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 (SCEVAddExpr::op_iterator I = SA->op_begin(), E = SA->op_end();
1104 DiffOps.push_back(*I);
1106 if (DiffOps.size() == SA->getNumOperands())
1109 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1110 // same three conditions that getSignExtendedExpr checks.
1112 // 1. NSW flags on the step increment.
1113 const SCEV *PreStart = SE->getAddExpr(DiffOps, SA->getNoWrapFlags());
1114 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1115 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1117 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1120 // 2. Direct overflow check on the step operation's expression.
1121 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1122 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1123 const SCEV *OperandExtendedStart =
1124 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1125 SE->getSignExtendExpr(Step, WideTy));
1126 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1127 // Cache knowledge of PreAR NSW.
1129 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1130 // FIXME: this optimization needs a unit test
1131 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1135 // 3. Loop precondition.
1136 ICmpInst::Predicate Pred;
1137 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1139 if (OverflowLimit &&
1140 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1146 // Get the normalized sign-extended expression for this AddRec's Start.
1147 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1149 ScalarEvolution *SE) {
1150 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1152 return SE->getSignExtendExpr(AR->getStart(), Ty);
1154 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1155 SE->getSignExtendExpr(PreStart, Ty));
1158 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1160 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1161 "This is not an extending conversion!");
1162 assert(isSCEVable(Ty) &&
1163 "This is not a conversion to a SCEVable type!");
1164 Ty = getEffectiveSCEVType(Ty);
1166 // Fold if the operand is constant.
1167 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1169 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(), Ty)));
1171 // sext(sext(x)) --> sext(x)
1172 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1173 return getSignExtendExpr(SS->getOperand(), Ty);
1175 // sext(zext(x)) --> zext(x)
1176 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1177 return getZeroExtendExpr(SZ->getOperand(), Ty);
1179 // Before doing any expensive analysis, check to see if we've already
1180 // computed a SCEV for this Op and Ty.
1181 FoldingSetNodeID ID;
1182 ID.AddInteger(scSignExtend);
1186 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1188 // If the input value is provably positive, build a zext instead.
1189 if (isKnownNonNegative(Op))
1190 return getZeroExtendExpr(Op, Ty);
1192 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1193 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1194 // It's possible the bits taken off by the truncate were all sign bits. If
1195 // so, we should be able to simplify this further.
1196 const SCEV *X = ST->getOperand();
1197 ConstantRange CR = getSignedRange(X);
1198 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1199 unsigned NewBits = getTypeSizeInBits(Ty);
1200 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1201 CR.sextOrTrunc(NewBits)))
1202 return getTruncateOrSignExtend(X, Ty);
1205 // If the input value is a chrec scev, and we can prove that the value
1206 // did not overflow the old, smaller, value, we can sign extend all of the
1207 // operands (often constants). This allows analysis of something like
1208 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1209 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1210 if (AR->isAffine()) {
1211 const SCEV *Start = AR->getStart();
1212 const SCEV *Step = AR->getStepRecurrence(*this);
1213 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1214 const Loop *L = AR->getLoop();
1216 // If we have special knowledge that this addrec won't overflow,
1217 // we don't need to do any further analysis.
1218 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1219 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1220 getSignExtendExpr(Step, Ty),
1223 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1224 // Note that this serves two purposes: It filters out loops that are
1225 // simply not analyzable, and it covers the case where this code is
1226 // being called from within backedge-taken count analysis, such that
1227 // attempting to ask for the backedge-taken count would likely result
1228 // in infinite recursion. In the later case, the analysis code will
1229 // cope with a conservative value, and it will take care to purge
1230 // that value once it has finished.
1231 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1232 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1233 // Manually compute the final value for AR, checking for
1236 // Check whether the backedge-taken count can be losslessly casted to
1237 // the addrec's type. The count is always unsigned.
1238 const SCEV *CastedMaxBECount =
1239 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1240 const SCEV *RecastedMaxBECount =
1241 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1242 if (MaxBECount == RecastedMaxBECount) {
1243 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1244 // Check whether Start+Step*MaxBECount has no signed overflow.
1245 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1246 const SCEV *SAdd = getSignExtendExpr(getAddExpr(Start, SMul), WideTy);
1247 const SCEV *WideStart = getSignExtendExpr(Start, WideTy);
1248 const SCEV *WideMaxBECount =
1249 getZeroExtendExpr(CastedMaxBECount, WideTy);
1250 const SCEV *OperandExtendedAdd =
1251 getAddExpr(WideStart,
1252 getMulExpr(WideMaxBECount,
1253 getSignExtendExpr(Step, WideTy)));
1254 if (SAdd == OperandExtendedAdd) {
1255 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1256 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1257 // Return the expression with the addrec on the outside.
1258 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1259 getSignExtendExpr(Step, Ty),
1260 L, AR->getNoWrapFlags());
1262 // Similar to above, only this time treat the step value as unsigned.
1263 // This covers loops that count up with an unsigned step.
1264 OperandExtendedAdd =
1265 getAddExpr(WideStart,
1266 getMulExpr(WideMaxBECount,
1267 getZeroExtendExpr(Step, WideTy)));
1268 if (SAdd == OperandExtendedAdd) {
1269 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1270 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1271 // Return the expression with the addrec on the outside.
1272 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1273 getZeroExtendExpr(Step, Ty),
1274 L, AR->getNoWrapFlags());
1278 // If the backedge is guarded by a comparison with the pre-inc value
1279 // the addrec is safe. Also, if the entry is guarded by a comparison
1280 // with the start value and the backedge is guarded by a comparison
1281 // with the post-inc value, the addrec is safe.
1282 ICmpInst::Predicate Pred;
1283 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1284 if (OverflowLimit &&
1285 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1286 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1287 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1289 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1290 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1291 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1292 getSignExtendExpr(Step, Ty),
1293 L, AR->getNoWrapFlags());
1298 // The cast wasn't folded; create an explicit cast node.
1299 // Recompute the insert position, as it may have been invalidated.
1300 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1301 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1303 UniqueSCEVs.InsertNode(S, IP);
1307 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1308 /// unspecified bits out to the given type.
1310 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1312 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1313 "This is not an extending conversion!");
1314 assert(isSCEVable(Ty) &&
1315 "This is not a conversion to a SCEVable type!");
1316 Ty = getEffectiveSCEVType(Ty);
1318 // Sign-extend negative constants.
1319 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1320 if (SC->getValue()->getValue().isNegative())
1321 return getSignExtendExpr(Op, Ty);
1323 // Peel off a truncate cast.
1324 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1325 const SCEV *NewOp = T->getOperand();
1326 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1327 return getAnyExtendExpr(NewOp, Ty);
1328 return getTruncateOrNoop(NewOp, Ty);
1331 // Next try a zext cast. If the cast is folded, use it.
1332 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1333 if (!isa<SCEVZeroExtendExpr>(ZExt))
1336 // Next try a sext cast. If the cast is folded, use it.
1337 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1338 if (!isa<SCEVSignExtendExpr>(SExt))
1341 // Force the cast to be folded into the operands of an addrec.
1342 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1343 SmallVector<const SCEV *, 4> Ops;
1344 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1346 Ops.push_back(getAnyExtendExpr(*I, Ty));
1347 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1350 // If the expression is obviously signed, use the sext cast value.
1351 if (isa<SCEVSMaxExpr>(Op))
1354 // Absent any other information, use the zext cast value.
1358 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1359 /// a list of operands to be added under the given scale, update the given
1360 /// map. This is a helper function for getAddRecExpr. As an example of
1361 /// what it does, given a sequence of operands that would form an add
1362 /// expression like this:
1364 /// m + n + 13 + (A * (o + p + (B * (q + m + 29)))) + r + (-1 * r)
1366 /// where A and B are constants, update the map with these values:
1368 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1370 /// and add 13 + A*B*29 to AccumulatedConstant.
1371 /// This will allow getAddRecExpr to produce this:
1373 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1375 /// This form often exposes folding opportunities that are hidden in
1376 /// the original operand list.
1378 /// Return true iff it appears that any interesting folding opportunities
1379 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1380 /// the common case where no interesting opportunities are present, and
1381 /// is also used as a check to avoid infinite recursion.
1384 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1385 SmallVectorImpl<const SCEV *> &NewOps,
1386 APInt &AccumulatedConstant,
1387 const SCEV *const *Ops, size_t NumOperands,
1389 ScalarEvolution &SE) {
1390 bool Interesting = false;
1392 // Iterate over the add operands. They are sorted, with constants first.
1394 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1396 // Pull a buried constant out to the outside.
1397 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1399 AccumulatedConstant += Scale * C->getValue()->getValue();
1402 // Next comes everything else. We're especially interested in multiplies
1403 // here, but they're in the middle, so just visit the rest with one loop.
1404 for (; i != NumOperands; ++i) {
1405 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1406 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1408 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1409 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1410 // A multiplication of a constant with another add; recurse.
1411 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1413 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1414 Add->op_begin(), Add->getNumOperands(),
1417 // A multiplication of a constant with some other value. Update
1419 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1420 const SCEV *Key = SE.getMulExpr(MulOps);
1421 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1422 M.insert(std::make_pair(Key, NewScale));
1424 NewOps.push_back(Pair.first->first);
1426 Pair.first->second += NewScale;
1427 // The map already had an entry for this value, which may indicate
1428 // a folding opportunity.
1433 // An ordinary operand. Update the map.
1434 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1435 M.insert(std::make_pair(Ops[i], Scale));
1437 NewOps.push_back(Pair.first->first);
1439 Pair.first->second += Scale;
1440 // The map already had an entry for this value, which may indicate
1441 // a folding opportunity.
1451 struct APIntCompare {
1452 bool operator()(const APInt &LHS, const APInt &RHS) const {
1453 return LHS.ult(RHS);
1458 /// getAddExpr - Get a canonical add expression, or something simpler if
1460 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1461 SCEV::NoWrapFlags Flags) {
1462 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1463 "only nuw or nsw allowed");
1464 assert(!Ops.empty() && "Cannot get empty add!");
1465 if (Ops.size() == 1) return Ops[0];
1467 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1468 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1469 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1470 "SCEVAddExpr operand types don't match!");
1473 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1475 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1476 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1477 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1479 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1480 E = Ops.end(); I != E; ++I)
1481 if (!isKnownNonNegative(*I)) {
1485 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1488 // Sort by complexity, this groups all similar expression types together.
1489 GroupByComplexity(Ops, LI);
1491 // If there are any constants, fold them together.
1493 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1495 assert(Idx < Ops.size());
1496 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1497 // We found two constants, fold them together!
1498 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1499 RHSC->getValue()->getValue());
1500 if (Ops.size() == 2) return Ops[0];
1501 Ops.erase(Ops.begin()+1); // Erase the folded element
1502 LHSC = cast<SCEVConstant>(Ops[0]);
1505 // If we are left with a constant zero being added, strip it off.
1506 if (LHSC->getValue()->isZero()) {
1507 Ops.erase(Ops.begin());
1511 if (Ops.size() == 1) return Ops[0];
1514 // Okay, check to see if the same value occurs in the operand list more than
1515 // once. If so, merge them together into an multiply expression. Since we
1516 // sorted the list, these values are required to be adjacent.
1517 Type *Ty = Ops[0]->getType();
1518 bool FoundMatch = false;
1519 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1520 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1521 // Scan ahead to count how many equal operands there are.
1523 while (i+Count != e && Ops[i+Count] == Ops[i])
1525 // Merge the values into a multiply.
1526 const SCEV *Scale = getConstant(Ty, Count);
1527 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1528 if (Ops.size() == Count)
1531 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1532 --i; e -= Count - 1;
1536 return getAddExpr(Ops, Flags);
1538 // Check for truncates. If all the operands are truncated from the same
1539 // type, see if factoring out the truncate would permit the result to be
1540 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1541 // if the contents of the resulting outer trunc fold to something simple.
1542 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1543 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1544 Type *DstType = Trunc->getType();
1545 Type *SrcType = Trunc->getOperand()->getType();
1546 SmallVector<const SCEV *, 8> LargeOps;
1548 // Check all the operands to see if they can be represented in the
1549 // source type of the truncate.
1550 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1551 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1552 if (T->getOperand()->getType() != SrcType) {
1556 LargeOps.push_back(T->getOperand());
1557 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1558 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1559 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1560 SmallVector<const SCEV *, 8> LargeMulOps;
1561 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1562 if (const SCEVTruncateExpr *T =
1563 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1564 if (T->getOperand()->getType() != SrcType) {
1568 LargeMulOps.push_back(T->getOperand());
1569 } else if (const SCEVConstant *C =
1570 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1571 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1578 LargeOps.push_back(getMulExpr(LargeMulOps));
1585 // Evaluate the expression in the larger type.
1586 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1587 // If it folds to something simple, use it. Otherwise, don't.
1588 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1589 return getTruncateExpr(Fold, DstType);
1593 // Skip past any other cast SCEVs.
1594 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1597 // If there are add operands they would be next.
1598 if (Idx < Ops.size()) {
1599 bool DeletedAdd = false;
1600 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1601 // If we have an add, expand the add operands onto the end of the operands
1603 Ops.erase(Ops.begin()+Idx);
1604 Ops.append(Add->op_begin(), Add->op_end());
1608 // If we deleted at least one add, we added operands to the end of the list,
1609 // and they are not necessarily sorted. Recurse to resort and resimplify
1610 // any operands we just acquired.
1612 return getAddExpr(Ops);
1615 // Skip over the add expression until we get to a multiply.
1616 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1619 // Check to see if there are any folding opportunities present with
1620 // operands multiplied by constant values.
1621 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1622 uint64_t BitWidth = getTypeSizeInBits(Ty);
1623 DenseMap<const SCEV *, APInt> M;
1624 SmallVector<const SCEV *, 8> NewOps;
1625 APInt AccumulatedConstant(BitWidth, 0);
1626 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1627 Ops.data(), Ops.size(),
1628 APInt(BitWidth, 1), *this)) {
1629 // Some interesting folding opportunity is present, so its worthwhile to
1630 // re-generate the operands list. Group the operands by constant scale,
1631 // to avoid multiplying by the same constant scale multiple times.
1632 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1633 for (SmallVectorImpl<const SCEV *>::const_iterator I = NewOps.begin(),
1634 E = NewOps.end(); I != E; ++I)
1635 MulOpLists[M.find(*I)->second].push_back(*I);
1636 // Re-generate the operands list.
1638 if (AccumulatedConstant != 0)
1639 Ops.push_back(getConstant(AccumulatedConstant));
1640 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1641 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1643 Ops.push_back(getMulExpr(getConstant(I->first),
1644 getAddExpr(I->second)));
1646 return getConstant(Ty, 0);
1647 if (Ops.size() == 1)
1649 return getAddExpr(Ops);
1653 // If we are adding something to a multiply expression, make sure the
1654 // something is not already an operand of the multiply. If so, merge it into
1656 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1657 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1658 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1659 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1660 if (isa<SCEVConstant>(MulOpSCEV))
1662 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1663 if (MulOpSCEV == Ops[AddOp]) {
1664 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1665 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1666 if (Mul->getNumOperands() != 2) {
1667 // If the multiply has more than two operands, we must get the
1669 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1670 Mul->op_begin()+MulOp);
1671 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1672 InnerMul = getMulExpr(MulOps);
1674 const SCEV *One = getConstant(Ty, 1);
1675 const SCEV *AddOne = getAddExpr(One, InnerMul);
1676 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1677 if (Ops.size() == 2) return OuterMul;
1679 Ops.erase(Ops.begin()+AddOp);
1680 Ops.erase(Ops.begin()+Idx-1);
1682 Ops.erase(Ops.begin()+Idx);
1683 Ops.erase(Ops.begin()+AddOp-1);
1685 Ops.push_back(OuterMul);
1686 return getAddExpr(Ops);
1689 // Check this multiply against other multiplies being added together.
1690 for (unsigned OtherMulIdx = Idx+1;
1691 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1693 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1694 // If MulOp occurs in OtherMul, we can fold the two multiplies
1696 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1697 OMulOp != e; ++OMulOp)
1698 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1699 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1700 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1701 if (Mul->getNumOperands() != 2) {
1702 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1703 Mul->op_begin()+MulOp);
1704 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1705 InnerMul1 = getMulExpr(MulOps);
1707 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1708 if (OtherMul->getNumOperands() != 2) {
1709 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1710 OtherMul->op_begin()+OMulOp);
1711 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1712 InnerMul2 = getMulExpr(MulOps);
1714 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1715 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1716 if (Ops.size() == 2) return OuterMul;
1717 Ops.erase(Ops.begin()+Idx);
1718 Ops.erase(Ops.begin()+OtherMulIdx-1);
1719 Ops.push_back(OuterMul);
1720 return getAddExpr(Ops);
1726 // If there are any add recurrences in the operands list, see if any other
1727 // added values are loop invariant. If so, we can fold them into the
1729 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1732 // Scan over all recurrences, trying to fold loop invariants into them.
1733 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1734 // Scan all of the other operands to this add and add them to the vector if
1735 // they are loop invariant w.r.t. the recurrence.
1736 SmallVector<const SCEV *, 8> LIOps;
1737 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1738 const Loop *AddRecLoop = AddRec->getLoop();
1739 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1740 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1741 LIOps.push_back(Ops[i]);
1742 Ops.erase(Ops.begin()+i);
1746 // If we found some loop invariants, fold them into the recurrence.
1747 if (!LIOps.empty()) {
1748 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1749 LIOps.push_back(AddRec->getStart());
1751 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1753 AddRecOps[0] = getAddExpr(LIOps);
1755 // Build the new addrec. Propagate the NUW and NSW flags if both the
1756 // outer add and the inner addrec are guaranteed to have no overflow.
1757 // Always propagate NW.
1758 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1759 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1761 // If all of the other operands were loop invariant, we are done.
1762 if (Ops.size() == 1) return NewRec;
1764 // Otherwise, add the folded AddRec by the non-invariant parts.
1765 for (unsigned i = 0;; ++i)
1766 if (Ops[i] == AddRec) {
1770 return getAddExpr(Ops);
1773 // Okay, if there weren't any loop invariants to be folded, check to see if
1774 // there are multiple AddRec's with the same loop induction variable being
1775 // added together. If so, we can fold them.
1776 for (unsigned OtherIdx = Idx+1;
1777 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1779 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1780 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1781 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1783 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1785 if (const SCEVAddRecExpr *OtherAddRec =
1786 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1787 if (OtherAddRec->getLoop() == AddRecLoop) {
1788 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1790 if (i >= AddRecOps.size()) {
1791 AddRecOps.append(OtherAddRec->op_begin()+i,
1792 OtherAddRec->op_end());
1795 AddRecOps[i] = getAddExpr(AddRecOps[i],
1796 OtherAddRec->getOperand(i));
1798 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1800 // Step size has changed, so we cannot guarantee no self-wraparound.
1801 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1802 return getAddExpr(Ops);
1805 // Otherwise couldn't fold anything into this recurrence. Move onto the
1809 // Okay, it looks like we really DO need an add expr. Check to see if we
1810 // already have one, otherwise create a new one.
1811 FoldingSetNodeID ID;
1812 ID.AddInteger(scAddExpr);
1813 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1814 ID.AddPointer(Ops[i]);
1817 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1819 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1820 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1821 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1823 UniqueSCEVs.InsertNode(S, IP);
1825 S->setNoWrapFlags(Flags);
1829 static uint64_t umul_ov(uint64_t i, uint64_t j, bool &Overflow) {
1831 if (j > 1 && k / j != i) Overflow = true;
1835 /// Compute the result of "n choose k", the binomial coefficient. If an
1836 /// intermediate computation overflows, Overflow will be set and the return will
1837 /// be garbage. Overflow is not cleared on absence of overflow.
1838 static uint64_t Choose(uint64_t n, uint64_t k, bool &Overflow) {
1839 // We use the multiplicative formula:
1840 // n(n-1)(n-2)...(n-(k-1)) / k(k-1)(k-2)...1 .
1841 // At each iteration, we take the n-th term of the numeral and divide by the
1842 // (k-n)th term of the denominator. This division will always produce an
1843 // integral result, and helps reduce the chance of overflow in the
1844 // intermediate computations. However, we can still overflow even when the
1845 // final result would fit.
1847 if (n == 0 || n == k) return 1;
1848 if (k > n) return 0;
1854 for (uint64_t i = 1; i <= k; ++i) {
1855 r = umul_ov(r, n-(i-1), Overflow);
1861 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1863 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1864 SCEV::NoWrapFlags Flags) {
1865 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1866 "only nuw or nsw allowed");
1867 assert(!Ops.empty() && "Cannot get empty mul!");
1868 if (Ops.size() == 1) return Ops[0];
1870 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1871 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1872 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1873 "SCEVMulExpr operand types don't match!");
1876 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1878 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1879 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1880 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1882 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1883 E = Ops.end(); I != E; ++I)
1884 if (!isKnownNonNegative(*I)) {
1888 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1891 // Sort by complexity, this groups all similar expression types together.
1892 GroupByComplexity(Ops, LI);
1894 // If there are any constants, fold them together.
1896 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1898 // C1*(C2+V) -> C1*C2 + C1*V
1899 if (Ops.size() == 2)
1900 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1901 if (Add->getNumOperands() == 2 &&
1902 isa<SCEVConstant>(Add->getOperand(0)))
1903 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1904 getMulExpr(LHSC, Add->getOperand(1)));
1907 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1908 // We found two constants, fold them together!
1909 ConstantInt *Fold = ConstantInt::get(getContext(),
1910 LHSC->getValue()->getValue() *
1911 RHSC->getValue()->getValue());
1912 Ops[0] = getConstant(Fold);
1913 Ops.erase(Ops.begin()+1); // Erase the folded element
1914 if (Ops.size() == 1) return Ops[0];
1915 LHSC = cast<SCEVConstant>(Ops[0]);
1918 // If we are left with a constant one being multiplied, strip it off.
1919 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1920 Ops.erase(Ops.begin());
1922 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1923 // If we have a multiply of zero, it will always be zero.
1925 } else if (Ops[0]->isAllOnesValue()) {
1926 // If we have a mul by -1 of an add, try distributing the -1 among the
1928 if (Ops.size() == 2) {
1929 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1930 SmallVector<const SCEV *, 4> NewOps;
1931 bool AnyFolded = false;
1932 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1933 E = Add->op_end(); I != E; ++I) {
1934 const SCEV *Mul = getMulExpr(Ops[0], *I);
1935 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1936 NewOps.push_back(Mul);
1939 return getAddExpr(NewOps);
1941 else if (const SCEVAddRecExpr *
1942 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1943 // Negation preserves a recurrence's no self-wrap property.
1944 SmallVector<const SCEV *, 4> Operands;
1945 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1946 E = AddRec->op_end(); I != E; ++I) {
1947 Operands.push_back(getMulExpr(Ops[0], *I));
1949 return getAddRecExpr(Operands, AddRec->getLoop(),
1950 AddRec->getNoWrapFlags(SCEV::FlagNW));
1955 if (Ops.size() == 1)
1959 // Skip over the add expression until we get to a multiply.
1960 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1963 // If there are mul operands inline them all into this expression.
1964 if (Idx < Ops.size()) {
1965 bool DeletedMul = false;
1966 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1967 // If we have an mul, expand the mul operands onto the end of the operands
1969 Ops.erase(Ops.begin()+Idx);
1970 Ops.append(Mul->op_begin(), Mul->op_end());
1974 // If we deleted at least one mul, we added operands to the end of the list,
1975 // and they are not necessarily sorted. Recurse to resort and resimplify
1976 // any operands we just acquired.
1978 return getMulExpr(Ops);
1981 // If there are any add recurrences in the operands list, see if any other
1982 // added values are loop invariant. If so, we can fold them into the
1984 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1987 // Scan over all recurrences, trying to fold loop invariants into them.
1988 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1989 // Scan all of the other operands to this mul and add them to the vector if
1990 // they are loop invariant w.r.t. the recurrence.
1991 SmallVector<const SCEV *, 8> LIOps;
1992 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1993 const Loop *AddRecLoop = AddRec->getLoop();
1994 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1995 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1996 LIOps.push_back(Ops[i]);
1997 Ops.erase(Ops.begin()+i);
2001 // If we found some loop invariants, fold them into the recurrence.
2002 if (!LIOps.empty()) {
2003 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
2004 SmallVector<const SCEV *, 4> NewOps;
2005 NewOps.reserve(AddRec->getNumOperands());
2006 const SCEV *Scale = getMulExpr(LIOps);
2007 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
2008 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
2010 // Build the new addrec. Propagate the NUW and NSW flags if both the
2011 // outer mul and the inner addrec are guaranteed to have no overflow.
2013 // No self-wrap cannot be guaranteed after changing the step size, but
2014 // will be inferred if either NUW or NSW is true.
2015 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
2016 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
2018 // If all of the other operands were loop invariant, we are done.
2019 if (Ops.size() == 1) return NewRec;
2021 // Otherwise, multiply the folded AddRec by the non-invariant parts.
2022 for (unsigned i = 0;; ++i)
2023 if (Ops[i] == AddRec) {
2027 return getMulExpr(Ops);
2030 // Okay, if there weren't any loop invariants to be folded, check to see if
2031 // there are multiple AddRec's with the same loop induction variable being
2032 // multiplied together. If so, we can fold them.
2033 for (unsigned OtherIdx = Idx+1;
2034 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2036 if (AddRecLoop != cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop())
2039 // {A1,+,A2,+,...,+,An}<L> * {B1,+,B2,+,...,+,Bn}<L>
2040 // = {x=1 in [ sum y=x..2x [ sum z=max(y-x, y-n)..min(x,n) [
2041 // choose(x, 2x)*choose(2x-y, x-z)*A_{y-z}*B_z
2042 // ]]],+,...up to x=2n}.
2043 // Note that the arguments to choose() are always integers with values
2044 // known at compile time, never SCEV objects.
2046 // The implementation avoids pointless extra computations when the two
2047 // addrec's are of different length (mathematically, it's equivalent to
2048 // an infinite stream of zeros on the right).
2049 bool OpsModified = false;
2050 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
2052 const SCEVAddRecExpr *OtherAddRec =
2053 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]);
2054 if (!OtherAddRec || OtherAddRec->getLoop() != AddRecLoop)
2057 bool Overflow = false;
2058 Type *Ty = AddRec->getType();
2059 bool LargerThan64Bits = getTypeSizeInBits(Ty) > 64;
2060 SmallVector<const SCEV*, 7> AddRecOps;
2061 for (int x = 0, xe = AddRec->getNumOperands() +
2062 OtherAddRec->getNumOperands() - 1; x != xe && !Overflow; ++x) {
2063 const SCEV *Term = getConstant(Ty, 0);
2064 for (int y = x, ye = 2*x+1; y != ye && !Overflow; ++y) {
2065 uint64_t Coeff1 = Choose(x, 2*x - y, Overflow);
2066 for (int z = std::max(y-x, y-(int)AddRec->getNumOperands()+1),
2067 ze = std::min(x+1, (int)OtherAddRec->getNumOperands());
2068 z < ze && !Overflow; ++z) {
2069 uint64_t Coeff2 = Choose(2*x - y, x-z, Overflow);
2071 if (LargerThan64Bits)
2072 Coeff = umul_ov(Coeff1, Coeff2, Overflow);
2074 Coeff = Coeff1*Coeff2;
2075 const SCEV *CoeffTerm = getConstant(Ty, Coeff);
2076 const SCEV *Term1 = AddRec->getOperand(y-z);
2077 const SCEV *Term2 = OtherAddRec->getOperand(z);
2078 Term = getAddExpr(Term, getMulExpr(CoeffTerm, Term1,Term2));
2081 AddRecOps.push_back(Term);
2084 const SCEV *NewAddRec = getAddRecExpr(AddRecOps, AddRec->getLoop(),
2086 if (Ops.size() == 2) return NewAddRec;
2087 Ops[Idx] = NewAddRec;
2088 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2090 AddRec = dyn_cast<SCEVAddRecExpr>(NewAddRec);
2096 return getMulExpr(Ops);
2099 // Otherwise couldn't fold anything into this recurrence. Move onto the
2103 // Okay, it looks like we really DO need an mul expr. Check to see if we
2104 // already have one, otherwise create a new one.
2105 FoldingSetNodeID ID;
2106 ID.AddInteger(scMulExpr);
2107 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2108 ID.AddPointer(Ops[i]);
2111 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2113 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2114 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2115 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2117 UniqueSCEVs.InsertNode(S, IP);
2119 S->setNoWrapFlags(Flags);
2123 /// getUDivExpr - Get a canonical unsigned division expression, or something
2124 /// simpler if possible.
2125 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2127 assert(getEffectiveSCEVType(LHS->getType()) ==
2128 getEffectiveSCEVType(RHS->getType()) &&
2129 "SCEVUDivExpr operand types don't match!");
2131 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2132 if (RHSC->getValue()->equalsInt(1))
2133 return LHS; // X udiv 1 --> x
2134 // If the denominator is zero, the result of the udiv is undefined. Don't
2135 // try to analyze it, because the resolution chosen here may differ from
2136 // the resolution chosen in other parts of the compiler.
2137 if (!RHSC->getValue()->isZero()) {
2138 // Determine if the division can be folded into the operands of
2140 // TODO: Generalize this to non-constants by using known-bits information.
2141 Type *Ty = LHS->getType();
2142 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2143 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2144 // For non-power-of-two values, effectively round the value up to the
2145 // nearest power of two.
2146 if (!RHSC->getValue()->getValue().isPowerOf2())
2148 IntegerType *ExtTy =
2149 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2150 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2151 if (const SCEVConstant *Step =
2152 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2153 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2154 const APInt &StepInt = Step->getValue()->getValue();
2155 const APInt &DivInt = RHSC->getValue()->getValue();
2156 if (!StepInt.urem(DivInt) &&
2157 getZeroExtendExpr(AR, ExtTy) ==
2158 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2159 getZeroExtendExpr(Step, ExtTy),
2160 AR->getLoop(), SCEV::FlagAnyWrap)) {
2161 SmallVector<const SCEV *, 4> Operands;
2162 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2163 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2164 return getAddRecExpr(Operands, AR->getLoop(),
2167 /// Get a canonical UDivExpr for a recurrence.
2168 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2169 // We can currently only fold X%N if X is constant.
2170 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2171 if (StartC && !DivInt.urem(StepInt) &&
2172 getZeroExtendExpr(AR, ExtTy) ==
2173 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2174 getZeroExtendExpr(Step, ExtTy),
2175 AR->getLoop(), SCEV::FlagAnyWrap)) {
2176 const APInt &StartInt = StartC->getValue()->getValue();
2177 const APInt &StartRem = StartInt.urem(StepInt);
2179 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2180 AR->getLoop(), SCEV::FlagNW);
2183 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2184 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2185 SmallVector<const SCEV *, 4> Operands;
2186 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2187 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2188 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2189 // Find an operand that's safely divisible.
2190 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2191 const SCEV *Op = M->getOperand(i);
2192 const SCEV *Div = getUDivExpr(Op, RHSC);
2193 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2194 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2197 return getMulExpr(Operands);
2201 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2202 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2203 SmallVector<const SCEV *, 4> Operands;
2204 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2205 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2206 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2208 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2209 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2210 if (isa<SCEVUDivExpr>(Op) ||
2211 getMulExpr(Op, RHS) != A->getOperand(i))
2213 Operands.push_back(Op);
2215 if (Operands.size() == A->getNumOperands())
2216 return getAddExpr(Operands);
2220 // Fold if both operands are constant.
2221 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2222 Constant *LHSCV = LHSC->getValue();
2223 Constant *RHSCV = RHSC->getValue();
2224 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2230 FoldingSetNodeID ID;
2231 ID.AddInteger(scUDivExpr);
2235 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2236 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2238 UniqueSCEVs.InsertNode(S, IP);
2242 static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
2243 APInt A = C1->getValue()->getValue().abs();
2244 APInt B = C2->getValue()->getValue().abs();
2245 uint32_t ABW = A.getBitWidth();
2246 uint32_t BBW = B.getBitWidth();
2253 return APIntOps::GreatestCommonDivisor(A, B);
2256 /// getUDivExactExpr - Get a canonical unsigned division expression, or
2257 /// something simpler if possible. There is no representation for an exact udiv
2258 /// in SCEV IR, but we can attempt to remove factors from the LHS and RHS.
2259 /// We can't do this when it's not exact because the udiv may be clearing bits.
2260 const SCEV *ScalarEvolution::getUDivExactExpr(const SCEV *LHS,
2262 // TODO: we could try to find factors in all sorts of things, but for now we
2263 // just deal with u/exact (multiply, constant). See SCEVDivision towards the
2264 // end of this file for inspiration.
2266 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(LHS);
2268 return getUDivExpr(LHS, RHS);
2270 if (const SCEVConstant *RHSCst = dyn_cast<SCEVConstant>(RHS)) {
2271 // If the mulexpr multiplies by a constant, then that constant must be the
2272 // first element of the mulexpr.
2273 if (const SCEVConstant *LHSCst =
2274 dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
2275 if (LHSCst == RHSCst) {
2276 SmallVector<const SCEV *, 2> Operands;
2277 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2278 return getMulExpr(Operands);
2281 // We can't just assume that LHSCst divides RHSCst cleanly, it could be
2282 // that there's a factor provided by one of the other terms. We need to
2284 APInt Factor = gcd(LHSCst, RHSCst);
2285 if (!Factor.isIntN(1)) {
2286 LHSCst = cast<SCEVConstant>(
2287 getConstant(LHSCst->getValue()->getValue().udiv(Factor)));
2288 RHSCst = cast<SCEVConstant>(
2289 getConstant(RHSCst->getValue()->getValue().udiv(Factor)));
2290 SmallVector<const SCEV *, 2> Operands;
2291 Operands.push_back(LHSCst);
2292 Operands.append(Mul->op_begin() + 1, Mul->op_end());
2293 LHS = getMulExpr(Operands);
2295 Mul = dyn_cast<SCEVMulExpr>(LHS);
2297 return getUDivExactExpr(LHS, RHS);
2302 for (int i = 0, e = Mul->getNumOperands(); i != e; ++i) {
2303 if (Mul->getOperand(i) == RHS) {
2304 SmallVector<const SCEV *, 2> Operands;
2305 Operands.append(Mul->op_begin(), Mul->op_begin() + i);
2306 Operands.append(Mul->op_begin() + i + 1, Mul->op_end());
2307 return getMulExpr(Operands);
2311 return getUDivExpr(LHS, RHS);
2314 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2315 /// Simplify the expression as much as possible.
2316 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2318 SCEV::NoWrapFlags Flags) {
2319 SmallVector<const SCEV *, 4> Operands;
2320 Operands.push_back(Start);
2321 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2322 if (StepChrec->getLoop() == L) {
2323 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2324 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2327 Operands.push_back(Step);
2328 return getAddRecExpr(Operands, L, Flags);
2331 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2332 /// Simplify the expression as much as possible.
2334 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2335 const Loop *L, SCEV::NoWrapFlags Flags) {
2336 if (Operands.size() == 1) return Operands[0];
2338 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2339 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2340 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2341 "SCEVAddRecExpr operand types don't match!");
2342 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2343 assert(isLoopInvariant(Operands[i], L) &&
2344 "SCEVAddRecExpr operand is not loop-invariant!");
2347 if (Operands.back()->isZero()) {
2348 Operands.pop_back();
2349 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2352 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2353 // use that information to infer NUW and NSW flags. However, computing a
2354 // BE count requires calling getAddRecExpr, so we may not yet have a
2355 // meaningful BE count at this point (and if we don't, we'd be stuck
2356 // with a SCEVCouldNotCompute as the cached BE count).
2358 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2360 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2361 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2362 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2364 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2365 E = Operands.end(); I != E; ++I)
2366 if (!isKnownNonNegative(*I)) {
2370 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2373 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2374 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2375 const Loop *NestedLoop = NestedAR->getLoop();
2376 if (L->contains(NestedLoop) ?
2377 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2378 (!NestedLoop->contains(L) &&
2379 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2380 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2381 NestedAR->op_end());
2382 Operands[0] = NestedAR->getStart();
2383 // AddRecs require their operands be loop-invariant with respect to their
2384 // loops. Don't perform this transformation if it would break this
2386 bool AllInvariant = true;
2387 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2388 if (!isLoopInvariant(Operands[i], L)) {
2389 AllInvariant = false;
2393 // Create a recurrence for the outer loop with the same step size.
2395 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2396 // inner recurrence has the same property.
2397 SCEV::NoWrapFlags OuterFlags =
2398 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2400 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2401 AllInvariant = true;
2402 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2403 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2404 AllInvariant = false;
2408 // Ok, both add recurrences are valid after the transformation.
2410 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2411 // the outer recurrence has the same property.
2412 SCEV::NoWrapFlags InnerFlags =
2413 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2414 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2417 // Reset Operands to its original state.
2418 Operands[0] = NestedAR;
2422 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2423 // already have one, otherwise create a new one.
2424 FoldingSetNodeID ID;
2425 ID.AddInteger(scAddRecExpr);
2426 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2427 ID.AddPointer(Operands[i]);
2431 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2433 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2434 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2435 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2436 O, Operands.size(), L);
2437 UniqueSCEVs.InsertNode(S, IP);
2439 S->setNoWrapFlags(Flags);
2443 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2445 SmallVector<const SCEV *, 2> Ops;
2448 return getSMaxExpr(Ops);
2452 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2453 assert(!Ops.empty() && "Cannot get empty smax!");
2454 if (Ops.size() == 1) return Ops[0];
2456 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2457 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2458 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2459 "SCEVSMaxExpr operand types don't match!");
2462 // Sort by complexity, this groups all similar expression types together.
2463 GroupByComplexity(Ops, LI);
2465 // If there are any constants, fold them together.
2467 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2469 assert(Idx < Ops.size());
2470 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2471 // We found two constants, fold them together!
2472 ConstantInt *Fold = ConstantInt::get(getContext(),
2473 APIntOps::smax(LHSC->getValue()->getValue(),
2474 RHSC->getValue()->getValue()));
2475 Ops[0] = getConstant(Fold);
2476 Ops.erase(Ops.begin()+1); // Erase the folded element
2477 if (Ops.size() == 1) return Ops[0];
2478 LHSC = cast<SCEVConstant>(Ops[0]);
2481 // If we are left with a constant minimum-int, strip it off.
2482 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2483 Ops.erase(Ops.begin());
2485 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2486 // If we have an smax with a constant maximum-int, it will always be
2491 if (Ops.size() == 1) return Ops[0];
2494 // Find the first SMax
2495 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2498 // Check to see if one of the operands is an SMax. If so, expand its operands
2499 // onto our operand list, and recurse to simplify.
2500 if (Idx < Ops.size()) {
2501 bool DeletedSMax = false;
2502 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2503 Ops.erase(Ops.begin()+Idx);
2504 Ops.append(SMax->op_begin(), SMax->op_end());
2509 return getSMaxExpr(Ops);
2512 // Okay, check to see if the same value occurs in the operand list twice. If
2513 // so, delete one. Since we sorted the list, these values are required to
2515 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2516 // X smax Y smax Y --> X smax Y
2517 // X smax Y --> X, if X is always greater than Y
2518 if (Ops[i] == Ops[i+1] ||
2519 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2520 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2522 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2523 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2527 if (Ops.size() == 1) return Ops[0];
2529 assert(!Ops.empty() && "Reduced smax down to nothing!");
2531 // Okay, it looks like we really DO need an smax expr. Check to see if we
2532 // already have one, otherwise create a new one.
2533 FoldingSetNodeID ID;
2534 ID.AddInteger(scSMaxExpr);
2535 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2536 ID.AddPointer(Ops[i]);
2538 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2539 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2540 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2541 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2543 UniqueSCEVs.InsertNode(S, IP);
2547 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2549 SmallVector<const SCEV *, 2> Ops;
2552 return getUMaxExpr(Ops);
2556 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2557 assert(!Ops.empty() && "Cannot get empty umax!");
2558 if (Ops.size() == 1) return Ops[0];
2560 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2561 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2562 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2563 "SCEVUMaxExpr operand types don't match!");
2566 // Sort by complexity, this groups all similar expression types together.
2567 GroupByComplexity(Ops, LI);
2569 // If there are any constants, fold them together.
2571 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2573 assert(Idx < Ops.size());
2574 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2575 // We found two constants, fold them together!
2576 ConstantInt *Fold = ConstantInt::get(getContext(),
2577 APIntOps::umax(LHSC->getValue()->getValue(),
2578 RHSC->getValue()->getValue()));
2579 Ops[0] = getConstant(Fold);
2580 Ops.erase(Ops.begin()+1); // Erase the folded element
2581 if (Ops.size() == 1) return Ops[0];
2582 LHSC = cast<SCEVConstant>(Ops[0]);
2585 // If we are left with a constant minimum-int, strip it off.
2586 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2587 Ops.erase(Ops.begin());
2589 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2590 // If we have an umax with a constant maximum-int, it will always be
2595 if (Ops.size() == 1) return Ops[0];
2598 // Find the first UMax
2599 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2602 // Check to see if one of the operands is a UMax. If so, expand its operands
2603 // onto our operand list, and recurse to simplify.
2604 if (Idx < Ops.size()) {
2605 bool DeletedUMax = false;
2606 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2607 Ops.erase(Ops.begin()+Idx);
2608 Ops.append(UMax->op_begin(), UMax->op_end());
2613 return getUMaxExpr(Ops);
2616 // Okay, check to see if the same value occurs in the operand list twice. If
2617 // so, delete one. Since we sorted the list, these values are required to
2619 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2620 // X umax Y umax Y --> X umax Y
2621 // X umax Y --> X, if X is always greater than Y
2622 if (Ops[i] == Ops[i+1] ||
2623 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2624 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2626 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2627 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2631 if (Ops.size() == 1) return Ops[0];
2633 assert(!Ops.empty() && "Reduced umax down to nothing!");
2635 // Okay, it looks like we really DO need a umax expr. Check to see if we
2636 // already have one, otherwise create a new one.
2637 FoldingSetNodeID ID;
2638 ID.AddInteger(scUMaxExpr);
2639 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2640 ID.AddPointer(Ops[i]);
2642 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2643 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2644 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2645 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2647 UniqueSCEVs.InsertNode(S, IP);
2651 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2653 // ~smax(~x, ~y) == smin(x, y).
2654 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2657 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2659 // ~umax(~x, ~y) == umin(x, y)
2660 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2663 const SCEV *ScalarEvolution::getSizeOfExpr(Type *IntTy, Type *AllocTy) {
2664 // If we have DataLayout, we can bypass creating a target-independent
2665 // constant expression and then folding it back into a ConstantInt.
2666 // This is just a compile-time optimization.
2668 return getConstant(IntTy, DL->getTypeAllocSize(AllocTy));
2670 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2671 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2672 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2674 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2675 assert(Ty == IntTy && "Effective SCEV type doesn't match");
2676 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2679 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *IntTy,
2682 // If we have DataLayout, we can bypass creating a target-independent
2683 // constant expression and then folding it back into a ConstantInt.
2684 // This is just a compile-time optimization.
2686 return getConstant(IntTy,
2687 DL->getStructLayout(STy)->getElementOffset(FieldNo));
2690 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2691 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2692 if (Constant *Folded = ConstantFoldConstantExpression(CE, DL, TLI))
2695 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2696 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2699 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2700 // Don't attempt to do anything other than create a SCEVUnknown object
2701 // here. createSCEV only calls getUnknown after checking for all other
2702 // interesting possibilities, and any other code that calls getUnknown
2703 // is doing so in order to hide a value from SCEV canonicalization.
2705 FoldingSetNodeID ID;
2706 ID.AddInteger(scUnknown);
2709 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2710 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2711 "Stale SCEVUnknown in uniquing map!");
2714 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2716 FirstUnknown = cast<SCEVUnknown>(S);
2717 UniqueSCEVs.InsertNode(S, IP);
2721 //===----------------------------------------------------------------------===//
2722 // Basic SCEV Analysis and PHI Idiom Recognition Code
2725 /// isSCEVable - Test if values of the given type are analyzable within
2726 /// the SCEV framework. This primarily includes integer types, and it
2727 /// can optionally include pointer types if the ScalarEvolution class
2728 /// has access to target-specific information.
2729 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2730 // Integers and pointers are always SCEVable.
2731 return Ty->isIntegerTy() || Ty->isPointerTy();
2734 /// getTypeSizeInBits - Return the size in bits of the specified type,
2735 /// for which isSCEVable must return true.
2736 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2737 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2739 // If we have a DataLayout, use it!
2741 return DL->getTypeSizeInBits(Ty);
2743 // Integer types have fixed sizes.
2744 if (Ty->isIntegerTy())
2745 return Ty->getPrimitiveSizeInBits();
2747 // The only other support type is pointer. Without DataLayout, conservatively
2748 // assume pointers are 64-bit.
2749 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2753 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2754 /// the given type and which represents how SCEV will treat the given
2755 /// type, for which isSCEVable must return true. For pointer types,
2756 /// this is the pointer-sized integer type.
2757 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2758 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2760 if (Ty->isIntegerTy()) {
2764 // The only other support type is pointer.
2765 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2768 return DL->getIntPtrType(Ty);
2770 // Without DataLayout, conservatively assume pointers are 64-bit.
2771 return Type::getInt64Ty(getContext());
2774 const SCEV *ScalarEvolution::getCouldNotCompute() {
2775 return &CouldNotCompute;
2779 // Helper class working with SCEVTraversal to figure out if a SCEV contains
2780 // a SCEVUnknown with null value-pointer. FindInvalidSCEVUnknown::FindOne
2781 // is set iff if find such SCEVUnknown.
2783 struct FindInvalidSCEVUnknown {
2785 FindInvalidSCEVUnknown() { FindOne = false; }
2786 bool follow(const SCEV *S) {
2787 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
2791 if (!cast<SCEVUnknown>(S)->getValue())
2798 bool isDone() const { return FindOne; }
2802 bool ScalarEvolution::checkValidity(const SCEV *S) const {
2803 FindInvalidSCEVUnknown F;
2804 SCEVTraversal<FindInvalidSCEVUnknown> ST(F);
2810 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2811 /// expression and create a new one.
2812 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2813 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2815 ValueExprMapType::iterator I = ValueExprMap.find_as(V);
2816 if (I != ValueExprMap.end()) {
2817 const SCEV *S = I->second;
2818 if (checkValidity(S))
2821 ValueExprMap.erase(I);
2823 const SCEV *S = createSCEV(V);
2825 // The process of creating a SCEV for V may have caused other SCEVs
2826 // to have been created, so it's necessary to insert the new entry
2827 // from scratch, rather than trying to remember the insert position
2829 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2833 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2835 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2836 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2838 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2840 Type *Ty = V->getType();
2841 Ty = getEffectiveSCEVType(Ty);
2842 return getMulExpr(V,
2843 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2846 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2847 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2848 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2850 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2852 Type *Ty = V->getType();
2853 Ty = getEffectiveSCEVType(Ty);
2854 const SCEV *AllOnes =
2855 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2856 return getMinusSCEV(AllOnes, V);
2859 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2860 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2861 SCEV::NoWrapFlags Flags) {
2862 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2864 // Fast path: X - X --> 0.
2866 return getConstant(LHS->getType(), 0);
2869 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2872 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2873 /// input value to the specified type. If the type must be extended, it is zero
2876 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2877 Type *SrcTy = V->getType();
2878 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2879 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2880 "Cannot truncate or zero extend with non-integer arguments!");
2881 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2882 return V; // No conversion
2883 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2884 return getTruncateExpr(V, Ty);
2885 return getZeroExtendExpr(V, Ty);
2888 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2889 /// input value to the specified type. If the type must be extended, it is sign
2892 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2894 Type *SrcTy = V->getType();
2895 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2896 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2897 "Cannot truncate or zero extend with non-integer arguments!");
2898 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2899 return V; // No conversion
2900 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2901 return getTruncateExpr(V, Ty);
2902 return getSignExtendExpr(V, Ty);
2905 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2906 /// input value to the specified type. If the type must be extended, it is zero
2907 /// extended. The conversion must not be narrowing.
2909 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2910 Type *SrcTy = V->getType();
2911 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2912 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2913 "Cannot noop or zero extend with non-integer arguments!");
2914 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2915 "getNoopOrZeroExtend cannot truncate!");
2916 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2917 return V; // No conversion
2918 return getZeroExtendExpr(V, Ty);
2921 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2922 /// input value to the specified type. If the type must be extended, it is sign
2923 /// extended. The conversion must not be narrowing.
2925 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2926 Type *SrcTy = V->getType();
2927 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2928 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2929 "Cannot noop or sign extend with non-integer arguments!");
2930 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2931 "getNoopOrSignExtend cannot truncate!");
2932 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2933 return V; // No conversion
2934 return getSignExtendExpr(V, Ty);
2937 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2938 /// the input value to the specified type. If the type must be extended,
2939 /// it is extended with unspecified bits. The conversion must not be
2942 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2943 Type *SrcTy = V->getType();
2944 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2945 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2946 "Cannot noop or any extend with non-integer arguments!");
2947 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2948 "getNoopOrAnyExtend cannot truncate!");
2949 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2950 return V; // No conversion
2951 return getAnyExtendExpr(V, Ty);
2954 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2955 /// input value to the specified type. The conversion must not be widening.
2957 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2958 Type *SrcTy = V->getType();
2959 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2960 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2961 "Cannot truncate or noop with non-integer arguments!");
2962 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2963 "getTruncateOrNoop cannot extend!");
2964 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2965 return V; // No conversion
2966 return getTruncateExpr(V, Ty);
2969 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2970 /// the types using zero-extension, and then perform a umax operation
2972 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2974 const SCEV *PromotedLHS = LHS;
2975 const SCEV *PromotedRHS = RHS;
2977 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2978 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2980 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2982 return getUMaxExpr(PromotedLHS, PromotedRHS);
2985 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2986 /// the types using zero-extension, and then perform a umin operation
2988 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2990 const SCEV *PromotedLHS = LHS;
2991 const SCEV *PromotedRHS = RHS;
2993 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2994 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2996 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2998 return getUMinExpr(PromotedLHS, PromotedRHS);
3001 /// getPointerBase - Transitively follow the chain of pointer-type operands
3002 /// until reaching a SCEV that does not have a single pointer operand. This
3003 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
3004 /// but corner cases do exist.
3005 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
3006 // A pointer operand may evaluate to a nonpointer expression, such as null.
3007 if (!V->getType()->isPointerTy())
3010 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
3011 return getPointerBase(Cast->getOperand());
3013 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
3014 const SCEV *PtrOp = nullptr;
3015 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
3017 if ((*I)->getType()->isPointerTy()) {
3018 // Cannot find the base of an expression with multiple pointer operands.
3026 return getPointerBase(PtrOp);
3031 /// PushDefUseChildren - Push users of the given Instruction
3032 /// onto the given Worklist.
3034 PushDefUseChildren(Instruction *I,
3035 SmallVectorImpl<Instruction *> &Worklist) {
3036 // Push the def-use children onto the Worklist stack.
3037 for (User *U : I->users())
3038 Worklist.push_back(cast<Instruction>(U));
3041 /// ForgetSymbolicValue - This looks up computed SCEV values for all
3042 /// instructions that depend on the given instruction and removes them from
3043 /// the ValueExprMapType map if they reference SymName. This is used during PHI
3046 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
3047 SmallVector<Instruction *, 16> Worklist;
3048 PushDefUseChildren(PN, Worklist);
3050 SmallPtrSet<Instruction *, 8> Visited;
3052 while (!Worklist.empty()) {
3053 Instruction *I = Worklist.pop_back_val();
3054 if (!Visited.insert(I)) continue;
3056 ValueExprMapType::iterator It =
3057 ValueExprMap.find_as(static_cast<Value *>(I));
3058 if (It != ValueExprMap.end()) {
3059 const SCEV *Old = It->second;
3061 // Short-circuit the def-use traversal if the symbolic name
3062 // ceases to appear in expressions.
3063 if (Old != SymName && !hasOperand(Old, SymName))
3066 // SCEVUnknown for a PHI either means that it has an unrecognized
3067 // structure, it's a PHI that's in the progress of being computed
3068 // by createNodeForPHI, or it's a single-value PHI. In the first case,
3069 // additional loop trip count information isn't going to change anything.
3070 // In the second case, createNodeForPHI will perform the necessary
3071 // updates on its own when it gets to that point. In the third, we do
3072 // want to forget the SCEVUnknown.
3073 if (!isa<PHINode>(I) ||
3074 !isa<SCEVUnknown>(Old) ||
3075 (I != PN && Old == SymName)) {
3076 forgetMemoizedResults(Old);
3077 ValueExprMap.erase(It);
3081 PushDefUseChildren(I, Worklist);
3085 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
3086 /// a loop header, making it a potential recurrence, or it doesn't.
3088 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
3089 if (const Loop *L = LI->getLoopFor(PN->getParent()))
3090 if (L->getHeader() == PN->getParent()) {
3091 // The loop may have multiple entrances or multiple exits; we can analyze
3092 // this phi as an addrec if it has a unique entry value and a unique
3094 Value *BEValueV = nullptr, *StartValueV = nullptr;
3095 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
3096 Value *V = PN->getIncomingValue(i);
3097 if (L->contains(PN->getIncomingBlock(i))) {
3100 } else if (BEValueV != V) {
3104 } else if (!StartValueV) {
3106 } else if (StartValueV != V) {
3107 StartValueV = nullptr;
3111 if (BEValueV && StartValueV) {
3112 // While we are analyzing this PHI node, handle its value symbolically.
3113 const SCEV *SymbolicName = getUnknown(PN);
3114 assert(ValueExprMap.find_as(PN) == ValueExprMap.end() &&
3115 "PHI node already processed?");
3116 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
3118 // Using this symbolic name for the PHI, analyze the value coming around
3120 const SCEV *BEValue = getSCEV(BEValueV);
3122 // NOTE: If BEValue is loop invariant, we know that the PHI node just
3123 // has a special value for the first iteration of the loop.
3125 // If the value coming around the backedge is an add with the symbolic
3126 // value we just inserted, then we found a simple induction variable!
3127 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
3128 // If there is a single occurrence of the symbolic value, replace it
3129 // with a recurrence.
3130 unsigned FoundIndex = Add->getNumOperands();
3131 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3132 if (Add->getOperand(i) == SymbolicName)
3133 if (FoundIndex == e) {
3138 if (FoundIndex != Add->getNumOperands()) {
3139 // Create an add with everything but the specified operand.
3140 SmallVector<const SCEV *, 8> Ops;
3141 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
3142 if (i != FoundIndex)
3143 Ops.push_back(Add->getOperand(i));
3144 const SCEV *Accum = getAddExpr(Ops);
3146 // This is not a valid addrec if the step amount is varying each
3147 // loop iteration, but is not itself an addrec in this loop.
3148 if (isLoopInvariant(Accum, L) ||
3149 (isa<SCEVAddRecExpr>(Accum) &&
3150 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
3151 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
3153 // If the increment doesn't overflow, then neither the addrec nor
3154 // the post-increment will overflow.
3155 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
3156 if (OBO->hasNoUnsignedWrap())
3157 Flags = setFlags(Flags, SCEV::FlagNUW);
3158 if (OBO->hasNoSignedWrap())
3159 Flags = setFlags(Flags, SCEV::FlagNSW);
3160 } else if (GEPOperator *GEP = dyn_cast<GEPOperator>(BEValueV)) {
3161 // If the increment is an inbounds GEP, then we know the address
3162 // space cannot be wrapped around. We cannot make any guarantee
3163 // about signed or unsigned overflow because pointers are
3164 // unsigned but we may have a negative index from the base
3165 // pointer. We can guarantee that no unsigned wrap occurs if the
3166 // indices form a positive value.
3167 if (GEP->isInBounds()) {
3168 Flags = setFlags(Flags, SCEV::FlagNW);
3170 const SCEV *Ptr = getSCEV(GEP->getPointerOperand());
3171 if (isKnownPositive(getMinusSCEV(getSCEV(GEP), Ptr)))
3172 Flags = setFlags(Flags, SCEV::FlagNUW);
3174 } else if (const SubOperator *OBO =
3175 dyn_cast<SubOperator>(BEValueV)) {
3176 if (OBO->hasNoUnsignedWrap())
3177 Flags = setFlags(Flags, SCEV::FlagNUW);
3178 if (OBO->hasNoSignedWrap())
3179 Flags = setFlags(Flags, SCEV::FlagNSW);
3182 const SCEV *StartVal = getSCEV(StartValueV);
3183 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
3185 // Since the no-wrap flags are on the increment, they apply to the
3186 // post-incremented value as well.
3187 if (isLoopInvariant(Accum, L))
3188 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
3191 // Okay, for the entire analysis of this edge we assumed the PHI
3192 // to be symbolic. We now need to go back and purge all of the
3193 // entries for the scalars that use the symbolic expression.
3194 ForgetSymbolicName(PN, SymbolicName);
3195 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3199 } else if (const SCEVAddRecExpr *AddRec =
3200 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3201 // Otherwise, this could be a loop like this:
3202 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3203 // In this case, j = {1,+,1} and BEValue is j.
3204 // Because the other in-value of i (0) fits the evolution of BEValue
3205 // i really is an addrec evolution.
3206 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3207 const SCEV *StartVal = getSCEV(StartValueV);
3209 // If StartVal = j.start - j.stride, we can use StartVal as the
3210 // initial step of the addrec evolution.
3211 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3212 AddRec->getOperand(1))) {
3213 // FIXME: For constant StartVal, we should be able to infer
3215 const SCEV *PHISCEV =
3216 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3219 // Okay, for the entire analysis of this edge we assumed the PHI
3220 // to be symbolic. We now need to go back and purge all of the
3221 // entries for the scalars that use the symbolic expression.
3222 ForgetSymbolicName(PN, SymbolicName);
3223 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3231 // If the PHI has a single incoming value, follow that value, unless the
3232 // PHI's incoming blocks are in a different loop, in which case doing so
3233 // risks breaking LCSSA form. Instcombine would normally zap these, but
3234 // it doesn't have DominatorTree information, so it may miss cases.
3235 if (Value *V = SimplifyInstruction(PN, DL, TLI, DT))
3236 if (LI->replacementPreservesLCSSAForm(PN, V))
3239 // If it's not a loop phi, we can't handle it yet.
3240 return getUnknown(PN);
3243 /// createNodeForGEP - Expand GEP instructions into add and multiply
3244 /// operations. This allows them to be analyzed by regular SCEV code.
3246 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3247 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3248 Value *Base = GEP->getOperand(0);
3249 // Don't attempt to analyze GEPs over unsized objects.
3250 if (!Base->getType()->getPointerElementType()->isSized())
3251 return getUnknown(GEP);
3253 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3254 // Add expression, because the Instruction may be guarded by control flow
3255 // and the no-overflow bits may not be valid for the expression in any
3257 SCEV::NoWrapFlags Wrap = GEP->isInBounds() ? SCEV::FlagNSW : SCEV::FlagAnyWrap;
3259 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3260 gep_type_iterator GTI = gep_type_begin(GEP);
3261 for (GetElementPtrInst::op_iterator I = std::next(GEP->op_begin()),
3265 // Compute the (potentially symbolic) offset in bytes for this index.
3266 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3267 // For a struct, add the member offset.
3268 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3269 const SCEV *FieldOffset = getOffsetOfExpr(IntPtrTy, STy, FieldNo);
3271 // Add the field offset to the running total offset.
3272 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3274 // For an array, add the element offset, explicitly scaled.
3275 const SCEV *ElementSize = getSizeOfExpr(IntPtrTy, *GTI);
3276 const SCEV *IndexS = getSCEV(Index);
3277 // Getelementptr indices are signed.
3278 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3280 // Multiply the index by the element size to compute the element offset.
3281 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize, Wrap);
3283 // Add the element offset to the running total offset.
3284 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3288 // Get the SCEV for the GEP base.
3289 const SCEV *BaseS = getSCEV(Base);
3291 // Add the total offset from all the GEP indices to the base.
3292 return getAddExpr(BaseS, TotalOffset, Wrap);
3295 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3296 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3297 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3298 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3300 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3301 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3302 return C->getValue()->getValue().countTrailingZeros();
3304 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3305 return std::min(GetMinTrailingZeros(T->getOperand()),
3306 (uint32_t)getTypeSizeInBits(T->getType()));
3308 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3309 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3310 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3311 getTypeSizeInBits(E->getType()) : OpRes;
3314 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3315 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3316 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3317 getTypeSizeInBits(E->getType()) : OpRes;
3320 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3321 // The result is the min of all operands results.
3322 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3323 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3324 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3328 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3329 // The result is the sum of all operands results.
3330 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3331 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3332 for (unsigned i = 1, e = M->getNumOperands();
3333 SumOpRes != BitWidth && i != e; ++i)
3334 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3339 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3340 // The result is the min of all operands results.
3341 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3342 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3343 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3347 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3348 // The result is the min of all operands results.
3349 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3350 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3351 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3355 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3356 // The result is the min of all operands results.
3357 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3358 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3359 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3363 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3364 // For a SCEVUnknown, ask ValueTracking.
3365 unsigned BitWidth = getTypeSizeInBits(U->getType());
3366 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3367 ComputeMaskedBits(U->getValue(), Zeros, Ones);
3368 return Zeros.countTrailingOnes();
3375 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3378 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3379 // See if we've computed this range already.
3380 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3381 if (I != UnsignedRanges.end())
3384 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3385 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3387 unsigned BitWidth = getTypeSizeInBits(S->getType());
3388 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3390 // If the value has known zeros, the maximum unsigned value will have those
3391 // known zeros as well.
3392 uint32_t TZ = GetMinTrailingZeros(S);
3394 ConservativeResult =
3395 ConstantRange(APInt::getMinValue(BitWidth),
3396 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3398 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3399 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3400 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3401 X = X.add(getUnsignedRange(Add->getOperand(i)));
3402 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3405 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3406 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3407 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3408 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3409 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3412 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3413 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3414 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3415 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3416 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3419 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3420 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3421 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3422 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3423 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3426 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3427 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3428 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3429 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3432 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3433 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3434 return setUnsignedRange(ZExt,
3435 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3438 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3439 ConstantRange X = getUnsignedRange(SExt->getOperand());
3440 return setUnsignedRange(SExt,
3441 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3444 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3445 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3446 return setUnsignedRange(Trunc,
3447 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3450 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3451 // If there's no unsigned wrap, the value will never be less than its
3453 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3454 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3455 if (!C->getValue()->isZero())
3456 ConservativeResult =
3457 ConservativeResult.intersectWith(
3458 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3460 // TODO: non-affine addrec
3461 if (AddRec->isAffine()) {
3462 Type *Ty = AddRec->getType();
3463 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3464 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3465 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3466 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3468 const SCEV *Start = AddRec->getStart();
3469 const SCEV *Step = AddRec->getStepRecurrence(*this);
3471 ConstantRange StartRange = getUnsignedRange(Start);
3472 ConstantRange StepRange = getSignedRange(Step);
3473 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3474 ConstantRange EndRange =
3475 StartRange.add(MaxBECountRange.multiply(StepRange));
3477 // Check for overflow. This must be done with ConstantRange arithmetic
3478 // because we could be called from within the ScalarEvolution overflow
3480 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3481 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3482 ConstantRange ExtMaxBECountRange =
3483 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3484 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3485 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3487 return setUnsignedRange(AddRec, ConservativeResult);
3489 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3490 EndRange.getUnsignedMin());
3491 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3492 EndRange.getUnsignedMax());
3493 if (Min.isMinValue() && Max.isMaxValue())
3494 return setUnsignedRange(AddRec, ConservativeResult);
3495 return setUnsignedRange(AddRec,
3496 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3500 return setUnsignedRange(AddRec, ConservativeResult);
3503 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3504 // For a SCEVUnknown, ask ValueTracking.
3505 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3506 ComputeMaskedBits(U->getValue(), Zeros, Ones, DL);
3507 if (Ones == ~Zeros + 1)
3508 return setUnsignedRange(U, ConservativeResult);
3509 return setUnsignedRange(U,
3510 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3513 return setUnsignedRange(S, ConservativeResult);
3516 /// getSignedRange - Determine the signed range for a particular SCEV.
3519 ScalarEvolution::getSignedRange(const SCEV *S) {
3520 // See if we've computed this range already.
3521 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3522 if (I != SignedRanges.end())
3525 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3526 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3528 unsigned BitWidth = getTypeSizeInBits(S->getType());
3529 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3531 // If the value has known zeros, the maximum signed value will have those
3532 // known zeros as well.
3533 uint32_t TZ = GetMinTrailingZeros(S);
3535 ConservativeResult =
3536 ConstantRange(APInt::getSignedMinValue(BitWidth),
3537 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3539 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3540 ConstantRange X = getSignedRange(Add->getOperand(0));
3541 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3542 X = X.add(getSignedRange(Add->getOperand(i)));
3543 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3546 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3547 ConstantRange X = getSignedRange(Mul->getOperand(0));
3548 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3549 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3550 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3553 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3554 ConstantRange X = getSignedRange(SMax->getOperand(0));
3555 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3556 X = X.smax(getSignedRange(SMax->getOperand(i)));
3557 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3560 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3561 ConstantRange X = getSignedRange(UMax->getOperand(0));
3562 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3563 X = X.umax(getSignedRange(UMax->getOperand(i)));
3564 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3567 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3568 ConstantRange X = getSignedRange(UDiv->getLHS());
3569 ConstantRange Y = getSignedRange(UDiv->getRHS());
3570 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3573 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3574 ConstantRange X = getSignedRange(ZExt->getOperand());
3575 return setSignedRange(ZExt,
3576 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3579 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3580 ConstantRange X = getSignedRange(SExt->getOperand());
3581 return setSignedRange(SExt,
3582 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3585 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3586 ConstantRange X = getSignedRange(Trunc->getOperand());
3587 return setSignedRange(Trunc,
3588 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3591 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3592 // If there's no signed wrap, and all the operands have the same sign or
3593 // zero, the value won't ever change sign.
3594 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3595 bool AllNonNeg = true;
3596 bool AllNonPos = true;
3597 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3598 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3599 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3602 ConservativeResult = ConservativeResult.intersectWith(
3603 ConstantRange(APInt(BitWidth, 0),
3604 APInt::getSignedMinValue(BitWidth)));
3606 ConservativeResult = ConservativeResult.intersectWith(
3607 ConstantRange(APInt::getSignedMinValue(BitWidth),
3608 APInt(BitWidth, 1)));
3611 // TODO: non-affine addrec
3612 if (AddRec->isAffine()) {
3613 Type *Ty = AddRec->getType();
3614 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3615 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3616 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3617 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3619 const SCEV *Start = AddRec->getStart();
3620 const SCEV *Step = AddRec->getStepRecurrence(*this);
3622 ConstantRange StartRange = getSignedRange(Start);
3623 ConstantRange StepRange = getSignedRange(Step);
3624 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3625 ConstantRange EndRange =
3626 StartRange.add(MaxBECountRange.multiply(StepRange));
3628 // Check for overflow. This must be done with ConstantRange arithmetic
3629 // because we could be called from within the ScalarEvolution overflow
3631 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3632 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3633 ConstantRange ExtMaxBECountRange =
3634 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3635 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3636 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3638 return setSignedRange(AddRec, ConservativeResult);
3640 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3641 EndRange.getSignedMin());
3642 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3643 EndRange.getSignedMax());
3644 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3645 return setSignedRange(AddRec, ConservativeResult);
3646 return setSignedRange(AddRec,
3647 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3651 return setSignedRange(AddRec, ConservativeResult);
3654 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3655 // For a SCEVUnknown, ask ValueTracking.
3656 if (!U->getValue()->getType()->isIntegerTy() && !DL)
3657 return setSignedRange(U, ConservativeResult);
3658 unsigned NS = ComputeNumSignBits(U->getValue(), DL);
3660 return setSignedRange(U, ConservativeResult);
3661 return setSignedRange(U, ConservativeResult.intersectWith(
3662 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3663 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3666 return setSignedRange(S, ConservativeResult);
3669 /// createSCEV - We know that there is no SCEV for the specified value.
3670 /// Analyze the expression.
3672 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3673 if (!isSCEVable(V->getType()))
3674 return getUnknown(V);
3676 unsigned Opcode = Instruction::UserOp1;
3677 if (Instruction *I = dyn_cast<Instruction>(V)) {
3678 Opcode = I->getOpcode();
3680 // Don't attempt to analyze instructions in blocks that aren't
3681 // reachable. Such instructions don't matter, and they aren't required
3682 // to obey basic rules for definitions dominating uses which this
3683 // analysis depends on.
3684 if (!DT->isReachableFromEntry(I->getParent()))
3685 return getUnknown(V);
3686 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3687 Opcode = CE->getOpcode();
3688 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3689 return getConstant(CI);
3690 else if (isa<ConstantPointerNull>(V))
3691 return getConstant(V->getType(), 0);
3692 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3693 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3695 return getUnknown(V);
3697 Operator *U = cast<Operator>(V);
3699 case Instruction::Add: {
3700 // The simple thing to do would be to just call getSCEV on both operands
3701 // and call getAddExpr with the result. However if we're looking at a
3702 // bunch of things all added together, this can be quite inefficient,
3703 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3704 // Instead, gather up all the operands and make a single getAddExpr call.
3705 // LLVM IR canonical form means we need only traverse the left operands.
3707 // Don't apply this instruction's NSW or NUW flags to the new
3708 // expression. The instruction may be guarded by control flow that the
3709 // no-wrap behavior depends on. Non-control-equivalent instructions can be
3710 // mapped to the same SCEV expression, and it would be incorrect to transfer
3711 // NSW/NUW semantics to those operations.
3712 SmallVector<const SCEV *, 4> AddOps;
3713 AddOps.push_back(getSCEV(U->getOperand(1)));
3714 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3715 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3716 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3718 U = cast<Operator>(Op);
3719 const SCEV *Op1 = getSCEV(U->getOperand(1));
3720 if (Opcode == Instruction::Sub)
3721 AddOps.push_back(getNegativeSCEV(Op1));
3723 AddOps.push_back(Op1);
3725 AddOps.push_back(getSCEV(U->getOperand(0)));
3726 return getAddExpr(AddOps);
3728 case Instruction::Mul: {
3729 // Don't transfer NSW/NUW for the same reason as AddExpr.
3730 SmallVector<const SCEV *, 4> MulOps;
3731 MulOps.push_back(getSCEV(U->getOperand(1)));
3732 for (Value *Op = U->getOperand(0);
3733 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3734 Op = U->getOperand(0)) {
3735 U = cast<Operator>(Op);
3736 MulOps.push_back(getSCEV(U->getOperand(1)));
3738 MulOps.push_back(getSCEV(U->getOperand(0)));
3739 return getMulExpr(MulOps);
3741 case Instruction::UDiv:
3742 return getUDivExpr(getSCEV(U->getOperand(0)),
3743 getSCEV(U->getOperand(1)));
3744 case Instruction::Sub:
3745 return getMinusSCEV(getSCEV(U->getOperand(0)),
3746 getSCEV(U->getOperand(1)));
3747 case Instruction::And:
3748 // For an expression like x&255 that merely masks off the high bits,
3749 // use zext(trunc(x)) as the SCEV expression.
3750 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3751 if (CI->isNullValue())
3752 return getSCEV(U->getOperand(1));
3753 if (CI->isAllOnesValue())
3754 return getSCEV(U->getOperand(0));
3755 const APInt &A = CI->getValue();
3757 // Instcombine's ShrinkDemandedConstant may strip bits out of
3758 // constants, obscuring what would otherwise be a low-bits mask.
3759 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3760 // knew about to reconstruct a low-bits mask value.
3761 unsigned LZ = A.countLeadingZeros();
3762 unsigned TZ = A.countTrailingZeros();
3763 unsigned BitWidth = A.getBitWidth();
3764 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3765 ComputeMaskedBits(U->getOperand(0), KnownZero, KnownOne, DL);
3767 APInt EffectiveMask =
3768 APInt::getLowBitsSet(BitWidth, BitWidth - LZ - TZ).shl(TZ);
3769 if ((LZ != 0 || TZ != 0) && !((~A & ~KnownZero) & EffectiveMask)) {
3770 const SCEV *MulCount = getConstant(
3771 ConstantInt::get(getContext(), APInt::getOneBitSet(BitWidth, TZ)));
3775 getUDivExactExpr(getSCEV(U->getOperand(0)), MulCount),
3776 IntegerType::get(getContext(), BitWidth - LZ - TZ)),
3783 case Instruction::Or:
3784 // If the RHS of the Or is a constant, we may have something like:
3785 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3786 // optimizations will transparently handle this case.
3788 // In order for this transformation to be safe, the LHS must be of the
3789 // form X*(2^n) and the Or constant must be less than 2^n.
3790 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3791 const SCEV *LHS = getSCEV(U->getOperand(0));
3792 const APInt &CIVal = CI->getValue();
3793 if (GetMinTrailingZeros(LHS) >=
3794 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3795 // Build a plain add SCEV.
3796 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3797 // If the LHS of the add was an addrec and it has no-wrap flags,
3798 // transfer the no-wrap flags, since an or won't introduce a wrap.
3799 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3800 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3801 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3802 OldAR->getNoWrapFlags());
3808 case Instruction::Xor:
3809 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3810 // If the RHS of the xor is a signbit, then this is just an add.
3811 // Instcombine turns add of signbit into xor as a strength reduction step.
3812 if (CI->getValue().isSignBit())
3813 return getAddExpr(getSCEV(U->getOperand(0)),
3814 getSCEV(U->getOperand(1)));
3816 // If the RHS of xor is -1, then this is a not operation.
3817 if (CI->isAllOnesValue())
3818 return getNotSCEV(getSCEV(U->getOperand(0)));
3820 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3821 // This is a variant of the check for xor with -1, and it handles
3822 // the case where instcombine has trimmed non-demanded bits out
3823 // of an xor with -1.
3824 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3825 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3826 if (BO->getOpcode() == Instruction::And &&
3827 LCI->getValue() == CI->getValue())
3828 if (const SCEVZeroExtendExpr *Z =
3829 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3830 Type *UTy = U->getType();
3831 const SCEV *Z0 = Z->getOperand();
3832 Type *Z0Ty = Z0->getType();
3833 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3835 // If C is a low-bits mask, the zero extend is serving to
3836 // mask off the high bits. Complement the operand and
3837 // re-apply the zext.
3838 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3839 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3841 // If C is a single bit, it may be in the sign-bit position
3842 // before the zero-extend. In this case, represent the xor
3843 // using an add, which is equivalent, and re-apply the zext.
3844 APInt Trunc = CI->getValue().trunc(Z0TySize);
3845 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3847 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3853 case Instruction::Shl:
3854 // Turn shift left of a constant amount into a multiply.
3855 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3856 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3858 // If the shift count is not less than the bitwidth, the result of
3859 // the shift is undefined. Don't try to analyze it, because the
3860 // resolution chosen here may differ from the resolution chosen in
3861 // other parts of the compiler.
3862 if (SA->getValue().uge(BitWidth))
3865 Constant *X = ConstantInt::get(getContext(),
3866 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3867 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3871 case Instruction::LShr:
3872 // Turn logical shift right of a constant into a unsigned divide.
3873 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3874 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3876 // If the shift count is not less than the bitwidth, the result of
3877 // the shift is undefined. Don't try to analyze it, because the
3878 // resolution chosen here may differ from the resolution chosen in
3879 // other parts of the compiler.
3880 if (SA->getValue().uge(BitWidth))
3883 Constant *X = ConstantInt::get(getContext(),
3884 APInt::getOneBitSet(BitWidth, SA->getZExtValue()));
3885 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3889 case Instruction::AShr:
3890 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3891 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3892 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3893 if (L->getOpcode() == Instruction::Shl &&
3894 L->getOperand(1) == U->getOperand(1)) {
3895 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3897 // If the shift count is not less than the bitwidth, the result of
3898 // the shift is undefined. Don't try to analyze it, because the
3899 // resolution chosen here may differ from the resolution chosen in
3900 // other parts of the compiler.
3901 if (CI->getValue().uge(BitWidth))
3904 uint64_t Amt = BitWidth - CI->getZExtValue();
3905 if (Amt == BitWidth)
3906 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3908 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3909 IntegerType::get(getContext(),
3915 case Instruction::Trunc:
3916 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3918 case Instruction::ZExt:
3919 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3921 case Instruction::SExt:
3922 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3924 case Instruction::BitCast:
3925 // BitCasts are no-op casts so we just eliminate the cast.
3926 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3927 return getSCEV(U->getOperand(0));
3930 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3931 // lead to pointer expressions which cannot safely be expanded to GEPs,
3932 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3933 // simplifying integer expressions.
3935 case Instruction::GetElementPtr:
3936 return createNodeForGEP(cast<GEPOperator>(U));
3938 case Instruction::PHI:
3939 return createNodeForPHI(cast<PHINode>(U));
3941 case Instruction::Select:
3942 // This could be a smax or umax that was lowered earlier.
3943 // Try to recover it.
3944 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3945 Value *LHS = ICI->getOperand(0);
3946 Value *RHS = ICI->getOperand(1);
3947 switch (ICI->getPredicate()) {
3948 case ICmpInst::ICMP_SLT:
3949 case ICmpInst::ICMP_SLE:
3950 std::swap(LHS, RHS);
3952 case ICmpInst::ICMP_SGT:
3953 case ICmpInst::ICMP_SGE:
3954 // a >s b ? a+x : b+x -> smax(a, b)+x
3955 // a >s b ? b+x : a+x -> smin(a, b)+x
3956 if (LHS->getType() == U->getType()) {
3957 const SCEV *LS = getSCEV(LHS);
3958 const SCEV *RS = getSCEV(RHS);
3959 const SCEV *LA = getSCEV(U->getOperand(1));
3960 const SCEV *RA = getSCEV(U->getOperand(2));
3961 const SCEV *LDiff = getMinusSCEV(LA, LS);
3962 const SCEV *RDiff = getMinusSCEV(RA, RS);
3964 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3965 LDiff = getMinusSCEV(LA, RS);
3966 RDiff = getMinusSCEV(RA, LS);
3968 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3971 case ICmpInst::ICMP_ULT:
3972 case ICmpInst::ICMP_ULE:
3973 std::swap(LHS, RHS);
3975 case ICmpInst::ICMP_UGT:
3976 case ICmpInst::ICMP_UGE:
3977 // a >u b ? a+x : b+x -> umax(a, b)+x
3978 // a >u b ? b+x : a+x -> umin(a, b)+x
3979 if (LHS->getType() == U->getType()) {
3980 const SCEV *LS = getSCEV(LHS);
3981 const SCEV *RS = getSCEV(RHS);
3982 const SCEV *LA = getSCEV(U->getOperand(1));
3983 const SCEV *RA = getSCEV(U->getOperand(2));
3984 const SCEV *LDiff = getMinusSCEV(LA, LS);
3985 const SCEV *RDiff = getMinusSCEV(RA, RS);
3987 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3988 LDiff = getMinusSCEV(LA, RS);
3989 RDiff = getMinusSCEV(RA, LS);
3991 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3994 case ICmpInst::ICMP_NE:
3995 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3996 if (LHS->getType() == U->getType() &&
3997 isa<ConstantInt>(RHS) &&
3998 cast<ConstantInt>(RHS)->isZero()) {
3999 const SCEV *One = getConstant(LHS->getType(), 1);
4000 const SCEV *LS = getSCEV(LHS);
4001 const SCEV *LA = getSCEV(U->getOperand(1));
4002 const SCEV *RA = getSCEV(U->getOperand(2));
4003 const SCEV *LDiff = getMinusSCEV(LA, LS);
4004 const SCEV *RDiff = getMinusSCEV(RA, One);
4006 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4009 case ICmpInst::ICMP_EQ:
4010 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
4011 if (LHS->getType() == U->getType() &&
4012 isa<ConstantInt>(RHS) &&
4013 cast<ConstantInt>(RHS)->isZero()) {
4014 const SCEV *One = getConstant(LHS->getType(), 1);
4015 const SCEV *LS = getSCEV(LHS);
4016 const SCEV *LA = getSCEV(U->getOperand(1));
4017 const SCEV *RA = getSCEV(U->getOperand(2));
4018 const SCEV *LDiff = getMinusSCEV(LA, One);
4019 const SCEV *RDiff = getMinusSCEV(RA, LS);
4021 return getAddExpr(getUMaxExpr(One, LS), LDiff);
4029 default: // We cannot analyze this expression.
4033 return getUnknown(V);
4038 //===----------------------------------------------------------------------===//
4039 // Iteration Count Computation Code
4042 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
4043 /// normal unsigned value. Returns 0 if the trip count is unknown or not
4044 /// constant. Will also return 0 if the maximum trip count is very large (>=
4047 /// This "trip count" assumes that control exits via ExitingBlock. More
4048 /// precisely, it is the number of times that control may reach ExitingBlock
4049 /// before taking the branch. For loops with multiple exits, it may not be the
4050 /// number times that the loop header executes because the loop may exit
4051 /// prematurely via another branch.
4053 /// FIXME: We conservatively call getBackedgeTakenCount(L) instead of
4054 /// getExitCount(L, ExitingBlock) to compute a safe trip count considering all
4055 /// loop exits. getExitCount() may return an exact count for this branch
4056 /// assuming no-signed-wrap. The number of well-defined iterations may actually
4057 /// be higher than this trip count if this exit test is skipped and the loop
4058 /// exits via a different branch. Ideally, getExitCount() would know whether it
4059 /// depends on a NSW assumption, and we would only fall back to a conservative
4060 /// trip count in that case.
4061 unsigned ScalarEvolution::
4062 getSmallConstantTripCount(Loop *L, BasicBlock * /*ExitingBlock*/) {
4063 const SCEVConstant *ExitCount =
4064 dyn_cast<SCEVConstant>(getBackedgeTakenCount(L));
4068 ConstantInt *ExitConst = ExitCount->getValue();
4070 // Guard against huge trip counts.
4071 if (ExitConst->getValue().getActiveBits() > 32)
4074 // In case of integer overflow, this returns 0, which is correct.
4075 return ((unsigned)ExitConst->getZExtValue()) + 1;
4078 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
4079 /// trip count of this loop as a normal unsigned value, if possible. This
4080 /// means that the actual trip count is always a multiple of the returned
4081 /// value (don't forget the trip count could very well be zero as well!).
4083 /// Returns 1 if the trip count is unknown or not guaranteed to be the
4084 /// multiple of a constant (which is also the case if the trip count is simply
4085 /// constant, use getSmallConstantTripCount for that case), Will also return 1
4086 /// if the trip count is very large (>= 2^32).
4088 /// As explained in the comments for getSmallConstantTripCount, this assumes
4089 /// that control exits the loop via ExitingBlock.
4090 unsigned ScalarEvolution::
4091 getSmallConstantTripMultiple(Loop *L, BasicBlock * /*ExitingBlock*/) {
4092 const SCEV *ExitCount = getBackedgeTakenCount(L);
4093 if (ExitCount == getCouldNotCompute())
4096 // Get the trip count from the BE count by adding 1.
4097 const SCEV *TCMul = getAddExpr(ExitCount,
4098 getConstant(ExitCount->getType(), 1));
4099 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
4100 // to factor simple cases.
4101 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
4102 TCMul = Mul->getOperand(0);
4104 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
4108 ConstantInt *Result = MulC->getValue();
4110 // Guard against huge trip counts (this requires checking
4111 // for zero to handle the case where the trip count == -1 and the
4113 if (!Result || Result->getValue().getActiveBits() > 32 ||
4114 Result->getValue().getActiveBits() == 0)
4117 return (unsigned)Result->getZExtValue();
4120 // getExitCount - Get the expression for the number of loop iterations for which
4121 // this loop is guaranteed not to exit via ExitingBlock. Otherwise return
4122 // SCEVCouldNotCompute.
4123 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
4124 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
4127 /// getBackedgeTakenCount - If the specified loop has a predictable
4128 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
4129 /// object. The backedge-taken count is the number of times the loop header
4130 /// will be branched to from within the loop. This is one less than the
4131 /// trip count of the loop, since it doesn't count the first iteration,
4132 /// when the header is branched to from outside the loop.
4134 /// Note that it is not valid to call this method on a loop without a
4135 /// loop-invariant backedge-taken count (see
4136 /// hasLoopInvariantBackedgeTakenCount).
4138 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
4139 return getBackedgeTakenInfo(L).getExact(this);
4142 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
4143 /// return the least SCEV value that is known never to be less than the
4144 /// actual backedge taken count.
4145 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
4146 return getBackedgeTakenInfo(L).getMax(this);
4149 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
4150 /// onto the given Worklist.
4152 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
4153 BasicBlock *Header = L->getHeader();
4155 // Push all Loop-header PHIs onto the Worklist stack.
4156 for (BasicBlock::iterator I = Header->begin();
4157 PHINode *PN = dyn_cast<PHINode>(I); ++I)
4158 Worklist.push_back(PN);
4161 const ScalarEvolution::BackedgeTakenInfo &
4162 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
4163 // Initially insert an invalid entry for this loop. If the insertion
4164 // succeeds, proceed to actually compute a backedge-taken count and
4165 // update the value. The temporary CouldNotCompute value tells SCEV
4166 // code elsewhere that it shouldn't attempt to request a new
4167 // backedge-taken count, which could result in infinite recursion.
4168 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
4169 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
4171 return Pair.first->second;
4173 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
4174 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
4175 // must be cleared in this scope.
4176 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
4178 if (Result.getExact(this) != getCouldNotCompute()) {
4179 assert(isLoopInvariant(Result.getExact(this), L) &&
4180 isLoopInvariant(Result.getMax(this), L) &&
4181 "Computed backedge-taken count isn't loop invariant for loop!");
4182 ++NumTripCountsComputed;
4184 else if (Result.getMax(this) == getCouldNotCompute() &&
4185 isa<PHINode>(L->getHeader()->begin())) {
4186 // Only count loops that have phi nodes as not being computable.
4187 ++NumTripCountsNotComputed;
4190 // Now that we know more about the trip count for this loop, forget any
4191 // existing SCEV values for PHI nodes in this loop since they are only
4192 // conservative estimates made without the benefit of trip count
4193 // information. This is similar to the code in forgetLoop, except that
4194 // it handles SCEVUnknown PHI nodes specially.
4195 if (Result.hasAnyInfo()) {
4196 SmallVector<Instruction *, 16> Worklist;
4197 PushLoopPHIs(L, Worklist);
4199 SmallPtrSet<Instruction *, 8> Visited;
4200 while (!Worklist.empty()) {
4201 Instruction *I = Worklist.pop_back_val();
4202 if (!Visited.insert(I)) continue;
4204 ValueExprMapType::iterator It =
4205 ValueExprMap.find_as(static_cast<Value *>(I));
4206 if (It != ValueExprMap.end()) {
4207 const SCEV *Old = It->second;
4209 // SCEVUnknown for a PHI either means that it has an unrecognized
4210 // structure, or it's a PHI that's in the progress of being computed
4211 // by createNodeForPHI. In the former case, additional loop trip
4212 // count information isn't going to change anything. In the later
4213 // case, createNodeForPHI will perform the necessary updates on its
4214 // own when it gets to that point.
4215 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
4216 forgetMemoizedResults(Old);
4217 ValueExprMap.erase(It);
4219 if (PHINode *PN = dyn_cast<PHINode>(I))
4220 ConstantEvolutionLoopExitValue.erase(PN);
4223 PushDefUseChildren(I, Worklist);
4227 // Re-lookup the insert position, since the call to
4228 // ComputeBackedgeTakenCount above could result in a
4229 // recusive call to getBackedgeTakenInfo (on a different
4230 // loop), which would invalidate the iterator computed
4232 return BackedgeTakenCounts.find(L)->second = Result;
4235 /// forgetLoop - This method should be called by the client when it has
4236 /// changed a loop in a way that may effect ScalarEvolution's ability to
4237 /// compute a trip count, or if the loop is deleted.
4238 void ScalarEvolution::forgetLoop(const Loop *L) {
4239 // Drop any stored trip count value.
4240 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4241 BackedgeTakenCounts.find(L);
4242 if (BTCPos != BackedgeTakenCounts.end()) {
4243 BTCPos->second.clear();
4244 BackedgeTakenCounts.erase(BTCPos);
4247 // Drop information about expressions based on loop-header PHIs.
4248 SmallVector<Instruction *, 16> Worklist;
4249 PushLoopPHIs(L, Worklist);
4251 SmallPtrSet<Instruction *, 8> Visited;
4252 while (!Worklist.empty()) {
4253 Instruction *I = Worklist.pop_back_val();
4254 if (!Visited.insert(I)) continue;
4256 ValueExprMapType::iterator It =
4257 ValueExprMap.find_as(static_cast<Value *>(I));
4258 if (It != ValueExprMap.end()) {
4259 forgetMemoizedResults(It->second);
4260 ValueExprMap.erase(It);
4261 if (PHINode *PN = dyn_cast<PHINode>(I))
4262 ConstantEvolutionLoopExitValue.erase(PN);
4265 PushDefUseChildren(I, Worklist);
4268 // Forget all contained loops too, to avoid dangling entries in the
4269 // ValuesAtScopes map.
4270 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4274 /// forgetValue - This method should be called by the client when it has
4275 /// changed a value in a way that may effect its value, or which may
4276 /// disconnect it from a def-use chain linking it to a loop.
4277 void ScalarEvolution::forgetValue(Value *V) {
4278 Instruction *I = dyn_cast<Instruction>(V);
4281 // Drop information about expressions based on loop-header PHIs.
4282 SmallVector<Instruction *, 16> Worklist;
4283 Worklist.push_back(I);
4285 SmallPtrSet<Instruction *, 8> Visited;
4286 while (!Worklist.empty()) {
4287 I = Worklist.pop_back_val();
4288 if (!Visited.insert(I)) continue;
4290 ValueExprMapType::iterator It =
4291 ValueExprMap.find_as(static_cast<Value *>(I));
4292 if (It != ValueExprMap.end()) {
4293 forgetMemoizedResults(It->second);
4294 ValueExprMap.erase(It);
4295 if (PHINode *PN = dyn_cast<PHINode>(I))
4296 ConstantEvolutionLoopExitValue.erase(PN);
4299 PushDefUseChildren(I, Worklist);
4303 /// getExact - Get the exact loop backedge taken count considering all loop
4304 /// exits. A computable result can only be return for loops with a single exit.
4305 /// Returning the minimum taken count among all exits is incorrect because one
4306 /// of the loop's exit limit's may have been skipped. HowFarToZero assumes that
4307 /// the limit of each loop test is never skipped. This is a valid assumption as
4308 /// long as the loop exits via that test. For precise results, it is the
4309 /// caller's responsibility to specify the relevant loop exit using
4310 /// getExact(ExitingBlock, SE).
4312 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4313 // If any exits were not computable, the loop is not computable.
4314 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4316 // We need exactly one computable exit.
4317 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4318 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4320 const SCEV *BECount = nullptr;
4321 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4322 ENT != nullptr; ENT = ENT->getNextExit()) {
4324 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4327 BECount = ENT->ExactNotTaken;
4328 else if (BECount != ENT->ExactNotTaken)
4329 return SE->getCouldNotCompute();
4331 assert(BECount && "Invalid not taken count for loop exit");
4335 /// getExact - Get the exact not taken count for this loop exit.
4337 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4338 ScalarEvolution *SE) const {
4339 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4340 ENT != nullptr; ENT = ENT->getNextExit()) {
4342 if (ENT->ExitingBlock == ExitingBlock)
4343 return ENT->ExactNotTaken;
4345 return SE->getCouldNotCompute();
4348 /// getMax - Get the max backedge taken count for the loop.
4350 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4351 return Max ? Max : SE->getCouldNotCompute();
4354 bool ScalarEvolution::BackedgeTakenInfo::hasOperand(const SCEV *S,
4355 ScalarEvolution *SE) const {
4356 if (Max && Max != SE->getCouldNotCompute() && SE->hasOperand(Max, S))
4359 if (!ExitNotTaken.ExitingBlock)
4362 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4363 ENT != nullptr; ENT = ENT->getNextExit()) {
4365 if (ENT->ExactNotTaken != SE->getCouldNotCompute()
4366 && SE->hasOperand(ENT->ExactNotTaken, S)) {
4373 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4374 /// computable exit into a persistent ExitNotTakenInfo array.
4375 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4376 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4377 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4380 ExitNotTaken.setIncomplete();
4382 unsigned NumExits = ExitCounts.size();
4383 if (NumExits == 0) return;
4385 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4386 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4387 if (NumExits == 1) return;
4389 // Handle the rare case of multiple computable exits.
4390 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4392 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4393 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4394 PrevENT->setNextExit(ENT);
4395 ENT->ExitingBlock = ExitCounts[i].first;
4396 ENT->ExactNotTaken = ExitCounts[i].second;
4400 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4401 void ScalarEvolution::BackedgeTakenInfo::clear() {
4402 ExitNotTaken.ExitingBlock = nullptr;
4403 ExitNotTaken.ExactNotTaken = nullptr;
4404 delete[] ExitNotTaken.getNextExit();
4407 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4408 /// of the specified loop will execute.
4409 ScalarEvolution::BackedgeTakenInfo
4410 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4411 SmallVector<BasicBlock *, 8> ExitingBlocks;
4412 L->getExitingBlocks(ExitingBlocks);
4414 // Examine all exits and pick the most conservative values.
4415 const SCEV *MaxBECount = getCouldNotCompute();
4416 bool CouldComputeBECount = true;
4417 BasicBlock *Latch = L->getLoopLatch(); // may be NULL.
4418 const SCEV *LatchMaxCount = nullptr;
4419 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4420 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4421 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4422 if (EL.Exact == getCouldNotCompute())
4423 // We couldn't compute an exact value for this exit, so
4424 // we won't be able to compute an exact value for the loop.
4425 CouldComputeBECount = false;
4427 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4429 if (MaxBECount == getCouldNotCompute())
4430 MaxBECount = EL.Max;
4431 else if (EL.Max != getCouldNotCompute()) {
4432 // We cannot take the "min" MaxBECount, because non-unit stride loops may
4433 // skip some loop tests. Taking the max over the exits is sufficiently
4434 // conservative. TODO: We could do better taking into consideration
4435 // non-latch exits that dominate the latch.
4436 if (EL.MustExit && ExitingBlocks[i] == Latch)
4437 LatchMaxCount = EL.Max;
4439 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, EL.Max);
4442 // Be more precise in the easy case of a loop latch that must exit.
4443 if (LatchMaxCount) {
4444 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, LatchMaxCount);
4446 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4449 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4450 /// loop will execute if it exits via the specified block.
4451 ScalarEvolution::ExitLimit
4452 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4454 // Okay, we've chosen an exiting block. See what condition causes us to
4455 // exit at this block and remember the exit block and whether all other targets
4456 // lead to the loop header.
4457 bool MustExecuteLoopHeader = true;
4458 BasicBlock *Exit = nullptr;
4459 for (succ_iterator SI = succ_begin(ExitingBlock), SE = succ_end(ExitingBlock);
4461 if (!L->contains(*SI)) {
4462 if (Exit) // Multiple exit successors.
4463 return getCouldNotCompute();
4465 } else if (*SI != L->getHeader()) {
4466 MustExecuteLoopHeader = false;
4469 // At this point, we know we have a conditional branch that determines whether
4470 // the loop is exited. However, we don't know if the branch is executed each
4471 // time through the loop. If not, then the execution count of the branch will
4472 // not be equal to the trip count of the loop.
4474 // Currently we check for this by checking to see if the Exit branch goes to
4475 // the loop header. If so, we know it will always execute the same number of
4476 // times as the loop. We also handle the case where the exit block *is* the
4477 // loop header. This is common for un-rotated loops.
4479 // If both of those tests fail, walk up the unique predecessor chain to the
4480 // header, stopping if there is an edge that doesn't exit the loop. If the
4481 // header is reached, the execution count of the branch will be equal to the
4482 // trip count of the loop.
4484 // More extensive analysis could be done to handle more cases here.
4486 if (!MustExecuteLoopHeader && ExitingBlock != L->getHeader()) {
4487 // The simple checks failed, try climbing the unique predecessor chain
4488 // up to the header.
4490 for (BasicBlock *BB = ExitingBlock; BB; ) {
4491 BasicBlock *Pred = BB->getUniquePredecessor();
4493 return getCouldNotCompute();
4494 TerminatorInst *PredTerm = Pred->getTerminator();
4495 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4496 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4499 // If the predecessor has a successor that isn't BB and isn't
4500 // outside the loop, assume the worst.
4501 if (L->contains(PredSucc))
4502 return getCouldNotCompute();
4504 if (Pred == L->getHeader()) {
4511 return getCouldNotCompute();
4514 TerminatorInst *Term = ExitingBlock->getTerminator();
4515 if (BranchInst *BI = dyn_cast<BranchInst>(Term)) {
4516 assert(BI->isConditional() && "If unconditional, it can't be in loop!");
4517 // Proceed to the next level to examine the exit condition expression.
4518 return ComputeExitLimitFromCond(L, BI->getCondition(), BI->getSuccessor(0),
4519 BI->getSuccessor(1),
4520 /*IsSubExpr=*/false);
4523 if (SwitchInst *SI = dyn_cast<SwitchInst>(Term))
4524 return ComputeExitLimitFromSingleExitSwitch(L, SI, Exit,
4525 /*IsSubExpr=*/false);
4527 return getCouldNotCompute();
4530 /// ComputeExitLimitFromCond - Compute the number of times the
4531 /// backedge of the specified loop will execute if its exit condition
4532 /// were a conditional branch of ExitCond, TBB, and FBB.
4534 /// @param IsSubExpr is true if ExitCond does not directly control the exit
4535 /// branch. In this case, we cannot assume that the loop only exits when the
4536 /// condition is true and cannot infer that failing to meet the condition prior
4537 /// to integer wraparound results in undefined behavior.
4538 ScalarEvolution::ExitLimit
4539 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4544 // Check if the controlling expression for this loop is an And or Or.
4545 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4546 if (BO->getOpcode() == Instruction::And) {
4547 // Recurse on the operands of the and.
4548 bool EitherMayExit = L->contains(TBB);
4549 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4550 IsSubExpr || EitherMayExit);
4551 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4552 IsSubExpr || EitherMayExit);
4553 const SCEV *BECount = getCouldNotCompute();
4554 const SCEV *MaxBECount = getCouldNotCompute();
4555 bool MustExit = false;
4556 if (EitherMayExit) {
4557 // Both conditions must be true for the loop to continue executing.
4558 // Choose the less conservative count.
4559 if (EL0.Exact == getCouldNotCompute() ||
4560 EL1.Exact == getCouldNotCompute())
4561 BECount = getCouldNotCompute();
4563 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4564 if (EL0.Max == getCouldNotCompute())
4565 MaxBECount = EL1.Max;
4566 else if (EL1.Max == getCouldNotCompute())
4567 MaxBECount = EL0.Max;
4569 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4570 MustExit = EL0.MustExit || EL1.MustExit;
4572 // Both conditions must be true at the same time for the loop to exit.
4573 // For now, be conservative.
4574 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4575 if (EL0.Max == EL1.Max)
4576 MaxBECount = EL0.Max;
4577 if (EL0.Exact == EL1.Exact)
4578 BECount = EL0.Exact;
4579 MustExit = EL0.MustExit && EL1.MustExit;
4582 return ExitLimit(BECount, MaxBECount, MustExit);
4584 if (BO->getOpcode() == Instruction::Or) {
4585 // Recurse on the operands of the or.
4586 bool EitherMayExit = L->contains(FBB);
4587 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB,
4588 IsSubExpr || EitherMayExit);
4589 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB,
4590 IsSubExpr || EitherMayExit);
4591 const SCEV *BECount = getCouldNotCompute();
4592 const SCEV *MaxBECount = getCouldNotCompute();
4593 bool MustExit = false;
4594 if (EitherMayExit) {
4595 // Both conditions must be false for the loop to continue executing.
4596 // Choose the less conservative count.
4597 if (EL0.Exact == getCouldNotCompute() ||
4598 EL1.Exact == getCouldNotCompute())
4599 BECount = getCouldNotCompute();
4601 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4602 if (EL0.Max == getCouldNotCompute())
4603 MaxBECount = EL1.Max;
4604 else if (EL1.Max == getCouldNotCompute())
4605 MaxBECount = EL0.Max;
4607 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4608 MustExit = EL0.MustExit || EL1.MustExit;
4610 // Both conditions must be false at the same time for the loop to exit.
4611 // For now, be conservative.
4612 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4613 if (EL0.Max == EL1.Max)
4614 MaxBECount = EL0.Max;
4615 if (EL0.Exact == EL1.Exact)
4616 BECount = EL0.Exact;
4617 MustExit = EL0.MustExit && EL1.MustExit;
4620 return ExitLimit(BECount, MaxBECount, MustExit);
4624 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4625 // Proceed to the next level to examine the icmp.
4626 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4627 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB, IsSubExpr);
4629 // Check for a constant condition. These are normally stripped out by
4630 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4631 // preserve the CFG and is temporarily leaving constant conditions
4633 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4634 if (L->contains(FBB) == !CI->getZExtValue())
4635 // The backedge is always taken.
4636 return getCouldNotCompute();
4638 // The backedge is never taken.
4639 return getConstant(CI->getType(), 0);
4642 // If it's not an integer or pointer comparison then compute it the hard way.
4643 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4646 /// ComputeExitLimitFromICmp - Compute the number of times the
4647 /// backedge of the specified loop will execute if its exit condition
4648 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4649 ScalarEvolution::ExitLimit
4650 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4656 // If the condition was exit on true, convert the condition to exit on false
4657 ICmpInst::Predicate Cond;
4658 if (!L->contains(FBB))
4659 Cond = ExitCond->getPredicate();
4661 Cond = ExitCond->getInversePredicate();
4663 // Handle common loops like: for (X = "string"; *X; ++X)
4664 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4665 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4667 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4668 if (ItCnt.hasAnyInfo())
4672 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4673 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4675 // Try to evaluate any dependencies out of the loop.
4676 LHS = getSCEVAtScope(LHS, L);
4677 RHS = getSCEVAtScope(RHS, L);
4679 // At this point, we would like to compute how many iterations of the
4680 // loop the predicate will return true for these inputs.
4681 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4682 // If there is a loop-invariant, force it into the RHS.
4683 std::swap(LHS, RHS);
4684 Cond = ICmpInst::getSwappedPredicate(Cond);
4687 // Simplify the operands before analyzing them.
4688 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4690 // If we have a comparison of a chrec against a constant, try to use value
4691 // ranges to answer this query.
4692 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4693 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4694 if (AddRec->getLoop() == L) {
4695 // Form the constant range.
4696 ConstantRange CompRange(
4697 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4699 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4700 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4704 case ICmpInst::ICMP_NE: { // while (X != Y)
4705 // Convert to: while (X-Y != 0)
4706 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4707 if (EL.hasAnyInfo()) return EL;
4710 case ICmpInst::ICMP_EQ: { // while (X == Y)
4711 // Convert to: while (X-Y == 0)
4712 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4713 if (EL.hasAnyInfo()) return EL;
4716 case ICmpInst::ICMP_SLT:
4717 case ICmpInst::ICMP_ULT: { // while (X < Y)
4718 bool IsSigned = Cond == ICmpInst::ICMP_SLT;
4719 ExitLimit EL = HowManyLessThans(LHS, RHS, L, IsSigned, IsSubExpr);
4720 if (EL.hasAnyInfo()) return EL;
4723 case ICmpInst::ICMP_SGT:
4724 case ICmpInst::ICMP_UGT: { // while (X > Y)
4725 bool IsSigned = Cond == ICmpInst::ICMP_SGT;
4726 ExitLimit EL = HowManyGreaterThans(LHS, RHS, L, IsSigned, IsSubExpr);
4727 if (EL.hasAnyInfo()) return EL;
4732 dbgs() << "ComputeBackedgeTakenCount ";
4733 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4734 dbgs() << "[unsigned] ";
4735 dbgs() << *LHS << " "
4736 << Instruction::getOpcodeName(Instruction::ICmp)
4737 << " " << *RHS << "\n";
4741 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4744 ScalarEvolution::ExitLimit
4745 ScalarEvolution::ComputeExitLimitFromSingleExitSwitch(const Loop *L,
4747 BasicBlock *ExitingBlock,
4749 assert(!L->contains(ExitingBlock) && "Not an exiting block!");
4751 // Give up if the exit is the default dest of a switch.
4752 if (Switch->getDefaultDest() == ExitingBlock)
4753 return getCouldNotCompute();
4755 assert(L->contains(Switch->getDefaultDest()) &&
4756 "Default case must not exit the loop!");
4757 const SCEV *LHS = getSCEVAtScope(Switch->getCondition(), L);
4758 const SCEV *RHS = getConstant(Switch->findCaseDest(ExitingBlock));
4760 // while (X != Y) --> while (X-Y != 0)
4761 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L, IsSubExpr);
4762 if (EL.hasAnyInfo())
4765 return getCouldNotCompute();
4768 static ConstantInt *
4769 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4770 ScalarEvolution &SE) {
4771 const SCEV *InVal = SE.getConstant(C);
4772 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4773 assert(isa<SCEVConstant>(Val) &&
4774 "Evaluation of SCEV at constant didn't fold correctly?");
4775 return cast<SCEVConstant>(Val)->getValue();
4778 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4779 /// 'icmp op load X, cst', try to see if we can compute the backedge
4780 /// execution count.
4781 ScalarEvolution::ExitLimit
4782 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4786 ICmpInst::Predicate predicate) {
4788 if (LI->isVolatile()) return getCouldNotCompute();
4790 // Check to see if the loaded pointer is a getelementptr of a global.
4791 // TODO: Use SCEV instead of manually grubbing with GEPs.
4792 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4793 if (!GEP) return getCouldNotCompute();
4795 // Make sure that it is really a constant global we are gepping, with an
4796 // initializer, and make sure the first IDX is really 0.
4797 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4798 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4799 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4800 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4801 return getCouldNotCompute();
4803 // Okay, we allow one non-constant index into the GEP instruction.
4804 Value *VarIdx = nullptr;
4805 std::vector<Constant*> Indexes;
4806 unsigned VarIdxNum = 0;
4807 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4808 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4809 Indexes.push_back(CI);
4810 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4811 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4812 VarIdx = GEP->getOperand(i);
4814 Indexes.push_back(nullptr);
4817 // Loop-invariant loads may be a byproduct of loop optimization. Skip them.
4819 return getCouldNotCompute();
4821 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4822 // Check to see if X is a loop variant variable value now.
4823 const SCEV *Idx = getSCEV(VarIdx);
4824 Idx = getSCEVAtScope(Idx, L);
4826 // We can only recognize very limited forms of loop index expressions, in
4827 // particular, only affine AddRec's like {C1,+,C2}.
4828 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4829 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4830 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4831 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4832 return getCouldNotCompute();
4834 unsigned MaxSteps = MaxBruteForceIterations;
4835 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4836 ConstantInt *ItCst = ConstantInt::get(
4837 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4838 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4840 // Form the GEP offset.
4841 Indexes[VarIdxNum] = Val;
4843 Constant *Result = ConstantFoldLoadThroughGEPIndices(GV->getInitializer(),
4845 if (!Result) break; // Cannot compute!
4847 // Evaluate the condition for this iteration.
4848 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4849 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4850 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4852 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4853 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4856 ++NumArrayLenItCounts;
4857 return getConstant(ItCst); // Found terminating iteration!
4860 return getCouldNotCompute();
4864 /// CanConstantFold - Return true if we can constant fold an instruction of the
4865 /// specified type, assuming that all operands were constants.
4866 static bool CanConstantFold(const Instruction *I) {
4867 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4868 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I) ||
4872 if (const CallInst *CI = dyn_cast<CallInst>(I))
4873 if (const Function *F = CI->getCalledFunction())
4874 return canConstantFoldCallTo(F);
4878 /// Determine whether this instruction can constant evolve within this loop
4879 /// assuming its operands can all constant evolve.
4880 static bool canConstantEvolve(Instruction *I, const Loop *L) {
4881 // An instruction outside of the loop can't be derived from a loop PHI.
4882 if (!L->contains(I)) return false;
4884 if (isa<PHINode>(I)) {
4885 if (L->getHeader() == I->getParent())
4888 // We don't currently keep track of the control flow needed to evaluate
4889 // PHIs, so we cannot handle PHIs inside of loops.
4893 // If we won't be able to constant fold this expression even if the operands
4894 // are constants, bail early.
4895 return CanConstantFold(I);
4898 /// getConstantEvolvingPHIOperands - Implement getConstantEvolvingPHI by
4899 /// recursing through each instruction operand until reaching a loop header phi.
4901 getConstantEvolvingPHIOperands(Instruction *UseInst, const Loop *L,
4902 DenseMap<Instruction *, PHINode *> &PHIMap) {
4904 // Otherwise, we can evaluate this instruction if all of its operands are
4905 // constant or derived from a PHI node themselves.
4906 PHINode *PHI = nullptr;
4907 for (Instruction::op_iterator OpI = UseInst->op_begin(),
4908 OpE = UseInst->op_end(); OpI != OpE; ++OpI) {
4910 if (isa<Constant>(*OpI)) continue;
4912 Instruction *OpInst = dyn_cast<Instruction>(*OpI);
4913 if (!OpInst || !canConstantEvolve(OpInst, L)) return nullptr;
4915 PHINode *P = dyn_cast<PHINode>(OpInst);
4917 // If this operand is already visited, reuse the prior result.
4918 // We may have P != PHI if this is the deepest point at which the
4919 // inconsistent paths meet.
4920 P = PHIMap.lookup(OpInst);
4922 // Recurse and memoize the results, whether a phi is found or not.
4923 // This recursive call invalidates pointers into PHIMap.
4924 P = getConstantEvolvingPHIOperands(OpInst, L, PHIMap);
4928 return nullptr; // Not evolving from PHI
4929 if (PHI && PHI != P)
4930 return nullptr; // Evolving from multiple different PHIs.
4933 // This is a expression evolving from a constant PHI!
4937 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4938 /// in the loop that V is derived from. We allow arbitrary operations along the
4939 /// way, but the operands of an operation must either be constants or a value
4940 /// derived from a constant PHI. If this expression does not fit with these
4941 /// constraints, return null.
4942 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4943 Instruction *I = dyn_cast<Instruction>(V);
4944 if (!I || !canConstantEvolve(I, L)) return nullptr;
4946 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4950 // Record non-constant instructions contained by the loop.
4951 DenseMap<Instruction *, PHINode *> PHIMap;
4952 return getConstantEvolvingPHIOperands(I, L, PHIMap);
4955 /// EvaluateExpression - Given an expression that passes the
4956 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4957 /// in the loop has the value PHIVal. If we can't fold this expression for some
4958 /// reason, return null.
4959 static Constant *EvaluateExpression(Value *V, const Loop *L,
4960 DenseMap<Instruction *, Constant *> &Vals,
4961 const DataLayout *DL,
4962 const TargetLibraryInfo *TLI) {
4963 // Convenient constant check, but redundant for recursive calls.
4964 if (Constant *C = dyn_cast<Constant>(V)) return C;
4965 Instruction *I = dyn_cast<Instruction>(V);
4966 if (!I) return nullptr;
4968 if (Constant *C = Vals.lookup(I)) return C;
4970 // An instruction inside the loop depends on a value outside the loop that we
4971 // weren't given a mapping for, or a value such as a call inside the loop.
4972 if (!canConstantEvolve(I, L)) return nullptr;
4974 // An unmapped PHI can be due to a branch or another loop inside this loop,
4975 // or due to this not being the initial iteration through a loop where we
4976 // couldn't compute the evolution of this particular PHI last time.
4977 if (isa<PHINode>(I)) return nullptr;
4979 std::vector<Constant*> Operands(I->getNumOperands());
4981 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4982 Instruction *Operand = dyn_cast<Instruction>(I->getOperand(i));
4984 Operands[i] = dyn_cast<Constant>(I->getOperand(i));
4985 if (!Operands[i]) return nullptr;
4988 Constant *C = EvaluateExpression(Operand, L, Vals, DL, TLI);
4990 if (!C) return nullptr;
4994 if (CmpInst *CI = dyn_cast<CmpInst>(I))
4995 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4996 Operands[1], DL, TLI);
4997 if (LoadInst *LI = dyn_cast<LoadInst>(I)) {
4998 if (!LI->isVolatile())
4999 return ConstantFoldLoadFromConstPtr(Operands[0], DL);
5001 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, DL,
5005 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
5006 /// in the header of its containing loop, we know the loop executes a
5007 /// constant number of times, and the PHI node is just a recurrence
5008 /// involving constants, fold it.
5010 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
5013 DenseMap<PHINode*, Constant*>::const_iterator I =
5014 ConstantEvolutionLoopExitValue.find(PN);
5015 if (I != ConstantEvolutionLoopExitValue.end())
5018 if (BEs.ugt(MaxBruteForceIterations))
5019 return ConstantEvolutionLoopExitValue[PN] = nullptr; // Not going to evaluate it.
5021 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
5023 DenseMap<Instruction *, Constant *> CurrentIterVals;
5024 BasicBlock *Header = L->getHeader();
5025 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5027 // Since the loop is canonicalized, the PHI node must have two entries. One
5028 // entry must be a constant (coming in from outside of the loop), and the
5029 // second must be derived from the same PHI.
5030 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5031 PHINode *PHI = nullptr;
5032 for (BasicBlock::iterator I = Header->begin();
5033 (PHI = dyn_cast<PHINode>(I)); ++I) {
5034 Constant *StartCST =
5035 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5036 if (!StartCST) continue;
5037 CurrentIterVals[PHI] = StartCST;
5039 if (!CurrentIterVals.count(PN))
5040 return RetVal = nullptr;
5042 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
5044 // Execute the loop symbolically to determine the exit value.
5045 if (BEs.getActiveBits() >= 32)
5046 return RetVal = nullptr; // More than 2^32-1 iterations?? Not doing it!
5048 unsigned NumIterations = BEs.getZExtValue(); // must be in range
5049 unsigned IterationNum = 0;
5050 for (; ; ++IterationNum) {
5051 if (IterationNum == NumIterations)
5052 return RetVal = CurrentIterVals[PN]; // Got exit value!
5054 // Compute the value of the PHIs for the next iteration.
5055 // EvaluateExpression adds non-phi values to the CurrentIterVals map.
5056 DenseMap<Instruction *, Constant *> NextIterVals;
5057 Constant *NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL,
5060 return nullptr; // Couldn't evaluate!
5061 NextIterVals[PN] = NextPHI;
5063 bool StoppedEvolving = NextPHI == CurrentIterVals[PN];
5065 // Also evaluate the other PHI nodes. However, we don't get to stop if we
5066 // cease to be able to evaluate one of them or if they stop evolving,
5067 // because that doesn't necessarily prevent us from computing PN.
5068 SmallVector<std::pair<PHINode *, Constant *>, 8> PHIsToCompute;
5069 for (DenseMap<Instruction *, Constant *>::const_iterator
5070 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5071 PHINode *PHI = dyn_cast<PHINode>(I->first);
5072 if (!PHI || PHI == PN || PHI->getParent() != Header) continue;
5073 PHIsToCompute.push_back(std::make_pair(PHI, I->second));
5075 // We use two distinct loops because EvaluateExpression may invalidate any
5076 // iterators into CurrentIterVals.
5077 for (SmallVectorImpl<std::pair<PHINode *, Constant*> >::const_iterator
5078 I = PHIsToCompute.begin(), E = PHIsToCompute.end(); I != E; ++I) {
5079 PHINode *PHI = I->first;
5080 Constant *&NextPHI = NextIterVals[PHI];
5081 if (!NextPHI) { // Not already computed.
5082 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5083 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5085 if (NextPHI != I->second)
5086 StoppedEvolving = false;
5089 // If all entries in CurrentIterVals == NextIterVals then we can stop
5090 // iterating, the loop can't continue to change.
5091 if (StoppedEvolving)
5092 return RetVal = CurrentIterVals[PN];
5094 CurrentIterVals.swap(NextIterVals);
5098 /// ComputeExitCountExhaustively - If the loop is known to execute a
5099 /// constant number of times (the condition evolves only from constants),
5100 /// try to evaluate a few iterations of the loop until we get the exit
5101 /// condition gets a value of ExitWhen (true or false). If we cannot
5102 /// evaluate the trip count of the loop, return getCouldNotCompute().
5103 const SCEV *ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
5106 PHINode *PN = getConstantEvolvingPHI(Cond, L);
5107 if (!PN) return getCouldNotCompute();
5109 // If the loop is canonicalized, the PHI will have exactly two entries.
5110 // That's the only form we support here.
5111 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
5113 DenseMap<Instruction *, Constant *> CurrentIterVals;
5114 BasicBlock *Header = L->getHeader();
5115 assert(PN->getParent() == Header && "Can't evaluate PHI not in loop header!");
5117 // One entry must be a constant (coming in from outside of the loop), and the
5118 // second must be derived from the same PHI.
5119 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
5120 PHINode *PHI = nullptr;
5121 for (BasicBlock::iterator I = Header->begin();
5122 (PHI = dyn_cast<PHINode>(I)); ++I) {
5123 Constant *StartCST =
5124 dyn_cast<Constant>(PHI->getIncomingValue(!SecondIsBackedge));
5125 if (!StartCST) continue;
5126 CurrentIterVals[PHI] = StartCST;
5128 if (!CurrentIterVals.count(PN))
5129 return getCouldNotCompute();
5131 // Okay, we find a PHI node that defines the trip count of this loop. Execute
5132 // the loop symbolically to determine when the condition gets a value of
5135 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
5136 for (unsigned IterationNum = 0; IterationNum != MaxIterations;++IterationNum){
5137 ConstantInt *CondVal =
5138 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, L, CurrentIterVals,
5141 // Couldn't symbolically evaluate.
5142 if (!CondVal) return getCouldNotCompute();
5144 if (CondVal->getValue() == uint64_t(ExitWhen)) {
5145 ++NumBruteForceTripCountsComputed;
5146 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
5149 // Update all the PHI nodes for the next iteration.
5150 DenseMap<Instruction *, Constant *> NextIterVals;
5152 // Create a list of which PHIs we need to compute. We want to do this before
5153 // calling EvaluateExpression on them because that may invalidate iterators
5154 // into CurrentIterVals.
5155 SmallVector<PHINode *, 8> PHIsToCompute;
5156 for (DenseMap<Instruction *, Constant *>::const_iterator
5157 I = CurrentIterVals.begin(), E = CurrentIterVals.end(); I != E; ++I){
5158 PHINode *PHI = dyn_cast<PHINode>(I->first);
5159 if (!PHI || PHI->getParent() != Header) continue;
5160 PHIsToCompute.push_back(PHI);
5162 for (SmallVectorImpl<PHINode *>::const_iterator I = PHIsToCompute.begin(),
5163 E = PHIsToCompute.end(); I != E; ++I) {
5165 Constant *&NextPHI = NextIterVals[PHI];
5166 if (NextPHI) continue; // Already computed!
5168 Value *BEValue = PHI->getIncomingValue(SecondIsBackedge);
5169 NextPHI = EvaluateExpression(BEValue, L, CurrentIterVals, DL, TLI);
5171 CurrentIterVals.swap(NextIterVals);
5174 // Too many iterations were needed to evaluate.
5175 return getCouldNotCompute();
5178 /// getSCEVAtScope - Return a SCEV expression for the specified value
5179 /// at the specified scope in the program. The L value specifies a loop
5180 /// nest to evaluate the expression at, where null is the top-level or a
5181 /// specified loop is immediately inside of the loop.
5183 /// This method can be used to compute the exit value for a variable defined
5184 /// in a loop by querying what the value will hold in the parent loop.
5186 /// In the case that a relevant loop exit value cannot be computed, the
5187 /// original value V is returned.
5188 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
5189 // Check to see if we've folded this expression at this loop before.
5190 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values = ValuesAtScopes[V];
5191 for (unsigned u = 0; u < Values.size(); u++) {
5192 if (Values[u].first == L)
5193 return Values[u].second ? Values[u].second : V;
5195 Values.push_back(std::make_pair(L, static_cast<const SCEV *>(nullptr)));
5196 // Otherwise compute it.
5197 const SCEV *C = computeSCEVAtScope(V, L);
5198 SmallVector<std::pair<const Loop *, const SCEV *>, 2> &Values2 = ValuesAtScopes[V];
5199 for (unsigned u = Values2.size(); u > 0; u--) {
5200 if (Values2[u - 1].first == L) {
5201 Values2[u - 1].second = C;
5208 /// This builds up a Constant using the ConstantExpr interface. That way, we
5209 /// will return Constants for objects which aren't represented by a
5210 /// SCEVConstant, because SCEVConstant is restricted to ConstantInt.
5211 /// Returns NULL if the SCEV isn't representable as a Constant.
5212 static Constant *BuildConstantFromSCEV(const SCEV *V) {
5213 switch (static_cast<SCEVTypes>(V->getSCEVType())) {
5214 case scCouldNotCompute:
5218 return cast<SCEVConstant>(V)->getValue();
5220 return dyn_cast<Constant>(cast<SCEVUnknown>(V)->getValue());
5221 case scSignExtend: {
5222 const SCEVSignExtendExpr *SS = cast<SCEVSignExtendExpr>(V);
5223 if (Constant *CastOp = BuildConstantFromSCEV(SS->getOperand()))
5224 return ConstantExpr::getSExt(CastOp, SS->getType());
5227 case scZeroExtend: {
5228 const SCEVZeroExtendExpr *SZ = cast<SCEVZeroExtendExpr>(V);
5229 if (Constant *CastOp = BuildConstantFromSCEV(SZ->getOperand()))
5230 return ConstantExpr::getZExt(CastOp, SZ->getType());
5234 const SCEVTruncateExpr *ST = cast<SCEVTruncateExpr>(V);
5235 if (Constant *CastOp = BuildConstantFromSCEV(ST->getOperand()))
5236 return ConstantExpr::getTrunc(CastOp, ST->getType());
5240 const SCEVAddExpr *SA = cast<SCEVAddExpr>(V);
5241 if (Constant *C = BuildConstantFromSCEV(SA->getOperand(0))) {
5242 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5243 unsigned AS = PTy->getAddressSpace();
5244 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5245 C = ConstantExpr::getBitCast(C, DestPtrTy);
5247 for (unsigned i = 1, e = SA->getNumOperands(); i != e; ++i) {
5248 Constant *C2 = BuildConstantFromSCEV(SA->getOperand(i));
5249 if (!C2) return nullptr;
5252 if (!C->getType()->isPointerTy() && C2->getType()->isPointerTy()) {
5253 unsigned AS = C2->getType()->getPointerAddressSpace();
5255 Type *DestPtrTy = Type::getInt8PtrTy(C->getContext(), AS);
5256 // The offsets have been converted to bytes. We can add bytes to an
5257 // i8* by GEP with the byte count in the first index.
5258 C = ConstantExpr::getBitCast(C, DestPtrTy);
5261 // Don't bother trying to sum two pointers. We probably can't
5262 // statically compute a load that results from it anyway.
5263 if (C2->getType()->isPointerTy())
5266 if (PointerType *PTy = dyn_cast<PointerType>(C->getType())) {
5267 if (PTy->getElementType()->isStructTy())
5268 C2 = ConstantExpr::getIntegerCast(
5269 C2, Type::getInt32Ty(C->getContext()), true);
5270 C = ConstantExpr::getGetElementPtr(C, C2);
5272 C = ConstantExpr::getAdd(C, C2);
5279 const SCEVMulExpr *SM = cast<SCEVMulExpr>(V);
5280 if (Constant *C = BuildConstantFromSCEV(SM->getOperand(0))) {
5281 // Don't bother with pointers at all.
5282 if (C->getType()->isPointerTy()) return nullptr;
5283 for (unsigned i = 1, e = SM->getNumOperands(); i != e; ++i) {
5284 Constant *C2 = BuildConstantFromSCEV(SM->getOperand(i));
5285 if (!C2 || C2->getType()->isPointerTy()) return nullptr;
5286 C = ConstantExpr::getMul(C, C2);
5293 const SCEVUDivExpr *SU = cast<SCEVUDivExpr>(V);
5294 if (Constant *LHS = BuildConstantFromSCEV(SU->getLHS()))
5295 if (Constant *RHS = BuildConstantFromSCEV(SU->getRHS()))
5296 if (LHS->getType() == RHS->getType())
5297 return ConstantExpr::getUDiv(LHS, RHS);
5302 break; // TODO: smax, umax.
5307 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
5308 if (isa<SCEVConstant>(V)) return V;
5310 // If this instruction is evolved from a constant-evolving PHI, compute the
5311 // exit value from the loop without using SCEVs.
5312 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
5313 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
5314 const Loop *LI = (*this->LI)[I->getParent()];
5315 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
5316 if (PHINode *PN = dyn_cast<PHINode>(I))
5317 if (PN->getParent() == LI->getHeader()) {
5318 // Okay, there is no closed form solution for the PHI node. Check
5319 // to see if the loop that contains it has a known backedge-taken
5320 // count. If so, we may be able to force computation of the exit
5322 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
5323 if (const SCEVConstant *BTCC =
5324 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
5325 // Okay, we know how many times the containing loop executes. If
5326 // this is a constant evolving PHI node, get the final value at
5327 // the specified iteration number.
5328 Constant *RV = getConstantEvolutionLoopExitValue(PN,
5329 BTCC->getValue()->getValue(),
5331 if (RV) return getSCEV(RV);
5335 // Okay, this is an expression that we cannot symbolically evaluate
5336 // into a SCEV. Check to see if it's possible to symbolically evaluate
5337 // the arguments into constants, and if so, try to constant propagate the
5338 // result. This is particularly useful for computing loop exit values.
5339 if (CanConstantFold(I)) {
5340 SmallVector<Constant *, 4> Operands;
5341 bool MadeImprovement = false;
5342 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
5343 Value *Op = I->getOperand(i);
5344 if (Constant *C = dyn_cast<Constant>(Op)) {
5345 Operands.push_back(C);
5349 // If any of the operands is non-constant and if they are
5350 // non-integer and non-pointer, don't even try to analyze them
5351 // with scev techniques.
5352 if (!isSCEVable(Op->getType()))
5355 const SCEV *OrigV = getSCEV(Op);
5356 const SCEV *OpV = getSCEVAtScope(OrigV, L);
5357 MadeImprovement |= OrigV != OpV;
5359 Constant *C = BuildConstantFromSCEV(OpV);
5361 if (C->getType() != Op->getType())
5362 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
5366 Operands.push_back(C);
5369 // Check to see if getSCEVAtScope actually made an improvement.
5370 if (MadeImprovement) {
5371 Constant *C = nullptr;
5372 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
5373 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
5374 Operands[0], Operands[1], DL,
5376 else if (const LoadInst *LI = dyn_cast<LoadInst>(I)) {
5377 if (!LI->isVolatile())
5378 C = ConstantFoldLoadFromConstPtr(Operands[0], DL);
5380 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
5388 // This is some other type of SCEVUnknown, just return it.
5392 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
5393 // Avoid performing the look-up in the common case where the specified
5394 // expression has no loop-variant portions.
5395 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
5396 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5397 if (OpAtScope != Comm->getOperand(i)) {
5398 // Okay, at least one of these operands is loop variant but might be
5399 // foldable. Build a new instance of the folded commutative expression.
5400 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
5401 Comm->op_begin()+i);
5402 NewOps.push_back(OpAtScope);
5404 for (++i; i != e; ++i) {
5405 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
5406 NewOps.push_back(OpAtScope);
5408 if (isa<SCEVAddExpr>(Comm))
5409 return getAddExpr(NewOps);
5410 if (isa<SCEVMulExpr>(Comm))
5411 return getMulExpr(NewOps);
5412 if (isa<SCEVSMaxExpr>(Comm))
5413 return getSMaxExpr(NewOps);
5414 if (isa<SCEVUMaxExpr>(Comm))
5415 return getUMaxExpr(NewOps);
5416 llvm_unreachable("Unknown commutative SCEV type!");
5419 // If we got here, all operands are loop invariant.
5423 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
5424 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
5425 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
5426 if (LHS == Div->getLHS() && RHS == Div->getRHS())
5427 return Div; // must be loop invariant
5428 return getUDivExpr(LHS, RHS);
5431 // If this is a loop recurrence for a loop that does not contain L, then we
5432 // are dealing with the final value computed by the loop.
5433 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
5434 // First, attempt to evaluate each operand.
5435 // Avoid performing the look-up in the common case where the specified
5436 // expression has no loop-variant portions.
5437 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
5438 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
5439 if (OpAtScope == AddRec->getOperand(i))
5442 // Okay, at least one of these operands is loop variant but might be
5443 // foldable. Build a new instance of the folded commutative expression.
5444 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
5445 AddRec->op_begin()+i);
5446 NewOps.push_back(OpAtScope);
5447 for (++i; i != e; ++i)
5448 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
5450 const SCEV *FoldedRec =
5451 getAddRecExpr(NewOps, AddRec->getLoop(),
5452 AddRec->getNoWrapFlags(SCEV::FlagNW));
5453 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
5454 // The addrec may be folded to a nonrecurrence, for example, if the
5455 // induction variable is multiplied by zero after constant folding. Go
5456 // ahead and return the folded value.
5462 // If the scope is outside the addrec's loop, evaluate it by using the
5463 // loop exit value of the addrec.
5464 if (!AddRec->getLoop()->contains(L)) {
5465 // To evaluate this recurrence, we need to know how many times the AddRec
5466 // loop iterates. Compute this now.
5467 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
5468 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
5470 // Then, evaluate the AddRec.
5471 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
5477 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
5478 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5479 if (Op == Cast->getOperand())
5480 return Cast; // must be loop invariant
5481 return getZeroExtendExpr(Op, Cast->getType());
5484 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
5485 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5486 if (Op == Cast->getOperand())
5487 return Cast; // must be loop invariant
5488 return getSignExtendExpr(Op, Cast->getType());
5491 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
5492 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
5493 if (Op == Cast->getOperand())
5494 return Cast; // must be loop invariant
5495 return getTruncateExpr(Op, Cast->getType());
5498 llvm_unreachable("Unknown SCEV type!");
5501 /// getSCEVAtScope - This is a convenience function which does
5502 /// getSCEVAtScope(getSCEV(V), L).
5503 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
5504 return getSCEVAtScope(getSCEV(V), L);
5507 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
5508 /// following equation:
5510 /// A * X = B (mod N)
5512 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
5513 /// A and B isn't important.
5515 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
5516 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5517 ScalarEvolution &SE) {
5518 uint32_t BW = A.getBitWidth();
5519 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5520 assert(A != 0 && "A must be non-zero.");
5524 // The gcd of A and N may have only one prime factor: 2. The number of
5525 // trailing zeros in A is its multiplicity
5526 uint32_t Mult2 = A.countTrailingZeros();
5529 // 2. Check if B is divisible by D.
5531 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5532 // is not less than multiplicity of this prime factor for D.
5533 if (B.countTrailingZeros() < Mult2)
5534 return SE.getCouldNotCompute();
5536 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5539 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5540 // bit width during computations.
5541 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5542 APInt Mod(BW + 1, 0);
5543 Mod.setBit(BW - Mult2); // Mod = N / D
5544 APInt I = AD.multiplicativeInverse(Mod);
5546 // 4. Compute the minimum unsigned root of the equation:
5547 // I * (B / D) mod (N / D)
5548 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5550 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5552 return SE.getConstant(Result.trunc(BW));
5555 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5556 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5557 /// might be the same) or two SCEVCouldNotCompute objects.
5559 static std::pair<const SCEV *,const SCEV *>
5560 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5561 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5562 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5563 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5564 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5566 // We currently can only solve this if the coefficients are constants.
5567 if (!LC || !MC || !NC) {
5568 const SCEV *CNC = SE.getCouldNotCompute();
5569 return std::make_pair(CNC, CNC);
5572 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5573 const APInt &L = LC->getValue()->getValue();
5574 const APInt &M = MC->getValue()->getValue();
5575 const APInt &N = NC->getValue()->getValue();
5576 APInt Two(BitWidth, 2);
5577 APInt Four(BitWidth, 4);
5580 using namespace APIntOps;
5582 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5583 // The B coefficient is M-N/2
5587 // The A coefficient is N/2
5588 APInt A(N.sdiv(Two));
5590 // Compute the B^2-4ac term.
5593 SqrtTerm -= Four * (A * C);
5595 if (SqrtTerm.isNegative()) {
5596 // The loop is provably infinite.
5597 const SCEV *CNC = SE.getCouldNotCompute();
5598 return std::make_pair(CNC, CNC);
5601 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5602 // integer value or else APInt::sqrt() will assert.
5603 APInt SqrtVal(SqrtTerm.sqrt());
5605 // Compute the two solutions for the quadratic formula.
5606 // The divisions must be performed as signed divisions.
5609 if (TwoA.isMinValue()) {
5610 const SCEV *CNC = SE.getCouldNotCompute();
5611 return std::make_pair(CNC, CNC);
5614 LLVMContext &Context = SE.getContext();
5616 ConstantInt *Solution1 =
5617 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5618 ConstantInt *Solution2 =
5619 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5621 return std::make_pair(SE.getConstant(Solution1),
5622 SE.getConstant(Solution2));
5623 } // end APIntOps namespace
5626 /// HowFarToZero - Return the number of times a backedge comparing the specified
5627 /// value to zero will execute. If not computable, return CouldNotCompute.
5629 /// This is only used for loops with a "x != y" exit test. The exit condition is
5630 /// now expressed as a single expression, V = x-y. So the exit test is
5631 /// effectively V != 0. We know and take advantage of the fact that this
5632 /// expression only being used in a comparison by zero context.
5633 ScalarEvolution::ExitLimit
5634 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L, bool IsSubExpr) {
5635 // If the value is a constant
5636 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5637 // If the value is already zero, the branch will execute zero times.
5638 if (C->getValue()->isZero()) return C;
5639 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5642 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5643 if (!AddRec || AddRec->getLoop() != L)
5644 return getCouldNotCompute();
5646 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5647 // the quadratic equation to solve it.
5648 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5649 std::pair<const SCEV *,const SCEV *> Roots =
5650 SolveQuadraticEquation(AddRec, *this);
5651 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5652 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5655 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5656 << " sol#2: " << *R2 << "\n";
5658 // Pick the smallest positive root value.
5659 if (ConstantInt *CB =
5660 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5663 if (CB->getZExtValue() == false)
5664 std::swap(R1, R2); // R1 is the minimum root now.
5666 // We can only use this value if the chrec ends up with an exact zero
5667 // value at this index. When solving for "X*X != 5", for example, we
5668 // should not accept a root of 2.
5669 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5671 return R1; // We found a quadratic root!
5674 return getCouldNotCompute();
5677 // Otherwise we can only handle this if it is affine.
5678 if (!AddRec->isAffine())
5679 return getCouldNotCompute();
5681 // If this is an affine expression, the execution count of this branch is
5682 // the minimum unsigned root of the following equation:
5684 // Start + Step*N = 0 (mod 2^BW)
5688 // Step*N = -Start (mod 2^BW)
5690 // where BW is the common bit width of Start and Step.
5692 // Get the initial value for the loop.
5693 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5694 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5696 // For now we handle only constant steps.
5698 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5699 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5700 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5701 // We have not yet seen any such cases.
5702 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5703 if (!StepC || StepC->getValue()->equalsInt(0))
5704 return getCouldNotCompute();
5706 // For positive steps (counting up until unsigned overflow):
5707 // N = -Start/Step (as unsigned)
5708 // For negative steps (counting down to zero):
5710 // First compute the unsigned distance from zero in the direction of Step.
5711 bool CountDown = StepC->getValue()->getValue().isNegative();
5712 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5714 // Handle unitary steps, which cannot wraparound.
5715 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5716 // N = Distance (as unsigned)
5717 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue()) {
5718 ConstantRange CR = getUnsignedRange(Start);
5719 const SCEV *MaxBECount;
5720 if (!CountDown && CR.getUnsignedMin().isMinValue())
5721 // When counting up, the worst starting value is 1, not 0.
5722 MaxBECount = CR.getUnsignedMax().isMinValue()
5723 ? getConstant(APInt::getMinValue(CR.getBitWidth()))
5724 : getConstant(APInt::getMaxValue(CR.getBitWidth()));
5726 MaxBECount = getConstant(CountDown ? CR.getUnsignedMax()
5727 : -CR.getUnsignedMin());
5728 return ExitLimit(Distance, MaxBECount, /*MustExit=*/true);
5731 // If the recurrence is known not to wraparound, unsigned divide computes the
5732 // back edge count. (Ideally we would have an "isexact" bit for udiv). We know
5733 // that the value will either become zero (and thus the loop terminates), that
5734 // the loop will terminate through some other exit condition first, or that
5735 // the loop has undefined behavior. This means we can't "miss" the exit
5736 // value, even with nonunit stride, and exit later via the same branch. Note
5737 // that we can skip this exit if loop later exits via a different
5738 // branch. Hence MustExit=false.
5740 // This is only valid for expressions that directly compute the loop exit. It
5741 // is invalid for subexpressions in which the loop may exit through this
5742 // branch even if this subexpression is false. In that case, the trip count
5743 // computed by this udiv could be smaller than the number of well-defined
5745 if (!IsSubExpr && AddRec->getNoWrapFlags(SCEV::FlagNW)) {
5747 getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5748 return ExitLimit(Exact, Exact, /*MustExit=*/false);
5751 // If Step is a power of two that evenly divides Start we know that the loop
5752 // will always terminate. Start may not be a constant so we just have the
5753 // number of trailing zeros available. This is safe even in presence of
5754 // overflow as the recurrence will overflow to exactly 0.
5755 const APInt &StepV = StepC->getValue()->getValue();
5756 if (StepV.isPowerOf2() &&
5757 GetMinTrailingZeros(getNegativeSCEV(Start)) >= StepV.countTrailingZeros())
5758 return getUDivExactExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5760 // Then, try to solve the above equation provided that Start is constant.
5761 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5762 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5763 -StartC->getValue()->getValue(),
5765 return getCouldNotCompute();
5768 /// HowFarToNonZero - Return the number of times a backedge checking the
5769 /// specified value for nonzero will execute. If not computable, return
5771 ScalarEvolution::ExitLimit
5772 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5773 // Loops that look like: while (X == 0) are very strange indeed. We don't
5774 // handle them yet except for the trivial case. This could be expanded in the
5775 // future as needed.
5777 // If the value is a constant, check to see if it is known to be non-zero
5778 // already. If so, the backedge will execute zero times.
5779 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5780 if (!C->getValue()->isNullValue())
5781 return getConstant(C->getType(), 0);
5782 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5785 // We could implement others, but I really doubt anyone writes loops like
5786 // this, and if they did, they would already be constant folded.
5787 return getCouldNotCompute();
5790 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5791 /// (which may not be an immediate predecessor) which has exactly one
5792 /// successor from which BB is reachable, or null if no such block is
5795 std::pair<BasicBlock *, BasicBlock *>
5796 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5797 // If the block has a unique predecessor, then there is no path from the
5798 // predecessor to the block that does not go through the direct edge
5799 // from the predecessor to the block.
5800 if (BasicBlock *Pred = BB->getSinglePredecessor())
5801 return std::make_pair(Pred, BB);
5803 // A loop's header is defined to be a block that dominates the loop.
5804 // If the header has a unique predecessor outside the loop, it must be
5805 // a block that has exactly one successor that can reach the loop.
5806 if (Loop *L = LI->getLoopFor(BB))
5807 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5809 return std::pair<BasicBlock *, BasicBlock *>();
5812 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5813 /// testing whether two expressions are equal, however for the purposes of
5814 /// looking for a condition guarding a loop, it can be useful to be a little
5815 /// more general, since a front-end may have replicated the controlling
5818 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5819 // Quick check to see if they are the same SCEV.
5820 if (A == B) return true;
5822 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5823 // two different instructions with the same value. Check for this case.
5824 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5825 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5826 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5827 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5828 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5831 // Otherwise assume they may have a different value.
5835 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5836 /// predicate Pred. Return true iff any changes were made.
5838 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5839 const SCEV *&LHS, const SCEV *&RHS,
5841 bool Changed = false;
5843 // If we hit the max recursion limit bail out.
5847 // Canonicalize a constant to the right side.
5848 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5849 // Check for both operands constant.
5850 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5851 if (ConstantExpr::getICmp(Pred,
5853 RHSC->getValue())->isNullValue())
5854 goto trivially_false;
5856 goto trivially_true;
5858 // Otherwise swap the operands to put the constant on the right.
5859 std::swap(LHS, RHS);
5860 Pred = ICmpInst::getSwappedPredicate(Pred);
5864 // If we're comparing an addrec with a value which is loop-invariant in the
5865 // addrec's loop, put the addrec on the left. Also make a dominance check,
5866 // as both operands could be addrecs loop-invariant in each other's loop.
5867 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5868 const Loop *L = AR->getLoop();
5869 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5870 std::swap(LHS, RHS);
5871 Pred = ICmpInst::getSwappedPredicate(Pred);
5876 // If there's a constant operand, canonicalize comparisons with boundary
5877 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5878 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5879 const APInt &RA = RC->getValue()->getValue();
5881 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5882 case ICmpInst::ICMP_EQ:
5883 case ICmpInst::ICMP_NE:
5884 // Fold ((-1) * %a) + %b == 0 (equivalent to %b-%a == 0) into %a == %b.
5886 if (const SCEVAddExpr *AE = dyn_cast<SCEVAddExpr>(LHS))
5887 if (const SCEVMulExpr *ME = dyn_cast<SCEVMulExpr>(AE->getOperand(0)))
5888 if (AE->getNumOperands() == 2 && ME->getNumOperands() == 2 &&
5889 ME->getOperand(0)->isAllOnesValue()) {
5890 RHS = AE->getOperand(1);
5891 LHS = ME->getOperand(1);
5895 case ICmpInst::ICMP_UGE:
5896 if ((RA - 1).isMinValue()) {
5897 Pred = ICmpInst::ICMP_NE;
5898 RHS = getConstant(RA - 1);
5902 if (RA.isMaxValue()) {
5903 Pred = ICmpInst::ICMP_EQ;
5907 if (RA.isMinValue()) goto trivially_true;
5909 Pred = ICmpInst::ICMP_UGT;
5910 RHS = getConstant(RA - 1);
5913 case ICmpInst::ICMP_ULE:
5914 if ((RA + 1).isMaxValue()) {
5915 Pred = ICmpInst::ICMP_NE;
5916 RHS = getConstant(RA + 1);
5920 if (RA.isMinValue()) {
5921 Pred = ICmpInst::ICMP_EQ;
5925 if (RA.isMaxValue()) goto trivially_true;
5927 Pred = ICmpInst::ICMP_ULT;
5928 RHS = getConstant(RA + 1);
5931 case ICmpInst::ICMP_SGE:
5932 if ((RA - 1).isMinSignedValue()) {
5933 Pred = ICmpInst::ICMP_NE;
5934 RHS = getConstant(RA - 1);
5938 if (RA.isMaxSignedValue()) {
5939 Pred = ICmpInst::ICMP_EQ;
5943 if (RA.isMinSignedValue()) goto trivially_true;
5945 Pred = ICmpInst::ICMP_SGT;
5946 RHS = getConstant(RA - 1);
5949 case ICmpInst::ICMP_SLE:
5950 if ((RA + 1).isMaxSignedValue()) {
5951 Pred = ICmpInst::ICMP_NE;
5952 RHS = getConstant(RA + 1);
5956 if (RA.isMinSignedValue()) {
5957 Pred = ICmpInst::ICMP_EQ;
5961 if (RA.isMaxSignedValue()) goto trivially_true;
5963 Pred = ICmpInst::ICMP_SLT;
5964 RHS = getConstant(RA + 1);
5967 case ICmpInst::ICMP_UGT:
5968 if (RA.isMinValue()) {
5969 Pred = ICmpInst::ICMP_NE;
5973 if ((RA + 1).isMaxValue()) {
5974 Pred = ICmpInst::ICMP_EQ;
5975 RHS = getConstant(RA + 1);
5979 if (RA.isMaxValue()) goto trivially_false;
5981 case ICmpInst::ICMP_ULT:
5982 if (RA.isMaxValue()) {
5983 Pred = ICmpInst::ICMP_NE;
5987 if ((RA - 1).isMinValue()) {
5988 Pred = ICmpInst::ICMP_EQ;
5989 RHS = getConstant(RA - 1);
5993 if (RA.isMinValue()) goto trivially_false;
5995 case ICmpInst::ICMP_SGT:
5996 if (RA.isMinSignedValue()) {
5997 Pred = ICmpInst::ICMP_NE;
6001 if ((RA + 1).isMaxSignedValue()) {
6002 Pred = ICmpInst::ICMP_EQ;
6003 RHS = getConstant(RA + 1);
6007 if (RA.isMaxSignedValue()) goto trivially_false;
6009 case ICmpInst::ICMP_SLT:
6010 if (RA.isMaxSignedValue()) {
6011 Pred = ICmpInst::ICMP_NE;
6015 if ((RA - 1).isMinSignedValue()) {
6016 Pred = ICmpInst::ICMP_EQ;
6017 RHS = getConstant(RA - 1);
6021 if (RA.isMinSignedValue()) goto trivially_false;
6026 // Check for obvious equality.
6027 if (HasSameValue(LHS, RHS)) {
6028 if (ICmpInst::isTrueWhenEqual(Pred))
6029 goto trivially_true;
6030 if (ICmpInst::isFalseWhenEqual(Pred))
6031 goto trivially_false;
6034 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
6035 // adding or subtracting 1 from one of the operands.
6037 case ICmpInst::ICMP_SLE:
6038 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
6039 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6041 Pred = ICmpInst::ICMP_SLT;
6043 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
6044 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6046 Pred = ICmpInst::ICMP_SLT;
6050 case ICmpInst::ICMP_SGE:
6051 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
6052 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6054 Pred = ICmpInst::ICMP_SGT;
6056 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
6057 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6059 Pred = ICmpInst::ICMP_SGT;
6063 case ICmpInst::ICMP_ULE:
6064 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
6065 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
6067 Pred = ICmpInst::ICMP_ULT;
6069 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
6070 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
6072 Pred = ICmpInst::ICMP_ULT;
6076 case ICmpInst::ICMP_UGE:
6077 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
6078 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
6080 Pred = ICmpInst::ICMP_UGT;
6082 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
6083 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
6085 Pred = ICmpInst::ICMP_UGT;
6093 // TODO: More simplifications are possible here.
6095 // Recursively simplify until we either hit a recursion limit or nothing
6098 return SimplifyICmpOperands(Pred, LHS, RHS, Depth+1);
6104 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6105 Pred = ICmpInst::ICMP_EQ;
6110 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
6111 Pred = ICmpInst::ICMP_NE;
6115 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
6116 return getSignedRange(S).getSignedMax().isNegative();
6119 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
6120 return getSignedRange(S).getSignedMin().isStrictlyPositive();
6123 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
6124 return !getSignedRange(S).getSignedMin().isNegative();
6127 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
6128 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
6131 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
6132 return isKnownNegative(S) || isKnownPositive(S);
6135 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
6136 const SCEV *LHS, const SCEV *RHS) {
6137 // Canonicalize the inputs first.
6138 (void)SimplifyICmpOperands(Pred, LHS, RHS);
6140 // If LHS or RHS is an addrec, check to see if the condition is true in
6141 // every iteration of the loop.
6142 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
6143 if (isLoopEntryGuardedByCond(
6144 AR->getLoop(), Pred, AR->getStart(), RHS) &&
6145 isLoopBackedgeGuardedByCond(
6146 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
6148 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
6149 if (isLoopEntryGuardedByCond(
6150 AR->getLoop(), Pred, LHS, AR->getStart()) &&
6151 isLoopBackedgeGuardedByCond(
6152 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
6155 // Otherwise see what can be done with known constant ranges.
6156 return isKnownPredicateWithRanges(Pred, LHS, RHS);
6160 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
6161 const SCEV *LHS, const SCEV *RHS) {
6162 if (HasSameValue(LHS, RHS))
6163 return ICmpInst::isTrueWhenEqual(Pred);
6165 // This code is split out from isKnownPredicate because it is called from
6166 // within isLoopEntryGuardedByCond.
6169 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6170 case ICmpInst::ICMP_SGT:
6171 std::swap(LHS, RHS);
6172 case ICmpInst::ICMP_SLT: {
6173 ConstantRange LHSRange = getSignedRange(LHS);
6174 ConstantRange RHSRange = getSignedRange(RHS);
6175 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
6177 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
6181 case ICmpInst::ICMP_SGE:
6182 std::swap(LHS, RHS);
6183 case ICmpInst::ICMP_SLE: {
6184 ConstantRange LHSRange = getSignedRange(LHS);
6185 ConstantRange RHSRange = getSignedRange(RHS);
6186 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
6188 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
6192 case ICmpInst::ICMP_UGT:
6193 std::swap(LHS, RHS);
6194 case ICmpInst::ICMP_ULT: {
6195 ConstantRange LHSRange = getUnsignedRange(LHS);
6196 ConstantRange RHSRange = getUnsignedRange(RHS);
6197 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
6199 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
6203 case ICmpInst::ICMP_UGE:
6204 std::swap(LHS, RHS);
6205 case ICmpInst::ICMP_ULE: {
6206 ConstantRange LHSRange = getUnsignedRange(LHS);
6207 ConstantRange RHSRange = getUnsignedRange(RHS);
6208 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
6210 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
6214 case ICmpInst::ICMP_NE: {
6215 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
6217 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
6220 const SCEV *Diff = getMinusSCEV(LHS, RHS);
6221 if (isKnownNonZero(Diff))
6225 case ICmpInst::ICMP_EQ:
6226 // The check at the top of the function catches the case where
6227 // the values are known to be equal.
6233 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
6234 /// protected by a conditional between LHS and RHS. This is used to
6235 /// to eliminate casts.
6237 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
6238 ICmpInst::Predicate Pred,
6239 const SCEV *LHS, const SCEV *RHS) {
6240 // Interpret a null as meaning no loop, where there is obviously no guard
6241 // (interprocedural conditions notwithstanding).
6242 if (!L) return true;
6244 BasicBlock *Latch = L->getLoopLatch();
6248 BranchInst *LoopContinuePredicate =
6249 dyn_cast<BranchInst>(Latch->getTerminator());
6250 if (!LoopContinuePredicate ||
6251 LoopContinuePredicate->isUnconditional())
6254 return isImpliedCond(Pred, LHS, RHS,
6255 LoopContinuePredicate->getCondition(),
6256 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
6259 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
6260 /// by a conditional between LHS and RHS. This is used to help avoid max
6261 /// expressions in loop trip counts, and to eliminate casts.
6263 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
6264 ICmpInst::Predicate Pred,
6265 const SCEV *LHS, const SCEV *RHS) {
6266 // Interpret a null as meaning no loop, where there is obviously no guard
6267 // (interprocedural conditions notwithstanding).
6268 if (!L) return false;
6270 // Starting at the loop predecessor, climb up the predecessor chain, as long
6271 // as there are predecessors that can be found that have unique successors
6272 // leading to the original header.
6273 for (std::pair<BasicBlock *, BasicBlock *>
6274 Pair(L->getLoopPredecessor(), L->getHeader());
6276 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
6278 BranchInst *LoopEntryPredicate =
6279 dyn_cast<BranchInst>(Pair.first->getTerminator());
6280 if (!LoopEntryPredicate ||
6281 LoopEntryPredicate->isUnconditional())
6284 if (isImpliedCond(Pred, LHS, RHS,
6285 LoopEntryPredicate->getCondition(),
6286 LoopEntryPredicate->getSuccessor(0) != Pair.second))
6293 /// RAII wrapper to prevent recursive application of isImpliedCond.
6294 /// ScalarEvolution's PendingLoopPredicates set must be empty unless we are
6295 /// currently evaluating isImpliedCond.
6296 struct MarkPendingLoopPredicate {
6298 DenseSet<Value*> &LoopPreds;
6301 MarkPendingLoopPredicate(Value *C, DenseSet<Value*> &LP)
6302 : Cond(C), LoopPreds(LP) {
6303 Pending = !LoopPreds.insert(Cond).second;
6305 ~MarkPendingLoopPredicate() {
6307 LoopPreds.erase(Cond);
6311 /// isImpliedCond - Test whether the condition described by Pred, LHS,
6312 /// and RHS is true whenever the given Cond value evaluates to true.
6313 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
6314 const SCEV *LHS, const SCEV *RHS,
6315 Value *FoundCondValue,
6317 MarkPendingLoopPredicate Mark(FoundCondValue, PendingLoopPredicates);
6321 // Recursively handle And and Or conditions.
6322 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
6323 if (BO->getOpcode() == Instruction::And) {
6325 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6326 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6327 } else if (BO->getOpcode() == Instruction::Or) {
6329 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
6330 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
6334 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
6335 if (!ICI) return false;
6337 // Bail if the ICmp's operands' types are wider than the needed type
6338 // before attempting to call getSCEV on them. This avoids infinite
6339 // recursion, since the analysis of widening casts can require loop
6340 // exit condition information for overflow checking, which would
6342 if (getTypeSizeInBits(LHS->getType()) <
6343 getTypeSizeInBits(ICI->getOperand(0)->getType()))
6346 // Now that we found a conditional branch that dominates the loop or controls
6347 // the loop latch. Check to see if it is the comparison we are looking for.
6348 ICmpInst::Predicate FoundPred;
6350 FoundPred = ICI->getInversePredicate();
6352 FoundPred = ICI->getPredicate();
6354 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
6355 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
6357 // Balance the types. The case where FoundLHS' type is wider than
6358 // LHS' type is checked for above.
6359 if (getTypeSizeInBits(LHS->getType()) >
6360 getTypeSizeInBits(FoundLHS->getType())) {
6361 if (CmpInst::isSigned(FoundPred)) {
6362 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
6363 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
6365 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
6366 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
6370 // Canonicalize the query to match the way instcombine will have
6371 // canonicalized the comparison.
6372 if (SimplifyICmpOperands(Pred, LHS, RHS))
6374 return CmpInst::isTrueWhenEqual(Pred);
6375 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
6376 if (FoundLHS == FoundRHS)
6377 return CmpInst::isFalseWhenEqual(FoundPred);
6379 // Check to see if we can make the LHS or RHS match.
6380 if (LHS == FoundRHS || RHS == FoundLHS) {
6381 if (isa<SCEVConstant>(RHS)) {
6382 std::swap(FoundLHS, FoundRHS);
6383 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
6385 std::swap(LHS, RHS);
6386 Pred = ICmpInst::getSwappedPredicate(Pred);
6390 // Check whether the found predicate is the same as the desired predicate.
6391 if (FoundPred == Pred)
6392 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
6394 // Check whether swapping the found predicate makes it the same as the
6395 // desired predicate.
6396 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
6397 if (isa<SCEVConstant>(RHS))
6398 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
6400 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
6401 RHS, LHS, FoundLHS, FoundRHS);
6404 // Check whether the actual condition is beyond sufficient.
6405 if (FoundPred == ICmpInst::ICMP_EQ)
6406 if (ICmpInst::isTrueWhenEqual(Pred))
6407 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
6409 if (Pred == ICmpInst::ICMP_NE)
6410 if (!ICmpInst::isTrueWhenEqual(FoundPred))
6411 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
6414 // Otherwise assume the worst.
6418 /// isImpliedCondOperands - Test whether the condition described by Pred,
6419 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
6420 /// and FoundRHS is true.
6421 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
6422 const SCEV *LHS, const SCEV *RHS,
6423 const SCEV *FoundLHS,
6424 const SCEV *FoundRHS) {
6425 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
6426 FoundLHS, FoundRHS) ||
6427 // ~x < ~y --> x > y
6428 isImpliedCondOperandsHelper(Pred, LHS, RHS,
6429 getNotSCEV(FoundRHS),
6430 getNotSCEV(FoundLHS));
6433 /// isImpliedCondOperandsHelper - Test whether the condition described by
6434 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
6435 /// FoundLHS, and FoundRHS is true.
6437 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
6438 const SCEV *LHS, const SCEV *RHS,
6439 const SCEV *FoundLHS,
6440 const SCEV *FoundRHS) {
6442 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
6443 case ICmpInst::ICMP_EQ:
6444 case ICmpInst::ICMP_NE:
6445 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
6448 case ICmpInst::ICMP_SLT:
6449 case ICmpInst::ICMP_SLE:
6450 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
6451 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
6454 case ICmpInst::ICMP_SGT:
6455 case ICmpInst::ICMP_SGE:
6456 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
6457 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
6460 case ICmpInst::ICMP_ULT:
6461 case ICmpInst::ICMP_ULE:
6462 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
6463 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
6466 case ICmpInst::ICMP_UGT:
6467 case ICmpInst::ICMP_UGE:
6468 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
6469 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
6477 // Verify if an linear IV with positive stride can overflow when in a
6478 // less-than comparison, knowing the invariant term of the comparison, the
6479 // stride and the knowledge of NSW/NUW flags on the recurrence.
6480 bool ScalarEvolution::doesIVOverflowOnLT(const SCEV *RHS, const SCEV *Stride,
6481 bool IsSigned, bool NoWrap) {
6482 if (NoWrap) return false;
6484 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6485 const SCEV *One = getConstant(Stride->getType(), 1);
6488 APInt MaxRHS = getSignedRange(RHS).getSignedMax();
6489 APInt MaxValue = APInt::getSignedMaxValue(BitWidth);
6490 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6493 // SMaxRHS + SMaxStrideMinusOne > SMaxValue => overflow!
6494 return (MaxValue - MaxStrideMinusOne).slt(MaxRHS);
6497 APInt MaxRHS = getUnsignedRange(RHS).getUnsignedMax();
6498 APInt MaxValue = APInt::getMaxValue(BitWidth);
6499 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6502 // UMaxRHS + UMaxStrideMinusOne > UMaxValue => overflow!
6503 return (MaxValue - MaxStrideMinusOne).ult(MaxRHS);
6506 // Verify if an linear IV with negative stride can overflow when in a
6507 // greater-than comparison, knowing the invariant term of the comparison,
6508 // the stride and the knowledge of NSW/NUW flags on the recurrence.
6509 bool ScalarEvolution::doesIVOverflowOnGT(const SCEV *RHS, const SCEV *Stride,
6510 bool IsSigned, bool NoWrap) {
6511 if (NoWrap) return false;
6513 unsigned BitWidth = getTypeSizeInBits(RHS->getType());
6514 const SCEV *One = getConstant(Stride->getType(), 1);
6517 APInt MinRHS = getSignedRange(RHS).getSignedMin();
6518 APInt MinValue = APInt::getSignedMinValue(BitWidth);
6519 APInt MaxStrideMinusOne = getSignedRange(getMinusSCEV(Stride, One))
6522 // SMinRHS - SMaxStrideMinusOne < SMinValue => overflow!
6523 return (MinValue + MaxStrideMinusOne).sgt(MinRHS);
6526 APInt MinRHS = getUnsignedRange(RHS).getUnsignedMin();
6527 APInt MinValue = APInt::getMinValue(BitWidth);
6528 APInt MaxStrideMinusOne = getUnsignedRange(getMinusSCEV(Stride, One))
6531 // UMinRHS - UMaxStrideMinusOne < UMinValue => overflow!
6532 return (MinValue + MaxStrideMinusOne).ugt(MinRHS);
6535 // Compute the backedge taken count knowing the interval difference, the
6536 // stride and presence of the equality in the comparison.
6537 const SCEV *ScalarEvolution::computeBECount(const SCEV *Delta, const SCEV *Step,
6539 const SCEV *One = getConstant(Step->getType(), 1);
6540 Delta = Equality ? getAddExpr(Delta, Step)
6541 : getAddExpr(Delta, getMinusSCEV(Step, One));
6542 return getUDivExpr(Delta, Step);
6545 /// HowManyLessThans - Return the number of times a backedge containing the
6546 /// specified less-than comparison will execute. If not computable, return
6547 /// CouldNotCompute.
6549 /// @param IsSubExpr is true when the LHS < RHS condition does not directly
6550 /// control the branch. In this case, we can only compute an iteration count for
6551 /// a subexpression that cannot overflow before evaluating true.
6552 ScalarEvolution::ExitLimit
6553 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
6554 const Loop *L, bool IsSigned,
6556 // We handle only IV < Invariant
6557 if (!isLoopInvariant(RHS, L))
6558 return getCouldNotCompute();
6560 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6562 // Avoid weird loops
6563 if (!IV || IV->getLoop() != L || !IV->isAffine())
6564 return getCouldNotCompute();
6566 bool NoWrap = !IsSubExpr &&
6567 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6569 const SCEV *Stride = IV->getStepRecurrence(*this);
6571 // Avoid negative or zero stride values
6572 if (!isKnownPositive(Stride))
6573 return getCouldNotCompute();
6575 // Avoid proven overflow cases: this will ensure that the backedge taken count
6576 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6577 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6578 // behaviors like the case of C language.
6579 if (!Stride->isOne() && doesIVOverflowOnLT(RHS, Stride, IsSigned, NoWrap))
6580 return getCouldNotCompute();
6582 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SLT
6583 : ICmpInst::ICMP_ULT;
6584 const SCEV *Start = IV->getStart();
6585 const SCEV *End = RHS;
6586 if (!isLoopEntryGuardedByCond(L, Cond, getMinusSCEV(Start, Stride), RHS))
6587 End = IsSigned ? getSMaxExpr(RHS, Start)
6588 : getUMaxExpr(RHS, Start);
6590 const SCEV *BECount = computeBECount(getMinusSCEV(End, Start), Stride, false);
6592 APInt MinStart = IsSigned ? getSignedRange(Start).getSignedMin()
6593 : getUnsignedRange(Start).getUnsignedMin();
6595 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6596 : getUnsignedRange(Stride).getUnsignedMin();
6598 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6599 APInt Limit = IsSigned ? APInt::getSignedMaxValue(BitWidth) - (MinStride - 1)
6600 : APInt::getMaxValue(BitWidth) - (MinStride - 1);
6602 // Although End can be a MAX expression we estimate MaxEnd considering only
6603 // the case End = RHS. This is safe because in the other case (End - Start)
6604 // is zero, leading to a zero maximum backedge taken count.
6606 IsSigned ? APIntOps::smin(getSignedRange(RHS).getSignedMax(), Limit)
6607 : APIntOps::umin(getUnsignedRange(RHS).getUnsignedMax(), Limit);
6609 const SCEV *MaxBECount;
6610 if (isa<SCEVConstant>(BECount))
6611 MaxBECount = BECount;
6613 MaxBECount = computeBECount(getConstant(MaxEnd - MinStart),
6614 getConstant(MinStride), false);
6616 if (isa<SCEVCouldNotCompute>(MaxBECount))
6617 MaxBECount = BECount;
6619 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6622 ScalarEvolution::ExitLimit
6623 ScalarEvolution::HowManyGreaterThans(const SCEV *LHS, const SCEV *RHS,
6624 const Loop *L, bool IsSigned,
6626 // We handle only IV > Invariant
6627 if (!isLoopInvariant(RHS, L))
6628 return getCouldNotCompute();
6630 const SCEVAddRecExpr *IV = dyn_cast<SCEVAddRecExpr>(LHS);
6632 // Avoid weird loops
6633 if (!IV || IV->getLoop() != L || !IV->isAffine())
6634 return getCouldNotCompute();
6636 bool NoWrap = !IsSubExpr &&
6637 IV->getNoWrapFlags(IsSigned ? SCEV::FlagNSW : SCEV::FlagNUW);
6639 const SCEV *Stride = getNegativeSCEV(IV->getStepRecurrence(*this));
6641 // Avoid negative or zero stride values
6642 if (!isKnownPositive(Stride))
6643 return getCouldNotCompute();
6645 // Avoid proven overflow cases: this will ensure that the backedge taken count
6646 // will not generate any unsigned overflow. Relaxed no-overflow conditions
6647 // exploit NoWrapFlags, allowing to optimize in presence of undefined
6648 // behaviors like the case of C language.
6649 if (!Stride->isOne() && doesIVOverflowOnGT(RHS, Stride, IsSigned, NoWrap))
6650 return getCouldNotCompute();
6652 ICmpInst::Predicate Cond = IsSigned ? ICmpInst::ICMP_SGT
6653 : ICmpInst::ICMP_UGT;
6655 const SCEV *Start = IV->getStart();
6656 const SCEV *End = RHS;
6657 if (!isLoopEntryGuardedByCond(L, Cond, getAddExpr(Start, Stride), RHS))
6658 End = IsSigned ? getSMinExpr(RHS, Start)
6659 : getUMinExpr(RHS, Start);
6661 const SCEV *BECount = computeBECount(getMinusSCEV(Start, End), Stride, false);
6663 APInt MaxStart = IsSigned ? getSignedRange(Start).getSignedMax()
6664 : getUnsignedRange(Start).getUnsignedMax();
6666 APInt MinStride = IsSigned ? getSignedRange(Stride).getSignedMin()
6667 : getUnsignedRange(Stride).getUnsignedMin();
6669 unsigned BitWidth = getTypeSizeInBits(LHS->getType());
6670 APInt Limit = IsSigned ? APInt::getSignedMinValue(BitWidth) + (MinStride - 1)
6671 : APInt::getMinValue(BitWidth) + (MinStride - 1);
6673 // Although End can be a MIN expression we estimate MinEnd considering only
6674 // the case End = RHS. This is safe because in the other case (Start - End)
6675 // is zero, leading to a zero maximum backedge taken count.
6677 IsSigned ? APIntOps::smax(getSignedRange(RHS).getSignedMin(), Limit)
6678 : APIntOps::umax(getUnsignedRange(RHS).getUnsignedMin(), Limit);
6681 const SCEV *MaxBECount = getCouldNotCompute();
6682 if (isa<SCEVConstant>(BECount))
6683 MaxBECount = BECount;
6685 MaxBECount = computeBECount(getConstant(MaxStart - MinEnd),
6686 getConstant(MinStride), false);
6688 if (isa<SCEVCouldNotCompute>(MaxBECount))
6689 MaxBECount = BECount;
6691 return ExitLimit(BECount, MaxBECount, /*MustExit=*/true);
6694 /// getNumIterationsInRange - Return the number of iterations of this loop that
6695 /// produce values in the specified constant range. Another way of looking at
6696 /// this is that it returns the first iteration number where the value is not in
6697 /// the condition, thus computing the exit count. If the iteration count can't
6698 /// be computed, an instance of SCEVCouldNotCompute is returned.
6699 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6700 ScalarEvolution &SE) const {
6701 if (Range.isFullSet()) // Infinite loop.
6702 return SE.getCouldNotCompute();
6704 // If the start is a non-zero constant, shift the range to simplify things.
6705 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6706 if (!SC->getValue()->isZero()) {
6707 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6708 Operands[0] = SE.getConstant(SC->getType(), 0);
6709 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6710 getNoWrapFlags(FlagNW));
6711 if (const SCEVAddRecExpr *ShiftedAddRec =
6712 dyn_cast<SCEVAddRecExpr>(Shifted))
6713 return ShiftedAddRec->getNumIterationsInRange(
6714 Range.subtract(SC->getValue()->getValue()), SE);
6715 // This is strange and shouldn't happen.
6716 return SE.getCouldNotCompute();
6719 // The only time we can solve this is when we have all constant indices.
6720 // Otherwise, we cannot determine the overflow conditions.
6721 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6722 if (!isa<SCEVConstant>(getOperand(i)))
6723 return SE.getCouldNotCompute();
6726 // Okay at this point we know that all elements of the chrec are constants and
6727 // that the start element is zero.
6729 // First check to see if the range contains zero. If not, the first
6731 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6732 if (!Range.contains(APInt(BitWidth, 0)))
6733 return SE.getConstant(getType(), 0);
6736 // If this is an affine expression then we have this situation:
6737 // Solve {0,+,A} in Range === Ax in Range
6739 // We know that zero is in the range. If A is positive then we know that
6740 // the upper value of the range must be the first possible exit value.
6741 // If A is negative then the lower of the range is the last possible loop
6742 // value. Also note that we already checked for a full range.
6743 APInt One(BitWidth,1);
6744 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6745 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6747 // The exit value should be (End+A)/A.
6748 APInt ExitVal = (End + A).udiv(A);
6749 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6751 // Evaluate at the exit value. If we really did fall out of the valid
6752 // range, then we computed our trip count, otherwise wrap around or other
6753 // things must have happened.
6754 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6755 if (Range.contains(Val->getValue()))
6756 return SE.getCouldNotCompute(); // Something strange happened
6758 // Ensure that the previous value is in the range. This is a sanity check.
6759 assert(Range.contains(
6760 EvaluateConstantChrecAtConstant(this,
6761 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6762 "Linear scev computation is off in a bad way!");
6763 return SE.getConstant(ExitValue);
6764 } else if (isQuadratic()) {
6765 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6766 // quadratic equation to solve it. To do this, we must frame our problem in
6767 // terms of figuring out when zero is crossed, instead of when
6768 // Range.getUpper() is crossed.
6769 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6770 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6771 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6772 // getNoWrapFlags(FlagNW)
6775 // Next, solve the constructed addrec
6776 std::pair<const SCEV *,const SCEV *> Roots =
6777 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6778 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6779 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6781 // Pick the smallest positive root value.
6782 if (ConstantInt *CB =
6783 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6784 R1->getValue(), R2->getValue()))) {
6785 if (CB->getZExtValue() == false)
6786 std::swap(R1, R2); // R1 is the minimum root now.
6788 // Make sure the root is not off by one. The returned iteration should
6789 // not be in the range, but the previous one should be. When solving
6790 // for "X*X < 5", for example, we should not return a root of 2.
6791 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6794 if (Range.contains(R1Val->getValue())) {
6795 // The next iteration must be out of the range...
6796 ConstantInt *NextVal =
6797 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6799 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6800 if (!Range.contains(R1Val->getValue()))
6801 return SE.getConstant(NextVal);
6802 return SE.getCouldNotCompute(); // Something strange happened
6805 // If R1 was not in the range, then it is a good return value. Make
6806 // sure that R1-1 WAS in the range though, just in case.
6807 ConstantInt *NextVal =
6808 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6809 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6810 if (Range.contains(R1Val->getValue()))
6812 return SE.getCouldNotCompute(); // Something strange happened
6817 return SE.getCouldNotCompute();
6820 static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
6821 APInt A = C1->getValue()->getValue();
6822 APInt B = C2->getValue()->getValue();
6823 uint32_t ABW = A.getBitWidth();
6824 uint32_t BBW = B.getBitWidth();
6831 return APIntOps::srem(A, B);
6834 static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
6835 APInt A = C1->getValue()->getValue();
6836 APInt B = C2->getValue()->getValue();
6837 uint32_t ABW = A.getBitWidth();
6838 uint32_t BBW = B.getBitWidth();
6845 return APIntOps::sdiv(A, B);
6849 struct SCEVGCD : public SCEVVisitor<SCEVGCD, const SCEV *> {
6851 // Pattern match Step into Start. When Step is a multiply expression, find
6852 // the largest subexpression of Step that appears in Start. When Start is an
6853 // add expression, try to match Step in the subexpressions of Start, non
6854 // matching subexpressions are returned under Remainder.
6855 static const SCEV *findGCD(ScalarEvolution &SE, const SCEV *Start,
6856 const SCEV *Step, const SCEV **Remainder) {
6857 assert(Remainder && "Remainder should not be NULL");
6858 SCEVGCD R(SE, Step, SE.getConstant(Step->getType(), 0));
6859 const SCEV *Res = R.visit(Start);
6860 *Remainder = R.Remainder;
6864 SCEVGCD(ScalarEvolution &S, const SCEV *G, const SCEV *R)
6865 : SE(S), GCD(G), Remainder(R) {
6866 Zero = SE.getConstant(GCD->getType(), 0);
6867 One = SE.getConstant(GCD->getType(), 1);
6870 const SCEV *visitConstant(const SCEVConstant *Constant) {
6871 if (GCD == Constant || Constant == Zero)
6874 if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD)) {
6875 const SCEV *Res = SE.getConstant(gcd(Constant, CGCD));
6879 Remainder = SE.getConstant(srem(Constant, CGCD));
6880 Constant = cast<SCEVConstant>(SE.getMinusSCEV(Constant, Remainder));
6881 Res = SE.getConstant(gcd(Constant, CGCD));
6885 // When GCD is not a constant, it could be that the GCD is an Add, Mul,
6886 // AddRec, etc., in which case we want to find out how many times the
6887 // Constant divides the GCD: we then return that as the new GCD.
6888 const SCEV *Rem = Zero;
6889 const SCEV *Res = findGCD(SE, GCD, Constant, &Rem);
6891 if (Res == One || Rem != Zero) {
6892 Remainder = Constant;
6896 assert(isa<SCEVConstant>(Res) && "Res should be a constant");
6897 Remainder = SE.getConstant(srem(Constant, cast<SCEVConstant>(Res)));
6901 const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
6907 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
6913 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
6919 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
6923 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6924 const SCEV *Rem = Zero;
6925 const SCEV *Res = findGCD(SE, Expr->getOperand(e - 1 - i), GCD, &Rem);
6927 // FIXME: There may be ambiguous situations: for instance,
6928 // GCD(-4 + (3 * %m), 2 * %m) where 2 divides -4 and %m divides (3 * %m).
6929 // The order in which the AddExpr is traversed computes a different GCD
6934 Remainder = SE.getAddExpr(Remainder, Rem);
6940 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
6944 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6945 if (Expr->getOperand(i) == GCD)
6949 // If we have not returned yet, it means that GCD is not part of Expr.
6950 const SCEV *PartialGCD = One;
6951 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
6952 const SCEV *Rem = Zero;
6953 const SCEV *Res = findGCD(SE, Expr->getOperand(i), GCD, &Rem);
6955 // GCD does not divide Expr->getOperand(i).
6960 PartialGCD = SE.getMulExpr(PartialGCD, Res);
6961 if (PartialGCD == GCD)
6965 if (PartialGCD != One)
6968 // Failed to find a PartialGCD: set the Remainder to the full expression,
6969 // and return the GCD.
6971 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(GCD);
6975 // When the GCD is a multiply expression, try to decompose it:
6976 // this occurs when Step does not divide the Start expression
6977 // as in: {(-4 + (3 * %m)),+,(2 * %m)}
6978 for (int i = 0, e = Mul->getNumOperands(); i < e; ++i) {
6979 const SCEV *Rem = Zero;
6980 const SCEV *Res = findGCD(SE, Expr, Mul->getOperand(i), &Rem);
6990 const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
6996 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
7000 if (!Expr->isAffine()) {
7005 const SCEV *Rem = Zero;
7006 const SCEV *Res = findGCD(SE, Expr->getOperand(0), GCD, &Rem);
7007 if (Res == One || Res->isAllOnesValue()) {
7013 Remainder = SE.getAddExpr(Remainder, Rem);
7016 Res = findGCD(SE, Expr->getOperand(1), Res, &Rem);
7017 if (Rem != Zero || Res == One || Res->isAllOnesValue()) {
7025 const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
7031 const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
7037 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
7043 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
7048 ScalarEvolution &SE;
7049 const SCEV *GCD, *Remainder, *Zero, *One;
7052 struct SCEVDivision : public SCEVVisitor<SCEVDivision, const SCEV *> {
7054 // Remove from Start all multiples of Step.
7055 static const SCEV *divide(ScalarEvolution &SE, const SCEV *Start,
7057 SCEVDivision D(SE, Step);
7058 const SCEV *Rem = D.Zero;
7060 // The division is guaranteed to succeed: Step should divide Start with no
7062 assert(Step == SCEVGCD::findGCD(SE, Start, Step, &Rem) && Rem == D.Zero &&
7063 "Step should divide Start with no remainder.");
7064 return D.visit(Start);
7067 SCEVDivision(ScalarEvolution &S, const SCEV *G) : SE(S), GCD(G) {
7068 Zero = SE.getConstant(GCD->getType(), 0);
7069 One = SE.getConstant(GCD->getType(), 1);
7072 const SCEV *visitConstant(const SCEVConstant *Constant) {
7073 if (GCD == Constant)
7076 if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD))
7077 return SE.getConstant(sdiv(Constant, CGCD));
7081 const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
7087 const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
7093 const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
7099 const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
7103 SmallVector<const SCEV *, 2> Operands;
7104 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
7105 Operands.push_back(divide(SE, Expr->getOperand(i), GCD));
7107 if (Operands.size() == 1)
7109 return SE.getAddExpr(Operands);
7112 const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
7116 bool FoundGCDTerm = false;
7117 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
7118 if (Expr->getOperand(i) == GCD)
7119 FoundGCDTerm = true;
7121 SmallVector<const SCEV *, 2> Operands;
7123 FoundGCDTerm = false;
7124 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
7126 Operands.push_back(Expr->getOperand(i));
7127 else if (Expr->getOperand(i) == GCD)
7128 FoundGCDTerm = true;
7130 Operands.push_back(Expr->getOperand(i));
7133 const SCEV *PartialGCD = One;
7134 for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
7135 if (PartialGCD == GCD) {
7136 Operands.push_back(Expr->getOperand(i));
7140 const SCEV *Rem = Zero;
7141 const SCEV *Res = SCEVGCD::findGCD(SE, Expr->getOperand(i), GCD, &Rem);
7143 PartialGCD = SE.getMulExpr(PartialGCD, Res);
7144 Operands.push_back(divide(SE, Expr->getOperand(i), Res));
7146 Operands.push_back(Expr->getOperand(i));
7151 if (Operands.size() == 1)
7153 return SE.getMulExpr(Operands);
7156 const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
7162 const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
7166 assert(Expr->isAffine() && "Expr should be affine");
7168 const SCEV *Start = divide(SE, Expr->getStart(), GCD);
7169 const SCEV *Step = divide(SE, Expr->getStepRecurrence(SE), GCD);
7171 return SE.getAddRecExpr(Start, Step, Expr->getLoop(),
7172 Expr->getNoWrapFlags());
7175 const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
7181 const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
7187 const SCEV *visitUnknown(const SCEVUnknown *Expr) {
7193 const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
7198 ScalarEvolution &SE;
7199 const SCEV *GCD, *Zero, *One;
7203 /// Splits the SCEV into two vectors of SCEVs representing the subscripts and
7204 /// sizes of an array access. Returns the remainder of the delinearization that
7205 /// is the offset start of the array. The SCEV->delinearize algorithm computes
7206 /// the multiples of SCEV coefficients: that is a pattern matching of sub
7207 /// expressions in the stride and base of a SCEV corresponding to the
7208 /// computation of a GCD (greatest common divisor) of base and stride. When
7209 /// SCEV->delinearize fails, it returns the SCEV unchanged.
7211 /// For example: when analyzing the memory access A[i][j][k] in this loop nest
7213 /// void foo(long n, long m, long o, double A[n][m][o]) {
7215 /// for (long i = 0; i < n; i++)
7216 /// for (long j = 0; j < m; j++)
7217 /// for (long k = 0; k < o; k++)
7218 /// A[i][j][k] = 1.0;
7221 /// the delinearization input is the following AddRec SCEV:
7223 /// AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
7225 /// From this SCEV, we are able to say that the base offset of the access is %A
7226 /// because it appears as an offset that does not divide any of the strides in
7229 /// CHECK: Base offset: %A
7231 /// and then SCEV->delinearize determines the size of some of the dimensions of
7232 /// the array as these are the multiples by which the strides are happening:
7234 /// CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
7236 /// Note that the outermost dimension remains of UnknownSize because there are
7237 /// no strides that would help identifying the size of the last dimension: when
7238 /// the array has been statically allocated, one could compute the size of that
7239 /// dimension by dividing the overall size of the array by the size of the known
7240 /// dimensions: %m * %o * 8.
7242 /// Finally delinearize provides the access functions for the array reference
7243 /// that does correspond to A[i][j][k] of the above C testcase:
7245 /// CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
7247 /// The testcases are checking the output of a function pass:
7248 /// DelinearizationPass that walks through all loads and stores of a function
7249 /// asking for the SCEV of the memory access with respect to all enclosing
7250 /// loops, calling SCEV->delinearize on that and printing the results.
7253 SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
7254 SmallVectorImpl<const SCEV *> &Subscripts,
7255 SmallVectorImpl<const SCEV *> &Sizes) const {
7256 // Early exit in case this SCEV is not an affine multivariate function.
7257 if (!this->isAffine())
7260 const SCEV *Start = this->getStart();
7261 const SCEV *Step = this->getStepRecurrence(SE);
7263 // Build the SCEV representation of the canonical induction variable in the
7264 // loop of this SCEV.
7265 const SCEV *Zero = SE.getConstant(this->getType(), 0);
7266 const SCEV *One = SE.getConstant(this->getType(), 1);
7268 SE.getAddRecExpr(Zero, One, this->getLoop(), this->getNoWrapFlags());
7270 DEBUG(dbgs() << "(delinearize: " << *this << "\n");
7272 // When the stride of this SCEV is 1, do not compute the GCD: the size of this
7273 // subscript is 1, and this same SCEV for the access function.
7274 const SCEV *Remainder = Zero;
7275 const SCEV *GCD = One;
7277 // Find the GCD and Remainder of the Start and Step coefficients of this SCEV.
7278 if (Step != One && !Step->isAllOnesValue())
7279 GCD = SCEVGCD::findGCD(SE, Start, Step, &Remainder);
7281 DEBUG(dbgs() << "GCD: " << *GCD << "\n");
7282 DEBUG(dbgs() << "Remainder: " << *Remainder << "\n");
7284 const SCEV *Quotient = Start;
7285 if (GCD != One && !GCD->isAllOnesValue())
7286 // As findGCD computed Remainder, GCD divides "Start - Remainder." The
7287 // Quotient is then this SCEV without Remainder, scaled down by the GCD. The
7288 // Quotient is what will be used in the next subscript delinearization.
7289 Quotient = SCEVDivision::divide(SE, SE.getMinusSCEV(Start, Remainder), GCD);
7291 DEBUG(dbgs() << "Quotient: " << *Quotient << "\n");
7293 const SCEV *Rem = Quotient;
7294 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Quotient))
7295 // Recursively call delinearize on the Quotient until there are no more
7296 // multiples that can be recognized.
7297 Rem = AR->delinearize(SE, Subscripts, Sizes);
7299 // Scale up the canonical induction variable IV by whatever remains from the
7300 // Step after division by the GCD: the GCD is the size of all the sub-array.
7301 if (Step != One && !Step->isAllOnesValue() && GCD != One &&
7302 !GCD->isAllOnesValue() && Step != GCD) {
7303 Step = SCEVDivision::divide(SE, Step, GCD);
7304 IV = SE.getMulExpr(IV, Step);
7306 // The access function in the current subscript is computed as the canonical
7307 // induction variable IV (potentially scaled up by the step) and offset by
7308 // Rem, the offset of delinearization in the sub-array.
7309 const SCEV *Index = SE.getAddExpr(IV, Rem);
7311 // Record the access function and the size of the current subscript.
7312 Subscripts.push_back(Index);
7313 Sizes.push_back(GCD);
7316 int Size = Sizes.size();
7317 DEBUG(dbgs() << "succeeded to delinearize " << *this << "\n");
7318 DEBUG(dbgs() << "ArrayDecl[UnknownSize]");
7319 for (int i = 0; i < Size - 1; i++)
7320 DEBUG(dbgs() << "[" << *Sizes[i] << "]");
7321 DEBUG(dbgs() << " with elements of " << *Sizes[Size - 1] << " bytes.\n");
7323 DEBUG(dbgs() << "ArrayRef");
7324 for (int i = 0; i < Size; i++)
7325 DEBUG(dbgs() << "[" << *Subscripts[i] << "]");
7326 DEBUG(dbgs() << "\n)\n");
7332 //===----------------------------------------------------------------------===//
7333 // SCEVCallbackVH Class Implementation
7334 //===----------------------------------------------------------------------===//
7336 void ScalarEvolution::SCEVCallbackVH::deleted() {
7337 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7338 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
7339 SE->ConstantEvolutionLoopExitValue.erase(PN);
7340 SE->ValueExprMap.erase(getValPtr());
7341 // this now dangles!
7344 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
7345 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
7347 // Forget all the expressions associated with users of the old value,
7348 // so that future queries will recompute the expressions using the new
7350 Value *Old = getValPtr();
7351 SmallVector<User *, 16> Worklist(Old->user_begin(), Old->user_end());
7352 SmallPtrSet<User *, 8> Visited;
7353 while (!Worklist.empty()) {
7354 User *U = Worklist.pop_back_val();
7355 // Deleting the Old value will cause this to dangle. Postpone
7356 // that until everything else is done.
7359 if (!Visited.insert(U))
7361 if (PHINode *PN = dyn_cast<PHINode>(U))
7362 SE->ConstantEvolutionLoopExitValue.erase(PN);
7363 SE->ValueExprMap.erase(U);
7364 Worklist.insert(Worklist.end(), U->user_begin(), U->user_end());
7366 // Delete the Old value.
7367 if (PHINode *PN = dyn_cast<PHINode>(Old))
7368 SE->ConstantEvolutionLoopExitValue.erase(PN);
7369 SE->ValueExprMap.erase(Old);
7370 // this now dangles!
7373 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
7374 : CallbackVH(V), SE(se) {}
7376 //===----------------------------------------------------------------------===//
7377 // ScalarEvolution Class Implementation
7378 //===----------------------------------------------------------------------===//
7380 ScalarEvolution::ScalarEvolution()
7381 : FunctionPass(ID), ValuesAtScopes(64), LoopDispositions(64),
7382 BlockDispositions(64), FirstUnknown(nullptr) {
7383 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
7386 bool ScalarEvolution::runOnFunction(Function &F) {
7388 LI = &getAnalysis<LoopInfo>();
7389 DataLayoutPass *DLP = getAnalysisIfAvailable<DataLayoutPass>();
7390 DL = DLP ? &DLP->getDataLayout() : nullptr;
7391 TLI = &getAnalysis<TargetLibraryInfo>();
7392 DT = &getAnalysis<DominatorTreeWrapperPass>().getDomTree();
7396 void ScalarEvolution::releaseMemory() {
7397 // Iterate through all the SCEVUnknown instances and call their
7398 // destructors, so that they release their references to their values.
7399 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
7401 FirstUnknown = nullptr;
7403 ValueExprMap.clear();
7405 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
7406 // that a loop had multiple computable exits.
7407 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7408 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
7413 assert(PendingLoopPredicates.empty() && "isImpliedCond garbage");
7415 BackedgeTakenCounts.clear();
7416 ConstantEvolutionLoopExitValue.clear();
7417 ValuesAtScopes.clear();
7418 LoopDispositions.clear();
7419 BlockDispositions.clear();
7420 UnsignedRanges.clear();
7421 SignedRanges.clear();
7422 UniqueSCEVs.clear();
7423 SCEVAllocator.Reset();
7426 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
7427 AU.setPreservesAll();
7428 AU.addRequiredTransitive<LoopInfo>();
7429 AU.addRequiredTransitive<DominatorTreeWrapperPass>();
7430 AU.addRequired<TargetLibraryInfo>();
7433 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
7434 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
7437 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
7439 // Print all inner loops first
7440 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
7441 PrintLoopInfo(OS, SE, *I);
7444 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7447 SmallVector<BasicBlock *, 8> ExitBlocks;
7448 L->getExitBlocks(ExitBlocks);
7449 if (ExitBlocks.size() != 1)
7450 OS << "<multiple exits> ";
7452 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
7453 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
7455 OS << "Unpredictable backedge-taken count. ";
7460 L->getHeader()->printAsOperand(OS, /*PrintType=*/false);
7463 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
7464 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
7466 OS << "Unpredictable max backedge-taken count. ";
7472 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
7473 // ScalarEvolution's implementation of the print method is to print
7474 // out SCEV values of all instructions that are interesting. Doing
7475 // this potentially causes it to create new SCEV objects though,
7476 // which technically conflicts with the const qualifier. This isn't
7477 // observable from outside the class though, so casting away the
7478 // const isn't dangerous.
7479 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7481 OS << "Classifying expressions for: ";
7482 F->printAsOperand(OS, /*PrintType=*/false);
7484 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
7485 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
7488 const SCEV *SV = SE.getSCEV(&*I);
7491 const Loop *L = LI->getLoopFor((*I).getParent());
7493 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
7500 OS << "\t\t" "Exits: ";
7501 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
7502 if (!SE.isLoopInvariant(ExitValue, L)) {
7503 OS << "<<Unknown>>";
7512 OS << "Determining loop execution counts for: ";
7513 F->printAsOperand(OS, /*PrintType=*/false);
7515 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
7516 PrintLoopInfo(OS, &SE, *I);
7519 ScalarEvolution::LoopDisposition
7520 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
7521 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values = LoopDispositions[S];
7522 for (unsigned u = 0; u < Values.size(); u++) {
7523 if (Values[u].first == L)
7524 return Values[u].second;
7526 Values.push_back(std::make_pair(L, LoopVariant));
7527 LoopDisposition D = computeLoopDisposition(S, L);
7528 SmallVector<std::pair<const Loop *, LoopDisposition>, 2> &Values2 = LoopDispositions[S];
7529 for (unsigned u = Values2.size(); u > 0; u--) {
7530 if (Values2[u - 1].first == L) {
7531 Values2[u - 1].second = D;
7538 ScalarEvolution::LoopDisposition
7539 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
7540 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7542 return LoopInvariant;
7546 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
7547 case scAddRecExpr: {
7548 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7550 // If L is the addrec's loop, it's computable.
7551 if (AR->getLoop() == L)
7552 return LoopComputable;
7554 // Add recurrences are never invariant in the function-body (null loop).
7558 // This recurrence is variant w.r.t. L if L contains AR's loop.
7559 if (L->contains(AR->getLoop()))
7562 // This recurrence is invariant w.r.t. L if AR's loop contains L.
7563 if (AR->getLoop()->contains(L))
7564 return LoopInvariant;
7566 // This recurrence is variant w.r.t. L if any of its operands
7568 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
7570 if (!isLoopInvariant(*I, L))
7573 // Otherwise it's loop-invariant.
7574 return LoopInvariant;
7580 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7581 bool HasVarying = false;
7582 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7584 LoopDisposition D = getLoopDisposition(*I, L);
7585 if (D == LoopVariant)
7587 if (D == LoopComputable)
7590 return HasVarying ? LoopComputable : LoopInvariant;
7593 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7594 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
7595 if (LD == LoopVariant)
7597 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
7598 if (RD == LoopVariant)
7600 return (LD == LoopInvariant && RD == LoopInvariant) ?
7601 LoopInvariant : LoopComputable;
7604 // All non-instruction values are loop invariant. All instructions are loop
7605 // invariant if they are not contained in the specified loop.
7606 // Instructions are never considered invariant in the function body
7607 // (null loop) because they are defined within the "loop".
7608 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
7609 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
7610 return LoopInvariant;
7611 case scCouldNotCompute:
7612 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7614 llvm_unreachable("Unknown SCEV kind!");
7617 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
7618 return getLoopDisposition(S, L) == LoopInvariant;
7621 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
7622 return getLoopDisposition(S, L) == LoopComputable;
7625 ScalarEvolution::BlockDisposition
7626 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7627 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values = BlockDispositions[S];
7628 for (unsigned u = 0; u < Values.size(); u++) {
7629 if (Values[u].first == BB)
7630 return Values[u].second;
7632 Values.push_back(std::make_pair(BB, DoesNotDominateBlock));
7633 BlockDisposition D = computeBlockDisposition(S, BB);
7634 SmallVector<std::pair<const BasicBlock *, BlockDisposition>, 2> &Values2 = BlockDispositions[S];
7635 for (unsigned u = Values2.size(); u > 0; u--) {
7636 if (Values2[u - 1].first == BB) {
7637 Values2[u - 1].second = D;
7644 ScalarEvolution::BlockDisposition
7645 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
7646 switch (static_cast<SCEVTypes>(S->getSCEVType())) {
7648 return ProperlyDominatesBlock;
7652 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
7653 case scAddRecExpr: {
7654 // This uses a "dominates" query instead of "properly dominates" query
7655 // to test for proper dominance too, because the instruction which
7656 // produces the addrec's value is a PHI, and a PHI effectively properly
7657 // dominates its entire containing block.
7658 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
7659 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
7660 return DoesNotDominateBlock;
7662 // FALL THROUGH into SCEVNAryExpr handling.
7667 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
7669 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
7671 BlockDisposition D = getBlockDisposition(*I, BB);
7672 if (D == DoesNotDominateBlock)
7673 return DoesNotDominateBlock;
7674 if (D == DominatesBlock)
7677 return Proper ? ProperlyDominatesBlock : DominatesBlock;
7680 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
7681 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
7682 BlockDisposition LD = getBlockDisposition(LHS, BB);
7683 if (LD == DoesNotDominateBlock)
7684 return DoesNotDominateBlock;
7685 BlockDisposition RD = getBlockDisposition(RHS, BB);
7686 if (RD == DoesNotDominateBlock)
7687 return DoesNotDominateBlock;
7688 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
7689 ProperlyDominatesBlock : DominatesBlock;
7692 if (Instruction *I =
7693 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
7694 if (I->getParent() == BB)
7695 return DominatesBlock;
7696 if (DT->properlyDominates(I->getParent(), BB))
7697 return ProperlyDominatesBlock;
7698 return DoesNotDominateBlock;
7700 return ProperlyDominatesBlock;
7701 case scCouldNotCompute:
7702 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
7704 llvm_unreachable("Unknown SCEV kind!");
7707 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
7708 return getBlockDisposition(S, BB) >= DominatesBlock;
7711 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
7712 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
7716 // Search for a SCEV expression node within an expression tree.
7717 // Implements SCEVTraversal::Visitor.
7722 SCEVSearch(const SCEV *N): Node(N), IsFound(false) {}
7724 bool follow(const SCEV *S) {
7725 IsFound |= (S == Node);
7728 bool isDone() const { return IsFound; }
7732 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
7733 SCEVSearch Search(Op);
7734 visitAll(S, Search);
7735 return Search.IsFound;
7738 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
7739 ValuesAtScopes.erase(S);
7740 LoopDispositions.erase(S);
7741 BlockDispositions.erase(S);
7742 UnsignedRanges.erase(S);
7743 SignedRanges.erase(S);
7745 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
7746 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end(); I != E; ) {
7747 BackedgeTakenInfo &BEInfo = I->second;
7748 if (BEInfo.hasOperand(S, this)) {
7750 BackedgeTakenCounts.erase(I++);
7757 typedef DenseMap<const Loop *, std::string> VerifyMap;
7759 /// replaceSubString - Replaces all occurrences of From in Str with To.
7760 static void replaceSubString(std::string &Str, StringRef From, StringRef To) {
7762 while ((Pos = Str.find(From, Pos)) != std::string::npos) {
7763 Str.replace(Pos, From.size(), To.data(), To.size());
7768 /// getLoopBackedgeTakenCounts - Helper method for verifyAnalysis.
7770 getLoopBackedgeTakenCounts(Loop *L, VerifyMap &Map, ScalarEvolution &SE) {
7771 for (Loop::reverse_iterator I = L->rbegin(), E = L->rend(); I != E; ++I) {
7772 getLoopBackedgeTakenCounts(*I, Map, SE); // recurse.
7774 std::string &S = Map[L];
7776 raw_string_ostream OS(S);
7777 SE.getBackedgeTakenCount(L)->print(OS);
7779 // false and 0 are semantically equivalent. This can happen in dead loops.
7780 replaceSubString(OS.str(), "false", "0");
7781 // Remove wrap flags, their use in SCEV is highly fragile.
7782 // FIXME: Remove this when SCEV gets smarter about them.
7783 replaceSubString(OS.str(), "<nw>", "");
7784 replaceSubString(OS.str(), "<nsw>", "");
7785 replaceSubString(OS.str(), "<nuw>", "");
7790 void ScalarEvolution::verifyAnalysis() const {
7794 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
7796 // Gather stringified backedge taken counts for all loops using SCEV's caches.
7797 // FIXME: It would be much better to store actual values instead of strings,
7798 // but SCEV pointers will change if we drop the caches.
7799 VerifyMap BackedgeDumpsOld, BackedgeDumpsNew;
7800 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7801 getLoopBackedgeTakenCounts(*I, BackedgeDumpsOld, SE);
7803 // Gather stringified backedge taken counts for all loops without using
7806 for (LoopInfo::reverse_iterator I = LI->rbegin(), E = LI->rend(); I != E; ++I)
7807 getLoopBackedgeTakenCounts(*I, BackedgeDumpsNew, SE);
7809 // Now compare whether they're the same with and without caches. This allows
7810 // verifying that no pass changed the cache.
7811 assert(BackedgeDumpsOld.size() == BackedgeDumpsNew.size() &&
7812 "New loops suddenly appeared!");
7814 for (VerifyMap::iterator OldI = BackedgeDumpsOld.begin(),
7815 OldE = BackedgeDumpsOld.end(),
7816 NewI = BackedgeDumpsNew.begin();
7817 OldI != OldE; ++OldI, ++NewI) {
7818 assert(OldI->first == NewI->first && "Loop order changed!");
7820 // Compare the stringified SCEVs. We don't care if undef backedgetaken count
7822 // FIXME: We currently ignore SCEV changes from/to CouldNotCompute. This
7823 // means that a pass is buggy or SCEV has to learn a new pattern but is
7824 // usually not harmful.
7825 if (OldI->second != NewI->second &&
7826 OldI->second.find("undef") == std::string::npos &&
7827 NewI->second.find("undef") == std::string::npos &&
7828 OldI->second != "***COULDNOTCOMPUTE***" &&
7829 NewI->second != "***COULDNOTCOMPUTE***") {
7830 dbgs() << "SCEVValidator: SCEV for loop '"
7831 << OldI->first->getHeader()->getName()
7832 << "' changed from '" << OldI->second
7833 << "' to '" << NewI->second << "'!\n";
7838 // TODO: Verify more things.