3655 return setSignedRange(U, ConservativeResult);
3656 unsigned NS = ComputeNumSignBits(U->getValue(), DL);
3658 return setSignedRange(U, ConservativeResult);
3659 return setSignedRange(U, ConservativeResult.intersectWith(
3660 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3661 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3664 return setSignedRange(S, ConservativeResult);
3667 /// createSCEV - We know that there is no SCEV for the specified value.
3668 /// Analyze the expression.
3670 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3671 if (!isSCEVable(V->getType()))
3672 return getUnknown(V);
3674 unsigned Opcode = Instruction::UserOp1;
3675 if (Instruction *I = dyn_cast<Instruction>(V)) {
3676 Opcode = I->getOpcode();
3678 // Don't attempt to analyze instructions in blocks that aren't
3679 // reachable. Such instructions don't matter, and they aren't required
3680 // to obey basic rules for definitions dominating uses which this
3681 // analysis depends on.
3682 if (!DT->isReachableFromEntry(I->getParent()))
3683 return getUnknown(V);
3684 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3685 Opcode = CE->getOpcode();
3686 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3687 return getConstant(CI);
3688 else if (isa<ConstantPointerNull>(V))
3689 return getConstant(V->getType(), 0);
3690 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3691 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3693 return getUnknown(V);
3695 Operator *U = cast<Operator>(V);
3697 case Instruction::Add: {
3698 // The simple thing to do would be to just call getSCEV on both operands
3699 // and call getAddExpr with the result. However if we're looking at a
3700 // bunch of things all added together, this can be quite inefficient,
3701 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3702 // Instead, gather up all the operands and make a single getAddExpr call.
3703 // LLVM IR canonical form means we need only traverse the left operands.
3705 // Don't apply this instruction's NSW or NUW flags to the new
3706 // expression. The instruction may be guarded by control flow that the
3707 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3708 // mapped to the same SCEV expression, and it would be incorrect to transfer
3709 // NSW/NUW semantics to those operations.
3710 SmallVector<const SCEV *, 4> AddOps;
3711 AddOps.push_back(getSCEV(U->getOperand(1)));
3712 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3713 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3714 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3716 U = cast<Operator>(Op);
3717 const SCEV *Op1 = getSCEV(U->getOperand(1));
3718 if (Opcode == Instruction::Sub)
3719 AddOps.push_back(getNegativeSCEV(Op1));
3721 AddOps.push_back(Op1);
3723 AddOps.push_back(getSCEV(U->getOperand(0)));
3724 return getAddExpr(AddOps);
3726 case Instruction::Mul: {
3727 // Don't transfer NSW/NUW for the same reason as AddExpr.
3728 SmallVector<const SCEV *, 4> MulOps;
3729 MulOps.push_back(getSCEV(U->getOperand(1)));
3730 for (Value *Op = U->getOperand(0);
3731 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3732 Op = U->getOperand(0)) {
3733 U = cast<Operator>(Op);
3734 MulOps.push_back(getSCEV(U->getOperand(1)));
3736 MulOps.push_back(getSCEV(U->getOperand(0)));
3737 return getMulExpr(MulOps);
3739 case Instruction::UDiv:
3740 return getUDivExpr(getSCEV(U->getOperand(0)),
3741 getSCEV(U->getOperand(1)));
3742 case Instruction::Sub:
3743 return getMinusSCEV(getSCEV(U->getOperand(0)),
3744 getSCEV(U->getOperand(1)));
3745 case Instruction::And:
3746 // For an expression like x&255 that merely masks off the high bits,
3747 // use zext(trunc(x)) as the SCEV expression.
3748 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3749 if (CI->isNullValue())
3750 return getSCEV(U->getOperand(1));
3751 if (CI->isAllOnesValue())
3752 return getSCEV(U->getOperand(0));
3753 const APInt &A = CI->getValue();
3755 // Instcombine's ShrinkDemandedConstant may strip bits out of
3756 // constants, obscuring what would otherwise be a low-bits mask.
3757 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3758 // knew about to reconstruct a low-bits mask value.
3759 unsigned LZ = A.countLeadingZeros();
3760 unsigned TZ = A.countTrailingZeros();
3761 unsigned BitWidth = A.getBitWidth();
3762 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3763 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, DL);
3765 APInt EffectiveMask =
3766 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
3767 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
3768 const SCEV *MulCount = getConstant(
3769 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
3773 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
3774 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
3781 case Instruction::Or:
3782 // If the RHS of the Or is a constant, we may have something like:
3783 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3784 // optimizations will transparently handle this case.
3786 // In order for this transformation to be safe, the LHS must be of the
3787 // form X*(2^n) and the Or constant must be less than 2^n.
3788 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3789 const SCEV *LHS = getSCEV(U->getOperand(0));
3790 const APInt &CIVal = CI->getValue();
3791 if (GetMinTrailingZeros(LHS) >=
3792 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3793 // Build a plain add SCEV.
3794 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3795 // If the LHS of the add was an addrec and it has no-wrap flags,
3796 // transfer the no-wrap flags, since an or won't introduce a wrap.
3797 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3798 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3799 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3800 OldAR->getNoWrapFlags());
3806 case Instruction::Xor:
3807 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3808 // If the RHS of the xor is a signbit, then this is just an add.
3809 // Instcombine turns add of signbit into xor as a strength reduction step.
3810 if (CI->getValue().isSignBit())
3811 return getAddExpr(getSCEV(U->getOperand(0)),
3812 getSCEV(U->getOperand(1)));
3814 // If the RHS of xor is -1, then this is a not operation.
3815 if (CI->isAllOnesValue())
3816 return getNotSCEV(getSCEV(U->getOperand(0)));
3818 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3819 // This is a variant of the check for xor with -1, and it handles
3820 // the case where instcombine has trimmed non-demanded bits out
3821 // of an xor with -1.
3822 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3823 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3824 if (BO->getOpcode() == Instruction::And &&
3825 LCI->getValue() == CI->getValue())
3826 if (const SCEVZeroExtendExpr *Z =
3827 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3828 Type *UTy = U->getType();
3829 const SCEV *Z0 = Z->getOperand();
3830 Type *Z0Ty = Z0->getType();
3831 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3833 // If C is a low-bits mask, the zero extend is serving to
3834 // mask off the high bits. Complement the operand and
3835 // re-apply the zext.
3836 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3837 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3839 // If C is a single bit, it may be in the sign-bit position
3840 // before the zero-extend. In this case, represent the xor
3841 // using an add, which is equivalent, and re-apply the zext.
3842 APInt Trunc = CI->getValue().trunc(Z0TySize);
3843 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3845 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3851 case Instruction::Shl:
3852 // Turn shift left of a constant amount into a multiply.
3853 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3854 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3856 // If the shift count is not less than the bitwidth, the result of
3857 // the shift is undefined. Don't try to analyze it, because the
3858 // resolution chosen here may differ from the resolution chosen in
3859 // other parts of the compiler.
3860 if (SA->getValue().uge(BitWidth))
3863 Constant *X = ConstantInt::get(getContext(),
3864 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3865 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3869 case Instruction::LShr:
3870 // Turn logical shift right of a constant into a unsigned divide.
3871 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3872 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3874 // If the shift count is not less than the bitwidth, the result of
3875 // the shift is undefined. Don't try to analyze it, because the
3876 // resolution chosen here may differ from the resolution chosen in
3877 // other parts of the compiler.
3878 if (SA->getValue().uge(BitWidth))
3881 Constant *X = ConstantInt::get(getContext(),
3882 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3883 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3887 case Instruction::AShr:
3888 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3889 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3890 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3891 if (L->getOpcode() == Instruction::Shl &&
3892 L->getOperand(1) == U->getOperand(1)) {
3893 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3895 // If the shift count is not less than the bitwidth, the result of
3896 // the shift is undefined. Don't try to analyze it, because the
3897 // resolution chosen here may differ from the resolution chosen in
3898 // other parts of the compiler.
3899 if (CI->getValue().uge(BitWidth))
3902 uint64_t Amt = BitWidth - CI->getZExtValue();
3903 if (Amt == BitWidth)
3904 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3906 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3907 IntegerType::get(getContext(),
3913 case Instruction::Trunc:
3914 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3916 case Instruction::ZExt:
3917 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3919 case Instruction::SExt:
3920 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3922 case Instruction::BitCast:
3923 // BitCasts are no-op casts so we just eliminate the cast.
3924 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3925 return getSCEV(U->getOperand(0));
3928 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3929 // lead to pointer expressions which cannot safely be expanded to GEPs,
3930 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3931 // simplifying integer expressions.
3933 case Instruction::GetElementPtr:
3934 return createNodeForGEP(cast<GEPOperator>(U));
3936 case Instruction::PHI:
3937 return createNodeForPHI(cast<PHINode>(U));
3939 case Instruction::Select:
3940 // This could be a smax or umax that was lowered earlier.
3941 // Try to recover it.
3942 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3943 Value *LHS = ICI->getOperand(0);
3944 Value *RHS = ICI->getOperand(1);
3945 switch (ICI->getPredicate()) {
3946 case ICmpInst::ICMP_SLT:
3947 case ICmpInst::ICMP_SLE:
3948 std::swap(LHS, RHS);
3950 case ICmpInst::ICMP_SGT:
3951 case ICmpInst::ICMP_SGE:
3952 // a >s b ? a+x : b+x -> smax(a, b)+x
3953 // a >s b ? b+x : a+x -> smin(a, b)+x
3954 if (LHS->getType() == U->getType()) {
3955 const SCEV *LS = getSCEV(LHS);
3956 const SCEV *RS = getSCEV(RHS);
3957 const SCEV *LA = getSCEV(U->getOperand(1));
3958 const SCEV *RA = getSCEV(U->getOperand(2));
3959 const SCEV *LDiff = getMinusSCEV(LA, LS);
3960 const SCEV *RDiff = getMinusSCEV(RA, RS);
3962 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3963 LDiff = getMinusSCEV(LA, RS);
3964 RDiff = getMinusSCEV(RA, LS);
3966 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3969 case ICmpInst::ICMP_ULT:
3970 case ICmpInst::ICMP_ULE:
3971 std::swap(LHS, RHS);
3973 case ICmpInst::ICMP_UGT:
3974 case ICmpInst::ICMP_UGE:
3975 // a >u b ? a+x : b+x -> umax(a, b)+x
3976 // a >u b ? b+x : a+x -> umin(a, b)+x
3977 if (LHS->getType() == U->getType()) {
3978 const SCEV *LS = getSCEV(LHS);
3979 const SCEV *RS = getSCEV(RHS);
3980 const SCEV *LA = getSCEV(U->getOperand(1));
3981 const SCEV *RA = getSCEV(U->getOperand(2));
3982 const SCEV *LDiff = getMinusSCEV(LA, LS);
3983 const SCEV *RDiff = getMinusSCEV(RA, RS);
3985 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3986 LDiff = getMinusSCEV(LA, RS);
3987 RDiff = getMinusSCEV(RA, LS);
3989 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3992 case ICmpInst::ICMP_NE:
3993 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3994 if (LHS->getType() == U->getType() &&
3995 isa<ConstantInt>(RHS) &&
3996 cast<ConstantInt>(RHS)->isZero()) {
3997 const SCEV *One = getConstant(LHS->getType(), 1);
3998 const SCEV *LS = getSCEV(LHS);
3999 const SCEV *LA = getSCEV(U->getOperand(1));
4000 const SCEV *RA = getSCEV(U->getOperand(2));
4001 const SCEV *LDiff = getMinusSCEV(LA, LS);
4002 const SCEV *RDiff = getMinusSCEV(RA, One);
4004 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4007 case ICmpInst::ICMP_EQ:
4008 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4009 if (LHS->getType() == U->getType() &&
4010 isa<ConstantInt>(RHS) &&
4011 cast<ConstantInt>(RHS)->isZero()) {
4012 const SCEV *One = getConstant(LHS->getType(), 1);
4013 const SCEV *LS = getSCEV(LHS);
4014 const SCEV *LA = getSCEV(U->getOperand(1));
4015 const SCEV *RA = getSCEV(U->getOperand(2));
4016 const SCEV *LDiff = getMinusSCEV(LA, One);
4017 const SCEV *RDiff = getMinusSCEV(RA, LS);
4019 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4027 default: // We cannot analyze this expression.
4031 return getUnknown(V);
4036 //===----------------------------------------------------------------------===//
4037 // Iteration Count Computation Code
4040 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4041 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4042 /// constant. Will also return 0 if the maximum trip count is very large (>=
4045 /// This "trip count" assumes that control exits via ExitingBlock. More
4046 /// precisely, it is the number of times that control may reach ExitingBlock
4047 /// before taking the branch. For loops with multiple exits, it may not be the
4048 /// number times that the loop header executes because the loop may exit
4049 /// prematurely via another branch.
4051 /// FIXME: We conservatively call getBackedgeTakenCount(L) instead of
4052 /// getExitCount(L, ExitingBlock) to compute a safe trip count considering all
4053 /// loop exits. getExitCount() may return an exact count for this branch
4054 /// assuming no-signed-wrap. The number of well-defined iterations may actually
4055 /// be higher than this trip count if this exit test is skipped and the loop
4056 /// exits via a different branch. Ideally, getExitCount() would know whether it
4057 /// depends on a NSW assumption, and we would only fall back to a conservative
4058 /// trip count in that case.
4059 unsigned ScalarEvolution::
4060 getSmallConstantTripCount(Loop *L, BasicBlock * /*ExitingBlock*/) {
4061 const SCEVConstant *ExitCount =
4062 dyn_cast<SCEVConstant>(getBackedgeTakenCount(L));
4066 ConstantInt *ExitConst = ExitCount->getValue();
4068 // Guard against huge trip counts.
4069 if (ExitConst->getValue().getActiveBits() > 32)
4072 // In case of integer overflow, this returns 0, which is correct.
4073 return ((unsigned)ExitConst->getZExtValue()) + 1;
4076 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4077 /// trip count of this loop as a normal unsigned value, if possible. This
4078 /// means that the actual trip count is always a multiple of the returned
4079 /// value (don't forget the trip count could very well be zero as well!).
4081 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4082 /// multiple of a constant (which is also the case if the trip count is simply
4083 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4084 /// if the trip count is very large (>= 2^32).
4086 /// As explained in the comments for getSmallConstantTripCount, this assumes
4087 /// that control exits the loop via ExitingBlock.
4088 unsigned ScalarEvolution::
4089 getSmallConstantTripMultiple(Loop *L, BasicBlock * /*ExitingBlock*/) {
4090 const SCEV *ExitCount = getBackedgeTakenCount(L);
4091 if (ExitCount == getCouldNotCompute())
4094 // Get the trip count from the BE count by adding 1.
4095 const SCEV *TCMul = getAddExpr(ExitCount,
4096 getConstant(ExitCount->getType(), 1));
4097 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4098 // to factor simple cases.
4099 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4100 TCMul = Mul->getOperand(0);
4102 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4106 ConstantInt *Result = MulC->getValue();
4108 // Guard against huge trip counts (this requires checking
4109 // for zero to handle the case where the trip count == -1 and the
4111 if (!Result || Result->getValue().getActiveBits() > 32 ||
4112 Result->getValue().getActiveBits() == 0)
4115 return (unsigned)Result->getZExtValue();
4118 // getExitCount - Get the expression for the number of loop iterations for which
4119 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4120 // SCEVCouldNotCompute.
4121 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4122 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4125 /// getBackedgeTakenCount - If the specified loop has a predictable
4126 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4127 /// object. The backedge-taken count is the number of times the loop header
4128 /// will be branched to from within the loop. This is one less than the
4129 /// trip count of the loop, since it doesn't count the first iteration,
4130 /// when the header is branched to from outside the loop.
4132 /// Note that it is not valid to call this method on a loop without a
4133 /// loop-invariant backedge-taken count (see
4134 /// hasLoopInvariantBackedgeTakenCount).
4136 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4137 return getBackedgeTakenInfo(L).getExact(this);
4140 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4141 /// return the least SCEV value that is known never to be less than the
4142 /// actual backedge taken count.
4143 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4144 return getBackedgeTakenInfo(L).getMax(this);
4147 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4148 /// onto the given Worklist.
4150 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4151 BasicBlock *Header = L->getHeader();
4153 // Push all Loop-header PHIs onto the Worklist stack.
4154 for (BasicBlock::iterator I = Header->begin();
4155 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4156 Worklist.push_back(PN);
4159 const ScalarEvolution::BackedgeTakenInfo &
4160 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4161 // Initially insert an invalid entry for this loop. If the insertion
4162 // succeeds, proceed to actually compute a backedge-taken count and
4163 // update the value. The temporary CouldNotCompute value tells SCEV
4164 // code elsewhere that it shouldn't attempt to request a new
4165 // backedge-taken count, which could result in infinite recursion.
4166 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4167 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4169 return Pair.first->second;
4171 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4172 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4173 // must be cleared in this scope.
4174 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4176 if (Result.getExact(this) != getCouldNotCompute()) {
4177 assert(isLoopInvariant(Result.getExact(this), L) &&
4178 isLoopInvariant(Result.getMax(this), L) &&
4179 "Computed backedge-taken count isn't loop invariant for loop!");
4180 ++NumTripCountsComputed;
4182 else if (Result.getMax(this) == getCouldNotCompute() &&
4183 isa<PHINode>(L->getHeader()->begin())) {
4184 // Only count loops that have phi nodes as not being computable.
4185 ++NumTripCountsNotComputed;
4188 // Now that we know more about the trip count for this loop, forget any
4189 // existing SCEV values for PHI nodes in this loop since they are only
4190 // conservative estimates made without the benefit of trip count
4191 // information. This is similar to the code in forgetLoop, except that
4192 // it handles SCEVUnknown PHI nodes specially.
4193 if (Result.hasAnyInfo()) {
4194 SmallVector<Instruction *, 16> Worklist;
4195 PushLoopPHIs(L, Worklist);
4197 SmallPtrSet<Instruction *, 8> Visited;
4198 while (!Worklist.empty()) {
4199 Instruction *I = Worklist.pop_back_val();
4200 if (!Visited.insert(I)) continue;
4202 ValueExprMapType::iterator It =
4203 ValueExprMap.find_as(static_cast<Value *>(I));
4204 if (It != ValueExprMap.end()) {
4205 const SCEV *Old = It->second;
4207 // SCEVUnknown for a PHI either means that it has an unrecognized
4208 // structure, or it's a PHI that's in the progress of being computed
4209 // by createNodeForPHI. In the former case, additional loop trip
4210 // count information isn't going to change anything. In the later
4211 // case, createNodeForPHI will perform the necessary updates on its
4212 // own when it gets to that point.
4213 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4214 forgetMemoizedResults(Old);
4215 ValueExprMap.erase(It);
4217 if (PHINode *PN = dyn_cast<PHINode>(I))
4218 ConstantEvolutionLoopExitValue.erase(PN);
4221 PushDefUseChildren(I, Worklist);
4225 // Re-lookup the insert position, since the call to
4226 // ComputeBackedgeTakenCount above could result in a
4227 // recusive call to getBackedgeTakenInfo (on a different
4228 // loop), which would invalidate the iterator computed
4230 return BackedgeTakenCounts.find(L)->second = Result;
4233 /// forgetLoop - This method should be called by the client when it has
4234 /// changed a loop in a way that may effect ScalarEvolution's ability to
4235 /// compute a trip count, or if the loop is deleted.
4236 void ScalarEvolution::forgetLoop(const Loop *L) {
4237 // Drop any stored trip count value.
4238 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4239 BackedgeTakenCounts.find(L);
4240 if (BTCPos != BackedgeTakenCounts.end()) {
4241 BTCPos->second.clear();
4242 BackedgeTakenCounts.erase(BTCPos);
4245 // Drop information about expressions based on loop-header PHIs.
4246 SmallVector<Instruction *, 16> Worklist;
4247 PushLoopPHIs(L, Worklist);
4249 SmallPtrSet<Instruction *, 8> Visited;
4250 while (!Worklist.empty()) {
4251 Instruction *I = Worklist.pop_back_val();
4252 if (!Visited.insert(I)) continue;
4254 ValueExprMapType::iterator It =
4255 ValueExprMap.find_as(static_cast<Value *>(I));
4256 if (It != ValueExprMap.end()) {
4257 forgetMemoizedResults(It->second);
4258 ValueExprMap.erase(It);
4259 if (PHINode *PN = dyn_cast<PHINode>(I))
4260 ConstantEvolutionLoopExitValue.erase(PN);
4263 PushDefUseChildren(I, Worklist);
4266 // Forget all contained loops too, to avoid dangling entries in the
4267 // ValuesAtScopes map.
4268 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4272 /// forgetValue - This method should be called by the client when it has
4273 /// changed a value in a way that may effect its value, or which may
4274 /// disconnect it from a def-use chain linking it to a loop.
4275 void ScalarEvolution::forgetValue(Value *V) {
4276 Instruction *I = dyn_cast<Instruction>(V);
4279 // Drop information about expressions based on loop-header PHIs.
4280 SmallVector<Instruction *, 16> Worklist;
4281 Worklist.push_back(I);
4283 SmallPtrSet<Instruction *, 8> Visited;
4284 while (!Worklist.empty()) {
4285 I = Worklist.pop_back_val();
4286 if (!Visited.insert(I)) continue;
4288 ValueExprMapType::iterator It =
4289 ValueExprMap.find_as(static_cast<Value *>(I));
4290 if (It != ValueExprMap.end()) {
4291 forgetMemoizedResults(It->second);
4292 ValueExprMap.erase(It);
4293 if (PHINode *PN = dyn_cast<PHINode>(I))
4294 ConstantEvolutionLoopExitValue.erase(PN);
4297 PushDefUseChildren(I, Worklist);
4301 /// getExact - Get the exact loop backedge taken count considering all loop
4302 /// exits. A computable result can only be return for loops with a single exit.
4303 /// Returning the minimum taken count among all exits is incorrect because one
4304 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4305 /// the limit of each loop test is never skipped. This is a valid assumption as
4306 /// long as the loop exits via that test. For precise results, it is the
4307 /// caller's responsibility to specify the relevant loop exit using
4308 /// getExact(ExitingBlock, SE).
4310 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4311 // If any exits were not computable, the loop is not computable.
4312 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4314 // We need exactly one computable exit.
4315 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4316 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4318 const SCEV *BECount = nullptr;
4319 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4320 ENT != nullptr; ENT = ENT->getNextExit()) {
4322 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4325 BECount = ENT->ExactNotTaken;
4326 else if (BECount != ENT->ExactNotTaken)
4327 return SE->getCouldNotCompute();
4329 assert(BECount && "Invalid not taken count for loop exit");
4333 /// getExact - Get the exact not taken count for this loop exit.
4335 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4336 ScalarEvolution *SE) const {
4337 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4338 ENT != nullptr; ENT = ENT->getNextExit()) {
4340 if (ENT->ExitingBlock == ExitingBlock)
4341 return ENT->ExactNotTaken;
4343 return SE->getCouldNotCompute();
4346 /// getMax - Get the max backedge taken count for the loop.
4348 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4349 return Max ? Max : SE->getCouldNotCompute();
4352 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4353 ScalarEvolution *SE) const {
4354 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4357 if (!ExitNotTaken.ExitingBlock)
4360 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4361 ENT != nullptr; ENT = ENT->getNextExit()) {
4363 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4364 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4371 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4372 /// computable exit into a persistent ExitNotTakenInfo array.
4373 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4374 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4375 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4378 ExitNotTaken.setIncomplete();
4380 unsigned NumExits = ExitCounts.size();
4381 if (NumExits == 0) return;
4383 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4384 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4385 if (NumExits == 1) return;
4387 // Handle the rare case of multiple computable exits.
4388 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4390 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4391 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4392 PrevENT->setNextExit(ENT);
4393 ENT->ExitingBlock = ExitCounts[i].first;
4394 ENT->ExactNotTaken = ExitCounts[i].second;
4398 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4399 void ScalarEvolution::BackedgeTakenInfo::clear() {
4400 ExitNotTaken.ExitingBlock = nullptr;
4401 ExitNotTaken.ExactNotTaken = nullptr;
4402 delete[] ExitNotTaken.getNextExit();
4405 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4406 /// of the specified loop will execute.
4407 ScalarEvolution::BackedgeTakenInfo
4408 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4409 SmallVector<BasicBlock *, 8> ExitingBlocks;
4410 L->getExitingBlocks(ExitingBlocks);
4412 // Examine all exits and pick the most conservative values.
4413 const SCEV *MaxBECount = getCouldNotCompute();
4414 bool CouldComputeBECount = true;
4415 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4416 const SCEV *LatchMaxCount = nullptr;
4417 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4418 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4419 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4420 if (EL.Exact == getCouldNotCompute())
4421 // We couldn't compute an exact value for this exit, so
4422 // we won't be able to compute an exact value for the loop.
4423 CouldComputeBECount = false;
4425 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4427 if (MaxBECount == getCouldNotCompute())
4428 MaxBECount = EL.Max;
4429 else if (EL.Max != getCouldNotCompute()) {
4430 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4431 // skip some loop tests. Taking the max over the exits is sufficiently
4432 // conservative. TODO: We could do better taking into consideration
4433 // non-latch exits that dominate the latch.
4434 if (EL.MustExit && ExitingBlocks[i] == Latch)
4435 LatchMaxCount = EL.Max;
4437 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4440 // Be more precise in the easy case of a loop latch that must exit.
4441 if (LatchMaxCount) {
4442 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, LatchMaxCount);
4444 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4447 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4448 /// loop will execute if it exits via the specified block.
4449 ScalarEvolution::ExitLimit
4450 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4452 // Okay, we've chosen an exiting block. See what condition causes us to
4453 // exit at this block and remember the exit block and whether all other targets
4454 // lead to the loop header.
4455 bool MustExecuteLoopHeader = true;
4456 BasicBlock *Exit = nullptr;
4457 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4459 if (!L->contains(*SI)) {
4460 if (Exit) // Multiple exit successors.
4461 return getCouldNotCompute();
4463 } else if (*SI != L->getHeader()) {
4464 MustExecuteLoopHeader = false;
4467 // At this point, we know we have a conditional branch that determines whether
4468 // the loop is exited. However, we don't know if the branch is executed each
4469 // time through the loop. If not, then the execution count of the branch will
4470 // not be equal to the trip count of the loop.
4472 // Currently we check for this by checking to see if the Exit branch goes to
4473 // the loop header. If so, we know it will always execute the same number of
4474 // times as the loop. We also handle the case where the exit block *is* the
4475 // loop header. This is common for un-rotated loops.
4477 // If both of those tests fail, walk up the unique predecessor chain to the
4478 // header, stopping if there is an edge that doesn't exit the loop. If the
4479 // header is reached, the execution count of the branch will be equal to the
4480 // trip count of the loop.
4482 // More extensive analysis could be done to handle more cases here.
4484 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4485 // The simple checks failed, try climbing the unique predecessor chain
4486 // up to the header.
4488 for (BasicBlock *BB = ExitingBlock; BB; ) {
4489 BasicBlock *Pred = BB->getUniquePredecessor();
4491 return getCouldNotCompute();
4492 TerminatorInst *PredTerm = Pred->getTerminator();
4493 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4494 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4497 // If the predecessor has a successor that isn't BB and isn't
4498 // outside the loop, assume the worst.
4499 if (L->contains(PredSucc))
4500 return getCouldNotCompute();
4502 if (Pred == L->getHeader()) {
4509 return getCouldNotCompute();
4512 TerminatorInst *Term = ExitingBlock->getTerminator();
4513 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4514 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4515 // Proceed to the next level to examine the exit condition expression.
4516 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4517 BI->getSuccessor(1),
4518 /*IsSubExpr=*/false);
4521 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4522 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4523 /*IsSubExpr=*/false);
4525 return getCouldNotCompute();
4528 /// ComputeExitLimitFromCond - Compute the number of times the
4529 /// backedge of the specified loop will execute if its exit condition
4530 /// were a conditional branch of ExitCond, TBB, and FBB.
4532 /// @param IsSubExpr is true if ExitCond does not directly control the exit
4533 /// branch. In this case, we cannot assume that the loop only exits when the
4534 /// condition is true and cannot infer that failing to meet the condition prior
4535 /// to integer wraparound results in undefined behavior.
4536 ScalarEvolution::ExitLimit
4537 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4542 // Check if the controlling expression for this loop is an And or Or.
4543 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4544 if (BO->getOpcode() == Instruction::And) {
4545 // Recurse on the operands of the and.
4546 bool EitherMayExit = L->contains(TBB);
4547 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4548 IsSubExpr || EitherMayExit);
4549 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4550 IsSubExpr || EitherMayExit);
4551 const SCEV *BECount = getCouldNotCompute();
4552 const SCEV *MaxBECount = getCouldNotCompute();
4553 bool MustExit = false;
4554 if (EitherMayExit) {
4555 // Both conditions must be true for the loop to continue executing.
4556 // Choose the less conservative count.
4557 if (EL0.Exact == getCouldNotCompute() ||
4558 EL1.Exact == getCouldNotCompute())
4559 BECount = getCouldNotCompute();
4561 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4562 if (EL0.Max == getCouldNotCompute())
4563 MaxBECount = EL1.Max;
4564 else if (EL1.Max == getCouldNotCompute())
4565 MaxBECount = EL0.Max;
4567 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4568 MustExit = EL0.MustExit || EL1.MustExit;
4570 // Both conditions must be true at the same time for the loop to exit.
4571 // For now, be conservative.
4572 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4573 if (EL0.Max == EL1.Max)
4574 MaxBECount = EL0.Max;
4575 if (EL0.Exact == EL1.Exact)
4576 BECount = EL0.Exact;
4577 MustExit = EL0.MustExit && EL1.MustExit;
4580 return ExitLimit(BECount, MaxBECount, MustExit);
4582 if (BO->getOpcode() == Instruction::Or) {
4583 // Recurse on the operands of the or.
4584 bool EitherMayExit = L->contains(FBB);
4585 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4586 IsSubExpr || EitherMayExit);
4587 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4588 IsSubExpr || EitherMayExit);
4589 const SCEV *BECount = getCouldNotCompute();
4590 const SCEV *MaxBECount = getCouldNotCompute();
4591 bool MustExit = false;
4592 if (EitherMayExit) {
4593 // Both conditions must be false for the loop to continue executing.
4594 // Choose the less conservative count.
4595 if (EL0.Exact == getCouldNotCompute() ||
4596 EL1.Exact == getCouldNotCompute())
4597 BECount = getCouldNotCompute();
4599 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4600 if (EL0.Max == getCouldNotCompute())
4601 MaxBECount = EL1.Max;
4602 else if (EL1.Max == getCouldNotCompute())
4603 MaxBECount = EL0.Max;
4605 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4606 MustExit = EL0.MustExit || EL1.MustExit;
4608 // Both conditions must be false at the same time for the loop to exit.
4609 // For now, be conservative.
4610 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4611 if (EL0.Max == EL1.Max)
4612 MaxBECount = EL0.Max;
4613 if (EL0.Exact == EL1.Exact)
4614 BECount = EL0.Exact;
4615 MustExit = EL0.MustExit && EL1.MustExit;
4618 return ExitLimit(BECount, MaxBECount, MustExit);
4622 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4623 // Proceed to the next level to examine the icmp.
4624 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4625 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, IsSubExpr);
4627 // Check for a constant condition. These are normally stripped out by
4628 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4629 // preserve the CFG and is temporarily leaving constant conditions
4631 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4632 if (L->contains(FBB) == !CI->getZExtValue())
4633 // The backedge is always taken.
4634 return getCouldNotCompute();
4636 // The backedge is never taken.
4637 return getConstant(CI->getType(), 0);
4640 // If it's not an integer or pointer comparison then compute it the hard way.
4641 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4644 /// ComputeExitLimitFromICmp - Compute the number of times the
4645 /// backedge of the specified loop will execute if its exit condition
4646 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4647 ScalarEvolution::ExitLimit
4648 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4654 // If the condition was exit on true, convert the condition to exit on false
4655 ICmpInst::Predicate Cond;
4656 if (!L->contains(FBB))
4657 Cond = ExitCond->getPredicate();
4659 Cond = ExitCond->getInversePredicate();
4661 // Handle common loops like: for (X = "string"; *X; ++X)
4662 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4663 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4665 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4666 if (ItCnt.hasAnyInfo())
4670 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4671 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4673 // Try to evaluate any dependencies out of the loop.
4674 LHS = getSCEVAtScope(LHS, L);
4675 RHS = getSCEVAtScope(RHS, L);
4677 // At this point, we would like to compute how many iterations of the
4678 // loop the predicate will return true for these inputs.
4679 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4680 // If there is a loop-invariant, force it into the RHS.
4681 std::swap(LHS, RHS);
4682 Cond = ICmpInst::getSwappedPredicate(Cond);
4685 // Simplify the operands before analyzing them.
4686 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4688 // If we have a comparison of a chrec against a constant, try to use value
4689 // ranges to answer this query.
4690 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4691 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4692 if (AddRec->getLoop() == L) {
4693 // Form the constant range.
4694 ConstantRange CompRange(
4695 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4697 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4698 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4702 case ICmpInst::ICMP_NE: { // while (X != Y)
4703 // Convert to: while (X-Y != 0)
4704 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4705 if (EL.hasAnyInfo()) return EL;
4708 case ICmpInst::ICMP_EQ: { // while (X == Y)
4709 // Convert to: while (X-Y == 0)
4710 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4711 if (EL.hasAnyInfo()) return EL;
4714 case ICmpInst::ICMP_SLT:
4715 case ICmpInst::ICMP_ULT: { // while (X < Y)
4716 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
4717 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, IsSubExpr);
4718 if (EL.hasAnyInfo()) return EL;
4721 case ICmpInst::ICMP_SGT:
4722 case ICmpInst::ICMP_UGT: { // while (X > Y)
4723 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
4724 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, IsSubExpr);
4725 if (EL.hasAnyInfo()) return EL;
4730 dbgs() << "ComputeBackedgeTakenCount ";
4731 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4732 dbgs() << "[unsigned] ";
4733 dbgs() << *LHS << " "
4734 << Instruction::getOpcodeName(Instruction::ICmp)
4735 << " " << *RHS << "\n";
4739 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4742 ScalarEvolution::ExitLimit
4743 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
4745 BasicBlock *ExitingBlock,
4747 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
4749 // Give up if the exit is the default dest of a switch.
4750 if (Switch->getDefaultDest() == ExitingBlock)
4751 return getCouldNotCompute();
4753 assert(L->contains(Switch->getDefaultDest()) &&
4754 "Default case must not exit the loop!");
4755 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
4756 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
4758 // while (X != Y) --> while (X-Y != 0)
4759 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4760 if (EL.hasAnyInfo())
4763 return getCouldNotCompute();
4766 static ConstantInt *
4767 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4768 ScalarEvolution &SE) {
4769 const SCEV *InVal = SE.getConstant(C);
4770 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4771 assert(isa<SCEVConstant>(Val) &&
4772 "Evaluation of SCEV at constant didn't fold correctly?");
4773 return cast<SCEVConstant>(Val)->getValue();
4776 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4777 /// 'icmp op load X, cst', try to see if we can compute the backedge
4778 /// execution count.
4779 ScalarEvolution::ExitLimit
4780 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4784 ICmpInst::Predicate predicate) {
4786 if (LI->isVolatile()) return getCouldNotCompute();
4788 // Check to see if the loaded pointer is a getelementptr of a global.
4789 // TODO: Use SCEV instead of manually grubbing with GEPs.
4790 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4791 if (!GEP) return getCouldNotCompute();
4793 // Make sure that it is really a constant global we are gepping, with an
4794 // initializer, and make sure the first IDX is really 0.
4795 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4796 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4797 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4798 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4799 return getCouldNotCompute();
4801 // Okay, we allow one non-constant index into the GEP instruction.
4802 Value *VarIdx = nullptr;
4803 std::vector<Constant*> Indexes;
4804 unsigned VarIdxNum = 0;
4805 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4806 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4807 Indexes.push_back(CI);
4808 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4809 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4810 VarIdx = GEP->getOperand(i);
4812 Indexes.push_back(nullptr);
4815 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4817 return getCouldNotCompute();
4819 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4820 // Check to see if X is a loop variant variable value now.
4821 const SCEV *Idx = getSCEV(VarIdx);
4822 Idx = getSCEVAtScope(Idx, L);
4824 // We can only recognize very limited forms of loop index expressions, in
4825 // particular, only affine AddRec's like {C1,+,C2}.
4826 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4827 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4828 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4829 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4830 return getCouldNotCompute();
4832 unsigned MaxSteps = MaxBruteForceIterations;
4833 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4834 ConstantInt *ItCst = ConstantInt::get(
4835 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4836 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4838 // Form the GEP offset.
4839 Indexes[VarIdxNum] = Val;
4841 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4843 if (!Result) break; // Cannot compute!
4845 // Evaluate the condition for this iteration.
4846 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4847 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4848 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4850 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4851 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4854 ++NumArrayLenItCounts;
4855 return getConstant(ItCst); // Found terminating iteration!
4858 return getCouldNotCompute();
4862 /// CanConstantFold - Return true if we can constant fold an instruction of the
4863 /// specified type, assuming that all operands were constants.
4864 static bool CanConstantFold(const Instruction *I) {
4865 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4866 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4870 if (const CallInst *CI = dyn_cast<CallInst>(I))
4871 if (const Function *F = CI->getCalledFunction())
4872 return canConstantFoldCallTo(F);
4876 /// Determine whether this instruction can constant evolve within this loop
4877 /// assuming its operands can all constant evolve.
4878 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4879 // An instruction outside of the loop can't be derived from a loop PHI.
4880 if (!L->contains(I)) return false;
4882 if (isa<PHINode>(I)) {
4883 if (L->getHeader() == I->getParent())
4886 // We don't currently keep track of the control flow needed to evaluate
4887 // PHIs, so we cannot handle PHIs inside of loops.
4891 // If we won't be able to constant fold this expression even if the operands
4892 // are constants, bail early.
4893 return CanConstantFold(I);
4896 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4897 /// recursing through each instruction operand until reaching a loop header phi.
4899 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4900 DenseMap<Instruction *, PHINode *> &PHIMap) {
4902 // Otherwise, we can evaluate this instruction if all of its operands are
4903 // constant or derived from a PHI node themselves.
4904 PHINode *PHI = nullptr;
4905 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4906 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4908 if (isa<Constant>(*OpI)) continue;
4910 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4911 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
4913 PHINode *P = dyn_cast<PHINode>(OpInst);
4915 // If this operand is already visited, reuse the prior result.
4916 // We may have P != PHI if this is the deepest point at which the
4917 // inconsistent paths meet.
4918 P = PHIMap.lookup(OpInst);
4920 // Recurse and memoize the results, whether a phi is found or not.
4921 // This recursive call invalidates pointers into PHIMap.
4922 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4926 return nullptr; // Not evolving from PHI
4927 if (PHI && PHI != P)
4928 return nullptr; // Evolving from multiple different PHIs.
4931 // This is a expression evolving from a constant PHI!
4935 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4936 /// in the loop that V is derived from. We allow arbitrary operations along the
4937 /// way, but the operands of an operation must either be constants or a value
4938 /// derived from a constant PHI. If this expression does not fit with these
4939 /// constraints, return null.
4940 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4941 Instruction *I = dyn_cast<Instruction>(V);
4942 if (!I || !canConstantEvolve(I, L)) return nullptr;
4944 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4948 // Record non-constant instructions contained by the loop.
4949 DenseMap<Instruction *, PHINode *> PHIMap;
4950 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4953 /// EvaluateExpression - Given an expression that passes the
4954 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4955 /// in the loop has the value PHIVal. If we can't fold this expression for some
4956 /// reason, return null.
4957 static Constant *EvaluateExpression(Value *V, const Loop *L,
4958 DenseMap<Instruction *, Constant *> &Vals,
4959 const DataLayout *DL,
4960 const TargetLibraryInfo *TLI) {
4961 // Convenient constant check, but redundant for recursive calls.
4962 if (Constant *C = dyn_cast<Constant>(V)) return C;
4963 Instruction *I = dyn_cast<Instruction>(V);
4964 if (!I) return nullptr;
4966 if (Constant *C = Vals.lookup(I)) return C;
4968 // An instruction inside the loop depends on a value outside the loop that we
4969 // weren't given a mapping for, or a value such as a call inside the loop.
4970 if (!canConstantEvolve(I, L)) return nullptr;
4972 // An unmapped PHI can be due to a branch or another loop inside this loop,
4973 // or due to this not being the initial iteration through a loop where we
4974 // couldn't compute the evolution of this particular PHI last time.
4975 if (isa<PHINode>(I)) return nullptr;
4977 std::vector<Constant*> Operands(I->getNumOperands());
4979 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4980 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4982 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4983 if (!Operands[i]) return nullptr;
4986 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
4988 if (!C) return nullptr;
4992 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4993 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4994 Operands[1], DL, TLI);
4995 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4996 if (!LI->isVolatile())
4997 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
4999 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5003 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5004 /// in the header of its containing loop, we know the loop executes a
5005 /// constant number of times, and the PHI node is just a recurrence
5006 /// involving constants, fold it.
5008 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5011 DenseMap<PHINode*, Constant*>::const_iterator I =
5012 ConstantEvolutionLoopExitValue.find(PN);
5013 if (I != ConstantEvolutionLoopExitValue.end())
5016 if (BEs.ugt(MaxBruteForceIterations))
5017 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5019 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5021 DenseMap<Instruction *, Constant *> CurrentIterVals;
5022 BasicBlock *Header = L->getHeader();
5023 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5025 // Since the loop is canonicalized, the PHI node must have two entries. One
5026 // entry must be a constant (coming in from outside of the loop), and the
5027 // second must be derived from the same PHI.
5028 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5029 PHINode *PHI = nullptr;
5030 for (BasicBlock::iterator I = Header->begin();
5031 (PHI = dyn_cast<PHINode>(I)); ++I) {
5032 Constant *StartCST =
5033 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5034 if (!StartCST) continue;
5035 CurrentIterVals[PHI] = StartCST;
5037 if (!CurrentIterVals.count(PN))
5038 return RetVal = nullptr;
5040 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5042 // Execute the loop symbolically to determine the exit value.
5043 if (BEs.getActiveBits() >= 32)
5044 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5046 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5047 unsigned IterationNum = 0;
5048 for (; ; ++IterationNum) {
5049 if (IterationNum == NumIterations)
5050 return RetVal = CurrentIterVals[PN]; // Got exit value!
5052 // Compute the value of the PHIs for the next iteration.
5053 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5054 DenseMap<Instruction *, Constant *> NextIterVals;
5055 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5058 return nullptr; // Couldn't evaluate!
5059 NextIterVals[PN] = NextPHI;
5061 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5063 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5064 // cease to be able to evaluate one of them or if they stop evolving,
5065 // because that doesn't necessarily prevent us from computing PN.
5066 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5067 for (DenseMap<Instruction *, Constant *>::const_iterator
5068 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5069 PHINode *PHI = dyn_cast<PHINode>(I->first);
5070 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5071 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5073 // We use two distinct loops because EvaluateExpression may invalidate any
5074 // iterators into CurrentIterVals.
5075 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5076 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5077 PHINode *PHI = I->first;
5078 Constant *&NextPHI = NextIterVals[PHI];
5079 if (!NextPHI) { // Not already computed.
5080 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5081 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5083 if (NextPHI != I->second)
5084 StoppedEvolving = false;
5087 // If all entries in CurrentIterVals == NextIterVals then we can stop
5088 // iterating, the loop can't continue to change.
5089 if (StoppedEvolving)
5090 return RetVal = CurrentIterVals[PN];
5092 CurrentIterVals.swap(NextIterVals);
5096 /// ComputeExitCountExhaustively - If the loop is known to execute a
5097 /// constant number of times (the condition evolves only from constants),
5098 /// try to evaluate a few iterations of the loop until we get the exit
5099 /// condition gets a value of ExitWhen (true or false). If we cannot
5100 /// evaluate the trip count of the loop, return getCouldNotCompute().
5101 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5104 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5105 if (!PN) return getCouldNotCompute();
5107 // If the loop is canonicalized, the PHI will have exactly two entries.
5108 // That's the only form we support here.
5109 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5111 DenseMap<Instruction *, Constant *> CurrentIterVals;
5112 BasicBlock *Header = L->getHeader();
5113 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5115 // One entry must be a constant (coming in from outside of the loop), and the
5116 // second must be derived from the same PHI.
5117 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5118 PHINode *PHI = nullptr;
5119 for (BasicBlock::iterator I = Header->begin();
5120 (PHI = dyn_cast<PHINode>(I)); ++I) {
5121 Constant *StartCST =
5122 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5123 if (!StartCST) continue;
5124 CurrentIterVals[PHI] = StartCST;
5126 if (!CurrentIterVals.count(PN))
5127 return getCouldNotCompute();
5129 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5130 // the loop symbolically to determine when the condition gets a value of
5133 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5134 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5135 ConstantInt *CondVal =
5136 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5139 // Couldn't symbolically evaluate.
5140 if (!CondVal) return getCouldNotCompute();
5142 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5143 ++NumBruteForceTripCountsComputed;
5144 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5147 // Update all the PHI nodes for the next iteration.
5148 DenseMap<Instruction *, Constant *> NextIterVals;
5150 // Create a list of which PHIs we need to compute. We want to do this before
5151 // calling EvaluateExpression on them because that may invalidate iterators
5152 // into CurrentIterVals.
5153 SmallVector<PHINode *, 8> PHIsToCompute;
5154 for (DenseMap<Instruction *, Constant *>::const_iterator
5155 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5156 PHINode *PHI = dyn_cast<PHINode>(I->first);
5157 if (!PHI || PHI->getParent() != Header) continue;
5158 PHIsToCompute.push_back(PHI);
5160 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5161 E = PHIsToCompute.end(); I != E; ++I) {
5163 Constant *&NextPHI = NextIterVals[PHI];
5164 if (NextPHI) continue; // Already computed!
5166 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5167 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5169 CurrentIterVals.swap(NextIterVals);
5172 // Too many iterations were needed to evaluate.
5173 return getCouldNotCompute();
5176 /// getSCEVAtScope - Return a SCEV expression for the specified value
5177 /// at the specified scope in the program. The L value specifies a loop
5178 /// nest to evaluate the expression at, where null is the top-level or a
5179 /// specified loop is immediately inside of the loop.
5181 /// This method can be used to compute the exit value for a variable defined
5182 /// in a loop by querying what the value will hold in the parent loop.
5184 /// In the case that a relevant loop exit value cannot be computed, the
5185 /// original value V is returned.
5186 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5187 // Check to see if we've folded this expression at this loop before.
5188 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5189 for (unsigned u = 0; u < Values.size(); u++) {
5190 if (Values[u].first == L)
5191 return Values[u].second ? Values[u].second : V;
5193 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5194 // Otherwise compute it.
5195 const SCEV *C = computeSCEVAtScope(V, L);
5196 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5197 for (unsigned u = Values2.size(); u > 0; u--) {
5198 if (Values2[u - 1].first == L) {
5199 Values2[u - 1].second = C;
5206 /// This builds up a Constant using the ConstantExpr interface. That way, we
5207 /// will return Constants for objects which aren't represented by a
5208 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5209 /// Returns NULL if the SCEV isn't representable as a Constant.
5210 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5211 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5212 case scCouldNotCompute:
5216 return cast<SCEVConstant>(V)->getValue();
5218 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5219 case scSignExtend: {
5220 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5221 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5222 return ConstantExpr::getSExt(CastOp, SS->getType());
5225 case scZeroExtend: {
5226 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5227 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5228 return ConstantExpr::getZExt(CastOp, SZ->getType());
5232 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5233 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5234 return ConstantExpr::getTrunc(CastOp, ST->getType());
5238 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5239 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5240 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5241 unsigned AS = PTy->getAddressSpace();
5242 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5243 C = ConstantExpr::getBitCast(C, DestPtrTy);
5245 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5246 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5247 if (!C2) return nullptr;
5250 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5251 unsigned AS = C2->getType()->getPointerAddressSpace();
5253 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5254 // The offsets have been converted to bytes. We can add bytes to an
5255 // i8* by GEP with the byte count in the first index.
5256 C = ConstantExpr::getBitCast(C, DestPtrTy);
5259 // Don't bother trying to sum two pointers. We probably can't
5260 // statically compute a load that results from it anyway.
5261 if (C2->getType()->isPointerTy())
5264 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5265 if (PTy->getElementType()->isStructTy())
5266 C2 = ConstantExpr::getIntegerCast(
5267 C2, Type::getInt32Ty(C->getContext()), true);
5268 C = ConstantExpr::getGetElementPtr(C, C2);
5270 C = ConstantExpr::getAdd(C, C2);
5277 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5278 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5279 // Don't bother with pointers at all.
5280 if (C->getType()->isPointerTy()) return nullptr;
5281 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5282 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5283 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5284 C = ConstantExpr::getMul(C, C2);
5291 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5292 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5293 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5294 if (LHS->getType() == RHS->getType())
5295 return ConstantExpr::getUDiv(LHS, RHS);
5300 break; // TODO: smax, umax.
5305 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5306 if (isa<SCEVConstant>(V)) return V;
5308 // If this instruction is evolved from a constant-evolving PHI, compute the
5309 // exit value from the loop without using SCEVs.
5310 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5311 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5312 const Loop *LI = (*this->LI)[I->getParent()];
5313 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5314 if (PHINode *PN = dyn_cast<PHINode>(I))
5315 if (PN->getParent() == LI->getHeader()) {
5316 // Okay, there is no closed form solution for the PHI node. Check
5317 // to see if the loop that contains it has a known backedge-taken
5318 // count. If so, we may be able to force computation of the exit
5320 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5321 if (const SCEVConstant *BTCC =
5322 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5323 // Okay, we know how many times the containing loop executes. If
5324 // this is a constant evolving PHI node, get the final value at
5325 // the specified iteration number.
5326 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5327 BTCC->getValue()->getValue(),
5329 if (RV) return getSCEV(RV);
5333 // Okay, this is an expression that we cannot symbolically evaluate
5334 // into a SCEV. Check to see if it's possible to symbolically evaluate
5335 // the arguments into constants, and if so, try to constant propagate the
5336 // result. This is particularly useful for computing loop exit values.
5337 if (CanConstantFold(I)) {
5338 SmallVector<Constant *, 4> Operands;
5339 bool MadeImprovement = false;
5340 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5341 Value *Op = I->getOperand(i);
5342 if (Constant *C = dyn_cast<Constant>(Op)) {
5343 Operands.push_back(C);
5347 // If any of the operands is non-constant and if they are
5348 // non-integer and non-pointer, don't even try to analyze them
5349 // with scev techniques.
5350 if (!isSCEVable(Op->getType()))
5353 const SCEV *OrigV = getSCEV(Op);
5354 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5355 MadeImprovement |= OrigV != OpV;
5357 Constant *C = BuildConstantFromSCEV(OpV);
5359 if (C->getType() != Op->getType())
5360 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5364 Operands.push_back(C);
5367 // Check to see if getSCEVAtScope actually made an improvement.
5368 if (MadeImprovement) {
5369 Constant *C = nullptr;
5370 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5371 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5372 Operands[0], Operands[1], DL,
5374 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5375 if (!LI->isVolatile())
5376 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5378 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5386 // This is some other type of SCEVUnknown, just return it.
5390 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5391 // Avoid performing the look-up in the common case where the specified
5392 // expression has no loop-variant portions.
5393 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5394 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5395 if (OpAtScope != Comm->getOperand(i)) {
5396 // Okay, at least one of these operands is loop variant but might be
5397 // foldable. Build a new instance of the folded commutative expression.
5398 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5399 Comm->op_begin()+i);
5400 NewOps.push_back(OpAtScope);
5402 for (++i; i != e; ++i) {
5403 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5404 NewOps.push_back(OpAtScope);
5406 if (isa<SCEVAddExpr>(Comm))
5407 return getAddExpr(NewOps);
5408 if (isa<SCEVMulExpr>(Comm))
5409 return getMulExpr(NewOps);
5410 if (isa<SCEVSMaxExpr>(Comm))
5411 return getSMaxExpr(NewOps);
5412 if (isa<SCEVUMaxExpr>(Comm))
5413 return getUMaxExpr(NewOps);
5414 llvm_unreachable("Unknown commutative SCEV type!");
5417 // If we got here, all operands are loop invariant.
5421 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5422 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5423 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5424 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5425 return Div; // must be loop invariant
5426 return getUDivExpr(LHS, RHS);
5429 // If this is a loop recurrence for a loop that does not contain L, then we
5430 // are dealing with the final value computed by the loop.
5431 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5432 // First, attempt to evaluate each operand.
5433 // Avoid performing the look-up in the common case where the specified
5434 // expression has no loop-variant portions.
5435 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5436 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5437 if (OpAtScope == AddRec->getOperand(i))
5440 // Okay, at least one of these operands is loop variant but might be
5441 // foldable. Build a new instance of the folded commutative expression.
5442 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5443 AddRec->op_begin()+i);
5444 NewOps.push_back(OpAtScope);
5445 for (++i; i != e; ++i)
5446 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5448 const SCEV *FoldedRec =
5449 getAddRecExpr(NewOps, AddRec->getLoop(),
5450 AddRec->getNoWrapFlags(SCEV::FlagNW));
5451 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5452 // The addrec may be folded to a nonrecurrence, for example, if the
5453 // induction variable is multiplied by zero after constant folding. Go
5454 // ahead and return the folded value.
5460 // If the scope is outside the addrec's loop, evaluate it by using the
5461 // loop exit value of the addrec.
5462 if (!AddRec->getLoop()->contains(L)) {
5463 // To evaluate this recurrence, we need to know how many times the AddRec
5464 // loop iterates. Compute this now.
5465 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5466 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5468 // Then, evaluate the AddRec.
5469 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5475 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5476 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5477 if (Op == Cast->getOperand())
5478 return Cast; // must be loop invariant
5479 return getZeroExtendExpr(Op, Cast->getType());
5482 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5483 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5484 if (Op == Cast->getOperand())
5485 return Cast; // must be loop invariant
5486 return getSignExtendExpr(Op, Cast->getType());
5489 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5490 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5491 if (Op == Cast->getOperand())
5492 return Cast; // must be loop invariant
5493 return getTruncateExpr(Op, Cast->getType());
5496 llvm_unreachable("Unknown SCEV type!");
5499 /// getSCEVAtScope - This is a convenience function which does
5500 /// getSCEVAtScope(getSCEV(V), L).
5501 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5502 return getSCEVAtScope(getSCEV(V), L);
5505 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5506 /// following equation:
5508 /// A * X = B (mod N)
5510 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5511 /// A and B isn't important.
5513 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5514 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5515 ScalarEvolution &SE) {
5516 uint32_t BW = A.getBitWidth();
5517 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5518 assert(A != 0 && "A must be non-zero.");
5522 // The gcd of A and N may have only one prime factor: 2. The number of
5523 // trailing zeros in A is its multiplicity
5524 uint32_t Mult2 = A.countTrailingZeros();
5527 // 2. Check if B is divisible by D.
5529 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5530 // is not less than multiplicity of this prime factor for D.
5531 if (B.countTrailingZeros() < Mult2)
5532 return SE.getCouldNotCompute();
5534 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5537 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5538 // bit width during computations.
5539 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5540 APInt Mod(BW + 1, 0);
5541 Mod.setBit(BW - Mult2); // Mod = N / D
5542 APInt I = AD.multiplicativeInverse(Mod);
5544 // 4. Compute the minimum unsigned root of the equation:
5545 // I * (B / D) mod (N / D)
5546 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5548 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5550 return SE.getConstant(Result.trunc(BW));
5553 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5554 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5555 /// might be the same) or two SCEVCouldNotCompute objects.
5557 static std::pair<const SCEV *,const SCEV *>
5558 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5559 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5560 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5561 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5562 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5564 // We currently can only solve this if the coefficients are constants.
5565 if (!LC || !MC || !NC) {
5566 const SCEV *CNC = SE.getCouldNotCompute();
5567 return std::make_pair(CNC, CNC);
5570 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5571 const APInt &L = LC->getValue()->getValue();
5572 const APInt &M = MC->getValue()->getValue();
5573 const APInt &N = NC->getValue()->getValue();
5574 APInt Two(BitWidth, 2);
5575 APInt Four(BitWidth, 4);
5578 using namespace APIntOps;
5580 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5581 // The B coefficient is M-N/2
5585 // The A coefficient is N/2
5586 APInt A(N.sdiv(Two));
5588 // Compute the B^2-4ac term.
5591 SqrtTerm -= Four * (A * C);
5593 if (SqrtTerm.isNegative()) {
5594 // The loop is provably infinite.
5595 const SCEV *CNC = SE.getCouldNotCompute();
5596 return std::make_pair(CNC, CNC);
5599 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5600 // integer value or else APInt::sqrt() will assert.
5601 APInt SqrtVal(SqrtTerm.sqrt());
5603 // Compute the two solutions for the quadratic formula.
5604 // The divisions must be performed as signed divisions.
5607 if (TwoA.isMinValue()) {
5608 const SCEV *CNC = SE.getCouldNotCompute();
5609 return std::make_pair(CNC, CNC);
5612 LLVMContext &Context = SE.getContext();
5614 ConstantInt *Solution1 =
5615 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5616 ConstantInt *Solution2 =
5617 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5619 return std::make_pair(SE.getConstant(Solution1),
5620 SE.getConstant(Solution2));
5621 } // end APIntOps namespace
5624 /// HowFarToZero - Return the number of times a backedge comparing the specified
5625 /// value to zero will execute. If not computable, return CouldNotCompute.
5627 /// This is only used for loops with a "x != y" exit test. The exit condition is
5628 /// now expressed as a single expression, V = x-y. So the exit test is
5629 /// effectively V != 0. We know and take advantage of the fact that this
5630 /// expression only being used in a comparison by zero context.
5631 ScalarEvolution::ExitLimit
5632 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
5633 // If the value is a constant
5634 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5635 // If the value is already zero, the branch will execute zero times.
5636 if (C->getValue()->isZero()) return C;
5637 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5640 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5641 if (!AddRec || AddRec->getLoop() != L)
5642 return getCouldNotCompute();
5644 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5645 // the quadratic equation to solve it.
5646 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5647 std::pair<const SCEV *,const SCEV *> Roots =
5648 SolveQuadraticEquation(AddRec, *this);
5649 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5650 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5653 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5654 << " sol#2: " << *R2 << "\n";
5656 // Pick the smallest positive root value.
5657 if (ConstantInt *CB =
5658 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5661 if (CB->getZExtValue() == false)
5662 std::swap(R1, R2); // R1 is the minimum root now.
5664 // We can only use this value if the chrec ends up with an exact zero
5665 // value at this index. When solving for "X*X != 5", for example, we
5666 // should not accept a root of 2.
5667 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5669 return R1; // We found a quadratic root!
5672 return getCouldNotCompute();
5675 // Otherwise we can only handle this if it is affine.
5676 if (!AddRec->isAffine())
5677 return getCouldNotCompute();
5679 // If this is an affine expression, the execution count of this branch is
5680 // the minimum unsigned root of the following equation:
5682 // Start + Step*N = 0 (mod 2^BW)
5686 // Step*N = -Start (mod 2^BW)
5688 // where BW is the common bit width of Start and Step.
5690 // Get the initial value for the loop.
5691 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5692 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5694 // For now we handle only constant steps.
5696 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5697 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5698 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5699 // We have not yet seen any such cases.
5700 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5701 if (!StepC || StepC->getValue()->equalsInt(0))
5702 return getCouldNotCompute();
5704 // For positive steps (counting up until unsigned overflow):
5705 // N = -Start/Step (as unsigned)
5706 // For negative steps (counting down to zero):
5708 // First compute the unsigned distance from zero in the direction of Step.
5709 bool CountDown = StepC->getValue()->getValue().isNegative();
5710 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5712 // Handle unitary steps, which cannot wraparound.
5713 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5714 // N = Distance (as unsigned)
5715 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5716 ConstantRange CR = getUnsignedRange(Start);
5717 const SCEV *MaxBECount;
5718 if (!CountDown && CR.getUnsignedMin().isMinValue())
5719 // When counting up, the worst starting value is 1, not 0.
5720 MaxBECount = CR.getUnsignedMax().isMinValue()
5721 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5722 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5724 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5725 : -CR.getUnsignedMin());
5726 return ExitLimit(Distance, MaxBECount, /*MustExit=*/true);
5729 // If the recurrence is known not to wraparound, unsigned divide computes the
5730 // back edge count. (Ideally we would have an "isexact" bit for udiv). We know
5731 // that the value will either become zero (and thus the loop terminates), that
5732 // the loop will terminate through some other exit condition first, or that
5733 // the loop has undefined behavior. This means we can't "miss" the exit
5734 // value, even with nonunit stride, and exit later via the same branch. Note
5735 // that we can skip this exit if loop later exits via a different
5736 // branch. Hence MustExit=false.
5738 // This is only valid for expressions that directly compute the loop exit. It
5739 // is invalid for subexpressions in which the loop may exit through this
5740 // branch even if this subexpression is false. In that case, the trip count
5741 // computed by this udiv could be smaller than the number of well-defined
5743 if (!IsSubExpr && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5745 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5746 return ExitLimit(Exact, Exact, /*MustExit=*/false);
5749 // If Step is a power of two that evenly divides Start we know that the loop
5750 // will always terminate. Start may not be a constant so we just have the
5751 // number of trailing zeros available. This is safe even in presence of
5752 // overflow as the recurrence will overflow to exactly 0.
5753 const APInt &StepV = StepC->getValue()->getValue();
5754 if (StepV.isPowerOf2() &&
5755 GetMinTrailingZeros(getNegativeSCEV(Start)) >= StepV.countTrailingZeros())
5756 return getUDivExactExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5758 // Then, try to solve the above equation provided that Start is constant.
5759 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5760 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5761 -StartC->getValue()->getValue(),
5763 return getCouldNotCompute();
5766 /// HowFarToNonZero - Return the number of times a backedge checking the
5767 /// specified value for nonzero will execute. If not computable, return
5769 ScalarEvolution::ExitLimit
5770 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5771 // Loops that look like: while (X == 0) are very strange indeed. We don't
5772 // handle them yet except for the trivial case. This could be expanded in the
5773 // future as needed.
5775 // If the value is a constant, check to see if it is known to be non-zero
5776 // already. If so, the backedge will execute zero times.
5777 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5778 if (!C->getValue()->isNullValue())
5779 return getConstant(C->getType(), 0);
5780 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5783 // We could implement others, but I really doubt anyone writes loops like
5784 // this, and if they did, they would already be constant folded.
5785 return getCouldNotCompute();
5788 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5789 /// (which may not be an immediate predecessor) which has exactly one
5790 /// successor from which BB is reachable, or null if no such block is
5793 std::pair<BasicBlock *, BasicBlock *>
5794 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5795 // If the block has a unique predecessor, then there is no path from the
5796 // predecessor to the block that does not go through the direct edge
5797 // from the predecessor to the block.
5798 if (BasicBlock *Pred = BB->getSinglePredecessor())
5799 return std::make_pair(Pred, BB);
5801 // A loop's header is defined to be a block that dominates the loop.
5802 // If the header has a unique predecessor outside the loop, it must be
5803 // a block that has exactly one successor that can reach the loop.
5804 if (Loop *L = LI->getLoopFor(BB))
5805 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5807 return std::pair<BasicBlock *, BasicBlock *>();
5810 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5811 /// testing whether two expressions are equal, however for the purposes of
5812 /// looking for a condition guarding a loop, it can be useful to be a little
5813 /// more general, since a front-end may have replicated the controlling
5816 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5817 // Quick check to see if they are the same SCEV.
5818 if (A == B) return true;
5820 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5821 // two different instructions with the same value. Check for this case.
5822 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5823 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5824 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5825 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5826 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5829 // Otherwise assume they may have a different value.
5833 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5834 /// predicate Pred. Return true iff any changes were made.
5836 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5837 const SCEV *&LHS, const SCEV *&RHS,
5839 bool Changed = false;
5841 // If we hit the max recursion limit bail out.
5845 // Canonicalize a constant to the right side.
5846 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5847 // Check for both operands constant.
5848 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5849 if (ConstantExpr::getICmp(Pred,
5851 RHSC->getValue())->isNullValue())
5852 goto trivially_false;
5854 goto trivially_true;
5856 // Otherwise swap the operands to put the constant on the right.
5857 std::swap(LHS, RHS);
5858 Pred = ICmpInst::getSwappedPredicate(Pred);
5862 // If we're comparing an addrec with a value which is loop-invariant in the
5863 // addrec's loop, put the addrec on the left. Also make a dominance check,
5864 // as both operands could be addrecs loop-invariant in each other's loop.
5865 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5866 const Loop *L = AR->getLoop();
5867 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5868 std::swap(LHS, RHS);
5869 Pred = ICmpInst::getSwappedPredicate(Pred);
5874 // If there's a constant operand, canonicalize comparisons with boundary
5875 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5876 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5877 const APInt &RA = RC->getValue()->getValue();
5879 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5880 case ICmpInst::ICMP_EQ:
5881 case ICmpInst::ICMP_NE:
5882 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5884 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5885 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5886 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5887 ME->getOperand(0)->isAllOnesValue()) {
5888 RHS = AE->getOperand(1);
5889 LHS = ME->getOperand(1);
5893 case ICmpInst::ICMP_UGE:
5894 if ((RA - 1).isMinValue()) {
5895 Pred = ICmpInst::ICMP_NE;
5896 RHS = getConstant(RA - 1);
5900 if (RA.isMaxValue()) {
5901 Pred = ICmpInst::ICMP_EQ;
5905 if (RA.isMinValue()) goto trivially_true;
5907 Pred = ICmpInst::ICMP_UGT;
5908 RHS = getConstant(RA - 1);
5911 case ICmpInst::ICMP_ULE:
5912 if ((RA + 1).isMaxValue()) {
5913 Pred = ICmpInst::ICMP_NE;
5914 RHS = getConstant(RA + 1);
5918 if (RA.isMinValue()) {
5919 Pred = ICmpInst::ICMP_EQ;
5923 if (RA.isMaxValue()) goto trivially_true;
5925 Pred = ICmpInst::ICMP_ULT;
5926 RHS = getConstant(RA + 1);
5929 case ICmpInst::ICMP_SGE:
5930 if ((RA - 1).isMinSignedValue()) {
5931 Pred = ICmpInst::ICMP_NE;
5932 RHS = getConstant(RA - 1);
5936 if (RA.isMaxSignedValue()) {
5937 Pred = ICmpInst::ICMP_EQ;
5941 if (RA.isMinSignedValue()) goto trivially_true;
5943 Pred = ICmpInst::ICMP_SGT;
5944 RHS = getConstant(RA - 1);
5947 case ICmpInst::ICMP_SLE:
5948 if ((RA + 1).isMaxSignedValue()) {
5949 Pred = ICmpInst::ICMP_NE;
5950 RHS = getConstant(RA + 1);
5954 if (RA.isMinSignedValue()) {
5955 Pred = ICmpInst::ICMP_EQ;
5959 if (RA.isMaxSignedValue()) goto trivially_true;
5961 Pred = ICmpInst::ICMP_SLT;
5962 RHS = getConstant(RA + 1);
5965 case ICmpInst::ICMP_UGT:
5966 if (RA.isMinValue()) {
5967 Pred = ICmpInst::ICMP_NE;
5971 if ((RA + 1).isMaxValue()) {
5972 Pred = ICmpInst::ICMP_EQ;
5973 RHS = getConstant(RA + 1);
5977 if (RA.isMaxValue()) goto trivially_false;
5979 case ICmpInst::ICMP_ULT:
5980 if (RA.isMaxValue()) {
5981 Pred = ICmpInst::ICMP_NE;
5985 if ((RA - 1).isMinValue()) {
5986 Pred = ICmpInst::ICMP_EQ;
5987 RHS = getConstant(RA - 1);
5991 if (RA.isMinValue()) goto trivially_false;
5993 case ICmpInst::ICMP_SGT:
5994 if (RA.isMinSignedValue()) {
5995 Pred = ICmpInst::ICMP_NE;
5999 if ((RA + 1).isMaxSignedValue()) {
6000 Pred = ICmpInst::ICMP_EQ;
6001 RHS = getConstant(RA + 1);
6005 if (RA.isMaxSignedValue()) goto trivially_false;
6007 case ICmpInst::ICMP_SLT:
6008 if (RA.isMaxSignedValue()) {
6009 Pred = ICmpInst::ICMP_NE;
6013 if ((RA - 1).isMinSignedValue()) {
6014 Pred = ICmpInst::ICMP_EQ;
6015 RHS = getConstant(RA - 1);
6019 if (RA.isMinSignedValue()) goto trivially_false;
6024 // Check for obvious equality.
6025 if (HasSameValue(LHS, RHS)) {
6026 if (ICmpInst::isTrueWhenEqual(Pred))
6027 goto trivially_true;
6028 if (ICmpInst::isFalseWhenEqual(Pred))
6029 goto trivially_false;
6032 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6033 // adding or subtracting 1 from one of the operands.
6035 case ICmpInst::ICMP_SLE:
6036 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6037 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6039 Pred = ICmpInst::ICMP_SLT;
6041 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6042 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6044 Pred = ICmpInst::ICMP_SLT;
6048 case ICmpInst::ICMP_SGE:
6049 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6050 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6052 Pred = ICmpInst::ICMP_SGT;
6054 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6055 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6057 Pred = ICmpInst::ICMP_SGT;
6061 case ICmpInst::ICMP_ULE:
6062 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6063 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6065 Pred = ICmpInst::ICMP_ULT;
6067 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6068 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6070 Pred = ICmpInst::ICMP_ULT;
6074 case ICmpInst::ICMP_UGE:
6075 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6076 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6078 Pred = ICmpInst::ICMP_UGT;
6080 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6081 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6083 Pred = ICmpInst::ICMP_UGT;
6091 // TODO: More simplifications are possible here.
6093 // Recursively simplify until we either hit a recursion limit or nothing
6096 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6102 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6103 Pred = ICmpInst::ICMP_EQ;
6108 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6109 Pred = ICmpInst::ICMP_NE;
6113 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6114 return getSignedRange(S).getSignedMax().isNegative();
6117 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6118 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6121 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6122 return !getSignedRange(S).getSignedMin().isNegative();
6125 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6126 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6129 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6130 return isKnownNegative(S) || isKnownPositive(S);
6133 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6134 const SCEV *LHS, const SCEV *RHS) {
6135 // Canonicalize the inputs first.
6136 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6138 // If LHS or RHS is an addrec, check to see if the condition is true in
6139 // every iteration of the loop.
6140 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
6141 if (isLoopEntryGuardedByCond(
6142 AR->getLoop(), Pred, AR->getStart(), RHS) &&
6143 isLoopBackedgeGuardedByCond(
6144 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
6146 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
6147 if (isLoopEntryGuardedByCond(
6148 AR->getLoop(), Pred, LHS, AR->getStart()) &&
6149 isLoopBackedgeGuardedByCond(
6150 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
6153 // Otherwise see what can be done with known constant ranges.
6154 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6158 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6159 const SCEV *LHS, const SCEV *RHS) {
6160 if (HasSameValue(LHS, RHS))
6161 return ICmpInst::isTrueWhenEqual(Pred);
6163 // This code is split out from isKnownPredicate because it is called from
6164 // within isLoopEntryGuardedByCond.
6167 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6168 case ICmpInst::ICMP_SGT:
6169 std::swap(LHS, RHS);
6170 case ICmpInst::ICMP_SLT: {
6171 ConstantRange LHSRange = getSignedRange(LHS);
6172 ConstantRange RHSRange = getSignedRange(RHS);
6173 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6175 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6179 case ICmpInst::ICMP_SGE:
6180 std::swap(LHS, RHS);
6181 case ICmpInst::ICMP_SLE: {
6182 ConstantRange LHSRange = getSignedRange(LHS);
6183 ConstantRange RHSRange = getSignedRange(RHS);
6184 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6186 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6190 case ICmpInst::ICMP_UGT:
6191 std::swap(LHS, RHS);
6192 case ICmpInst::ICMP_ULT: {
6193 ConstantRange LHSRange = getUnsignedRange(LHS);
6194 ConstantRange RHSRange = getUnsignedRange(RHS);
6195 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6197 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6201 case ICmpInst::ICMP_UGE:
6202 std::swap(LHS, RHS);
6203 case ICmpInst::ICMP_ULE: {
6204 ConstantRange LHSRange = getUnsignedRange(LHS);
6205 ConstantRange RHSRange = getUnsignedRange(RHS);
6206 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6208 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6212 case ICmpInst::ICMP_NE: {
6213 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6215 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6218 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6219 if (isKnownNonZero(Diff))
6223 case ICmpInst::ICMP_EQ:
6224 // The check at the top of the function catches the case where
6225 // the values are known to be equal.
6231 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6232 /// protected by a conditional between LHS and RHS. This is used to
6233 /// to eliminate casts.
6235 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6236 ICmpInst::Predicate Pred,
6237 const SCEV *LHS, const SCEV *RHS) {
6238 // Interpret a null as meaning no loop, where there is obviously no guard
6239 // (interprocedural conditions notwithstanding).
6240 if (!L) return true;
6242 BasicBlock *Latch = L->getLoopLatch();
6246 BranchInst *LoopContinuePredicate =
6247 dyn_cast<BranchInst>(Latch->getTerminator());
6248 if (!LoopContinuePredicate ||
6249 LoopContinuePredicate->isUnconditional())
6252 return isImpliedCond(Pred, LHS, RHS,
6253 LoopContinuePredicate->getCondition(),
6254 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6257 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6258 /// by a conditional between LHS and RHS. This is used to help avoid max
6259 /// expressions in loop trip counts, and to eliminate casts.
6261 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6262 ICmpInst::Predicate Pred,
6263 const SCEV *LHS, const SCEV *RHS) {
6264 // Interpret a null as meaning no loop, where there is obviously no guard
6265 // (interprocedural conditions notwithstanding).
6266 if (!L) return false;
6268 // Starting at the loop predecessor, climb up the predecessor chain, as long
6269 // as there are predecessors that can be found that have unique successors
6270 // leading to the original header.
6271 for (std::pair<BasicBlock *, BasicBlock *>
6272 Pair(L->getLoopPredecessor(), L->getHeader());
6274 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6276 BranchInst *LoopEntryPredicate =
6277 dyn_cast<BranchInst>(Pair.first->getTerminator());
6278 if (!LoopEntryPredicate ||
6279 LoopEntryPredicate->isUnconditional())
6282 if (isImpliedCond(Pred, LHS, RHS,
6283 LoopEntryPredicate->getCondition(),
6284 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6291 /// RAII wrapper to prevent recursive application of isImpliedCond.
6292 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6293 /// currently evaluating isImpliedCond.
6294 struct MarkPendingLoopPredicate {
6296 DenseSet<Value*> &LoopPreds;
6299 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6300 : Cond(C), LoopPreds(LP) {
6301 Pending = !LoopPreds.insert(Cond).second;
6303 ~MarkPendingLoopPredicate() {
6305 LoopPreds.erase(Cond);
6309 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6310 /// and RHS is true whenever the given Cond value evaluates to true.
6311 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6312 const SCEV *LHS, const SCEV *RHS,
6313 Value *FoundCondValue,
6315 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6319 // Recursively handle And and Or conditions.
6320 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6321 if (BO->getOpcode() == Instruction::And) {
6323 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6324 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6325 } else if (BO->getOpcode() == Instruction::Or) {
6327 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6328 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6332 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6333 if (!ICI) return false;
6335 // Bail if the ICmp's operands' types are wider than the needed type
6336 // before attempting to call getSCEV on them. This avoids infinite
6337 // recursion, since the analysis of widening casts can require loop
6338 // exit condition information for overflow checking, which would
6340 if (getTypeSizeInBits(LHS->getType()) <
6341 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6344 // Now that we found a conditional branch that dominates the loop or controls
6345 // the loop latch. Check to see if it is the comparison we are looking for.
6346 ICmpInst::Predicate FoundPred;
6348 FoundPred = ICI->getInversePredicate();
6350 FoundPred = ICI->getPredicate();
6352 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6353 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6355 // Balance the types. The case where FoundLHS' type is wider than
6356 // LHS' type is checked for above.
6357 if (getTypeSizeInBits(LHS->getType()) >
6358 getTypeSizeInBits(FoundLHS->getType())) {
6359 if (CmpInst::isSigned(FoundPred)) {
6360 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6361 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6363 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6364 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6368 // Canonicalize the query to match the way instcombine will have
6369 // canonicalized the comparison.
6370 if (SimplifyICmpOperands(Pred, LHS, RHS))
6372 return CmpInst::isTrueWhenEqual(Pred);
6373 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6374 if (FoundLHS == FoundRHS)
6375 return CmpInst::isFalseWhenEqual(FoundPred);
6377 // Check to see if we can make the LHS or RHS match.
6378 if (LHS == FoundRHS || RHS == FoundLHS) {
6379 if (isa<SCEVConstant>(RHS)) {
6380 std::swap(FoundLHS, FoundRHS);
6381 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6383 std::swap(LHS, RHS);
6384 Pred = ICmpInst::getSwappedPredicate(Pred);
6388 // Check whether the found predicate is the same as the desired predicate.
6389 if (FoundPred == Pred)
6390 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6392 // Check whether swapping the found predicate makes it the same as the
6393 // desired predicate.
6394 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6395 if (isa<SCEVConstant>(RHS))
6396 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6398 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6399 RHS, LHS, FoundLHS, FoundRHS);
6402 // Check whether the actual condition is beyond sufficient.
6403 if (FoundPred == ICmpInst::ICMP_EQ)
6404 if (ICmpInst::isTrueWhenEqual(Pred))
6405 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6407 if (Pred == ICmpInst::ICMP_NE)
6408 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6409 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6412 // Otherwise assume the worst.
6416 /// isImpliedCondOperands - Test whether the condition described by Pred,
6417 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6418 /// and FoundRHS is true.
6419 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6420 const SCEV *LHS, const SCEV *RHS,
6421 const SCEV *FoundLHS,
6422 const SCEV *FoundRHS) {
6423 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6424 FoundLHS, FoundRHS) ||
6425 // ~x < ~y --> x > y
6426 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6427 getNotSCEV(FoundRHS),
6428 getNotSCEV(FoundLHS));
6431 /// isImpliedCondOperandsHelper - Test whether the condition described by
6432 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6433 /// FoundLHS, and FoundRHS is true.
6435 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6436 const SCEV *LHS, const SCEV *RHS,
6437 const SCEV *FoundLHS,
6438 const SCEV *FoundRHS) {
6440 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6441 case ICmpInst::ICMP_EQ:
6442 case ICmpInst::ICMP_NE:
6443 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6446 case ICmpInst::ICMP_SLT:
6447 case ICmpInst::ICMP_SLE:
6448 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6449 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6452 case ICmpInst::ICMP_SGT:
6453 case ICmpInst::ICMP_SGE:
6454 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6455 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6458 case ICmpInst::ICMP_ULT:
6459 case ICmpInst::ICMP_ULE:
6460 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6461 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6464 case ICmpInst::ICMP_UGT:
6465 case ICmpInst::ICMP_UGE:
6466 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6467 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6475 // Verify if an linear IV with positive stride can overflow when in a
6476 // less-than comparison, knowing the invariant term of the comparison, the
6477 // stride and the knowledge of NSW/NUW flags on the recurrence.
6478 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
6479 bool IsSigned, bool NoWrap) {
6480 if (NoWrap) return false;
6482 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6483 const SCEV *One = getConstant(Stride->getType(), 1);
6486 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
6487 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
6488 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6491 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
6492 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
6495 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
6496 APInt MaxValue = APInt::getMaxValue(BitWidth);
6497 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6500 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
6501 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
6504 // Verify if an linear IV with negative stride can overflow when in a
6505 // greater-than comparison, knowing the invariant term of the comparison,
6506 // the stride and the knowledge of NSW/NUW flags on the recurrence.
6507 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
6508 bool IsSigned, bool NoWrap) {
6509 if (NoWrap) return false;
6511 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6512 const SCEV *One = getConstant(Stride->getType(), 1);
6515 APInt MinRHS = getSignedRange(RHS).getSignedMin();
6516 APInt MinValue = APInt::getSignedMinValue(BitWidth);
6517 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6520 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
6521 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
6524 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
6525 APInt MinValue = APInt::getMinValue(BitWidth);
6526 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6529 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
6530 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
6533 // Compute the backedge taken count knowing the interval difference, the
6534 // stride and presence of the equality in the comparison.
6535 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
6537 const SCEV *One = getConstant(Step->getType(), 1);
6538 Delta = Equality ? getAddExpr(Delta, Step)
6539 : getAddExpr(Delta, getMinusSCEV(Step, One));
6540 return getUDivExpr(Delta, Step);
6543 /// HowManyLessThans - Return the number of times a backedge containing the
6544 /// specified less-than comparison will execute. If not computable, return
6545 /// CouldNotCompute.
6547 /// @param IsSubExpr is true when the LHS < RHS condition does not directly
6548 /// control the branch. In this case, we can only compute an iteration count for
6549 /// a subexpression that cannot overflow before evaluating true.
6550 ScalarEvolution::ExitLimit
6551 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6552 const Loop *L, bool IsSigned,
6554 // We handle only IV < Invariant
6555 if (!isLoopInvariant(RHS, L))
6556 return getCouldNotCompute();
6558 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6560 // Avoid weird loops
6561 if (!IV || IV->getLoop() != L || !IV->isAffine())
6562 return getCouldNotCompute();
6564 bool NoWrap = !IsSubExpr &&
6565 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6567 const SCEV *Stride = IV->getStepRecurrence(*this);
6569 // Avoid negative or zero stride values
6570 if (!isKnownPositive(Stride))
6571 return getCouldNotCompute();
6573 // Avoid proven overflow cases: this will ensure that the backedge taken count
6574 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6575 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6576 // behaviors like the case of C language.
6577 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
6578 return getCouldNotCompute();
6580 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
6581 : ICmpInst::ICMP_ULT;
6582 const SCEV *Start = IV->getStart();
6583 const SCEV *End = RHS;
6584 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
6585 End = IsSigned ? getSMaxExpr(RHS, Start)
6586 : getUMaxExpr(RHS, Start);
6588 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
6590 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
6591 : getUnsignedRange(Start).getUnsignedMin();
6593 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6594 : getUnsignedRange(Stride).getUnsignedMin();
6596 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6597 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
6598 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
6600 // Although End can be a MAX expression we estimate MaxEnd considering only
6601 // the case End = RHS. This is safe because in the other case (End - Start)
6602 // is zero, leading to a zero maximum backedge taken count.
6604 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
6605 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
6607 const SCEV *MaxBECount;
6608 if (isa<SCEVConstant>(BECount))
6609 MaxBECount = BECount;
6611 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
6612 getConstant(MinStride), false);
6614 if (isa<SCEVCouldNotCompute>(MaxBECount))
6615 MaxBECount = BECount;
6617 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6620 ScalarEvolution::ExitLimit
6621 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
6622 const Loop *L, bool IsSigned,
6624 // We handle only IV > Invariant
6625 if (!isLoopInvariant(RHS, L))
6626 return getCouldNotCompute();
6628 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6630 // Avoid weird loops
6631 if (!IV || IV->getLoop() != L || !IV->isAffine())
6632 return getCouldNotCompute();
6634 bool NoWrap = !IsSubExpr &&
6635 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6637 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
6639 // Avoid negative or zero stride values
6640 if (!isKnownPositive(Stride))
6641 return getCouldNotCompute();
6643 // Avoid proven overflow cases: this will ensure that the backedge taken count
6644 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6645 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6646 // behaviors like the case of C language.
6647 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
6648 return getCouldNotCompute();
6650 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
6651 : ICmpInst::ICMP_UGT;
6653 const SCEV *Start = IV->getStart();
6654 const SCEV *End = RHS;
6655 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
6656 End = IsSigned ? getSMinExpr(RHS, Start)
6657 : getUMinExpr(RHS, Start);
6659 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
6661 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
6662 : getUnsignedRange(Start).getUnsignedMax();
6664 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6665 : getUnsignedRange(Stride).getUnsignedMin();
6667 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6668 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
6669 : APInt::getMinValue(BitWidth) + (MinStride - 1);
6671 // Although End can be a MIN expression we estimate MinEnd considering only
6672 // the case End = RHS. This is safe because in the other case (Start - End)
6673 // is zero, leading to a zero maximum backedge taken count.
6675 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
6676 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
6679 const SCEV *MaxBECount = getCouldNotCompute();
6680 if (isa<SCEVConstant>(BECount))
6681 MaxBECount = BECount;
6683 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
6684 getConstant(MinStride), false);
6686 if (isa<SCEVCouldNotCompute>(MaxBECount))
6687 MaxBECount = BECount;
6689 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6692 /// getNumIterationsInRange - Return the number of iterations of this loop that
6693 /// produce values in the specified constant range. Another way of looking at
6694 /// this is that it returns the first iteration number where the value is not in
6695 /// the condition, thus computing the exit count. If the iteration count can't
6696 /// be computed, an instance of SCEVCouldNotCompute is returned.
6697 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6698 ScalarEvolution &SE) const {
6699 if (Range.isFullSet()) // Infinite loop.
6700 return SE.getCouldNotCompute();
6702 // If the start is a non-zero constant, shift the range to simplify things.
6703 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6704 if (!SC->getValue()->isZero()) {
6705 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6706 Operands[0] = SE.getConstant(SC->getType(), 0);
6707 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6708 getNoWrapFlags(FlagNW));
6709 if (const SCEVAddRecExpr *ShiftedAddRec =
6710 dyn_cast<SCEVAddRecExpr>(Shifted))
6711 return ShiftedAddRec->getNumIterationsInRange(
6712 Range.subtract(SC->getValue()->getValue()), SE);
6713 // This is strange and shouldn't happen.
6714 return SE.getCouldNotCompute();
6717 // The only time we can solve this is when we have all constant indices.
6718 // Otherwise, we cannot determine the overflow conditions.
6719 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6720 if (!isa<SCEVConstant>(getOperand(i)))
6721 return SE.getCouldNotCompute();
6724 // Okay at this point we know that all elements of the chrec are constants and
6725 // that the start element is zero.
6727 // First check to see if the range contains zero. If not, the first
6729 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6730 if (!Range.contains(APInt(BitWidth, 0)))
6731 return SE.getConstant(getType(), 0);
6734 // If this is an affine expression then we have this situation:
6735 // Solve {0,+,A} in Range === Ax in Range
6737 // We know that zero is in the range. If A is positive then we know that
6738 // the upper value of the range must be the first possible exit value.
6739 // If A is negative then the lower of the range is the last possible loop
6740 // value. Also note that we already checked for a full range.
6741 APInt One(BitWidth,1);
6742 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6743 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6745 // The exit value should be (End+A)/A.
6746 APInt ExitVal = (End + A).udiv(A);
6747 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6749 // Evaluate at the exit value. If we really did fall out of the valid
6750 // range, then we computed our trip count, otherwise wrap around or other
6751 // things must have happened.
6752 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6753 if (Range.contains(Val->getValue()))
6754 return SE.getCouldNotCompute(); // Something strange happened
6756 // Ensure that the previous value is in the range. This is a sanity check.
6757 assert(Range.contains(
6758 EvaluateConstantChrecAtConstant(this,
6759 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6760 "Linear scev computation is off in a bad way!");
6761 return SE.getConstant(ExitValue);
6762 } else if (isQuadratic()) {
6763 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6764 // quadratic equation to solve it. To do this, we must frame our problem in
6765 // terms of figuring out when zero is crossed, instead of when
6766 // Range.getUpper() is crossed.
6767 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6768 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6769 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6770 // getNoWrapFlags(FlagNW)
6773 // Next, solve the constructed addrec
6774 std::pair<const SCEV *,const SCEV *> Roots =
6775 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6776 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6777 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6779 // Pick the smallest positive root value.
6780 if (ConstantInt *CB =
6781 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6782 R1->getValue(), R2->getValue()))) {
6783 if (CB->getZExtValue() == false)
6784 std::swap(R1, R2); // R1 is the minimum root now.
6786 // Make sure the root is not off by one. The returned iteration should
6787 // not be in the range, but the previous one should be. When solving
6788 // for "X*X < 5", for example, we should not return a root of 2.
6789 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6792 if (Range.contains(R1Val->getValue())) {
6793 // The next iteration must be out of the range...
6794 ConstantInt *NextVal =
6795 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6797 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6798 if (!Range.contains(R1Val->getValue()))
6799 return SE.getConstant(NextVal);
6800 return SE.getCouldNotCompute(); // Something strange happened
6803 // If R1 was not in the range, then it is a good return value. Make
6804 // sure that R1-1 WAS in the range though, just in case.
6805 ConstantInt *NextVal =
6806 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6807 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6808 if (Range.contains(R1Val->getValue()))
6810 return SE.getCouldNotCompute(); // Something strange happened
6815 return SE.getCouldNotCompute();
6821 FindUndefs() : Found(false) {}
6823 bool follow(const SCEV *S) {
6824 if (const SCEVUnknown *C = dyn_cast<SCEVUnknown>(S)) {
6825 if (isa<UndefValue>(C->getValue()))
6827 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
6828 if (isa<UndefValue>(C->getValue()))
6832 // Keep looking if we haven't found it yet.
6835 bool isDone() const {
6836 // Stop recursion if we have found an undef.
6842 // Return true when S contains at least an undef value.
6844 containsUndefs(const SCEV *S) {
6846 SCEVTraversal<FindUndefs> ST(F);
6853 // Collect all steps of SCEV expressions.
6854 struct SCEVCollectStrides {
6855 ScalarEvolution &SE;
6856 SmallVectorImpl<const SCEV *> &Strides;
6858 SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
6859 : SE(SE), Strides(S) {}
6861 bool follow(const SCEV *S) {
6862 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
6863 Strides.push_back(AR->getStepRecurrence(SE));
6866 bool isDone() const { return false; }
6869 // Collect all SCEVUnknown and SCEVMulExpr expressions.
6870 struct SCEVCollectTerms {
6871 SmallVectorImpl<const SCEV *> &Terms;
6873 SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T)
6876 bool follow(const SCEV *S) {
6877 if (isa<SCEVUnknown>(S) || isa<SCEVConstant>(S) || isa<SCEVMulExpr>(S)) {
6878 if (!containsUndefs(S))
6881 // Stop recursion: once we collected a term, do not walk its operands.
6888 bool isDone() const { return false; }
6892 /// Find parametric terms in this SCEVAddRecExpr.
6893 void SCEVAddRecExpr::collectParametricTerms(
6894 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) const {
6895 SmallVector<const SCEV *, 4> Strides;
6896 SCEVCollectStrides StrideCollector(SE, Strides);
6897 visitAll(this, StrideCollector);
6900 dbgs() << "Strides:\n";
6901 for (const SCEV *S : Strides)
6902 dbgs() << *S << "\n";
6905 for (const SCEV *S : Strides) {
6906 SCEVCollectTerms TermCollector(Terms);
6907 visitAll(S, TermCollector);
6911 dbgs() << "Terms:\n";
6912 for (const SCEV *T : Terms)
6913 dbgs() << *T << "\n";
6917 static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
6918 APInt A = C1->getValue()->getValue();
6919 APInt B = C2->getValue()->getValue();
6920 uint32_t ABW = A.getBitWidth();
6921 uint32_t BBW = B.getBitWidth();
6928 return APIntOps::srem(A, B);
6931 static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
6932 APInt A = C1->getValue()->getValue();
6933 APInt B = C2->getValue()->getValue();
6934 uint32_t ABW = A.getBitWidth();
6935 uint32_t BBW = B.getBitWidth();
6942 return APIntOps::sdiv(A, B);
6946 struct FindSCEVSize {
6948 FindSCEVSize() : Size(0) {}
6950 bool follow(const SCEV *S) {
6952 // Keep looking at all operands of S.
6955 bool isDone() const {
6961 // Returns the size of the SCEV S.
6962 static inline int sizeOfSCEV(const SCEV *S) {
6964 SCEVTraversal<FindSCEVSize> ST(F);
6971 struct SCEVDivision : public SCEVVisitor<SCEVDivision, void> {
6973 // Computes the Quotient and Remainder of the division of Numerator by
6975 static void divide(ScalarEvolution &SE, const SCEV *Numerator,
6976 const SCEV *Denominator, const SCEV **Quotient,
6977 const SCEV **Remainder) {
6978 assert(Numerator && Denominator && "Uninitialized SCEV");
6980 SCEVDivision D(SE, Numerator, Denominator);
6982 // Check for the trivial case here to avoid having to check for it in the
6983 // rest of the code.
6984 if (Numerator == Denominator) {
6986 *Remainder = D.Zero;
6990 if (Numerator == D.Zero) {
6992 *Remainder = D.Zero;
6996 // Split the Denominator when it is a product.
6997 if (const SCEVMulExpr *T = dyn_cast<const SCEVMulExpr>(Denominator)) {
6999 *Quotient = Numerator;
7000 for (const SCEV *Op : T->operands()) {
7001 divide(SE, *Quotient, Op, &Q, &R);
7004 // Bail out when the Numerator is not divisible by one of the terms of
7008 *Remainder = Numerator;
7012 *Remainder = D.Zero;
7017 *Quotient = D.Quotient;
7018 *Remainder = D.Remainder;
7021 SCEVDivision(ScalarEvolution &S, const SCEV *Numerator, const SCEV *Denominator)
7022 : SE(S), Denominator(Denominator) {
7023 Zero = SE.getConstant(Denominator->getType(), 0);
7024 One = SE.getConstant(Denominator->getType(), 1);
7026 // By default, we don't know how to divide Expr by Denominator.
7027 // Providing the default here simplifies the rest of the code.
7029 Remainder = Numerator;
7032 // Except in the trivial case described above, we do not know how to divide
7033 // Expr by Denominator for the following functions with empty implementation.
7034 void visitTruncateExpr(const SCEVTruncateExpr *Numerator) {}
7035 void visitZeroExtendExpr(const SCEVZeroExtendExpr *Numerator) {}
7036 void visitSignExtendExpr(const SCEVSignExtendExpr *Numerator) {}
7037 void visitUDivExpr(const SCEVUDivExpr *Numerator) {}
7038 void visitSMaxExpr(const SCEVSMaxExpr *Numerator) {}
7039 void visitUMaxExpr(const SCEVUMaxExpr *Numerator) {}
7040 void visitUnknown(const SCEVUnknown *Numerator) {}
7041 void visitCouldNotCompute(const SCEVCouldNotCompute *Numerator) {}
7043 void visitConstant(const SCEVConstant *Numerator) {
7044 if (const SCEVConstant *D = dyn_cast<SCEVConstant>(Denominator)) {
7045 Quotient = SE.getConstant(sdiv(Numerator, D));
7046 Remainder = SE.getConstant(srem(Numerator, D));
7051 void visitAddRecExpr(const SCEVAddRecExpr *Numerator) {
7052 const SCEV *StartQ, *StartR, *StepQ, *StepR;
7053 assert(Numerator->isAffine() && "Numerator should be affine");
7054 divide(SE, Numerator->getStart(), Denominator, &StartQ, &StartR);
7055 divide(SE, Numerator->getStepRecurrence(SE), Denominator, &StepQ, &StepR);
7056 Quotient = SE.getAddRecExpr(StartQ, StepQ, Numerator->getLoop(),
7057 Numerator->getNoWrapFlags());
7058 Remainder = SE.getAddRecExpr(StartR, StepR, Numerator->getLoop(),
7059 Numerator->getNoWrapFlags());
7062 void visitAddExpr(const SCEVAddExpr *Numerator) {
7063 SmallVector<const SCEV *, 2> Qs, Rs;
7064 for (const SCEV *Op : Numerator->operands()) {
7066 divide(SE, Op, Denominator, &Q, &R);
7071 if (Qs.size() == 1) {
7077 Quotient = SE.getAddExpr(Qs);
7078 Remainder = SE.getAddExpr(Rs);
7081 void visitMulExpr(const SCEVMulExpr *Numerator) {
7082 SmallVector<const SCEV *, 2> Qs;
7084 bool FoundDenominatorTerm = false;
7085 for (const SCEV *Op : Numerator->operands()) {
7086 if (FoundDenominatorTerm) {
7091 // Check whether Denominator divides one of the product operands.
7093 divide(SE, Op, Denominator, &Q, &R);
7098 FoundDenominatorTerm = true;
7102 if (FoundDenominatorTerm) {
7107 Quotient = SE.getMulExpr(Qs);
7111 if (!isa<SCEVUnknown>(Denominator)) {
7113 Remainder = Numerator;
7117 // The Remainder is obtained by replacing Denominator by 0 in Numerator.
7118 ValueToValueMap RewriteMap;
7119 RewriteMap[cast<SCEVUnknown>(Denominator)->getValue()] =
7120 cast<SCEVConstant>(Zero)->getValue();
7121 Remainder = SCEVParameterRewriter::rewrite(Numerator, SE, RewriteMap, true);
7123 // Quotient is (Numerator - Remainder) divided by Denominator.
7125 const SCEV *Diff = SE.getMinusSCEV(Numerator, Remainder);
7126 if (sizeOfSCEV(Diff) > sizeOfSCEV(Numerator)) {
7127 // This SCEV does not seem to simplify: fail the division here.
7129 Remainder = Numerator;
7132 divide(SE, Diff, Denominator, &Q, &R);
7134 "(Numerator - Remainder) should evenly divide Denominator");
7139 ScalarEvolution &SE;
7140 const SCEV *Denominator, *Quotient, *Remainder, *Zero, *One;
7144 // Find the Greatest Common Divisor of A and B.
7146 findGCD(ScalarEvolution &SE, const SCEV *A, const SCEV *B) {
7148 if (const SCEVConstant *CA = dyn_cast<SCEVConstant>(A))
7149 if (const SCEVConstant *CB = dyn_cast<SCEVConstant>(B))
7150 return SE.getConstant(gcd(CA, CB));
7152 const SCEV *One = SE.getConstant(A->getType(), 1);
7153 if (isa<SCEVConstant>(A) && isa<SCEVUnknown>(B))
7155 if (isa<SCEVUnknown>(A) && isa<SCEVConstant>(B))
7159 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(A)) {
7160 SmallVector<const SCEV *, 2> Qs;
7161 for (const SCEV *Op : M->operands())
7162 Qs.push_back(findGCD(SE, Op, B));
7163 return SE.getMulExpr(Qs);
7165 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(B)) {
7166 SmallVector<const SCEV *, 2> Qs;
7167 for (const SCEV *Op : M->operands())
7168 Qs.push_back(findGCD(SE, A, Op));
7169 return SE.getMulExpr(Qs);
7172 const SCEV *Zero = SE.getConstant(A->getType(), 0);
7173 SCEVDivision::divide(SE, A, B, &Q, &R);
7177 SCEVDivision::divide(SE, B, A, &Q, &R);
7184 // Find the Greatest Common Divisor of all the SCEVs in Terms.
7186 findGCD(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms) {
7187 assert(Terms.size() > 0 && "Terms vector is empty");
7189 const SCEV *GCD = Terms[0];
7190 for (const SCEV *T : Terms)
7191 GCD = findGCD(SE, GCD, T);
7196 static void findArrayDimensionsRec(ScalarEvolution &SE,
7197 SmallVectorImpl<const SCEV *> &Terms,
7198 SmallVectorImpl<const SCEV *> &Sizes,
7199 const SCEV *Zero, const SCEV *One) {
7200 // The GCD of all Terms is the dimension of the innermost dimension.
7201 const SCEV *GCD = findGCD(SE, Terms);
7203 // End of recursion.
7204 if (Terms.size() == 1) {
7205 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(GCD)) {
7206 SmallVector<const SCEV *, 2> Qs;
7207 for (const SCEV *Op : M->operands())
7208 if (!isa<SCEVConstant>(Op))
7211 GCD = SE.getMulExpr(Qs);
7214 Sizes.push_back(GCD);
7218 for (unsigned I = 0; I < Terms.size(); ++I) {
7219 // Normalize the terms before the next call to findArrayDimensionsRec.
7221 SCEVDivision::divide(SE, Terms[I], GCD, &Q, &R);
7222 assert(R == Zero && "GCD does not evenly divide one of the terms");
7226 // Remove all SCEVConstants.
7227 for (unsigned I = 0; I < Terms.size();)
7228 if (isa<SCEVConstant>(Terms[I]))
7229 Terms.erase(Terms.begin() + I);
7233 if (Terms.size() > 0)
7234 findArrayDimensionsRec(SE, Terms, Sizes, Zero, One);
7235 Sizes.push_back(GCD);
7239 struct FindParameter {
7240 bool FoundParameter;
7241 FindParameter() : FoundParameter(false) {}
7243 bool follow(const SCEV *S) {
7244 if (isa<SCEVUnknown>(S)) {
7245 FoundParameter = true;
7246 // Stop recursion: we found a parameter.
7252 bool isDone() const {
7253 // Stop recursion if we have found a parameter.
7254 return FoundParameter;
7259 // Returns true when S contains at least a SCEVUnknown parameter.
7261 containsParameters(const SCEV *S) {
7263 SCEVTraversal<FindParameter> ST(F);
7266 return F.FoundParameter;
7269 // Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
7271 containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
7272 for (const SCEV *T : Terms)
7273 if (containsParameters(T))
7278 // Return the number of product terms in S.
7279 static inline int numberOfTerms(const SCEV *S) {
7280 if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
7281 return Expr->getNumOperands();
7285 /// Second step of delinearization: compute the array dimensions Sizes from the
7286 /// set of Terms extracted from the memory access function of this SCEVAddRec.
7287 void SCEVAddRecExpr::findArrayDimensions(
7288 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Terms,
7289 SmallVectorImpl<const SCEV *> &Sizes) const {
7291 if (Terms.size() < 2)
7294 // Early return when Terms do not contain parameters: we do not delinearize
7295 // non parametric SCEVs.
7296 if (!containsParameters(Terms))
7300 dbgs() << "Terms:\n";
7301 for (const SCEV *T : Terms)
7302 dbgs() << *T << "\n";
7305 // Remove duplicates.
7306 std::sort(Terms.begin(), Terms.end());
7307 Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
7309 // Put larger terms first.
7310 std::sort(Terms.begin(), Terms.end(), [](const SCEV *LHS, const SCEV *RHS) {
7311 return numberOfTerms(LHS) > numberOfTerms(RHS);
7315 dbgs() << "Terms after sorting:\n";
7316 for (const SCEV *T : Terms)
7317 dbgs() << *T << "\n";
7320 const SCEV *Zero = SE.getConstant(this->getType(), 0);
7321 const SCEV *One = SE.getConstant(this->getType(), 1);
7322 findArrayDimensionsRec(SE, Terms, Sizes, Zero, One);
7325 dbgs() << "Sizes:\n";
7326 for (const SCEV *S : Sizes)
7327 dbgs() << *S << "\n";
7331 /// Third step of delinearization: compute the access functions for the
7332 /// Subscripts based on the dimensions in Sizes.
7333 const SCEV *SCEVAddRecExpr::computeAccessFunctions(
7334 ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &Subscripts,
7335 SmallVectorImpl<const SCEV *> &Sizes) const {
7336 // Early exit in case this SCEV is not an affine multivariate function.
7337 const SCEV *Zero = SE.getConstant(this->getType(), 0);
7338 if (!this->isAffine())
7341 const SCEV *Res = this, *Remainder = Zero;
7342 int Last = Sizes.size() - 1;
7343 for (int i = Last; i >= 0; i--) {
7345 SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
7348 dbgs() << "Res: " << *Res << "\n";
7349 dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
7350 dbgs() << "Res divided by Sizes[i]:\n";
7351 dbgs() << "Quotient: " << *Q << "\n";
7352 dbgs() << "Remainder: " << *R << "\n";
7358 // Do not record the last subscript corresponding to the size of elements
7364 // Record the access function for the current subscript.
7365 Subscripts.push_back(R);
7368 // Also push in last position the remainder of the last division: it will be
7369 // the access function of the innermost dimension.
7370 Subscripts.push_back(Res);
7372 std::reverse(Subscripts.begin(), Subscripts.end());
7375 dbgs() << "Subscripts:\n";
7376 for (const SCEV *S : Subscripts)
7377 dbgs() << *S << "\n";
7382 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7383 /// sizes of an array access. Returns the remainder of the delinearization that
7384 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7385 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7386 /// expressions in the stride and base of a SCEV corresponding to the
7387 /// computation of a GCD (greatest common divisor) of base and stride. When
7388 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7390 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7392 /// void foo(long n, long m, long o, double A[n][m][o]) {
7394 /// for (long i = 0; i < n; i++)
7395 /// for (long j = 0; j < m; j++)
7396 /// for (long k = 0; k < o; k++)
7397 /// A[i][j][k] = 1.0;
7400 /// the delinearization input is the following AddRec SCEV:
7402 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7404 /// From this SCEV, we are able to say that the base offset of the access is %A
7405 /// because it appears as an offset that does not divide any of the strides in
7408 /// CHECK: Base offset: %A
7410 /// and then SCEV->delinearize determines the size of some of the dimensions of
7411 /// the array as these are the multiples by which the strides are happening:
7413 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7415 /// Note that the outermost dimension remains of UnknownSize because there are
7416 /// no strides that would help identifying the size of the last dimension: when
7417 /// the array has been statically allocated, one could compute the size of that
7418 /// dimension by dividing the overall size of the array by the size of the known
7419 /// dimensions: %m * %o * 8.
7421 /// Finally delinearize provides the access functions for the array reference
7422 /// that does correspond to A[i][j][k] of the above C testcase:
7424 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7426 /// The testcases are checking the output of a function pass:
7427 /// DelinearizationPass that walks through all loads and stores of a function
7428 /// asking for the SCEV of the memory access with respect to all enclosing
7429 /// loops, calling SCEV->delinearize on that and printing the results.
7432 SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7433 SmallVectorImpl<const SCEV *> &Subscripts,
7434 SmallVectorImpl<const SCEV *> &Sizes) const {
7435 // First step: collect parametric terms.
7436 SmallVector<const SCEV *, 4> Terms;
7437 collectParametricTerms(SE, Terms);
7439 // Second step: find subscript sizes.
7440 findArrayDimensions(SE, Terms, Sizes);
7442 // Third step: compute the access functions for each subscript.
7443 const SCEV *Remainder = computeAccessFunctions(SE, Subscripts, Sizes);
7446 dbgs() << "succeeded to delinearize " << *this << "\n";
7447 dbgs() << "ArrayDecl[UnknownSize]";
7448 for (const SCEV *S : Sizes)
7449 dbgs() << "[" << *S << "]";
7451 dbgs() << "ArrayRef";
7452 for (const SCEV *S : Sizes)
7453 dbgs() << "[" << *S << "]";
7460 //===----------------------------------------------------------------------===//
7461 // SCEVCallbackVH Class Implementation
7462 //===----------------------------------------------------------------------===//
7464 void ScalarEvolution::SCEVCallbackVH::deleted() {
7465 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7466 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7467 SE->ConstantEvolutionLoopExitValue.erase(PN);
7468 SE->ValueExprMap.erase(getValPtr());
7469 // this now dangles!
7472 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7473 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7475 // Forget all the expressions associated with users of the old value,
7476 // so that future queries will recompute the expressions using the new
7478 Value *Old = getValPtr();
7479 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7480 SmallPtrSet<User *, 8> Visited;
7481 while (!Worklist.empty()) {
7482 User *U = Worklist.pop_back_val();
7483 // Deleting the Old value will cause this to dangle. Postpone
7484 // that until everything else is done.
7487 if (!Visited.insert(U))
7489 if (PHINode *PN = dyn_cast<PHINode>(U))
7490 SE->ConstantEvolutionLoopExitValue.erase(PN);
7491 SE->ValueExprMap.erase(U);
7492 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7494 // Delete the Old value.
7495 if (PHINode *PN = dyn_cast<PHINode>(Old))
7496 SE->ConstantEvolutionLoopExitValue.erase(PN);
7497 SE->ValueExprMap.erase(Old);
7498 // this now dangles!
7501 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7502 : CallbackVH(V), SE(se) {}
7504 //===----------------------------------------------------------------------===//
7505 // ScalarEvolution Class Implementation
7506 //===----------------------------------------------------------------------===//
7508 ScalarEvolution::ScalarEvolution()
7509 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7510 BlockDispositions(64), FirstUnknown(nullptr) {
7511 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7514 bool ScalarEvolution::runOnFunction(Function &F) {
7516 LI = &getAnalysis<LoopInfo>();
7517 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7518 DL = DLP ? &DLP->getDataLayout() : nullptr;
7519 TLI = &getAnalysis<TargetLibraryInfo>();
7520 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7524 void ScalarEvolution::releaseMemory() {
7525 // Iterate through all the SCEVUnknown instances and call their
7526 // destructors, so that they release their references to their values.
7527 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7529 FirstUnknown = nullptr;
7531 ValueExprMap.clear();
7533 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7534 // that a loop had multiple computable exits.
7535 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7536 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7541 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7543 BackedgeTakenCounts.clear();
7544 ConstantEvolutionLoopExitValue.clear();
7545 ValuesAtScopes.clear();
7546 LoopDispositions.clear();
7547 BlockDispositions.clear();
7548 UnsignedRanges.clear();
7549 SignedRanges.clear();
7550 UniqueSCEVs.clear();
7551 SCEVAllocator.Reset();
7554 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7555 AU.setPreservesAll();
7556 AU.addRequiredTransitive<LoopInfo>();
7557 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7558 AU.addRequired<TargetLibraryInfo>();
7561 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7562 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7565 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7567 // Print all inner loops first
7568 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7569 PrintLoopInfo(OS, SE, *I);
7572 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7575 SmallVector<BasicBlock *, 8> ExitBlocks;
7576 L->getExitBlocks(ExitBlocks);
7577 if (ExitBlocks.size() != 1)
7578 OS << "<multiple exits> ";
7580 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7581 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7583 OS << "Unpredictable backedge-taken count. ";
7588 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7591 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7592 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7594 OS << "Unpredictable max backedge-taken count. ";
7600 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7601 // ScalarEvolution's implementation of the print method is to print
7602 // out SCEV values of all instructions that are interesting. Doing
7603 // this potentially causes it to create new SCEV objects though,
7604 // which technically conflicts with the const qualifier. This isn't
7605 // observable from outside the class though, so casting away the
7606 // const isn't dangerous.
7607 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7609 OS << "Classifying expressions for: ";
7610 F->printAsOperand(OS, /*PrintType=*/false);
7612 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7613 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7616 const SCEV *SV = SE.getSCEV(&*I);
7619 const Loop *L = LI->getLoopFor((*I).getParent());
7621 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
7628 OS << "\t\t" "Exits: ";
7629 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
7630 if (!SE.isLoopInvariant(ExitValue, L)) {
7631 OS << "<<Unknown>>";
7640 OS << "Determining loop execution counts for: ";
7641 F->printAsOperand(OS, /*PrintType=*/false);
7643 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
7644 PrintLoopInfo(OS, &SE, *I);
7647 ScalarEvolution::LoopDisposition
7648 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
7649 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
7650 for (unsigned u = 0; u < Values.size(); u++) {
7651 if (Values[u].first == L)
7652 return Values[u].second;
7654 Values.push_back(std::make_pair(L, LoopVariant));
7655 LoopDisposition D = computeLoopDisposition(S, L);
7656 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
7657 for (unsigned u = Values2.size(); u > 0; u--) {
7658 if (Values2[u - 1].first == L) {
7659 Values2[u - 1].second = D;
7666 ScalarEvolution::LoopDisposition
7667 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
7668 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7670 return LoopInvariant;
7674 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
7675 case scAddRecExpr: {
7676 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7678 // If L is the addrec's loop, it's computable.
7679 if (AR->getLoop() == L)
7680 return LoopComputable;
7682 // Add recurrences are never invariant in the function-body (null loop).
7686 // This recurrence is variant w.r.t. L if L contains AR's loop.
7687 if (L->contains(AR->getLoop()))
7690 // This recurrence is invariant w.r.t. L if AR's loop contains L.
7691 if (AR->getLoop()->contains(L))
7692 return LoopInvariant;
7694 // This recurrence is variant w.r.t. L if any of its operands
7696 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
7698 if (!isLoopInvariant(*I, L))
7701 // Otherwise it's loop-invariant.
7702 return LoopInvariant;
7708 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7709 bool HasVarying = false;
7710 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7712 LoopDisposition D = getLoopDisposition(*I, L);
7713 if (D == LoopVariant)
7715 if (D == LoopComputable)
7718 return HasVarying ? LoopComputable : LoopInvariant;
7721 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7722 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
7723 if (LD == LoopVariant)
7725 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
7726 if (RD == LoopVariant)
7728 return (LD == LoopInvariant && RD == LoopInvariant) ?
7729 LoopInvariant : LoopComputable;
7732 // All non-instruction values are loop invariant. All instructions are loop
7733 // invariant if they are not contained in the specified loop.
7734 // Instructions are never considered invariant in the function body
7735 // (null loop) because they are defined within the "loop".
7736 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
7737 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
7738 return LoopInvariant;
7739 case scCouldNotCompute:
7740 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7742 llvm_unreachable("Unknown SCEV kind!");
7745 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
7746 return getLoopDisposition(S, L) == LoopInvariant;
7749 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
7750 return getLoopDisposition(S, L) == LoopComputable;
7753 ScalarEvolution::BlockDisposition
7754 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7755 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
7756 for (unsigned u = 0; u < Values.size(); u++) {
7757 if (Values[u].first == BB)
7758 return Values[u].second;
7760 Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
7761 BlockDisposition D = computeBlockDisposition(S, BB);
7762 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
7763 for (unsigned u = Values2.size(); u > 0; u--) {
7764 if (Values2[u - 1].first == BB) {
7765 Values2[u - 1].second = D;
7772 ScalarEvolution::BlockDisposition
7773 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7774 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7776 return ProperlyDominatesBlock;
7780 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
7781 case scAddRecExpr: {
7782 // This uses a "dominates" query instead of "properly dominates" query
7783 // to test for proper dominance too, because the instruction which
7784 // produces the addrec's value is a PHI, and a PHI effectively properly
7785 // dominates its entire containing block.
7786 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7787 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
7788 return DoesNotDominateBlock;
7790 // FALL THROUGH into SCEVNAryExpr handling.
7795 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7797 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7799 BlockDisposition D = getBlockDisposition(*I, BB);
7800 if (D == DoesNotDominateBlock)
7801 return DoesNotDominateBlock;
7802 if (D == DominatesBlock)
7805 return Proper ? ProperlyDominatesBlock : DominatesBlock;
7808 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7809 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
7810 BlockDisposition LD = getBlockDisposition(LHS, BB);
7811 if (LD == DoesNotDominateBlock)
7812 return DoesNotDominateBlock;
7813 BlockDisposition RD = getBlockDisposition(RHS, BB);
7814 if (RD == DoesNotDominateBlock)
7815 return DoesNotDominateBlock;
7816 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
7817 ProperlyDominatesBlock : DominatesBlock;
7820 if (Instruction *I =
7821 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
7822 if (I->getParent() == BB)
7823 return DominatesBlock;
7824 if (DT->properlyDominates(I->getParent(), BB))
7825 return ProperlyDominatesBlock;
7826 return DoesNotDominateBlock;
7828 return ProperlyDominatesBlock;
7829 case scCouldNotCompute:
7830 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7832 llvm_unreachable("Unknown SCEV kind!");
7835 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
7836 return getBlockDisposition(S, BB) >= DominatesBlock;
7839 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
7840 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
7844 // Search for a SCEV expression node within an expression tree.
7845 // Implements SCEVTraversal::Visitor.
7850 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
7852 bool follow(const SCEV *S) {
7853 IsFound |= (S == Node);
7856 bool isDone() const { return IsFound; }
7860 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
7861 SCEVSearch Search(Op);
7862 visitAll(S, Search);
7863 return Search.IsFound;
7866 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
7867 ValuesAtScopes.erase(S);
7868 LoopDispositions.erase(S);
7869 BlockDispositions.erase(S);
7870 UnsignedRanges.erase(S);
7871 SignedRanges.erase(S);
7873 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7874 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
7875 BackedgeTakenInfo &BEInfo = I->second;
7876 if (BEInfo.hasOperand(S, this)) {
7878 BackedgeTakenCounts.erase(I++);
7885 typedef DenseMap<const Loop *, std::string> VerifyMap;
7887 /// replaceSubString - Replaces all occurrences of From in Str with To.
7888 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
7890 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
7891 Str.replace(Pos, From.size(), To.data(), To.size());
7896 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
7898 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
7899 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
7900 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
7902 std::string &S = Map[L];
7904 raw_string_ostream OS(S);
7905 SE.getBackedgeTakenCount(L)->print(OS);
7907 // false and 0 are semantically equivalent. This can happen in dead loops.
7908 replaceSubString(OS.str(), "false", "0");
7909 // Remove wrap flags, their use in SCEV is highly fragile.
7910 // FIXME: Remove this when SCEV gets smarter about them.
7911 replaceSubString(OS.str(), "<nw>", "");
7912 replaceSubString(OS.str(), "<nsw>", "");
7913 replaceSubString(OS.str(), "<nuw>", "");
7918 void ScalarEvolution::verifyAnalysis() const {
7922 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7924 // Gather stringified backedge taken counts for all loops using SCEV's caches.
7925 // FIXME: It would be much better to store actual values instead of strings,
7926 // but SCEV pointers will change if we drop the caches.
7927 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
7928 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7929 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
7931 // Gather stringified backedge taken counts for all loops without using
7934 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7935 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
7937 // Now compare whether they're the same with and without caches. This allows
7938 // verifying that no pass changed the cache.
7939 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
7940 "New loops suddenly appeared!");
7942 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
7943 OldE = BackedgeDumpsOld.end(),
7944 NewI = BackedgeDumpsNew.begin();
7945 OldI != OldE; ++OldI, ++NewI) {
7946 assert(OldI->first == NewI->first && "Loop order changed!");
7948 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
7950 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
7951 // means that a pass is buggy or SCEV has to learn a new pattern but is
7952 // usually not harmful.
7953 if (OldI->second != NewI->second &&
7954 OldI->second.find("undef") == std::string::npos &&
7955 NewI->second.find("undef") == std::string::npos &&
7956 OldI->second != "***COULDNOTCOMPUTE***" &&
7957 NewI->second != "***COULDNOTCOMPUTE***") {
7958 dbgs() << "SCEVValidator: SCEV for loop '"
7959 << OldI->first->getHeader()->getName()
7960 << "' changed from '" << OldI->second
7961 << "' to '" << NewI->second << "'!\n";
7966 // TODO: Verify more things.