1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #define DEBUG_TYPE "scalar-evolution"
62 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/GlobalAlias.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/Operator.h"
70 #include "llvm/Analysis/ConstantFolding.h"
71 #include "llvm/Analysis/Dominators.h"
72 #include "llvm/Analysis/InstructionSimplify.h"
73 #include "llvm/Analysis/LoopInfo.h"
74 #include "llvm/Analysis/ValueTracking.h"
75 #include "llvm/Assembly/Writer.h"
76 #include "llvm/Target/TargetData.h"
77 #include "llvm/Support/CommandLine.h"
78 #include "llvm/Support/ConstantRange.h"
79 #include "llvm/Support/Debug.h"
80 #include "llvm/Support/ErrorHandling.h"
81 #include "llvm/Support/GetElementPtrTypeIterator.h"
82 #include "llvm/Support/InstIterator.h"
83 #include "llvm/Support/MathExtras.h"
84 #include "llvm/Support/raw_ostream.h"
85 #include "llvm/ADT/Statistic.h"
86 #include "llvm/ADT/STLExtras.h"
87 #include "llvm/ADT/SmallPtrSet.h"
91 STATISTIC(NumArrayLenItCounts,
92 "Number of trip counts computed with array length");
93 STATISTIC(NumTripCountsComputed,
94 "Number of loops with predictable loop counts");
95 STATISTIC(NumTripCountsNotComputed,
96 "Number of loops without predictable loop counts");
97 STATISTIC(NumBruteForceTripCountsComputed,
98 "Number of loops with trip counts computed by force");
100 static cl::opt<unsigned>
101 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
102 cl::desc("Maximum number of iterations SCEV will "
103 "symbolically execute a constant "
107 INITIALIZE_PASS_BEGIN(ScalarEvolution, "scalar-evolution",
108 "Scalar Evolution Analysis", false, true)
109 INITIALIZE_PASS_DEPENDENCY(LoopInfo)
110 INITIALIZE_PASS_DEPENDENCY(DominatorTree)
111 INITIALIZE_PASS_END(ScalarEvolution, "scalar-evolution",
112 "Scalar Evolution Analysis", false, true)
113 char ScalarEvolution::ID = 0;
115 //===----------------------------------------------------------------------===//
116 // SCEV class definitions
117 //===----------------------------------------------------------------------===//
119 //===----------------------------------------------------------------------===//
120 // Implementation of the SCEV class.
123 void SCEV::dump() const {
128 void SCEV::print(raw_ostream &OS) const {
129 switch (getSCEVType()) {
131 WriteAsOperand(OS, cast<SCEVConstant>(this)->getValue(), false);
134 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(this);
135 const SCEV *Op = Trunc->getOperand();
136 OS << "(trunc " << *Op->getType() << " " << *Op << " to "
137 << *Trunc->getType() << ")";
141 const SCEVZeroExtendExpr *ZExt = cast<SCEVZeroExtendExpr>(this);
142 const SCEV *Op = ZExt->getOperand();
143 OS << "(zext " << *Op->getType() << " " << *Op << " to "
144 << *ZExt->getType() << ")";
148 const SCEVSignExtendExpr *SExt = cast<SCEVSignExtendExpr>(this);
149 const SCEV *Op = SExt->getOperand();
150 OS << "(sext " << *Op->getType() << " " << *Op << " to "
151 << *SExt->getType() << ")";
155 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(this);
156 OS << "{" << *AR->getOperand(0);
157 for (unsigned i = 1, e = AR->getNumOperands(); i != e; ++i)
158 OS << ",+," << *AR->getOperand(i);
160 if (AR->getNoWrapFlags(FlagNUW))
162 if (AR->getNoWrapFlags(FlagNSW))
164 if (AR->getNoWrapFlags(FlagNW) &&
165 !AR->getNoWrapFlags((NoWrapFlags)(FlagNUW | FlagNSW)))
167 WriteAsOperand(OS, AR->getLoop()->getHeader(), /*PrintType=*/false);
175 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(this);
176 const char *OpStr = 0;
177 switch (NAry->getSCEVType()) {
178 case scAddExpr: OpStr = " + "; break;
179 case scMulExpr: OpStr = " * "; break;
180 case scUMaxExpr: OpStr = " umax "; break;
181 case scSMaxExpr: OpStr = " smax "; break;
184 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
187 if (llvm::next(I) != E)
194 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(this);
195 OS << "(" << *UDiv->getLHS() << " /u " << *UDiv->getRHS() << ")";
199 const SCEVUnknown *U = cast<SCEVUnknown>(this);
201 if (U->isSizeOf(AllocTy)) {
202 OS << "sizeof(" << *AllocTy << ")";
205 if (U->isAlignOf(AllocTy)) {
206 OS << "alignof(" << *AllocTy << ")";
212 if (U->isOffsetOf(CTy, FieldNo)) {
213 OS << "offsetof(" << *CTy << ", ";
214 WriteAsOperand(OS, FieldNo, false);
219 // Otherwise just print it normally.
220 WriteAsOperand(OS, U->getValue(), false);
223 case scCouldNotCompute:
224 OS << "***COULDNOTCOMPUTE***";
228 llvm_unreachable("Unknown SCEV kind!");
231 Type *SCEV::getType() const {
232 switch (getSCEVType()) {
234 return cast<SCEVConstant>(this)->getType();
238 return cast<SCEVCastExpr>(this)->getType();
243 return cast<SCEVNAryExpr>(this)->getType();
245 return cast<SCEVAddExpr>(this)->getType();
247 return cast<SCEVUDivExpr>(this)->getType();
249 return cast<SCEVUnknown>(this)->getType();
250 case scCouldNotCompute:
251 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
255 llvm_unreachable("Unknown SCEV kind!");
259 bool SCEV::isZero() const {
260 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
261 return SC->getValue()->isZero();
265 bool SCEV::isOne() const {
266 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
267 return SC->getValue()->isOne();
271 bool SCEV::isAllOnesValue() const {
272 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
273 return SC->getValue()->isAllOnesValue();
277 SCEVCouldNotCompute::SCEVCouldNotCompute() :
278 SCEV(FoldingSetNodeIDRef(), scCouldNotCompute) {}
280 bool SCEVCouldNotCompute::classof(const SCEV *S) {
281 return S->getSCEVType() == scCouldNotCompute;
284 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
286 ID.AddInteger(scConstant);
289 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
290 SCEV *S = new (SCEVAllocator) SCEVConstant(ID.Intern(SCEVAllocator), V);
291 UniqueSCEVs.InsertNode(S, IP);
295 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
296 return getConstant(ConstantInt::get(getContext(), Val));
300 ScalarEvolution::getConstant(Type *Ty, uint64_t V, bool isSigned) {
301 IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
302 return getConstant(ConstantInt::get(ITy, V, isSigned));
305 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeIDRef ID,
306 unsigned SCEVTy, const SCEV *op, Type *ty)
307 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
309 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeIDRef ID,
310 const SCEV *op, Type *ty)
311 : SCEVCastExpr(ID, scTruncate, op, ty) {
312 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
313 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
314 "Cannot truncate non-integer value!");
317 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeIDRef ID,
318 const SCEV *op, Type *ty)
319 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
320 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
321 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
322 "Cannot zero extend non-integer value!");
325 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeIDRef ID,
326 const SCEV *op, Type *ty)
327 : SCEVCastExpr(ID, scSignExtend, op, ty) {
328 assert((Op->getType()->isIntegerTy() || Op->getType()->isPointerTy()) &&
329 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
330 "Cannot sign extend non-integer value!");
333 void SCEVUnknown::deleted() {
334 // Clear this SCEVUnknown from various maps.
335 SE->forgetMemoizedResults(this);
337 // Remove this SCEVUnknown from the uniquing map.
338 SE->UniqueSCEVs.RemoveNode(this);
340 // Release the value.
344 void SCEVUnknown::allUsesReplacedWith(Value *New) {
345 // Clear this SCEVUnknown from various maps.
346 SE->forgetMemoizedResults(this);
348 // Remove this SCEVUnknown from the uniquing map.
349 SE->UniqueSCEVs.RemoveNode(this);
351 // Update this SCEVUnknown to point to the new value. This is needed
352 // because there may still be outstanding SCEVs which still point to
357 bool SCEVUnknown::isSizeOf(Type *&AllocTy) const {
358 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
359 if (VCE->getOpcode() == Instruction::PtrToInt)
360 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
361 if (CE->getOpcode() == Instruction::GetElementPtr &&
362 CE->getOperand(0)->isNullValue() &&
363 CE->getNumOperands() == 2)
364 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(1)))
366 AllocTy = cast<PointerType>(CE->getOperand(0)->getType())
374 bool SCEVUnknown::isAlignOf(Type *&AllocTy) const {
375 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
376 if (VCE->getOpcode() == Instruction::PtrToInt)
377 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
378 if (CE->getOpcode() == Instruction::GetElementPtr &&
379 CE->getOperand(0)->isNullValue()) {
381 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
382 if (StructType *STy = dyn_cast<StructType>(Ty))
383 if (!STy->isPacked() &&
384 CE->getNumOperands() == 3 &&
385 CE->getOperand(1)->isNullValue()) {
386 if (ConstantInt *CI = dyn_cast<ConstantInt>(CE->getOperand(2)))
388 STy->getNumElements() == 2 &&
389 STy->getElementType(0)->isIntegerTy(1)) {
390 AllocTy = STy->getElementType(1);
399 bool SCEVUnknown::isOffsetOf(Type *&CTy, Constant *&FieldNo) const {
400 if (ConstantExpr *VCE = dyn_cast<ConstantExpr>(getValue()))
401 if (VCE->getOpcode() == Instruction::PtrToInt)
402 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(VCE->getOperand(0)))
403 if (CE->getOpcode() == Instruction::GetElementPtr &&
404 CE->getNumOperands() == 3 &&
405 CE->getOperand(0)->isNullValue() &&
406 CE->getOperand(1)->isNullValue()) {
408 cast<PointerType>(CE->getOperand(0)->getType())->getElementType();
409 // Ignore vector types here so that ScalarEvolutionExpander doesn't
410 // emit getelementptrs that index into vectors.
411 if (Ty->isStructTy() || Ty->isArrayTy()) {
413 FieldNo = CE->getOperand(2);
421 //===----------------------------------------------------------------------===//
423 //===----------------------------------------------------------------------===//
426 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
427 /// than the complexity of the RHS. This comparator is used to canonicalize
429 class SCEVComplexityCompare {
430 const LoopInfo *const LI;
432 explicit SCEVComplexityCompare(const LoopInfo *li) : LI(li) {}
434 // Return true or false if LHS is less than, or at least RHS, respectively.
435 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
436 return compare(LHS, RHS) < 0;
439 // Return negative, zero, or positive, if LHS is less than, equal to, or
440 // greater than RHS, respectively. A three-way result allows recursive
441 // comparisons to be more efficient.
442 int compare(const SCEV *LHS, const SCEV *RHS) const {
443 // Fast-path: SCEVs are uniqued so we can do a quick equality check.
447 // Primarily, sort the SCEVs by their getSCEVType().
448 unsigned LType = LHS->getSCEVType(), RType = RHS->getSCEVType();
450 return (int)LType - (int)RType;
452 // Aside from the getSCEVType() ordering, the particular ordering
453 // isn't very important except that it's beneficial to be consistent,
454 // so that (a + b) and (b + a) don't end up as different expressions.
457 const SCEVUnknown *LU = cast<SCEVUnknown>(LHS);
458 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
460 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
461 // not as complete as it could be.
462 const Value *LV = LU->getValue(), *RV = RU->getValue();
464 // Order pointer values after integer values. This helps SCEVExpander
466 bool LIsPointer = LV->getType()->isPointerTy(),
467 RIsPointer = RV->getType()->isPointerTy();
468 if (LIsPointer != RIsPointer)
469 return (int)LIsPointer - (int)RIsPointer;
471 // Compare getValueID values.
472 unsigned LID = LV->getValueID(),
473 RID = RV->getValueID();
475 return (int)LID - (int)RID;
477 // Sort arguments by their position.
478 if (const Argument *LA = dyn_cast<Argument>(LV)) {
479 const Argument *RA = cast<Argument>(RV);
480 unsigned LArgNo = LA->getArgNo(), RArgNo = RA->getArgNo();
481 return (int)LArgNo - (int)RArgNo;
484 // For instructions, compare their loop depth, and their operand
485 // count. This is pretty loose.
486 if (const Instruction *LInst = dyn_cast<Instruction>(LV)) {
487 const Instruction *RInst = cast<Instruction>(RV);
489 // Compare loop depths.
490 const BasicBlock *LParent = LInst->getParent(),
491 *RParent = RInst->getParent();
492 if (LParent != RParent) {
493 unsigned LDepth = LI->getLoopDepth(LParent),
494 RDepth = LI->getLoopDepth(RParent);
495 if (LDepth != RDepth)
496 return (int)LDepth - (int)RDepth;
499 // Compare the number of operands.
500 unsigned LNumOps = LInst->getNumOperands(),
501 RNumOps = RInst->getNumOperands();
502 return (int)LNumOps - (int)RNumOps;
509 const SCEVConstant *LC = cast<SCEVConstant>(LHS);
510 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
512 // Compare constant values.
513 const APInt &LA = LC->getValue()->getValue();
514 const APInt &RA = RC->getValue()->getValue();
515 unsigned LBitWidth = LA.getBitWidth(), RBitWidth = RA.getBitWidth();
516 if (LBitWidth != RBitWidth)
517 return (int)LBitWidth - (int)RBitWidth;
518 return LA.ult(RA) ? -1 : 1;
522 const SCEVAddRecExpr *LA = cast<SCEVAddRecExpr>(LHS);
523 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
525 // Compare addrec loop depths.
526 const Loop *LLoop = LA->getLoop(), *RLoop = RA->getLoop();
527 if (LLoop != RLoop) {
528 unsigned LDepth = LLoop->getLoopDepth(),
529 RDepth = RLoop->getLoopDepth();
530 if (LDepth != RDepth)
531 return (int)LDepth - (int)RDepth;
534 // Addrec complexity grows with operand count.
535 unsigned LNumOps = LA->getNumOperands(), RNumOps = RA->getNumOperands();
536 if (LNumOps != RNumOps)
537 return (int)LNumOps - (int)RNumOps;
539 // Lexicographically compare.
540 for (unsigned i = 0; i != LNumOps; ++i) {
541 long X = compare(LA->getOperand(i), RA->getOperand(i));
553 const SCEVNAryExpr *LC = cast<SCEVNAryExpr>(LHS);
554 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
556 // Lexicographically compare n-ary expressions.
557 unsigned LNumOps = LC->getNumOperands(), RNumOps = RC->getNumOperands();
558 for (unsigned i = 0; i != LNumOps; ++i) {
561 long X = compare(LC->getOperand(i), RC->getOperand(i));
565 return (int)LNumOps - (int)RNumOps;
569 const SCEVUDivExpr *LC = cast<SCEVUDivExpr>(LHS);
570 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
572 // Lexicographically compare udiv expressions.
573 long X = compare(LC->getLHS(), RC->getLHS());
576 return compare(LC->getRHS(), RC->getRHS());
582 const SCEVCastExpr *LC = cast<SCEVCastExpr>(LHS);
583 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
585 // Compare cast expressions by operand.
586 return compare(LC->getOperand(), RC->getOperand());
593 llvm_unreachable("Unknown SCEV kind!");
599 /// GroupByComplexity - Given a list of SCEV objects, order them by their
600 /// complexity, and group objects of the same complexity together by value.
601 /// When this routine is finished, we know that any duplicates in the vector are
602 /// consecutive and that complexity is monotonically increasing.
604 /// Note that we go take special precautions to ensure that we get deterministic
605 /// results from this routine. In other words, we don't want the results of
606 /// this to depend on where the addresses of various SCEV objects happened to
609 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
611 if (Ops.size() < 2) return; // Noop
612 if (Ops.size() == 2) {
613 // This is the common case, which also happens to be trivially simple.
615 const SCEV *&LHS = Ops[0], *&RHS = Ops[1];
616 if (SCEVComplexityCompare(LI)(RHS, LHS))
621 // Do the rough sort by complexity.
622 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
624 // Now that we are sorted by complexity, group elements of the same
625 // complexity. Note that this is, at worst, N^2, but the vector is likely to
626 // be extremely short in practice. Note that we take this approach because we
627 // do not want to depend on the addresses of the objects we are grouping.
628 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
629 const SCEV *S = Ops[i];
630 unsigned Complexity = S->getSCEVType();
632 // If there are any objects of the same complexity and same value as this
634 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
635 if (Ops[j] == S) { // Found a duplicate.
636 // Move it to immediately after i'th element.
637 std::swap(Ops[i+1], Ops[j]);
638 ++i; // no need to rescan it.
639 if (i == e-2) return; // Done!
647 //===----------------------------------------------------------------------===//
648 // Simple SCEV method implementations
649 //===----------------------------------------------------------------------===//
651 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
653 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
656 // Handle the simplest case efficiently.
658 return SE.getTruncateOrZeroExtend(It, ResultTy);
660 // We are using the following formula for BC(It, K):
662 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
664 // Suppose, W is the bitwidth of the return value. We must be prepared for
665 // overflow. Hence, we must assure that the result of our computation is
666 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
667 // safe in modular arithmetic.
669 // However, this code doesn't use exactly that formula; the formula it uses
670 // is something like the following, where T is the number of factors of 2 in
671 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
674 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
676 // This formula is trivially equivalent to the previous formula. However,
677 // this formula can be implemented much more efficiently. The trick is that
678 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
679 // arithmetic. To do exact division in modular arithmetic, all we have
680 // to do is multiply by the inverse. Therefore, this step can be done at
683 // The next issue is how to safely do the division by 2^T. The way this
684 // is done is by doing the multiplication step at a width of at least W + T
685 // bits. This way, the bottom W+T bits of the product are accurate. Then,
686 // when we perform the division by 2^T (which is equivalent to a right shift
687 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
688 // truncated out after the division by 2^T.
690 // In comparison to just directly using the first formula, this technique
691 // is much more efficient; using the first formula requires W * K bits,
692 // but this formula less than W + K bits. Also, the first formula requires
693 // a division step, whereas this formula only requires multiplies and shifts.
695 // It doesn't matter whether the subtraction step is done in the calculation
696 // width or the input iteration count's width; if the subtraction overflows,
697 // the result must be zero anyway. We prefer here to do it in the width of
698 // the induction variable because it helps a lot for certain cases; CodeGen
699 // isn't smart enough to ignore the overflow, which leads to much less
700 // efficient code if the width of the subtraction is wider than the native
703 // (It's possible to not widen at all by pulling out factors of 2 before
704 // the multiplication; for example, K=2 can be calculated as
705 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
706 // extra arithmetic, so it's not an obvious win, and it gets
707 // much more complicated for K > 3.)
709 // Protection from insane SCEVs; this bound is conservative,
710 // but it probably doesn't matter.
712 return SE.getCouldNotCompute();
714 unsigned W = SE.getTypeSizeInBits(ResultTy);
716 // Calculate K! / 2^T and T; we divide out the factors of two before
717 // multiplying for calculating K! / 2^T to avoid overflow.
718 // Other overflow doesn't matter because we only care about the bottom
719 // W bits of the result.
720 APInt OddFactorial(W, 1);
722 for (unsigned i = 3; i <= K; ++i) {
724 unsigned TwoFactors = Mult.countTrailingZeros();
726 Mult = Mult.lshr(TwoFactors);
727 OddFactorial *= Mult;
730 // We need at least W + T bits for the multiplication step
731 unsigned CalculationBits = W + T;
733 // Calculate 2^T, at width T+W.
734 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
736 // Calculate the multiplicative inverse of K! / 2^T;
737 // this multiplication factor will perform the exact division by
739 APInt Mod = APInt::getSignedMinValue(W+1);
740 APInt MultiplyFactor = OddFactorial.zext(W+1);
741 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
742 MultiplyFactor = MultiplyFactor.trunc(W);
744 // Calculate the product, at width T+W
745 IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
747 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
748 for (unsigned i = 1; i != K; ++i) {
749 const SCEV *S = SE.getMinusSCEV(It, SE.getConstant(It->getType(), i));
750 Dividend = SE.getMulExpr(Dividend,
751 SE.getTruncateOrZeroExtend(S, CalculationTy));
755 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
757 // Truncate the result, and divide by K! / 2^T.
759 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
760 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
763 /// evaluateAtIteration - Return the value of this chain of recurrences at
764 /// the specified iteration number. We can evaluate this recurrence by
765 /// multiplying each element in the chain by the binomial coefficient
766 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
768 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
770 /// where BC(It, k) stands for binomial coefficient.
772 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
773 ScalarEvolution &SE) const {
774 const SCEV *Result = getStart();
775 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
776 // The computation is correct in the face of overflow provided that the
777 // multiplication is performed _after_ the evaluation of the binomial
779 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
780 if (isa<SCEVCouldNotCompute>(Coeff))
783 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
788 //===----------------------------------------------------------------------===//
789 // SCEV Expression folder implementations
790 //===----------------------------------------------------------------------===//
792 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
794 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
795 "This is not a truncating conversion!");
796 assert(isSCEVable(Ty) &&
797 "This is not a conversion to a SCEVable type!");
798 Ty = getEffectiveSCEVType(Ty);
801 ID.AddInteger(scTruncate);
805 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
807 // Fold if the operand is constant.
808 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
810 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(),
811 getEffectiveSCEVType(Ty))));
813 // trunc(trunc(x)) --> trunc(x)
814 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
815 return getTruncateExpr(ST->getOperand(), Ty);
817 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
818 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
819 return getTruncateOrSignExtend(SS->getOperand(), Ty);
821 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
822 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
823 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
825 // trunc(x1+x2+...+xN) --> trunc(x1)+trunc(x2)+...+trunc(xN) if we can
826 // eliminate all the truncates.
827 if (const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Op)) {
828 SmallVector<const SCEV *, 4> Operands;
829 bool hasTrunc = false;
830 for (unsigned i = 0, e = SA->getNumOperands(); i != e && !hasTrunc; ++i) {
831 const SCEV *S = getTruncateExpr(SA->getOperand(i), Ty);
832 hasTrunc = isa<SCEVTruncateExpr>(S);
833 Operands.push_back(S);
836 return getAddExpr(Operands);
837 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
840 // trunc(x1*x2*...*xN) --> trunc(x1)*trunc(x2)*...*trunc(xN) if we can
841 // eliminate all the truncates.
842 if (const SCEVMulExpr *SM = dyn_cast<SCEVMulExpr>(Op)) {
843 SmallVector<const SCEV *, 4> Operands;
844 bool hasTrunc = false;
845 for (unsigned i = 0, e = SM->getNumOperands(); i != e && !hasTrunc; ++i) {
846 const SCEV *S = getTruncateExpr(SM->getOperand(i), Ty);
847 hasTrunc = isa<SCEVTruncateExpr>(S);
848 Operands.push_back(S);
851 return getMulExpr(Operands);
852 UniqueSCEVs.FindNodeOrInsertPos(ID, IP); // Mutates IP, returns NULL.
855 // If the input value is a chrec scev, truncate the chrec's operands.
856 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
857 SmallVector<const SCEV *, 4> Operands;
858 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
859 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
860 return getAddRecExpr(Operands, AddRec->getLoop(), SCEV::FlagAnyWrap);
863 // As a special case, fold trunc(undef) to undef. We don't want to
864 // know too much about SCEVUnknowns, but this special case is handy
866 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
867 if (isa<UndefValue>(U->getValue()))
868 return getSCEV(UndefValue::get(Ty));
870 // The cast wasn't folded; create an explicit cast node. We can reuse
871 // the existing insert position since if we get here, we won't have
872 // made any changes which would invalidate it.
873 SCEV *S = new (SCEVAllocator) SCEVTruncateExpr(ID.Intern(SCEVAllocator),
875 UniqueSCEVs.InsertNode(S, IP);
879 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
881 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
882 "This is not an extending conversion!");
883 assert(isSCEVable(Ty) &&
884 "This is not a conversion to a SCEVable type!");
885 Ty = getEffectiveSCEVType(Ty);
887 // Fold if the operand is constant.
888 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
890 cast<ConstantInt>(ConstantExpr::getZExt(SC->getValue(),
891 getEffectiveSCEVType(Ty))));
893 // zext(zext(x)) --> zext(x)
894 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
895 return getZeroExtendExpr(SZ->getOperand(), Ty);
897 // Before doing any expensive analysis, check to see if we've already
898 // computed a SCEV for this Op and Ty.
900 ID.AddInteger(scZeroExtend);
904 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
906 // zext(trunc(x)) --> zext(x) or x or trunc(x)
907 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
908 // It's possible the bits taken off by the truncate were all zero bits. If
909 // so, we should be able to simplify this further.
910 const SCEV *X = ST->getOperand();
911 ConstantRange CR = getUnsignedRange(X);
912 unsigned TruncBits = getTypeSizeInBits(ST->getType());
913 unsigned NewBits = getTypeSizeInBits(Ty);
914 if (CR.truncate(TruncBits).zeroExtend(NewBits).contains(
915 CR.zextOrTrunc(NewBits)))
916 return getTruncateOrZeroExtend(X, Ty);
919 // If the input value is a chrec scev, and we can prove that the value
920 // did not overflow the old, smaller, value, we can zero extend all of the
921 // operands (often constants). This allows analysis of something like
922 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
923 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
924 if (AR->isAffine()) {
925 const SCEV *Start = AR->getStart();
926 const SCEV *Step = AR->getStepRecurrence(*this);
927 unsigned BitWidth = getTypeSizeInBits(AR->getType());
928 const Loop *L = AR->getLoop();
930 // If we have special knowledge that this addrec won't overflow,
931 // we don't need to do any further analysis.
932 if (AR->getNoWrapFlags(SCEV::FlagNUW))
933 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
934 getZeroExtendExpr(Step, Ty),
935 L, AR->getNoWrapFlags());
937 // Check whether the backedge-taken count is SCEVCouldNotCompute.
938 // Note that this serves two purposes: It filters out loops that are
939 // simply not analyzable, and it covers the case where this code is
940 // being called from within backedge-taken count analysis, such that
941 // attempting to ask for the backedge-taken count would likely result
942 // in infinite recursion. In the later case, the analysis code will
943 // cope with a conservative value, and it will take care to purge
944 // that value once it has finished.
945 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
946 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
947 // Manually compute the final value for AR, checking for
950 // Check whether the backedge-taken count can be losslessly casted to
951 // the addrec's type. The count is always unsigned.
952 const SCEV *CastedMaxBECount =
953 getTruncateOrZeroExtend(MaxBECount, Start->getType());
954 const SCEV *RecastedMaxBECount =
955 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
956 if (MaxBECount == RecastedMaxBECount) {
957 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
958 // Check whether Start+Step*MaxBECount has no unsigned overflow.
959 const SCEV *ZMul = getMulExpr(CastedMaxBECount, Step);
960 const SCEV *Add = getAddExpr(Start, ZMul);
961 const SCEV *OperandExtendedAdd =
962 getAddExpr(getZeroExtendExpr(Start, WideTy),
963 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
964 getZeroExtendExpr(Step, WideTy)));
965 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
966 // Cache knowledge of AR NUW, which is propagated to this AddRec.
967 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
968 // Return the expression with the addrec on the outside.
969 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
970 getZeroExtendExpr(Step, Ty),
971 L, AR->getNoWrapFlags());
973 // Similar to above, only this time treat the step value as signed.
974 // This covers loops that count down.
975 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
976 Add = getAddExpr(Start, SMul);
978 getAddExpr(getZeroExtendExpr(Start, WideTy),
979 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
980 getSignExtendExpr(Step, WideTy)));
981 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd) {
982 // Cache knowledge of AR NW, which is propagated to this AddRec.
983 // Negative step causes unsigned wrap, but it still can't self-wrap.
984 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
985 // Return the expression with the addrec on the outside.
986 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
987 getSignExtendExpr(Step, Ty),
988 L, AR->getNoWrapFlags());
992 // If the backedge is guarded by a comparison with the pre-inc value
993 // the addrec is safe. Also, if the entry is guarded by a comparison
994 // with the start value and the backedge is guarded by a comparison
995 // with the post-inc value, the addrec is safe.
996 if (isKnownPositive(Step)) {
997 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
998 getUnsignedRange(Step).getUnsignedMax());
999 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
1000 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
1001 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
1002 AR->getPostIncExpr(*this), N))) {
1003 // Cache knowledge of AR NUW, which is propagated to this AddRec.
1004 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNUW);
1005 // Return the expression with the addrec on the outside.
1006 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1007 getZeroExtendExpr(Step, Ty),
1008 L, AR->getNoWrapFlags());
1010 } else if (isKnownNegative(Step)) {
1011 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
1012 getSignedRange(Step).getSignedMin());
1013 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) ||
1014 (isLoopEntryGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) &&
1015 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
1016 AR->getPostIncExpr(*this), N))) {
1017 // Cache knowledge of AR NW, which is propagated to this AddRec.
1018 // Negative step causes unsigned wrap, but it still can't self-wrap.
1019 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNW);
1020 // Return the expression with the addrec on the outside.
1021 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
1022 getSignExtendExpr(Step, Ty),
1023 L, AR->getNoWrapFlags());
1029 // The cast wasn't folded; create an explicit cast node.
1030 // Recompute the insert position, as it may have been invalidated.
1031 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1032 SCEV *S = new (SCEVAllocator) SCEVZeroExtendExpr(ID.Intern(SCEVAllocator),
1034 UniqueSCEVs.InsertNode(S, IP);
1038 // Get the limit of a recurrence such that incrementing by Step cannot cause
1039 // signed overflow as long as the value of the recurrence within the loop does
1040 // not exceed this limit before incrementing.
1041 static const SCEV *getOverflowLimitForStep(const SCEV *Step,
1042 ICmpInst::Predicate *Pred,
1043 ScalarEvolution *SE) {
1044 unsigned BitWidth = SE->getTypeSizeInBits(Step->getType());
1045 if (SE->isKnownPositive(Step)) {
1046 *Pred = ICmpInst::ICMP_SLT;
1047 return SE->getConstant(APInt::getSignedMinValue(BitWidth) -
1048 SE->getSignedRange(Step).getSignedMax());
1050 if (SE->isKnownNegative(Step)) {
1051 *Pred = ICmpInst::ICMP_SGT;
1052 return SE->getConstant(APInt::getSignedMaxValue(BitWidth) -
1053 SE->getSignedRange(Step).getSignedMin());
1058 // The recurrence AR has been shown to have no signed wrap. Typically, if we can
1059 // prove NSW for AR, then we can just as easily prove NSW for its preincrement
1060 // or postincrement sibling. This allows normalizing a sign extended AddRec as
1061 // such: {sext(Step + Start),+,Step} => {(Step + sext(Start),+,Step} As a
1062 // result, the expression "Step + sext(PreIncAR)" is congruent with
1063 // "sext(PostIncAR)"
1064 static const SCEV *getPreStartForSignExtend(const SCEVAddRecExpr *AR,
1066 ScalarEvolution *SE) {
1067 const Loop *L = AR->getLoop();
1068 const SCEV *Start = AR->getStart();
1069 const SCEV *Step = AR->getStepRecurrence(*SE);
1071 // Check for a simple looking step prior to loop entry.
1072 const SCEVAddExpr *SA = dyn_cast<SCEVAddExpr>(Start);
1073 if (!SA || SA->getNumOperands() != 2 || SA->getOperand(0) != Step)
1076 // This is a postinc AR. Check for overflow on the preinc recurrence using the
1077 // same three conditions that getSignExtendedExpr checks.
1079 // 1. NSW flags on the step increment.
1080 const SCEV *PreStart = SA->getOperand(1);
1081 const SCEVAddRecExpr *PreAR = dyn_cast<SCEVAddRecExpr>(
1082 SE->getAddRecExpr(PreStart, Step, L, SCEV::FlagAnyWrap));
1084 if (PreAR && PreAR->getNoWrapFlags(SCEV::FlagNSW))
1087 // 2. Direct overflow check on the step operation's expression.
1088 unsigned BitWidth = SE->getTypeSizeInBits(AR->getType());
1089 Type *WideTy = IntegerType::get(SE->getContext(), BitWidth * 2);
1090 const SCEV *OperandExtendedStart =
1091 SE->getAddExpr(SE->getSignExtendExpr(PreStart, WideTy),
1092 SE->getSignExtendExpr(Step, WideTy));
1093 if (SE->getSignExtendExpr(Start, WideTy) == OperandExtendedStart) {
1094 // Cache knowledge of PreAR NSW.
1096 const_cast<SCEVAddRecExpr *>(PreAR)->setNoWrapFlags(SCEV::FlagNSW);
1097 // FIXME: this optimization needs a unit test
1098 DEBUG(dbgs() << "SCEV: untested prestart overflow check\n");
1102 // 3. Loop precondition.
1103 ICmpInst::Predicate Pred;
1104 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, SE);
1106 if (OverflowLimit &&
1107 SE->isLoopEntryGuardedByCond(L, Pred, PreStart, OverflowLimit)) {
1113 // Get the normalized sign-extended expression for this AddRec's Start.
1114 static const SCEV *getSignExtendAddRecStart(const SCEVAddRecExpr *AR,
1116 ScalarEvolution *SE) {
1117 const SCEV *PreStart = getPreStartForSignExtend(AR, Ty, SE);
1119 return SE->getSignExtendExpr(AR->getStart(), Ty);
1121 return SE->getAddExpr(SE->getSignExtendExpr(AR->getStepRecurrence(*SE), Ty),
1122 SE->getSignExtendExpr(PreStart, Ty));
1125 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
1127 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1128 "This is not an extending conversion!");
1129 assert(isSCEVable(Ty) &&
1130 "This is not a conversion to a SCEVable type!");
1131 Ty = getEffectiveSCEVType(Ty);
1133 // Fold if the operand is constant.
1134 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1136 cast<ConstantInt>(ConstantExpr::getSExt(SC->getValue(),
1137 getEffectiveSCEVType(Ty))));
1139 // sext(sext(x)) --> sext(x)
1140 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
1141 return getSignExtendExpr(SS->getOperand(), Ty);
1143 // sext(zext(x)) --> zext(x)
1144 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
1145 return getZeroExtendExpr(SZ->getOperand(), Ty);
1147 // Before doing any expensive analysis, check to see if we've already
1148 // computed a SCEV for this Op and Ty.
1149 FoldingSetNodeID ID;
1150 ID.AddInteger(scSignExtend);
1154 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1156 // If the input value is provably positive, build a zext instead.
1157 if (isKnownNonNegative(Op))
1158 return getZeroExtendExpr(Op, Ty);
1160 // sext(trunc(x)) --> sext(x) or x or trunc(x)
1161 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op)) {
1162 // It's possible the bits taken off by the truncate were all sign bits. If
1163 // so, we should be able to simplify this further.
1164 const SCEV *X = ST->getOperand();
1165 ConstantRange CR = getSignedRange(X);
1166 unsigned TruncBits = getTypeSizeInBits(ST->getType());
1167 unsigned NewBits = getTypeSizeInBits(Ty);
1168 if (CR.truncate(TruncBits).signExtend(NewBits).contains(
1169 CR.sextOrTrunc(NewBits)))
1170 return getTruncateOrSignExtend(X, Ty);
1173 // If the input value is a chrec scev, and we can prove that the value
1174 // did not overflow the old, smaller, value, we can sign extend all of the
1175 // operands (often constants). This allows analysis of something like
1176 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
1177 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
1178 if (AR->isAffine()) {
1179 const SCEV *Start = AR->getStart();
1180 const SCEV *Step = AR->getStepRecurrence(*this);
1181 unsigned BitWidth = getTypeSizeInBits(AR->getType());
1182 const Loop *L = AR->getLoop();
1184 // If we have special knowledge that this addrec won't overflow,
1185 // we don't need to do any further analysis.
1186 if (AR->getNoWrapFlags(SCEV::FlagNSW))
1187 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1188 getSignExtendExpr(Step, Ty),
1191 // Check whether the backedge-taken count is SCEVCouldNotCompute.
1192 // Note that this serves two purposes: It filters out loops that are
1193 // simply not analyzable, and it covers the case where this code is
1194 // being called from within backedge-taken count analysis, such that
1195 // attempting to ask for the backedge-taken count would likely result
1196 // in infinite recursion. In the later case, the analysis code will
1197 // cope with a conservative value, and it will take care to purge
1198 // that value once it has finished.
1199 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
1200 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
1201 // Manually compute the final value for AR, checking for
1204 // Check whether the backedge-taken count can be losslessly casted to
1205 // the addrec's type. The count is always unsigned.
1206 const SCEV *CastedMaxBECount =
1207 getTruncateOrZeroExtend(MaxBECount, Start->getType());
1208 const SCEV *RecastedMaxBECount =
1209 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
1210 if (MaxBECount == RecastedMaxBECount) {
1211 Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
1212 // Check whether Start+Step*MaxBECount has no signed overflow.
1213 const SCEV *SMul = getMulExpr(CastedMaxBECount, Step);
1214 const SCEV *Add = getAddExpr(Start, SMul);
1215 const SCEV *OperandExtendedAdd =
1216 getAddExpr(getSignExtendExpr(Start, WideTy),
1217 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1218 getSignExtendExpr(Step, WideTy)));
1219 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1220 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1221 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1222 // Return the expression with the addrec on the outside.
1223 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1224 getSignExtendExpr(Step, Ty),
1225 L, AR->getNoWrapFlags());
1227 // Similar to above, only this time treat the step value as unsigned.
1228 // This covers loops that count up with an unsigned step.
1229 const SCEV *UMul = getMulExpr(CastedMaxBECount, Step);
1230 Add = getAddExpr(Start, UMul);
1231 OperandExtendedAdd =
1232 getAddExpr(getSignExtendExpr(Start, WideTy),
1233 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
1234 getZeroExtendExpr(Step, WideTy)));
1235 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd) {
1236 // Cache knowledge of AR NSW, which is propagated to this AddRec.
1237 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1238 // Return the expression with the addrec on the outside.
1239 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1240 getZeroExtendExpr(Step, Ty),
1241 L, AR->getNoWrapFlags());
1245 // If the backedge is guarded by a comparison with the pre-inc value
1246 // the addrec is safe. Also, if the entry is guarded by a comparison
1247 // with the start value and the backedge is guarded by a comparison
1248 // with the post-inc value, the addrec is safe.
1249 ICmpInst::Predicate Pred;
1250 const SCEV *OverflowLimit = getOverflowLimitForStep(Step, &Pred, this);
1251 if (OverflowLimit &&
1252 (isLoopBackedgeGuardedByCond(L, Pred, AR, OverflowLimit) ||
1253 (isLoopEntryGuardedByCond(L, Pred, Start, OverflowLimit) &&
1254 isLoopBackedgeGuardedByCond(L, Pred, AR->getPostIncExpr(*this),
1256 // Cache knowledge of AR NSW, then propagate NSW to the wide AddRec.
1257 const_cast<SCEVAddRecExpr *>(AR)->setNoWrapFlags(SCEV::FlagNSW);
1258 return getAddRecExpr(getSignExtendAddRecStart(AR, Ty, this),
1259 getSignExtendExpr(Step, Ty),
1260 L, AR->getNoWrapFlags());
1265 // The cast wasn't folded; create an explicit cast node.
1266 // Recompute the insert position, as it may have been invalidated.
1267 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1268 SCEV *S = new (SCEVAllocator) SCEVSignExtendExpr(ID.Intern(SCEVAllocator),
1270 UniqueSCEVs.InsertNode(S, IP);
1274 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1275 /// unspecified bits out to the given type.
1277 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1279 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1280 "This is not an extending conversion!");
1281 assert(isSCEVable(Ty) &&
1282 "This is not a conversion to a SCEVable type!");
1283 Ty = getEffectiveSCEVType(Ty);
1285 // Sign-extend negative constants.
1286 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1287 if (SC->getValue()->getValue().isNegative())
1288 return getSignExtendExpr(Op, Ty);
1290 // Peel off a truncate cast.
1291 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1292 const SCEV *NewOp = T->getOperand();
1293 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1294 return getAnyExtendExpr(NewOp, Ty);
1295 return getTruncateOrNoop(NewOp, Ty);
1298 // Next try a zext cast. If the cast is folded, use it.
1299 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1300 if (!isa<SCEVZeroExtendExpr>(ZExt))
1303 // Next try a sext cast. If the cast is folded, use it.
1304 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1305 if (!isa<SCEVSignExtendExpr>(SExt))
1308 // Force the cast to be folded into the operands of an addrec.
1309 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op)) {
1310 SmallVector<const SCEV *, 4> Ops;
1311 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
1313 Ops.push_back(getAnyExtendExpr(*I, Ty));
1314 return getAddRecExpr(Ops, AR->getLoop(), SCEV::FlagNW);
1317 // As a special case, fold anyext(undef) to undef. We don't want to
1318 // know too much about SCEVUnknowns, but this special case is handy
1320 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Op))
1321 if (isa<UndefValue>(U->getValue()))
1322 return getSCEV(UndefValue::get(Ty));
1324 // If the expression is obviously signed, use the sext cast value.
1325 if (isa<SCEVSMaxExpr>(Op))
1328 // Absent any other information, use the zext cast value.
1332 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1333 /// a list of operands to be added under the given scale, update the given
1334 /// map. This is a helper function for getAddRecExpr. As an example of
1335 /// what it does, given a sequence of operands that would form an add
1336 /// expression like this:
1338 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1340 /// where A and B are constants, update the map with these values:
1342 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1344 /// and add 13 + A*B*29 to AccumulatedConstant.
1345 /// This will allow getAddRecExpr to produce this:
1347 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1349 /// This form often exposes folding opportunities that are hidden in
1350 /// the original operand list.
1352 /// Return true iff it appears that any interesting folding opportunities
1353 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1354 /// the common case where no interesting opportunities are present, and
1355 /// is also used as a check to avoid infinite recursion.
1358 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1359 SmallVector<const SCEV *, 8> &NewOps,
1360 APInt &AccumulatedConstant,
1361 const SCEV *const *Ops, size_t NumOperands,
1363 ScalarEvolution &SE) {
1364 bool Interesting = false;
1366 // Iterate over the add operands. They are sorted, with constants first.
1368 while (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1370 // Pull a buried constant out to the outside.
1371 if (Scale != 1 || AccumulatedConstant != 0 || C->getValue()->isZero())
1373 AccumulatedConstant += Scale * C->getValue()->getValue();
1376 // Next comes everything else. We're especially interested in multiplies
1377 // here, but they're in the middle, so just visit the rest with one loop.
1378 for (; i != NumOperands; ++i) {
1379 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1380 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1382 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1383 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1384 // A multiplication of a constant with another add; recurse.
1385 const SCEVAddExpr *Add = cast<SCEVAddExpr>(Mul->getOperand(1));
1387 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1388 Add->op_begin(), Add->getNumOperands(),
1391 // A multiplication of a constant with some other value. Update
1393 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1394 const SCEV *Key = SE.getMulExpr(MulOps);
1395 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1396 M.insert(std::make_pair(Key, NewScale));
1398 NewOps.push_back(Pair.first->first);
1400 Pair.first->second += NewScale;
1401 // The map already had an entry for this value, which may indicate
1402 // a folding opportunity.
1407 // An ordinary operand. Update the map.
1408 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1409 M.insert(std::make_pair(Ops[i], Scale));
1411 NewOps.push_back(Pair.first->first);
1413 Pair.first->second += Scale;
1414 // The map already had an entry for this value, which may indicate
1415 // a folding opportunity.
1425 struct APIntCompare {
1426 bool operator()(const APInt &LHS, const APInt &RHS) const {
1427 return LHS.ult(RHS);
1432 /// getAddExpr - Get a canonical add expression, or something simpler if
1434 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops,
1435 SCEV::NoWrapFlags Flags) {
1436 assert(!(Flags & ~(SCEV::FlagNUW | SCEV::FlagNSW)) &&
1437 "only nuw or nsw allowed");
1438 assert(!Ops.empty() && "Cannot get empty add!");
1439 if (Ops.size() == 1) return Ops[0];
1441 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1442 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1443 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1444 "SCEVAddExpr operand types don't match!");
1447 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1449 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1450 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1451 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1453 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1454 E = Ops.end(); I != E; ++I)
1455 if (!isKnownNonNegative(*I)) {
1459 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1462 // Sort by complexity, this groups all similar expression types together.
1463 GroupByComplexity(Ops, LI);
1465 // If there are any constants, fold them together.
1467 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1469 assert(Idx < Ops.size());
1470 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1471 // We found two constants, fold them together!
1472 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1473 RHSC->getValue()->getValue());
1474 if (Ops.size() == 2) return Ops[0];
1475 Ops.erase(Ops.begin()+1); // Erase the folded element
1476 LHSC = cast<SCEVConstant>(Ops[0]);
1479 // If we are left with a constant zero being added, strip it off.
1480 if (LHSC->getValue()->isZero()) {
1481 Ops.erase(Ops.begin());
1485 if (Ops.size() == 1) return Ops[0];
1488 // Okay, check to see if the same value occurs in the operand list more than
1489 // once. If so, merge them together into an multiply expression. Since we
1490 // sorted the list, these values are required to be adjacent.
1491 Type *Ty = Ops[0]->getType();
1492 bool FoundMatch = false;
1493 for (unsigned i = 0, e = Ops.size(); i != e-1; ++i)
1494 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1495 // Scan ahead to count how many equal operands there are.
1497 while (i+Count != e && Ops[i+Count] == Ops[i])
1499 // Merge the values into a multiply.
1500 const SCEV *Scale = getConstant(Ty, Count);
1501 const SCEV *Mul = getMulExpr(Scale, Ops[i]);
1502 if (Ops.size() == Count)
1505 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+Count);
1506 --i; e -= Count - 1;
1510 return getAddExpr(Ops, Flags);
1512 // Check for truncates. If all the operands are truncated from the same
1513 // type, see if factoring out the truncate would permit the result to be
1514 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1515 // if the contents of the resulting outer trunc fold to something simple.
1516 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1517 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1518 Type *DstType = Trunc->getType();
1519 Type *SrcType = Trunc->getOperand()->getType();
1520 SmallVector<const SCEV *, 8> LargeOps;
1522 // Check all the operands to see if they can be represented in the
1523 // source type of the truncate.
1524 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1525 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1526 if (T->getOperand()->getType() != SrcType) {
1530 LargeOps.push_back(T->getOperand());
1531 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1532 LargeOps.push_back(getAnyExtendExpr(C, SrcType));
1533 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1534 SmallVector<const SCEV *, 8> LargeMulOps;
1535 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1536 if (const SCEVTruncateExpr *T =
1537 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1538 if (T->getOperand()->getType() != SrcType) {
1542 LargeMulOps.push_back(T->getOperand());
1543 } else if (const SCEVConstant *C =
1544 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1545 LargeMulOps.push_back(getAnyExtendExpr(C, SrcType));
1552 LargeOps.push_back(getMulExpr(LargeMulOps));
1559 // Evaluate the expression in the larger type.
1560 const SCEV *Fold = getAddExpr(LargeOps, Flags);
1561 // If it folds to something simple, use it. Otherwise, don't.
1562 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1563 return getTruncateExpr(Fold, DstType);
1567 // Skip past any other cast SCEVs.
1568 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1571 // If there are add operands they would be next.
1572 if (Idx < Ops.size()) {
1573 bool DeletedAdd = false;
1574 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1575 // If we have an add, expand the add operands onto the end of the operands
1577 Ops.erase(Ops.begin()+Idx);
1578 Ops.append(Add->op_begin(), Add->op_end());
1582 // If we deleted at least one add, we added operands to the end of the list,
1583 // and they are not necessarily sorted. Recurse to resort and resimplify
1584 // any operands we just acquired.
1586 return getAddExpr(Ops);
1589 // Skip over the add expression until we get to a multiply.
1590 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1593 // Check to see if there are any folding opportunities present with
1594 // operands multiplied by constant values.
1595 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1596 uint64_t BitWidth = getTypeSizeInBits(Ty);
1597 DenseMap<const SCEV *, APInt> M;
1598 SmallVector<const SCEV *, 8> NewOps;
1599 APInt AccumulatedConstant(BitWidth, 0);
1600 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1601 Ops.data(), Ops.size(),
1602 APInt(BitWidth, 1), *this)) {
1603 // Some interesting folding opportunity is present, so its worthwhile to
1604 // re-generate the operands list. Group the operands by constant scale,
1605 // to avoid multiplying by the same constant scale multiple times.
1606 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1607 for (SmallVector<const SCEV *, 8>::const_iterator I = NewOps.begin(),
1608 E = NewOps.end(); I != E; ++I)
1609 MulOpLists[M.find(*I)->second].push_back(*I);
1610 // Re-generate the operands list.
1612 if (AccumulatedConstant != 0)
1613 Ops.push_back(getConstant(AccumulatedConstant));
1614 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1615 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1617 Ops.push_back(getMulExpr(getConstant(I->first),
1618 getAddExpr(I->second)));
1620 return getConstant(Ty, 0);
1621 if (Ops.size() == 1)
1623 return getAddExpr(Ops);
1627 // If we are adding something to a multiply expression, make sure the
1628 // something is not already an operand of the multiply. If so, merge it into
1630 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1631 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1632 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1633 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1634 if (isa<SCEVConstant>(MulOpSCEV))
1636 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1637 if (MulOpSCEV == Ops[AddOp]) {
1638 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1639 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1640 if (Mul->getNumOperands() != 2) {
1641 // If the multiply has more than two operands, we must get the
1643 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1644 Mul->op_begin()+MulOp);
1645 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1646 InnerMul = getMulExpr(MulOps);
1648 const SCEV *One = getConstant(Ty, 1);
1649 const SCEV *AddOne = getAddExpr(One, InnerMul);
1650 const SCEV *OuterMul = getMulExpr(AddOne, MulOpSCEV);
1651 if (Ops.size() == 2) return OuterMul;
1653 Ops.erase(Ops.begin()+AddOp);
1654 Ops.erase(Ops.begin()+Idx-1);
1656 Ops.erase(Ops.begin()+Idx);
1657 Ops.erase(Ops.begin()+AddOp-1);
1659 Ops.push_back(OuterMul);
1660 return getAddExpr(Ops);
1663 // Check this multiply against other multiplies being added together.
1664 for (unsigned OtherMulIdx = Idx+1;
1665 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1667 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1668 // If MulOp occurs in OtherMul, we can fold the two multiplies
1670 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1671 OMulOp != e; ++OMulOp)
1672 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1673 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1674 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1675 if (Mul->getNumOperands() != 2) {
1676 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1677 Mul->op_begin()+MulOp);
1678 MulOps.append(Mul->op_begin()+MulOp+1, Mul->op_end());
1679 InnerMul1 = getMulExpr(MulOps);
1681 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1682 if (OtherMul->getNumOperands() != 2) {
1683 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1684 OtherMul->op_begin()+OMulOp);
1685 MulOps.append(OtherMul->op_begin()+OMulOp+1, OtherMul->op_end());
1686 InnerMul2 = getMulExpr(MulOps);
1688 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1689 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1690 if (Ops.size() == 2) return OuterMul;
1691 Ops.erase(Ops.begin()+Idx);
1692 Ops.erase(Ops.begin()+OtherMulIdx-1);
1693 Ops.push_back(OuterMul);
1694 return getAddExpr(Ops);
1700 // If there are any add recurrences in the operands list, see if any other
1701 // added values are loop invariant. If so, we can fold them into the
1703 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1706 // Scan over all recurrences, trying to fold loop invariants into them.
1707 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1708 // Scan all of the other operands to this add and add them to the vector if
1709 // they are loop invariant w.r.t. the recurrence.
1710 SmallVector<const SCEV *, 8> LIOps;
1711 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1712 const Loop *AddRecLoop = AddRec->getLoop();
1713 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1714 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1715 LIOps.push_back(Ops[i]);
1716 Ops.erase(Ops.begin()+i);
1720 // If we found some loop invariants, fold them into the recurrence.
1721 if (!LIOps.empty()) {
1722 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1723 LIOps.push_back(AddRec->getStart());
1725 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1727 AddRecOps[0] = getAddExpr(LIOps);
1729 // Build the new addrec. Propagate the NUW and NSW flags if both the
1730 // outer add and the inner addrec are guaranteed to have no overflow.
1731 // Always propagate NW.
1732 Flags = AddRec->getNoWrapFlags(setFlags(Flags, SCEV::FlagNW));
1733 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRecLoop, Flags);
1735 // If all of the other operands were loop invariant, we are done.
1736 if (Ops.size() == 1) return NewRec;
1738 // Otherwise, add the folded AddRec by the non-live parts.
1739 for (unsigned i = 0;; ++i)
1740 if (Ops[i] == AddRec) {
1744 return getAddExpr(Ops);
1747 // Okay, if there weren't any loop invariants to be folded, check to see if
1748 // there are multiple AddRec's with the same loop induction variable being
1749 // added together. If so, we can fold them.
1750 for (unsigned OtherIdx = Idx+1;
1751 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1753 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1754 // Other + {A,+,B}<L> + {C,+,D}<L> --> Other + {A+C,+,B+D}<L>
1755 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1757 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1759 if (const SCEVAddRecExpr *OtherAddRec =
1760 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1761 if (OtherAddRec->getLoop() == AddRecLoop) {
1762 for (unsigned i = 0, e = OtherAddRec->getNumOperands();
1764 if (i >= AddRecOps.size()) {
1765 AddRecOps.append(OtherAddRec->op_begin()+i,
1766 OtherAddRec->op_end());
1769 AddRecOps[i] = getAddExpr(AddRecOps[i],
1770 OtherAddRec->getOperand(i));
1772 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
1774 // Step size has changed, so we cannot guarantee no self-wraparound.
1775 Ops[Idx] = getAddRecExpr(AddRecOps, AddRecLoop, SCEV::FlagAnyWrap);
1776 return getAddExpr(Ops);
1779 // Otherwise couldn't fold anything into this recurrence. Move onto the
1783 // Okay, it looks like we really DO need an add expr. Check to see if we
1784 // already have one, otherwise create a new one.
1785 FoldingSetNodeID ID;
1786 ID.AddInteger(scAddExpr);
1787 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1788 ID.AddPointer(Ops[i]);
1791 static_cast<SCEVAddExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
1793 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
1794 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
1795 S = new (SCEVAllocator) SCEVAddExpr(ID.Intern(SCEVAllocator),
1797 UniqueSCEVs.InsertNode(S, IP);
1799 S->setNoWrapFlags(Flags);
1803 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1805 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops,
1806 SCEV::NoWrapFlags Flags) {
1807 assert(Flags == maskFlags(Flags, SCEV::FlagNUW | SCEV::FlagNSW) &&
1808 "only nuw or nsw allowed");
1809 assert(!Ops.empty() && "Cannot get empty mul!");
1810 if (Ops.size() == 1) return Ops[0];
1812 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
1813 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1814 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
1815 "SCEVMulExpr operand types don't match!");
1818 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
1820 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
1821 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
1822 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
1824 for (SmallVectorImpl<const SCEV *>::const_iterator I = Ops.begin(),
1825 E = Ops.end(); I != E; ++I)
1826 if (!isKnownNonNegative(*I)) {
1830 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
1833 // Sort by complexity, this groups all similar expression types together.
1834 GroupByComplexity(Ops, LI);
1836 // If there are any constants, fold them together.
1838 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1840 // C1*(C2+V) -> C1*C2 + C1*V
1841 if (Ops.size() == 2)
1842 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1843 if (Add->getNumOperands() == 2 &&
1844 isa<SCEVConstant>(Add->getOperand(0)))
1845 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1846 getMulExpr(LHSC, Add->getOperand(1)));
1849 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1850 // We found two constants, fold them together!
1851 ConstantInt *Fold = ConstantInt::get(getContext(),
1852 LHSC->getValue()->getValue() *
1853 RHSC->getValue()->getValue());
1854 Ops[0] = getConstant(Fold);
1855 Ops.erase(Ops.begin()+1); // Erase the folded element
1856 if (Ops.size() == 1) return Ops[0];
1857 LHSC = cast<SCEVConstant>(Ops[0]);
1860 // If we are left with a constant one being multiplied, strip it off.
1861 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1862 Ops.erase(Ops.begin());
1864 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1865 // If we have a multiply of zero, it will always be zero.
1867 } else if (Ops[0]->isAllOnesValue()) {
1868 // If we have a mul by -1 of an add, try distributing the -1 among the
1870 if (Ops.size() == 2) {
1871 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1])) {
1872 SmallVector<const SCEV *, 4> NewOps;
1873 bool AnyFolded = false;
1874 for (SCEVAddRecExpr::op_iterator I = Add->op_begin(),
1875 E = Add->op_end(); I != E; ++I) {
1876 const SCEV *Mul = getMulExpr(Ops[0], *I);
1877 if (!isa<SCEVMulExpr>(Mul)) AnyFolded = true;
1878 NewOps.push_back(Mul);
1881 return getAddExpr(NewOps);
1883 else if (const SCEVAddRecExpr *
1884 AddRec = dyn_cast<SCEVAddRecExpr>(Ops[1])) {
1885 // Negation preserves a recurrence's no self-wrap property.
1886 SmallVector<const SCEV *, 4> Operands;
1887 for (SCEVAddRecExpr::op_iterator I = AddRec->op_begin(),
1888 E = AddRec->op_end(); I != E; ++I) {
1889 Operands.push_back(getMulExpr(Ops[0], *I));
1891 return getAddRecExpr(Operands, AddRec->getLoop(),
1892 AddRec->getNoWrapFlags(SCEV::FlagNW));
1897 if (Ops.size() == 1)
1901 // Skip over the add expression until we get to a multiply.
1902 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1905 // If there are mul operands inline them all into this expression.
1906 if (Idx < Ops.size()) {
1907 bool DeletedMul = false;
1908 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1909 // If we have an mul, expand the mul operands onto the end of the operands
1911 Ops.erase(Ops.begin()+Idx);
1912 Ops.append(Mul->op_begin(), Mul->op_end());
1916 // If we deleted at least one mul, we added operands to the end of the list,
1917 // and they are not necessarily sorted. Recurse to resort and resimplify
1918 // any operands we just acquired.
1920 return getMulExpr(Ops);
1923 // If there are any add recurrences in the operands list, see if any other
1924 // added values are loop invariant. If so, we can fold them into the
1926 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1929 // Scan over all recurrences, trying to fold loop invariants into them.
1930 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1931 // Scan all of the other operands to this mul and add them to the vector if
1932 // they are loop invariant w.r.t. the recurrence.
1933 SmallVector<const SCEV *, 8> LIOps;
1934 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1935 const Loop *AddRecLoop = AddRec->getLoop();
1936 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1937 if (isLoopInvariant(Ops[i], AddRecLoop)) {
1938 LIOps.push_back(Ops[i]);
1939 Ops.erase(Ops.begin()+i);
1943 // If we found some loop invariants, fold them into the recurrence.
1944 if (!LIOps.empty()) {
1945 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1946 SmallVector<const SCEV *, 4> NewOps;
1947 NewOps.reserve(AddRec->getNumOperands());
1948 const SCEV *Scale = getMulExpr(LIOps);
1949 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1950 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1952 // Build the new addrec. Propagate the NUW and NSW flags if both the
1953 // outer mul and the inner addrec are guaranteed to have no overflow.
1955 // No self-wrap cannot be guaranteed after changing the step size, but
1956 // will be inferred if either NUW or NSW is true.
1957 Flags = AddRec->getNoWrapFlags(clearFlags(Flags, SCEV::FlagNW));
1958 const SCEV *NewRec = getAddRecExpr(NewOps, AddRecLoop, Flags);
1960 // If all of the other operands were loop invariant, we are done.
1961 if (Ops.size() == 1) return NewRec;
1963 // Otherwise, multiply the folded AddRec by the non-live parts.
1964 for (unsigned i = 0;; ++i)
1965 if (Ops[i] == AddRec) {
1969 return getMulExpr(Ops);
1972 // Okay, if there weren't any loop invariants to be folded, check to see if
1973 // there are multiple AddRec's with the same loop induction variable being
1974 // multiplied together. If so, we can fold them.
1975 for (unsigned OtherIdx = Idx+1;
1976 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1978 if (AddRecLoop == cast<SCEVAddRecExpr>(Ops[OtherIdx])->getLoop()) {
1979 // {A,+,B}<L> * {C,+,D}<L> --> {A*C,+,A*D + B*C + B*D,+,2*B*D}<L>
1980 for (; OtherIdx != Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);
1982 if (const SCEVAddRecExpr *OtherAddRec =
1983 dyn_cast<SCEVAddRecExpr>(Ops[OtherIdx]))
1984 if (OtherAddRec->getLoop() == AddRecLoop) {
1985 const SCEV *A = AddRec->getStart();
1986 const SCEV *B = AddRec->getStepRecurrence(*this);
1987 const SCEV *C = OtherAddRec->getStart();
1988 const SCEV *D = OtherAddRec->getStepRecurrence(*this);
1989 const SCEV *NewStart = getMulExpr(A, C);
1990 const SCEV *BD = getMulExpr(B, D);
1991 const SCEV *NewStep = getAddExpr(getMulExpr(A, D),
1992 getMulExpr(B, C), BD);
1993 const SCEV *NewSecondOrderStep =
1994 getMulExpr(BD, getConstant(BD->getType(), 2));
1996 SmallVector<const SCEV *, 3> AddRecOps;
1997 AddRecOps.push_back(NewStart);
1998 AddRecOps.push_back(NewStep);
1999 AddRecOps.push_back(NewSecondOrderStep);
2000 const SCEV *NewAddRec = getAddRecExpr(AddRecOps,
2003 if (Ops.size() == 2) return NewAddRec;
2004 Ops[Idx] = AddRec = cast<SCEVAddRecExpr>(NewAddRec);
2005 Ops.erase(Ops.begin() + OtherIdx); --OtherIdx;
2007 return getMulExpr(Ops);
2010 // Otherwise couldn't fold anything into this recurrence. Move onto the
2014 // Okay, it looks like we really DO need an mul expr. Check to see if we
2015 // already have one, otherwise create a new one.
2016 FoldingSetNodeID ID;
2017 ID.AddInteger(scMulExpr);
2018 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2019 ID.AddPointer(Ops[i]);
2022 static_cast<SCEVMulExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2024 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2025 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2026 S = new (SCEVAllocator) SCEVMulExpr(ID.Intern(SCEVAllocator),
2028 UniqueSCEVs.InsertNode(S, IP);
2030 S->setNoWrapFlags(Flags);
2034 /// getUDivExpr - Get a canonical unsigned division expression, or something
2035 /// simpler if possible.
2036 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
2038 assert(getEffectiveSCEVType(LHS->getType()) ==
2039 getEffectiveSCEVType(RHS->getType()) &&
2040 "SCEVUDivExpr operand types don't match!");
2042 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
2043 if (RHSC->getValue()->equalsInt(1))
2044 return LHS; // X udiv 1 --> x
2045 // If the denominator is zero, the result of the udiv is undefined. Don't
2046 // try to analyze it, because the resolution chosen here may differ from
2047 // the resolution chosen in other parts of the compiler.
2048 if (!RHSC->getValue()->isZero()) {
2049 // Determine if the division can be folded into the operands of
2051 // TODO: Generalize this to non-constants by using known-bits information.
2052 Type *Ty = LHS->getType();
2053 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
2054 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ - 1;
2055 // For non-power-of-two values, effectively round the value up to the
2056 // nearest power of two.
2057 if (!RHSC->getValue()->getValue().isPowerOf2())
2059 IntegerType *ExtTy =
2060 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
2061 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
2062 if (const SCEVConstant *Step =
2063 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this))) {
2064 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
2065 const APInt &StepInt = Step->getValue()->getValue();
2066 const APInt &DivInt = RHSC->getValue()->getValue();
2067 if (!StepInt.urem(DivInt) &&
2068 getZeroExtendExpr(AR, ExtTy) ==
2069 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2070 getZeroExtendExpr(Step, ExtTy),
2071 AR->getLoop(), SCEV::FlagAnyWrap)) {
2072 SmallVector<const SCEV *, 4> Operands;
2073 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
2074 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
2075 return getAddRecExpr(Operands, AR->getLoop(),
2078 /// Get a canonical UDivExpr for a recurrence.
2079 /// {X,+,N}/C => {Y,+,N}/C where Y=X-(X%N). Safe when C%N=0.
2080 // We can currently only fold X%N if X is constant.
2081 const SCEVConstant *StartC = dyn_cast<SCEVConstant>(AR->getStart());
2082 if (StartC && !DivInt.urem(StepInt) &&
2083 getZeroExtendExpr(AR, ExtTy) ==
2084 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
2085 getZeroExtendExpr(Step, ExtTy),
2086 AR->getLoop(), SCEV::FlagAnyWrap)) {
2087 const APInt &StartInt = StartC->getValue()->getValue();
2088 const APInt &StartRem = StartInt.urem(StepInt);
2090 LHS = getAddRecExpr(getConstant(StartInt - StartRem), Step,
2091 AR->getLoop(), SCEV::FlagNW);
2094 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
2095 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
2096 SmallVector<const SCEV *, 4> Operands;
2097 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
2098 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
2099 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
2100 // Find an operand that's safely divisible.
2101 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
2102 const SCEV *Op = M->getOperand(i);
2103 const SCEV *Div = getUDivExpr(Op, RHSC);
2104 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
2105 Operands = SmallVector<const SCEV *, 4>(M->op_begin(),
2108 return getMulExpr(Operands);
2112 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
2113 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(LHS)) {
2114 SmallVector<const SCEV *, 4> Operands;
2115 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
2116 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
2117 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
2119 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2120 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
2121 if (isa<SCEVUDivExpr>(Op) ||
2122 getMulExpr(Op, RHS) != A->getOperand(i))
2124 Operands.push_back(Op);
2126 if (Operands.size() == A->getNumOperands())
2127 return getAddExpr(Operands);
2131 // Fold if both operands are constant.
2132 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
2133 Constant *LHSCV = LHSC->getValue();
2134 Constant *RHSCV = RHSC->getValue();
2135 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
2141 FoldingSetNodeID ID;
2142 ID.AddInteger(scUDivExpr);
2146 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2147 SCEV *S = new (SCEVAllocator) SCEVUDivExpr(ID.Intern(SCEVAllocator),
2149 UniqueSCEVs.InsertNode(S, IP);
2154 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2155 /// Simplify the expression as much as possible.
2156 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start, const SCEV *Step,
2158 SCEV::NoWrapFlags Flags) {
2159 SmallVector<const SCEV *, 4> Operands;
2160 Operands.push_back(Start);
2161 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
2162 if (StepChrec->getLoop() == L) {
2163 Operands.append(StepChrec->op_begin(), StepChrec->op_end());
2164 return getAddRecExpr(Operands, L, maskFlags(Flags, SCEV::FlagNW));
2167 Operands.push_back(Step);
2168 return getAddRecExpr(Operands, L, Flags);
2171 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
2172 /// Simplify the expression as much as possible.
2174 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
2175 const Loop *L, SCEV::NoWrapFlags Flags) {
2176 if (Operands.size() == 1) return Operands[0];
2178 Type *ETy = getEffectiveSCEVType(Operands[0]->getType());
2179 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
2180 assert(getEffectiveSCEVType(Operands[i]->getType()) == ETy &&
2181 "SCEVAddRecExpr operand types don't match!");
2182 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2183 assert(isLoopInvariant(Operands[i], L) &&
2184 "SCEVAddRecExpr operand is not loop-invariant!");
2187 if (Operands.back()->isZero()) {
2188 Operands.pop_back();
2189 return getAddRecExpr(Operands, L, SCEV::FlagAnyWrap); // {X,+,0} --> X
2192 // It's tempting to want to call getMaxBackedgeTakenCount count here and
2193 // use that information to infer NUW and NSW flags. However, computing a
2194 // BE count requires calling getAddRecExpr, so we may not yet have a
2195 // meaningful BE count at this point (and if we don't, we'd be stuck
2196 // with a SCEVCouldNotCompute as the cached BE count).
2198 // If FlagNSW is true and all the operands are non-negative, infer FlagNUW.
2200 int SignOrUnsignMask = SCEV::FlagNUW | SCEV::FlagNSW;
2201 SCEV::NoWrapFlags SignOrUnsignWrap = maskFlags(Flags, SignOrUnsignMask);
2202 if (SignOrUnsignWrap && (SignOrUnsignWrap != SignOrUnsignMask)) {
2204 for (SmallVectorImpl<const SCEV *>::const_iterator I = Operands.begin(),
2205 E = Operands.end(); I != E; ++I)
2206 if (!isKnownNonNegative(*I)) {
2210 if (All) Flags = setFlags(Flags, (SCEV::NoWrapFlags)SignOrUnsignMask);
2213 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
2214 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
2215 const Loop *NestedLoop = NestedAR->getLoop();
2216 if (L->contains(NestedLoop) ?
2217 (L->getLoopDepth() < NestedLoop->getLoopDepth()) :
2218 (!NestedLoop->contains(L) &&
2219 DT->dominates(L->getHeader(), NestedLoop->getHeader()))) {
2220 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
2221 NestedAR->op_end());
2222 Operands[0] = NestedAR->getStart();
2223 // AddRecs require their operands be loop-invariant with respect to their
2224 // loops. Don't perform this transformation if it would break this
2226 bool AllInvariant = true;
2227 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2228 if (!isLoopInvariant(Operands[i], L)) {
2229 AllInvariant = false;
2233 // Create a recurrence for the outer loop with the same step size.
2235 // The outer recurrence keeps its NW flag but only keeps NUW/NSW if the
2236 // inner recurrence has the same property.
2237 SCEV::NoWrapFlags OuterFlags =
2238 maskFlags(Flags, SCEV::FlagNW | NestedAR->getNoWrapFlags());
2240 NestedOperands[0] = getAddRecExpr(Operands, L, OuterFlags);
2241 AllInvariant = true;
2242 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
2243 if (!isLoopInvariant(NestedOperands[i], NestedLoop)) {
2244 AllInvariant = false;
2248 // Ok, both add recurrences are valid after the transformation.
2250 // The inner recurrence keeps its NW flag but only keeps NUW/NSW if
2251 // the outer recurrence has the same property.
2252 SCEV::NoWrapFlags InnerFlags =
2253 maskFlags(NestedAR->getNoWrapFlags(), SCEV::FlagNW | Flags);
2254 return getAddRecExpr(NestedOperands, NestedLoop, InnerFlags);
2257 // Reset Operands to its original state.
2258 Operands[0] = NestedAR;
2262 // Okay, it looks like we really DO need an addrec expr. Check to see if we
2263 // already have one, otherwise create a new one.
2264 FoldingSetNodeID ID;
2265 ID.AddInteger(scAddRecExpr);
2266 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
2267 ID.AddPointer(Operands[i]);
2271 static_cast<SCEVAddRecExpr *>(UniqueSCEVs.FindNodeOrInsertPos(ID, IP));
2273 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Operands.size());
2274 std::uninitialized_copy(Operands.begin(), Operands.end(), O);
2275 S = new (SCEVAllocator) SCEVAddRecExpr(ID.Intern(SCEVAllocator),
2276 O, Operands.size(), L);
2277 UniqueSCEVs.InsertNode(S, IP);
2279 S->setNoWrapFlags(Flags);
2283 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
2285 SmallVector<const SCEV *, 2> Ops;
2288 return getSMaxExpr(Ops);
2292 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2293 assert(!Ops.empty() && "Cannot get empty smax!");
2294 if (Ops.size() == 1) return Ops[0];
2296 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2297 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2298 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2299 "SCEVSMaxExpr operand types don't match!");
2302 // Sort by complexity, this groups all similar expression types together.
2303 GroupByComplexity(Ops, LI);
2305 // If there are any constants, fold them together.
2307 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2309 assert(Idx < Ops.size());
2310 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2311 // We found two constants, fold them together!
2312 ConstantInt *Fold = ConstantInt::get(getContext(),
2313 APIntOps::smax(LHSC->getValue()->getValue(),
2314 RHSC->getValue()->getValue()));
2315 Ops[0] = getConstant(Fold);
2316 Ops.erase(Ops.begin()+1); // Erase the folded element
2317 if (Ops.size() == 1) return Ops[0];
2318 LHSC = cast<SCEVConstant>(Ops[0]);
2321 // If we are left with a constant minimum-int, strip it off.
2322 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
2323 Ops.erase(Ops.begin());
2325 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
2326 // If we have an smax with a constant maximum-int, it will always be
2331 if (Ops.size() == 1) return Ops[0];
2334 // Find the first SMax
2335 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
2338 // Check to see if one of the operands is an SMax. If so, expand its operands
2339 // onto our operand list, and recurse to simplify.
2340 if (Idx < Ops.size()) {
2341 bool DeletedSMax = false;
2342 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
2343 Ops.erase(Ops.begin()+Idx);
2344 Ops.append(SMax->op_begin(), SMax->op_end());
2349 return getSMaxExpr(Ops);
2352 // Okay, check to see if the same value occurs in the operand list twice. If
2353 // so, delete one. Since we sorted the list, these values are required to
2355 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2356 // X smax Y smax Y --> X smax Y
2357 // X smax Y --> X, if X is always greater than Y
2358 if (Ops[i] == Ops[i+1] ||
2359 isKnownPredicate(ICmpInst::ICMP_SGE, Ops[i], Ops[i+1])) {
2360 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2362 } else if (isKnownPredicate(ICmpInst::ICMP_SLE, Ops[i], Ops[i+1])) {
2363 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2367 if (Ops.size() == 1) return Ops[0];
2369 assert(!Ops.empty() && "Reduced smax down to nothing!");
2371 // Okay, it looks like we really DO need an smax expr. Check to see if we
2372 // already have one, otherwise create a new one.
2373 FoldingSetNodeID ID;
2374 ID.AddInteger(scSMaxExpr);
2375 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2376 ID.AddPointer(Ops[i]);
2378 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2379 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2380 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2381 SCEV *S = new (SCEVAllocator) SCEVSMaxExpr(ID.Intern(SCEVAllocator),
2383 UniqueSCEVs.InsertNode(S, IP);
2387 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
2389 SmallVector<const SCEV *, 2> Ops;
2392 return getUMaxExpr(Ops);
2396 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
2397 assert(!Ops.empty() && "Cannot get empty umax!");
2398 if (Ops.size() == 1) return Ops[0];
2400 Type *ETy = getEffectiveSCEVType(Ops[0]->getType());
2401 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
2402 assert(getEffectiveSCEVType(Ops[i]->getType()) == ETy &&
2403 "SCEVUMaxExpr operand types don't match!");
2406 // Sort by complexity, this groups all similar expression types together.
2407 GroupByComplexity(Ops, LI);
2409 // If there are any constants, fold them together.
2411 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
2413 assert(Idx < Ops.size());
2414 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
2415 // We found two constants, fold them together!
2416 ConstantInt *Fold = ConstantInt::get(getContext(),
2417 APIntOps::umax(LHSC->getValue()->getValue(),
2418 RHSC->getValue()->getValue()));
2419 Ops[0] = getConstant(Fold);
2420 Ops.erase(Ops.begin()+1); // Erase the folded element
2421 if (Ops.size() == 1) return Ops[0];
2422 LHSC = cast<SCEVConstant>(Ops[0]);
2425 // If we are left with a constant minimum-int, strip it off.
2426 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
2427 Ops.erase(Ops.begin());
2429 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
2430 // If we have an umax with a constant maximum-int, it will always be
2435 if (Ops.size() == 1) return Ops[0];
2438 // Find the first UMax
2439 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
2442 // Check to see if one of the operands is a UMax. If so, expand its operands
2443 // onto our operand list, and recurse to simplify.
2444 if (Idx < Ops.size()) {
2445 bool DeletedUMax = false;
2446 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2447 Ops.erase(Ops.begin()+Idx);
2448 Ops.append(UMax->op_begin(), UMax->op_end());
2453 return getUMaxExpr(Ops);
2456 // Okay, check to see if the same value occurs in the operand list twice. If
2457 // so, delete one. Since we sorted the list, these values are required to
2459 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2460 // X umax Y umax Y --> X umax Y
2461 // X umax Y --> X, if X is always greater than Y
2462 if (Ops[i] == Ops[i+1] ||
2463 isKnownPredicate(ICmpInst::ICMP_UGE, Ops[i], Ops[i+1])) {
2464 Ops.erase(Ops.begin()+i+1, Ops.begin()+i+2);
2466 } else if (isKnownPredicate(ICmpInst::ICMP_ULE, Ops[i], Ops[i+1])) {
2467 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2471 if (Ops.size() == 1) return Ops[0];
2473 assert(!Ops.empty() && "Reduced umax down to nothing!");
2475 // Okay, it looks like we really DO need a umax expr. Check to see if we
2476 // already have one, otherwise create a new one.
2477 FoldingSetNodeID ID;
2478 ID.AddInteger(scUMaxExpr);
2479 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2480 ID.AddPointer(Ops[i]);
2482 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2483 const SCEV **O = SCEVAllocator.Allocate<const SCEV *>(Ops.size());
2484 std::uninitialized_copy(Ops.begin(), Ops.end(), O);
2485 SCEV *S = new (SCEVAllocator) SCEVUMaxExpr(ID.Intern(SCEVAllocator),
2487 UniqueSCEVs.InsertNode(S, IP);
2491 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2493 // ~smax(~x, ~y) == smin(x, y).
2494 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2497 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2499 // ~umax(~x, ~y) == umin(x, y)
2500 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2503 const SCEV *ScalarEvolution::getSizeOfExpr(Type *AllocTy) {
2504 // If we have TargetData, we can bypass creating a target-independent
2505 // constant expression and then folding it back into a ConstantInt.
2506 // This is just a compile-time optimization.
2508 return getConstant(TD->getIntPtrType(getContext()),
2509 TD->getTypeAllocSize(AllocTy));
2511 Constant *C = ConstantExpr::getSizeOf(AllocTy);
2512 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2513 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2515 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2516 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2519 const SCEV *ScalarEvolution::getAlignOfExpr(Type *AllocTy) {
2520 Constant *C = ConstantExpr::getAlignOf(AllocTy);
2521 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2522 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2524 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(AllocTy));
2525 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2528 const SCEV *ScalarEvolution::getOffsetOfExpr(StructType *STy,
2530 // If we have TargetData, we can bypass creating a target-independent
2531 // constant expression and then folding it back into a ConstantInt.
2532 // This is just a compile-time optimization.
2534 return getConstant(TD->getIntPtrType(getContext()),
2535 TD->getStructLayout(STy)->getElementOffset(FieldNo));
2537 Constant *C = ConstantExpr::getOffsetOf(STy, FieldNo);
2538 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2539 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2541 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(STy));
2542 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2545 const SCEV *ScalarEvolution::getOffsetOfExpr(Type *CTy,
2546 Constant *FieldNo) {
2547 Constant *C = ConstantExpr::getOffsetOf(CTy, FieldNo);
2548 if (ConstantExpr *CE = dyn_cast<ConstantExpr>(C))
2549 if (Constant *Folded = ConstantFoldConstantExpression(CE, TD))
2551 Type *Ty = getEffectiveSCEVType(PointerType::getUnqual(CTy));
2552 return getTruncateOrZeroExtend(getSCEV(C), Ty);
2555 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2556 // Don't attempt to do anything other than create a SCEVUnknown object
2557 // here. createSCEV only calls getUnknown after checking for all other
2558 // interesting possibilities, and any other code that calls getUnknown
2559 // is doing so in order to hide a value from SCEV canonicalization.
2561 FoldingSetNodeID ID;
2562 ID.AddInteger(scUnknown);
2565 if (SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) {
2566 assert(cast<SCEVUnknown>(S)->getValue() == V &&
2567 "Stale SCEVUnknown in uniquing map!");
2570 SCEV *S = new (SCEVAllocator) SCEVUnknown(ID.Intern(SCEVAllocator), V, this,
2572 FirstUnknown = cast<SCEVUnknown>(S);
2573 UniqueSCEVs.InsertNode(S, IP);
2577 //===----------------------------------------------------------------------===//
2578 // Basic SCEV Analysis and PHI Idiom Recognition Code
2581 /// isSCEVable - Test if values of the given type are analyzable within
2582 /// the SCEV framework. This primarily includes integer types, and it
2583 /// can optionally include pointer types if the ScalarEvolution class
2584 /// has access to target-specific information.
2585 bool ScalarEvolution::isSCEVable(Type *Ty) const {
2586 // Integers and pointers are always SCEVable.
2587 return Ty->isIntegerTy() || Ty->isPointerTy();
2590 /// getTypeSizeInBits - Return the size in bits of the specified type,
2591 /// for which isSCEVable must return true.
2592 uint64_t ScalarEvolution::getTypeSizeInBits(Type *Ty) const {
2593 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2595 // If we have a TargetData, use it!
2597 return TD->getTypeSizeInBits(Ty);
2599 // Integer types have fixed sizes.
2600 if (Ty->isIntegerTy())
2601 return Ty->getPrimitiveSizeInBits();
2603 // The only other support type is pointer. Without TargetData, conservatively
2604 // assume pointers are 64-bit.
2605 assert(Ty->isPointerTy() && "isSCEVable permitted a non-SCEVable type!");
2609 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2610 /// the given type and which represents how SCEV will treat the given
2611 /// type, for which isSCEVable must return true. For pointer types,
2612 /// this is the pointer-sized integer type.
2613 Type *ScalarEvolution::getEffectiveSCEVType(Type *Ty) const {
2614 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2616 if (Ty->isIntegerTy())
2619 // The only other support type is pointer.
2620 assert(Ty->isPointerTy() && "Unexpected non-pointer non-integer type!");
2621 if (TD) return TD->getIntPtrType(getContext());
2623 // Without TargetData, conservatively assume pointers are 64-bit.
2624 return Type::getInt64Ty(getContext());
2627 const SCEV *ScalarEvolution::getCouldNotCompute() {
2628 return &CouldNotCompute;
2631 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2632 /// expression and create a new one.
2633 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2634 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2636 ValueExprMapType::const_iterator I = ValueExprMap.find(V);
2637 if (I != ValueExprMap.end()) return I->second;
2638 const SCEV *S = createSCEV(V);
2640 // The process of creating a SCEV for V may have caused other SCEVs
2641 // to have been created, so it's necessary to insert the new entry
2642 // from scratch, rather than trying to remember the insert position
2644 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2648 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2650 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2651 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2653 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2655 Type *Ty = V->getType();
2656 Ty = getEffectiveSCEVType(Ty);
2657 return getMulExpr(V,
2658 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2661 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2662 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2663 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2665 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2667 Type *Ty = V->getType();
2668 Ty = getEffectiveSCEVType(Ty);
2669 const SCEV *AllOnes =
2670 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2671 return getMinusSCEV(AllOnes, V);
2674 /// getMinusSCEV - Return LHS-RHS. Minus is represented in SCEV as A+B*-1.
2675 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS, const SCEV *RHS,
2676 SCEV::NoWrapFlags Flags) {
2677 assert(!maskFlags(Flags, SCEV::FlagNUW) && "subtraction does not have NUW");
2679 // Fast path: X - X --> 0.
2681 return getConstant(LHS->getType(), 0);
2684 return getAddExpr(LHS, getNegativeSCEV(RHS), Flags);
2687 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2688 /// input value to the specified type. If the type must be extended, it is zero
2691 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V, Type *Ty) {
2692 Type *SrcTy = V->getType();
2693 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2694 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2695 "Cannot truncate or zero extend with non-integer arguments!");
2696 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2697 return V; // No conversion
2698 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2699 return getTruncateExpr(V, Ty);
2700 return getZeroExtendExpr(V, Ty);
2703 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2704 /// input value to the specified type. If the type must be extended, it is sign
2707 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2709 Type *SrcTy = V->getType();
2710 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2711 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2712 "Cannot truncate or zero extend with non-integer arguments!");
2713 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2714 return V; // No conversion
2715 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2716 return getTruncateExpr(V, Ty);
2717 return getSignExtendExpr(V, Ty);
2720 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2721 /// input value to the specified type. If the type must be extended, it is zero
2722 /// extended. The conversion must not be narrowing.
2724 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, Type *Ty) {
2725 Type *SrcTy = V->getType();
2726 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2727 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2728 "Cannot noop or zero extend with non-integer arguments!");
2729 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2730 "getNoopOrZeroExtend cannot truncate!");
2731 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2732 return V; // No conversion
2733 return getZeroExtendExpr(V, Ty);
2736 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2737 /// input value to the specified type. If the type must be extended, it is sign
2738 /// extended. The conversion must not be narrowing.
2740 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, Type *Ty) {
2741 Type *SrcTy = V->getType();
2742 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2743 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2744 "Cannot noop or sign extend with non-integer arguments!");
2745 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2746 "getNoopOrSignExtend cannot truncate!");
2747 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2748 return V; // No conversion
2749 return getSignExtendExpr(V, Ty);
2752 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2753 /// the input value to the specified type. If the type must be extended,
2754 /// it is extended with unspecified bits. The conversion must not be
2757 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, Type *Ty) {
2758 Type *SrcTy = V->getType();
2759 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2760 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2761 "Cannot noop or any extend with non-integer arguments!");
2762 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2763 "getNoopOrAnyExtend cannot truncate!");
2764 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2765 return V; // No conversion
2766 return getAnyExtendExpr(V, Ty);
2769 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2770 /// input value to the specified type. The conversion must not be widening.
2772 ScalarEvolution::getTruncateOrNoop(const SCEV *V, Type *Ty) {
2773 Type *SrcTy = V->getType();
2774 assert((SrcTy->isIntegerTy() || SrcTy->isPointerTy()) &&
2775 (Ty->isIntegerTy() || Ty->isPointerTy()) &&
2776 "Cannot truncate or noop with non-integer arguments!");
2777 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2778 "getTruncateOrNoop cannot extend!");
2779 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2780 return V; // No conversion
2781 return getTruncateExpr(V, Ty);
2784 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2785 /// the types using zero-extension, and then perform a umax operation
2787 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2789 const SCEV *PromotedLHS = LHS;
2790 const SCEV *PromotedRHS = RHS;
2792 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2793 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2795 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2797 return getUMaxExpr(PromotedLHS, PromotedRHS);
2800 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2801 /// the types using zero-extension, and then perform a umin operation
2803 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2805 const SCEV *PromotedLHS = LHS;
2806 const SCEV *PromotedRHS = RHS;
2808 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2809 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2811 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2813 return getUMinExpr(PromotedLHS, PromotedRHS);
2816 /// getPointerBase - Transitively follow the chain of pointer-type operands
2817 /// until reaching a SCEV that does not have a single pointer operand. This
2818 /// returns a SCEVUnknown pointer for well-formed pointer-type expressions,
2819 /// but corner cases do exist.
2820 const SCEV *ScalarEvolution::getPointerBase(const SCEV *V) {
2821 // A pointer operand may evaluate to a nonpointer expression, such as null.
2822 if (!V->getType()->isPointerTy())
2825 if (const SCEVCastExpr *Cast = dyn_cast<SCEVCastExpr>(V)) {
2826 return getPointerBase(Cast->getOperand());
2828 else if (const SCEVNAryExpr *NAry = dyn_cast<SCEVNAryExpr>(V)) {
2829 const SCEV *PtrOp = 0;
2830 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
2832 if ((*I)->getType()->isPointerTy()) {
2833 // Cannot find the base of an expression with multiple pointer operands.
2841 return getPointerBase(PtrOp);
2846 /// PushDefUseChildren - Push users of the given Instruction
2847 /// onto the given Worklist.
2849 PushDefUseChildren(Instruction *I,
2850 SmallVectorImpl<Instruction *> &Worklist) {
2851 // Push the def-use children onto the Worklist stack.
2852 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2854 Worklist.push_back(cast<Instruction>(*UI));
2857 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2858 /// instructions that depend on the given instruction and removes them from
2859 /// the ValueExprMapType map if they reference SymName. This is used during PHI
2862 ScalarEvolution::ForgetSymbolicName(Instruction *PN, const SCEV *SymName) {
2863 SmallVector<Instruction *, 16> Worklist;
2864 PushDefUseChildren(PN, Worklist);
2866 SmallPtrSet<Instruction *, 8> Visited;
2868 while (!Worklist.empty()) {
2869 Instruction *I = Worklist.pop_back_val();
2870 if (!Visited.insert(I)) continue;
2872 ValueExprMapType::iterator It =
2873 ValueExprMap.find(static_cast<Value *>(I));
2874 if (It != ValueExprMap.end()) {
2875 const SCEV *Old = It->second;
2877 // Short-circuit the def-use traversal if the symbolic name
2878 // ceases to appear in expressions.
2879 if (Old != SymName && !hasOperand(Old, SymName))
2882 // SCEVUnknown for a PHI either means that it has an unrecognized
2883 // structure, it's a PHI that's in the progress of being computed
2884 // by createNodeForPHI, or it's a single-value PHI. In the first case,
2885 // additional loop trip count information isn't going to change anything.
2886 // In the second case, createNodeForPHI will perform the necessary
2887 // updates on its own when it gets to that point. In the third, we do
2888 // want to forget the SCEVUnknown.
2889 if (!isa<PHINode>(I) ||
2890 !isa<SCEVUnknown>(Old) ||
2891 (I != PN && Old == SymName)) {
2892 forgetMemoizedResults(Old);
2893 ValueExprMap.erase(It);
2897 PushDefUseChildren(I, Worklist);
2901 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2902 /// a loop header, making it a potential recurrence, or it doesn't.
2904 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2905 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2906 if (L->getHeader() == PN->getParent()) {
2907 // The loop may have multiple entrances or multiple exits; we can analyze
2908 // this phi as an addrec if it has a unique entry value and a unique
2910 Value *BEValueV = 0, *StartValueV = 0;
2911 for (unsigned i = 0, e = PN->getNumIncomingValues(); i != e; ++i) {
2912 Value *V = PN->getIncomingValue(i);
2913 if (L->contains(PN->getIncomingBlock(i))) {
2916 } else if (BEValueV != V) {
2920 } else if (!StartValueV) {
2922 } else if (StartValueV != V) {
2927 if (BEValueV && StartValueV) {
2928 // While we are analyzing this PHI node, handle its value symbolically.
2929 const SCEV *SymbolicName = getUnknown(PN);
2930 assert(ValueExprMap.find(PN) == ValueExprMap.end() &&
2931 "PHI node already processed?");
2932 ValueExprMap.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2934 // Using this symbolic name for the PHI, analyze the value coming around
2936 const SCEV *BEValue = getSCEV(BEValueV);
2938 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2939 // has a special value for the first iteration of the loop.
2941 // If the value coming around the backedge is an add with the symbolic
2942 // value we just inserted, then we found a simple induction variable!
2943 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2944 // If there is a single occurrence of the symbolic value, replace it
2945 // with a recurrence.
2946 unsigned FoundIndex = Add->getNumOperands();
2947 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2948 if (Add->getOperand(i) == SymbolicName)
2949 if (FoundIndex == e) {
2954 if (FoundIndex != Add->getNumOperands()) {
2955 // Create an add with everything but the specified operand.
2956 SmallVector<const SCEV *, 8> Ops;
2957 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2958 if (i != FoundIndex)
2959 Ops.push_back(Add->getOperand(i));
2960 const SCEV *Accum = getAddExpr(Ops);
2962 // This is not a valid addrec if the step amount is varying each
2963 // loop iteration, but is not itself an addrec in this loop.
2964 if (isLoopInvariant(Accum, L) ||
2965 (isa<SCEVAddRecExpr>(Accum) &&
2966 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2967 SCEV::NoWrapFlags Flags = SCEV::FlagAnyWrap;
2969 // If the increment doesn't overflow, then neither the addrec nor
2970 // the post-increment will overflow.
2971 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV)) {
2972 if (OBO->hasNoUnsignedWrap())
2973 Flags = setFlags(Flags, SCEV::FlagNUW);
2974 if (OBO->hasNoSignedWrap())
2975 Flags = setFlags(Flags, SCEV::FlagNSW);
2976 } else if (const GEPOperator *GEP =
2977 dyn_cast<GEPOperator>(BEValueV)) {
2978 // If the increment is an inbounds GEP, then we know the address
2979 // space cannot be wrapped around. We cannot make any guarantee
2980 // about signed or unsigned overflow because pointers are
2981 // unsigned but we may have a negative index from the base
2983 if (GEP->isInBounds())
2984 Flags = setFlags(Flags, SCEV::FlagNW);
2987 const SCEV *StartVal = getSCEV(StartValueV);
2988 const SCEV *PHISCEV = getAddRecExpr(StartVal, Accum, L, Flags);
2990 // Since the no-wrap flags are on the increment, they apply to the
2991 // post-incremented value as well.
2992 if (isLoopInvariant(Accum, L))
2993 (void)getAddRecExpr(getAddExpr(StartVal, Accum),
2996 // Okay, for the entire analysis of this edge we assumed the PHI
2997 // to be symbolic. We now need to go back and purge all of the
2998 // entries for the scalars that use the symbolic expression.
2999 ForgetSymbolicName(PN, SymbolicName);
3000 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3004 } else if (const SCEVAddRecExpr *AddRec =
3005 dyn_cast<SCEVAddRecExpr>(BEValue)) {
3006 // Otherwise, this could be a loop like this:
3007 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
3008 // In this case, j = {1,+,1} and BEValue is j.
3009 // Because the other in-value of i (0) fits the evolution of BEValue
3010 // i really is an addrec evolution.
3011 if (AddRec->getLoop() == L && AddRec->isAffine()) {
3012 const SCEV *StartVal = getSCEV(StartValueV);
3014 // If StartVal = j.start - j.stride, we can use StartVal as the
3015 // initial step of the addrec evolution.
3016 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
3017 AddRec->getOperand(1))) {
3018 // FIXME: For constant StartVal, we should be able to infer
3020 const SCEV *PHISCEV =
3021 getAddRecExpr(StartVal, AddRec->getOperand(1), L,
3024 // Okay, for the entire analysis of this edge we assumed the PHI
3025 // to be symbolic. We now need to go back and purge all of the
3026 // entries for the scalars that use the symbolic expression.
3027 ForgetSymbolicName(PN, SymbolicName);
3028 ValueExprMap[SCEVCallbackVH(PN, this)] = PHISCEV;
3036 // If the PHI has a single incoming value, follow that value, unless the
3037 // PHI's incoming blocks are in a different loop, in which case doing so
3038 // risks breaking LCSSA form. Instcombine would normally zap these, but
3039 // it doesn't have DominatorTree information, so it may miss cases.
3040 if (Value *V = SimplifyInstruction(PN, TD, DT))
3041 if (LI->replacementPreservesLCSSAForm(PN, V))
3044 // If it's not a loop phi, we can't handle it yet.
3045 return getUnknown(PN);
3048 /// createNodeForGEP - Expand GEP instructions into add and multiply
3049 /// operations. This allows them to be analyzed by regular SCEV code.
3051 const SCEV *ScalarEvolution::createNodeForGEP(GEPOperator *GEP) {
3053 // Don't blindly transfer the inbounds flag from the GEP instruction to the
3054 // Add expression, because the Instruction may be guarded by control flow
3055 // and the no-overflow bits may not be valid for the expression in any
3057 bool isInBounds = GEP->isInBounds();
3059 Type *IntPtrTy = getEffectiveSCEVType(GEP->getType());
3060 Value *Base = GEP->getOperand(0);
3061 // Don't attempt to analyze GEPs over unsized objects.
3062 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
3063 return getUnknown(GEP);
3064 const SCEV *TotalOffset = getConstant(IntPtrTy, 0);
3065 gep_type_iterator GTI = gep_type_begin(GEP);
3066 for (GetElementPtrInst::op_iterator I = llvm::next(GEP->op_begin()),
3070 // Compute the (potentially symbolic) offset in bytes for this index.
3071 if (StructType *STy = dyn_cast<StructType>(*GTI++)) {
3072 // For a struct, add the member offset.
3073 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
3074 const SCEV *FieldOffset = getOffsetOfExpr(STy, FieldNo);
3076 // Add the field offset to the running total offset.
3077 TotalOffset = getAddExpr(TotalOffset, FieldOffset);
3079 // For an array, add the element offset, explicitly scaled.
3080 const SCEV *ElementSize = getSizeOfExpr(*GTI);
3081 const SCEV *IndexS = getSCEV(Index);
3082 // Getelementptr indices are signed.
3083 IndexS = getTruncateOrSignExtend(IndexS, IntPtrTy);
3085 // Multiply the index by the element size to compute the element offset.
3086 const SCEV *LocalOffset = getMulExpr(IndexS, ElementSize,
3087 isInBounds ? SCEV::FlagNSW :
3090 // Add the element offset to the running total offset.
3091 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
3095 // Get the SCEV for the GEP base.
3096 const SCEV *BaseS = getSCEV(Base);
3098 // Add the total offset from all the GEP indices to the base.
3099 return getAddExpr(BaseS, TotalOffset,
3100 isInBounds ? SCEV::FlagNSW : SCEV::FlagAnyWrap);
3103 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
3104 /// guaranteed to end in (at every loop iteration). It is, at the same time,
3105 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
3106 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
3108 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
3109 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3110 return C->getValue()->getValue().countTrailingZeros();
3112 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
3113 return std::min(GetMinTrailingZeros(T->getOperand()),
3114 (uint32_t)getTypeSizeInBits(T->getType()));
3116 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
3117 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3118 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3119 getTypeSizeInBits(E->getType()) : OpRes;
3122 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
3123 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
3124 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
3125 getTypeSizeInBits(E->getType()) : OpRes;
3128 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
3129 // The result is the min of all operands results.
3130 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3131 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3132 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3136 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
3137 // The result is the sum of all operands results.
3138 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
3139 uint32_t BitWidth = getTypeSizeInBits(M->getType());
3140 for (unsigned i = 1, e = M->getNumOperands();
3141 SumOpRes != BitWidth && i != e; ++i)
3142 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
3147 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
3148 // The result is the min of all operands results.
3149 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
3150 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
3151 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
3155 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
3156 // The result is the min of all operands results.
3157 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3158 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3159 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3163 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
3164 // The result is the min of all operands results.
3165 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
3166 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
3167 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
3171 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3172 // For a SCEVUnknown, ask ValueTracking.
3173 unsigned BitWidth = getTypeSizeInBits(U->getType());
3174 APInt Mask = APInt::getAllOnesValue(BitWidth);
3175 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3176 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
3177 return Zeros.countTrailingOnes();
3184 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
3187 ScalarEvolution::getUnsignedRange(const SCEV *S) {
3188 // See if we've computed this range already.
3189 DenseMap<const SCEV *, ConstantRange>::iterator I = UnsignedRanges.find(S);
3190 if (I != UnsignedRanges.end())
3193 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3194 return setUnsignedRange(C, ConstantRange(C->getValue()->getValue()));
3196 unsigned BitWidth = getTypeSizeInBits(S->getType());
3197 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3199 // If the value has known zeros, the maximum unsigned value will have those
3200 // known zeros as well.
3201 uint32_t TZ = GetMinTrailingZeros(S);
3203 ConservativeResult =
3204 ConstantRange(APInt::getMinValue(BitWidth),
3205 APInt::getMaxValue(BitWidth).lshr(TZ).shl(TZ) + 1);
3207 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3208 ConstantRange X = getUnsignedRange(Add->getOperand(0));
3209 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3210 X = X.add(getUnsignedRange(Add->getOperand(i)));
3211 return setUnsignedRange(Add, ConservativeResult.intersectWith(X));
3214 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3215 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
3216 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3217 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
3218 return setUnsignedRange(Mul, ConservativeResult.intersectWith(X));
3221 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3222 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
3223 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3224 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
3225 return setUnsignedRange(SMax, ConservativeResult.intersectWith(X));
3228 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3229 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
3230 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3231 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
3232 return setUnsignedRange(UMax, ConservativeResult.intersectWith(X));
3235 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3236 ConstantRange X = getUnsignedRange(UDiv->getLHS());
3237 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
3238 return setUnsignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3241 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3242 ConstantRange X = getUnsignedRange(ZExt->getOperand());
3243 return setUnsignedRange(ZExt,
3244 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3247 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3248 ConstantRange X = getUnsignedRange(SExt->getOperand());
3249 return setUnsignedRange(SExt,
3250 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3253 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3254 ConstantRange X = getUnsignedRange(Trunc->getOperand());
3255 return setUnsignedRange(Trunc,
3256 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3259 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3260 // If there's no unsigned wrap, the value will never be less than its
3262 if (AddRec->getNoWrapFlags(SCEV::FlagNUW))
3263 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(AddRec->getStart()))
3264 if (!C->getValue()->isZero())
3265 ConservativeResult =
3266 ConservativeResult.intersectWith(
3267 ConstantRange(C->getValue()->getValue(), APInt(BitWidth, 0)));
3269 // TODO: non-affine addrec
3270 if (AddRec->isAffine()) {
3271 Type *Ty = AddRec->getType();
3272 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3273 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3274 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3275 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3277 const SCEV *Start = AddRec->getStart();
3278 const SCEV *Step = AddRec->getStepRecurrence(*this);
3280 ConstantRange StartRange = getUnsignedRange(Start);
3281 ConstantRange StepRange = getSignedRange(Step);
3282 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3283 ConstantRange EndRange =
3284 StartRange.add(MaxBECountRange.multiply(StepRange));
3286 // Check for overflow. This must be done with ConstantRange arithmetic
3287 // because we could be called from within the ScalarEvolution overflow
3289 ConstantRange ExtStartRange = StartRange.zextOrTrunc(BitWidth*2+1);
3290 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3291 ConstantRange ExtMaxBECountRange =
3292 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3293 ConstantRange ExtEndRange = EndRange.zextOrTrunc(BitWidth*2+1);
3294 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3296 return setUnsignedRange(AddRec, ConservativeResult);
3298 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
3299 EndRange.getUnsignedMin());
3300 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
3301 EndRange.getUnsignedMax());
3302 if (Min.isMinValue() && Max.isMaxValue())
3303 return setUnsignedRange(AddRec, ConservativeResult);
3304 return setUnsignedRange(AddRec,
3305 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3309 return setUnsignedRange(AddRec, ConservativeResult);
3312 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3313 // For a SCEVUnknown, ask ValueTracking.
3314 APInt Mask = APInt::getAllOnesValue(BitWidth);
3315 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
3316 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
3317 if (Ones == ~Zeros + 1)
3318 return setUnsignedRange(U, ConservativeResult);
3319 return setUnsignedRange(U,
3320 ConservativeResult.intersectWith(ConstantRange(Ones, ~Zeros + 1)));
3323 return setUnsignedRange(S, ConservativeResult);
3326 /// getSignedRange - Determine the signed range for a particular SCEV.
3329 ScalarEvolution::getSignedRange(const SCEV *S) {
3330 // See if we've computed this range already.
3331 DenseMap<const SCEV *, ConstantRange>::iterator I = SignedRanges.find(S);
3332 if (I != SignedRanges.end())
3335 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
3336 return setSignedRange(C, ConstantRange(C->getValue()->getValue()));
3338 unsigned BitWidth = getTypeSizeInBits(S->getType());
3339 ConstantRange ConservativeResult(BitWidth, /*isFullSet=*/true);
3341 // If the value has known zeros, the maximum signed value will have those
3342 // known zeros as well.
3343 uint32_t TZ = GetMinTrailingZeros(S);
3345 ConservativeResult =
3346 ConstantRange(APInt::getSignedMinValue(BitWidth),
3347 APInt::getSignedMaxValue(BitWidth).ashr(TZ).shl(TZ) + 1);
3349 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
3350 ConstantRange X = getSignedRange(Add->getOperand(0));
3351 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
3352 X = X.add(getSignedRange(Add->getOperand(i)));
3353 return setSignedRange(Add, ConservativeResult.intersectWith(X));
3356 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
3357 ConstantRange X = getSignedRange(Mul->getOperand(0));
3358 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
3359 X = X.multiply(getSignedRange(Mul->getOperand(i)));
3360 return setSignedRange(Mul, ConservativeResult.intersectWith(X));
3363 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
3364 ConstantRange X = getSignedRange(SMax->getOperand(0));
3365 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
3366 X = X.smax(getSignedRange(SMax->getOperand(i)));
3367 return setSignedRange(SMax, ConservativeResult.intersectWith(X));
3370 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
3371 ConstantRange X = getSignedRange(UMax->getOperand(0));
3372 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
3373 X = X.umax(getSignedRange(UMax->getOperand(i)));
3374 return setSignedRange(UMax, ConservativeResult.intersectWith(X));
3377 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
3378 ConstantRange X = getSignedRange(UDiv->getLHS());
3379 ConstantRange Y = getSignedRange(UDiv->getRHS());
3380 return setSignedRange(UDiv, ConservativeResult.intersectWith(X.udiv(Y)));
3383 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
3384 ConstantRange X = getSignedRange(ZExt->getOperand());
3385 return setSignedRange(ZExt,
3386 ConservativeResult.intersectWith(X.zeroExtend(BitWidth)));
3389 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
3390 ConstantRange X = getSignedRange(SExt->getOperand());
3391 return setSignedRange(SExt,
3392 ConservativeResult.intersectWith(X.signExtend(BitWidth)));
3395 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
3396 ConstantRange X = getSignedRange(Trunc->getOperand());
3397 return setSignedRange(Trunc,
3398 ConservativeResult.intersectWith(X.truncate(BitWidth)));
3401 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
3402 // If there's no signed wrap, and all the operands have the same sign or
3403 // zero, the value won't ever change sign.
3404 if (AddRec->getNoWrapFlags(SCEV::FlagNSW)) {
3405 bool AllNonNeg = true;
3406 bool AllNonPos = true;
3407 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
3408 if (!isKnownNonNegative(AddRec->getOperand(i))) AllNonNeg = false;
3409 if (!isKnownNonPositive(AddRec->getOperand(i))) AllNonPos = false;
3412 ConservativeResult = ConservativeResult.intersectWith(
3413 ConstantRange(APInt(BitWidth, 0),
3414 APInt::getSignedMinValue(BitWidth)));
3416 ConservativeResult = ConservativeResult.intersectWith(
3417 ConstantRange(APInt::getSignedMinValue(BitWidth),
3418 APInt(BitWidth, 1)));
3421 // TODO: non-affine addrec
3422 if (AddRec->isAffine()) {
3423 Type *Ty = AddRec->getType();
3424 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
3425 if (!isa<SCEVCouldNotCompute>(MaxBECount) &&
3426 getTypeSizeInBits(MaxBECount->getType()) <= BitWidth) {
3427 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
3429 const SCEV *Start = AddRec->getStart();
3430 const SCEV *Step = AddRec->getStepRecurrence(*this);
3432 ConstantRange StartRange = getSignedRange(Start);
3433 ConstantRange StepRange = getSignedRange(Step);
3434 ConstantRange MaxBECountRange = getUnsignedRange(MaxBECount);
3435 ConstantRange EndRange =
3436 StartRange.add(MaxBECountRange.multiply(StepRange));
3438 // Check for overflow. This must be done with ConstantRange arithmetic
3439 // because we could be called from within the ScalarEvolution overflow
3441 ConstantRange ExtStartRange = StartRange.sextOrTrunc(BitWidth*2+1);
3442 ConstantRange ExtStepRange = StepRange.sextOrTrunc(BitWidth*2+1);
3443 ConstantRange ExtMaxBECountRange =
3444 MaxBECountRange.zextOrTrunc(BitWidth*2+1);
3445 ConstantRange ExtEndRange = EndRange.sextOrTrunc(BitWidth*2+1);
3446 if (ExtStartRange.add(ExtMaxBECountRange.multiply(ExtStepRange)) !=
3448 return setSignedRange(AddRec, ConservativeResult);
3450 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
3451 EndRange.getSignedMin());
3452 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
3453 EndRange.getSignedMax());
3454 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
3455 return setSignedRange(AddRec, ConservativeResult);
3456 return setSignedRange(AddRec,
3457 ConservativeResult.intersectWith(ConstantRange(Min, Max+1)));
3461 return setSignedRange(AddRec, ConservativeResult);
3464 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
3465 // For a SCEVUnknown, ask ValueTracking.
3466 if (!U->getValue()->getType()->isIntegerTy() && !TD)
3467 return setSignedRange(U, ConservativeResult);
3468 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
3470 return setSignedRange(U, ConservativeResult);
3471 return setSignedRange(U, ConservativeResult.intersectWith(
3472 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
3473 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1)));
3476 return setSignedRange(S, ConservativeResult);
3479 /// createSCEV - We know that there is no SCEV for the specified value.
3480 /// Analyze the expression.
3482 const SCEV *ScalarEvolution::createSCEV(Value *V) {
3483 if (!isSCEVable(V->getType()))
3484 return getUnknown(V);
3486 unsigned Opcode = Instruction::UserOp1;
3487 if (Instruction *I = dyn_cast<Instruction>(V)) {
3488 Opcode = I->getOpcode();
3490 // Don't attempt to analyze instructions in blocks that aren't
3491 // reachable. Such instructions don't matter, and they aren't required
3492 // to obey basic rules for definitions dominating uses which this
3493 // analysis depends on.
3494 if (!DT->isReachableFromEntry(I->getParent()))
3495 return getUnknown(V);
3496 } else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
3497 Opcode = CE->getOpcode();
3498 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
3499 return getConstant(CI);
3500 else if (isa<ConstantPointerNull>(V))
3501 return getConstant(V->getType(), 0);
3502 else if (GlobalAlias *GA = dyn_cast<GlobalAlias>(V))
3503 return GA->mayBeOverridden() ? getUnknown(V) : getSCEV(GA->getAliasee());
3505 return getUnknown(V);
3507 Operator *U = cast<Operator>(V);
3509 case Instruction::Add: {
3510 // The simple thing to do would be to just call getSCEV on both operands
3511 // and call getAddExpr with the result. However if we're looking at a
3512 // bunch of things all added together, this can be quite inefficient,
3513 // because it leads to N-1 getAddExpr calls for N ultimate operands.
3514 // Instead, gather up all the operands and make a single getAddExpr call.
3515 // LLVM IR canonical form means we need only traverse the left operands.
3516 SmallVector<const SCEV *, 4> AddOps;
3517 AddOps.push_back(getSCEV(U->getOperand(1)));
3518 for (Value *Op = U->getOperand(0); ; Op = U->getOperand(0)) {
3519 unsigned Opcode = Op->getValueID() - Value::InstructionVal;
3520 if (Opcode != Instruction::Add && Opcode != Instruction::Sub)
3522 U = cast<Operator>(Op);
3523 const SCEV *Op1 = getSCEV(U->getOperand(1));
3524 if (Opcode == Instruction::Sub)
3525 AddOps.push_back(getNegativeSCEV(Op1));
3527 AddOps.push_back(Op1);
3529 AddOps.push_back(getSCEV(U->getOperand(0)));
3530 return getAddExpr(AddOps);
3532 case Instruction::Mul: {
3533 // See the Add code above.
3534 SmallVector<const SCEV *, 4> MulOps;
3535 MulOps.push_back(getSCEV(U->getOperand(1)));
3536 for (Value *Op = U->getOperand(0);
3537 Op->getValueID() == Instruction::Mul + Value::InstructionVal;
3538 Op = U->getOperand(0)) {
3539 U = cast<Operator>(Op);
3540 MulOps.push_back(getSCEV(U->getOperand(1)));
3542 MulOps.push_back(getSCEV(U->getOperand(0)));
3543 return getMulExpr(MulOps);
3545 case Instruction::UDiv:
3546 return getUDivExpr(getSCEV(U->getOperand(0)),
3547 getSCEV(U->getOperand(1)));
3548 case Instruction::Sub:
3549 return getMinusSCEV(getSCEV(U->getOperand(0)),
3550 getSCEV(U->getOperand(1)));
3551 case Instruction::And:
3552 // For an expression like x&255 that merely masks off the high bits,
3553 // use zext(trunc(x)) as the SCEV expression.
3554 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3555 if (CI->isNullValue())
3556 return getSCEV(U->getOperand(1));
3557 if (CI->isAllOnesValue())
3558 return getSCEV(U->getOperand(0));
3559 const APInt &A = CI->getValue();
3561 // Instcombine's ShrinkDemandedConstant may strip bits out of
3562 // constants, obscuring what would otherwise be a low-bits mask.
3563 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
3564 // knew about to reconstruct a low-bits mask value.
3565 unsigned LZ = A.countLeadingZeros();
3566 unsigned BitWidth = A.getBitWidth();
3567 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
3568 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
3569 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
3571 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
3573 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
3575 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
3576 IntegerType::get(getContext(), BitWidth - LZ)),
3581 case Instruction::Or:
3582 // If the RHS of the Or is a constant, we may have something like:
3583 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
3584 // optimizations will transparently handle this case.
3586 // In order for this transformation to be safe, the LHS must be of the
3587 // form X*(2^n) and the Or constant must be less than 2^n.
3588 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3589 const SCEV *LHS = getSCEV(U->getOperand(0));
3590 const APInt &CIVal = CI->getValue();
3591 if (GetMinTrailingZeros(LHS) >=
3592 (CIVal.getBitWidth() - CIVal.countLeadingZeros())) {
3593 // Build a plain add SCEV.
3594 const SCEV *S = getAddExpr(LHS, getSCEV(CI));
3595 // If the LHS of the add was an addrec and it has no-wrap flags,
3596 // transfer the no-wrap flags, since an or won't introduce a wrap.
3597 if (const SCEVAddRecExpr *NewAR = dyn_cast<SCEVAddRecExpr>(S)) {
3598 const SCEVAddRecExpr *OldAR = cast<SCEVAddRecExpr>(LHS);
3599 const_cast<SCEVAddRecExpr *>(NewAR)->setNoWrapFlags(
3600 OldAR->getNoWrapFlags());
3606 case Instruction::Xor:
3607 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
3608 // If the RHS of the xor is a signbit, then this is just an add.
3609 // Instcombine turns add of signbit into xor as a strength reduction step.
3610 if (CI->getValue().isSignBit())
3611 return getAddExpr(getSCEV(U->getOperand(0)),
3612 getSCEV(U->getOperand(1)));
3614 // If the RHS of xor is -1, then this is a not operation.
3615 if (CI->isAllOnesValue())
3616 return getNotSCEV(getSCEV(U->getOperand(0)));
3618 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
3619 // This is a variant of the check for xor with -1, and it handles
3620 // the case where instcombine has trimmed non-demanded bits out
3621 // of an xor with -1.
3622 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
3623 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
3624 if (BO->getOpcode() == Instruction::And &&
3625 LCI->getValue() == CI->getValue())
3626 if (const SCEVZeroExtendExpr *Z =
3627 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
3628 Type *UTy = U->getType();
3629 const SCEV *Z0 = Z->getOperand();
3630 Type *Z0Ty = Z0->getType();
3631 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
3633 // If C is a low-bits mask, the zero extend is serving to
3634 // mask off the high bits. Complement the operand and
3635 // re-apply the zext.
3636 if (APIntOps::isMask(Z0TySize, CI->getValue()))
3637 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
3639 // If C is a single bit, it may be in the sign-bit position
3640 // before the zero-extend. In this case, represent the xor
3641 // using an add, which is equivalent, and re-apply the zext.
3642 APInt Trunc = CI->getValue().trunc(Z0TySize);
3643 if (Trunc.zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
3645 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
3651 case Instruction::Shl:
3652 // Turn shift left of a constant amount into a multiply.
3653 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3654 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3656 // If the shift count is not less than the bitwidth, the result of
3657 // the shift is undefined. Don't try to analyze it, because the
3658 // resolution chosen here may differ from the resolution chosen in
3659 // other parts of the compiler.
3660 if (SA->getValue().uge(BitWidth))
3663 Constant *X = ConstantInt::get(getContext(),
3664 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3665 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3669 case Instruction::LShr:
3670 // Turn logical shift right of a constant into a unsigned divide.
3671 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
3672 uint32_t BitWidth = cast<IntegerType>(U->getType())->getBitWidth();
3674 // If the shift count is not less than the bitwidth, the result of
3675 // the shift is undefined. Don't try to analyze it, because the
3676 // resolution chosen here may differ from the resolution chosen in
3677 // other parts of the compiler.
3678 if (SA->getValue().uge(BitWidth))
3681 Constant *X = ConstantInt::get(getContext(),
3682 APInt(BitWidth, 1).shl(SA->getZExtValue()));
3683 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
3687 case Instruction::AShr:
3688 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
3689 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
3690 if (Operator *L = dyn_cast<Operator>(U->getOperand(0)))
3691 if (L->getOpcode() == Instruction::Shl &&
3692 L->getOperand(1) == U->getOperand(1)) {
3693 uint64_t BitWidth = getTypeSizeInBits(U->getType());
3695 // If the shift count is not less than the bitwidth, the result of
3696 // the shift is undefined. Don't try to analyze it, because the
3697 // resolution chosen here may differ from the resolution chosen in
3698 // other parts of the compiler.
3699 if (CI->getValue().uge(BitWidth))
3702 uint64_t Amt = BitWidth - CI->getZExtValue();
3703 if (Amt == BitWidth)
3704 return getSCEV(L->getOperand(0)); // shift by zero --> noop
3706 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
3707 IntegerType::get(getContext(),
3713 case Instruction::Trunc:
3714 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
3716 case Instruction::ZExt:
3717 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3719 case Instruction::SExt:
3720 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
3722 case Instruction::BitCast:
3723 // BitCasts are no-op casts so we just eliminate the cast.
3724 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
3725 return getSCEV(U->getOperand(0));
3728 // It's tempting to handle inttoptr and ptrtoint as no-ops, however this can
3729 // lead to pointer expressions which cannot safely be expanded to GEPs,
3730 // because ScalarEvolution doesn't respect the GEP aliasing rules when
3731 // simplifying integer expressions.
3733 case Instruction::GetElementPtr:
3734 return createNodeForGEP(cast<GEPOperator>(U));
3736 case Instruction::PHI:
3737 return createNodeForPHI(cast<PHINode>(U));
3739 case Instruction::Select:
3740 // This could be a smax or umax that was lowered earlier.
3741 // Try to recover it.
3742 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
3743 Value *LHS = ICI->getOperand(0);
3744 Value *RHS = ICI->getOperand(1);
3745 switch (ICI->getPredicate()) {
3746 case ICmpInst::ICMP_SLT:
3747 case ICmpInst::ICMP_SLE:
3748 std::swap(LHS, RHS);
3750 case ICmpInst::ICMP_SGT:
3751 case ICmpInst::ICMP_SGE:
3752 // a >s b ? a+x : b+x -> smax(a, b)+x
3753 // a >s b ? b+x : a+x -> smin(a, b)+x
3754 if (LHS->getType() == U->getType()) {
3755 const SCEV *LS = getSCEV(LHS);
3756 const SCEV *RS = getSCEV(RHS);
3757 const SCEV *LA = getSCEV(U->getOperand(1));
3758 const SCEV *RA = getSCEV(U->getOperand(2));
3759 const SCEV *LDiff = getMinusSCEV(LA, LS);
3760 const SCEV *RDiff = getMinusSCEV(RA, RS);
3762 return getAddExpr(getSMaxExpr(LS, RS), LDiff);
3763 LDiff = getMinusSCEV(LA, RS);
3764 RDiff = getMinusSCEV(RA, LS);
3766 return getAddExpr(getSMinExpr(LS, RS), LDiff);
3769 case ICmpInst::ICMP_ULT:
3770 case ICmpInst::ICMP_ULE:
3771 std::swap(LHS, RHS);
3773 case ICmpInst::ICMP_UGT:
3774 case ICmpInst::ICMP_UGE:
3775 // a >u b ? a+x : b+x -> umax(a, b)+x
3776 // a >u b ? b+x : a+x -> umin(a, b)+x
3777 if (LHS->getType() == U->getType()) {
3778 const SCEV *LS = getSCEV(LHS);
3779 const SCEV *RS = getSCEV(RHS);
3780 const SCEV *LA = getSCEV(U->getOperand(1));
3781 const SCEV *RA = getSCEV(U->getOperand(2));
3782 const SCEV *LDiff = getMinusSCEV(LA, LS);
3783 const SCEV *RDiff = getMinusSCEV(RA, RS);
3785 return getAddExpr(getUMaxExpr(LS, RS), LDiff);
3786 LDiff = getMinusSCEV(LA, RS);
3787 RDiff = getMinusSCEV(RA, LS);
3789 return getAddExpr(getUMinExpr(LS, RS), LDiff);
3792 case ICmpInst::ICMP_NE:
3793 // n != 0 ? n+x : 1+x -> umax(n, 1)+x
3794 if (LHS->getType() == U->getType() &&
3795 isa<ConstantInt>(RHS) &&
3796 cast<ConstantInt>(RHS)->isZero()) {
3797 const SCEV *One = getConstant(LHS->getType(), 1);
3798 const SCEV *LS = getSCEV(LHS);
3799 const SCEV *LA = getSCEV(U->getOperand(1));
3800 const SCEV *RA = getSCEV(U->getOperand(2));
3801 const SCEV *LDiff = getMinusSCEV(LA, LS);
3802 const SCEV *RDiff = getMinusSCEV(RA, One);
3804 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3807 case ICmpInst::ICMP_EQ:
3808 // n == 0 ? 1+x : n+x -> umax(n, 1)+x
3809 if (LHS->getType() == U->getType() &&
3810 isa<ConstantInt>(RHS) &&
3811 cast<ConstantInt>(RHS)->isZero()) {
3812 const SCEV *One = getConstant(LHS->getType(), 1);
3813 const SCEV *LS = getSCEV(LHS);
3814 const SCEV *LA = getSCEV(U->getOperand(1));
3815 const SCEV *RA = getSCEV(U->getOperand(2));
3816 const SCEV *LDiff = getMinusSCEV(LA, One);
3817 const SCEV *RDiff = getMinusSCEV(RA, LS);
3819 return getAddExpr(getUMaxExpr(One, LS), LDiff);
3827 default: // We cannot analyze this expression.
3831 return getUnknown(V);
3836 //===----------------------------------------------------------------------===//
3837 // Iteration Count Computation Code
3840 /// getSmallConstantTripCount - Returns the maximum trip count of this loop as a
3841 /// normal unsigned value, if possible. Returns 0 if the trip count is unknown
3842 /// or not constant. Will also return 0 if the maximum trip count is very large
3844 unsigned ScalarEvolution::getSmallConstantTripCount(Loop *L,
3845 BasicBlock *ExitBlock) {
3846 const SCEVConstant *ExitCount =
3847 dyn_cast<SCEVConstant>(getExitCount(L, ExitBlock));
3851 ConstantInt *ExitConst = ExitCount->getValue();
3853 // Guard against huge trip counts.
3854 if (ExitConst->getValue().getActiveBits() > 32)
3857 // In case of integer overflow, this returns 0, which is correct.
3858 return ((unsigned)ExitConst->getZExtValue()) + 1;
3861 /// getSmallConstantTripMultiple - Returns the largest constant divisor of the
3862 /// trip count of this loop as a normal unsigned value, if possible. This
3863 /// means that the actual trip count is always a multiple of the returned
3864 /// value (don't forget the trip count could very well be zero as well!).
3866 /// Returns 1 if the trip count is unknown or not guaranteed to be the
3867 /// multiple of a constant (which is also the case if the trip count is simply
3868 /// constant, use getSmallConstantTripCount for that case), Will also return 1
3869 /// if the trip count is very large (>= 2^32).
3870 unsigned ScalarEvolution::getSmallConstantTripMultiple(Loop *L,
3871 BasicBlock *ExitBlock) {
3872 const SCEV *ExitCount = getExitCount(L, ExitBlock);
3873 if (ExitCount == getCouldNotCompute())
3876 // Get the trip count from the BE count by adding 1.
3877 const SCEV *TCMul = getAddExpr(ExitCount,
3878 getConstant(ExitCount->getType(), 1));
3879 // FIXME: SCEV distributes multiplication as V1*C1 + V2*C1. We could attempt
3880 // to factor simple cases.
3881 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(TCMul))
3882 TCMul = Mul->getOperand(0);
3884 const SCEVConstant *MulC = dyn_cast<SCEVConstant>(TCMul);
3888 ConstantInt *Result = MulC->getValue();
3890 // Guard against huge trip counts.
3891 if (!Result || Result->getValue().getActiveBits() > 32)
3894 return (unsigned)Result->getZExtValue();
3897 // getExitCount - Get the expression for the number of loop iterations for which
3898 // this loop is guaranteed not to exit via ExitintBlock. Otherwise return
3899 // SCEVCouldNotCompute.
3900 const SCEV *ScalarEvolution::getExitCount(Loop *L, BasicBlock *ExitingBlock) {
3901 return getBackedgeTakenInfo(L).getExact(ExitingBlock, this);
3904 /// getBackedgeTakenCount - If the specified loop has a predictable
3905 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3906 /// object. The backedge-taken count is the number of times the loop header
3907 /// will be branched to from within the loop. This is one less than the
3908 /// trip count of the loop, since it doesn't count the first iteration,
3909 /// when the header is branched to from outside the loop.
3911 /// Note that it is not valid to call this method on a loop without a
3912 /// loop-invariant backedge-taken count (see
3913 /// hasLoopInvariantBackedgeTakenCount).
3915 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3916 return getBackedgeTakenInfo(L).getExact(this);
3919 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3920 /// return the least SCEV value that is known never to be less than the
3921 /// actual backedge taken count.
3922 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3923 return getBackedgeTakenInfo(L).getMax(this);
3926 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3927 /// onto the given Worklist.
3929 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3930 BasicBlock *Header = L->getHeader();
3932 // Push all Loop-header PHIs onto the Worklist stack.
3933 for (BasicBlock::iterator I = Header->begin();
3934 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3935 Worklist.push_back(PN);
3938 const ScalarEvolution::BackedgeTakenInfo &
3939 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3940 // Initially insert an invalid entry for this loop. If the insertion
3941 // succeeds, proceed to actually compute a backedge-taken count and
3942 // update the value. The temporary CouldNotCompute value tells SCEV
3943 // code elsewhere that it shouldn't attempt to request a new
3944 // backedge-taken count, which could result in infinite recursion.
3945 std::pair<DenseMap<const Loop *, BackedgeTakenInfo>::iterator, bool> Pair =
3946 BackedgeTakenCounts.insert(std::make_pair(L, BackedgeTakenInfo()));
3948 return Pair.first->second;
3950 // ComputeBackedgeTakenCount may allocate memory for its result. Inserting it
3951 // into the BackedgeTakenCounts map transfers ownership. Otherwise, the result
3952 // must be cleared in this scope.
3953 BackedgeTakenInfo Result = ComputeBackedgeTakenCount(L);
3955 if (Result.getExact(this) != getCouldNotCompute()) {
3956 assert(isLoopInvariant(Result.getExact(this), L) &&
3957 isLoopInvariant(Result.getMax(this), L) &&
3958 "Computed backedge-taken count isn't loop invariant for loop!");
3959 ++NumTripCountsComputed;
3961 else if (Result.getMax(this) == getCouldNotCompute() &&
3962 isa<PHINode>(L->getHeader()->begin())) {
3963 // Only count loops that have phi nodes as not being computable.
3964 ++NumTripCountsNotComputed;
3967 // Now that we know more about the trip count for this loop, forget any
3968 // existing SCEV values for PHI nodes in this loop since they are only
3969 // conservative estimates made without the benefit of trip count
3970 // information. This is similar to the code in forgetLoop, except that
3971 // it handles SCEVUnknown PHI nodes specially.
3972 if (Result.hasAnyInfo()) {
3973 SmallVector<Instruction *, 16> Worklist;
3974 PushLoopPHIs(L, Worklist);
3976 SmallPtrSet<Instruction *, 8> Visited;
3977 while (!Worklist.empty()) {
3978 Instruction *I = Worklist.pop_back_val();
3979 if (!Visited.insert(I)) continue;
3981 ValueExprMapType::iterator It =
3982 ValueExprMap.find(static_cast<Value *>(I));
3983 if (It != ValueExprMap.end()) {
3984 const SCEV *Old = It->second;
3986 // SCEVUnknown for a PHI either means that it has an unrecognized
3987 // structure, or it's a PHI that's in the progress of being computed
3988 // by createNodeForPHI. In the former case, additional loop trip
3989 // count information isn't going to change anything. In the later
3990 // case, createNodeForPHI will perform the necessary updates on its
3991 // own when it gets to that point.
3992 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(Old)) {
3993 forgetMemoizedResults(Old);
3994 ValueExprMap.erase(It);
3996 if (PHINode *PN = dyn_cast<PHINode>(I))
3997 ConstantEvolutionLoopExitValue.erase(PN);
4000 PushDefUseChildren(I, Worklist);
4004 // Re-lookup the insert position, since the call to
4005 // ComputeBackedgeTakenCount above could result in a
4006 // recusive call to getBackedgeTakenInfo (on a different
4007 // loop), which would invalidate the iterator computed
4009 return BackedgeTakenCounts.find(L)->second = Result;
4012 /// forgetLoop - This method should be called by the client when it has
4013 /// changed a loop in a way that may effect ScalarEvolution's ability to
4014 /// compute a trip count, or if the loop is deleted.
4015 void ScalarEvolution::forgetLoop(const Loop *L) {
4016 // Drop any stored trip count value.
4017 DenseMap<const Loop*, BackedgeTakenInfo>::iterator BTCPos =
4018 BackedgeTakenCounts.find(L);
4019 if (BTCPos != BackedgeTakenCounts.end()) {
4020 BTCPos->second.clear();
4021 BackedgeTakenCounts.erase(BTCPos);
4024 // Drop information about expressions based on loop-header PHIs.
4025 SmallVector<Instruction *, 16> Worklist;
4026 PushLoopPHIs(L, Worklist);
4028 SmallPtrSet<Instruction *, 8> Visited;
4029 while (!Worklist.empty()) {
4030 Instruction *I = Worklist.pop_back_val();
4031 if (!Visited.insert(I)) continue;
4033 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4034 if (It != ValueExprMap.end()) {
4035 forgetMemoizedResults(It->second);
4036 ValueExprMap.erase(It);
4037 if (PHINode *PN = dyn_cast<PHINode>(I))
4038 ConstantEvolutionLoopExitValue.erase(PN);
4041 PushDefUseChildren(I, Worklist);
4044 // Forget all contained loops too, to avoid dangling entries in the
4045 // ValuesAtScopes map.
4046 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4050 /// forgetValue - This method should be called by the client when it has
4051 /// changed a value in a way that may effect its value, or which may
4052 /// disconnect it from a def-use chain linking it to a loop.
4053 void ScalarEvolution::forgetValue(Value *V) {
4054 Instruction *I = dyn_cast<Instruction>(V);
4057 // Drop information about expressions based on loop-header PHIs.
4058 SmallVector<Instruction *, 16> Worklist;
4059 Worklist.push_back(I);
4061 SmallPtrSet<Instruction *, 8> Visited;
4062 while (!Worklist.empty()) {
4063 I = Worklist.pop_back_val();
4064 if (!Visited.insert(I)) continue;
4066 ValueExprMapType::iterator It = ValueExprMap.find(static_cast<Value *>(I));
4067 if (It != ValueExprMap.end()) {
4068 forgetMemoizedResults(It->second);
4069 ValueExprMap.erase(It);
4070 if (PHINode *PN = dyn_cast<PHINode>(I))
4071 ConstantEvolutionLoopExitValue.erase(PN);
4074 PushDefUseChildren(I, Worklist);
4078 /// getExact - Get the exact loop backedge taken count considering all loop
4079 /// exits. If all exits are computable, this is the minimum computed count.
4081 ScalarEvolution::BackedgeTakenInfo::getExact(ScalarEvolution *SE) const {
4082 // If any exits were not computable, the loop is not computable.
4083 if (!ExitNotTaken.isCompleteList()) return SE->getCouldNotCompute();
4085 // We need at least one computable exit.
4086 if (!ExitNotTaken.ExitingBlock) return SE->getCouldNotCompute();
4087 assert(ExitNotTaken.ExactNotTaken && "uninitialized not-taken info");
4089 const SCEV *BECount = 0;
4090 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4091 ENT != 0; ENT = ENT->getNextExit()) {
4093 assert(ENT->ExactNotTaken != SE->getCouldNotCompute() && "bad exit SCEV");
4096 BECount = ENT->ExactNotTaken;
4098 BECount = SE->getUMinFromMismatchedTypes(BECount, ENT->ExactNotTaken);
4100 assert(BECount && "Invalid not taken count for loop exit");
4104 /// getExact - Get the exact not taken count for this loop exit.
4106 ScalarEvolution::BackedgeTakenInfo::getExact(BasicBlock *ExitingBlock,
4107 ScalarEvolution *SE) const {
4108 for (const ExitNotTakenInfo *ENT = &ExitNotTaken;
4109 ENT != 0; ENT = ENT->getNextExit()) {
4111 if (ENT->ExitingBlock == ExitingBlock)
4112 return ENT->ExactNotTaken;
4114 return SE->getCouldNotCompute();
4117 /// getMax - Get the max backedge taken count for the loop.
4119 ScalarEvolution::BackedgeTakenInfo::getMax(ScalarEvolution *SE) const {
4120 return Max ? Max : SE->getCouldNotCompute();
4123 /// Allocate memory for BackedgeTakenInfo and copy the not-taken count of each
4124 /// computable exit into a persistent ExitNotTakenInfo array.
4125 ScalarEvolution::BackedgeTakenInfo::BackedgeTakenInfo(
4126 SmallVectorImpl< std::pair<BasicBlock *, const SCEV *> > &ExitCounts,
4127 bool Complete, const SCEV *MaxCount) : Max(MaxCount) {
4130 ExitNotTaken.setIncomplete();
4132 unsigned NumExits = ExitCounts.size();
4133 if (NumExits == 0) return;
4135 ExitNotTaken.ExitingBlock = ExitCounts[0].first;
4136 ExitNotTaken.ExactNotTaken = ExitCounts[0].second;
4137 if (NumExits == 1) return;
4139 // Handle the rare case of multiple computable exits.
4140 ExitNotTakenInfo *ENT = new ExitNotTakenInfo[NumExits-1];
4142 ExitNotTakenInfo *PrevENT = &ExitNotTaken;
4143 for (unsigned i = 1; i < NumExits; ++i, PrevENT = ENT, ++ENT) {
4144 PrevENT->setNextExit(ENT);
4145 ENT->ExitingBlock = ExitCounts[i].first;
4146 ENT->ExactNotTaken = ExitCounts[i].second;
4150 /// clear - Invalidate this result and free the ExitNotTakenInfo array.
4151 void ScalarEvolution::BackedgeTakenInfo::clear() {
4152 ExitNotTaken.ExitingBlock = 0;
4153 ExitNotTaken.ExactNotTaken = 0;
4154 delete[] ExitNotTaken.getNextExit();
4157 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
4158 /// of the specified loop will execute.
4159 ScalarEvolution::BackedgeTakenInfo
4160 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
4161 SmallVector<BasicBlock *, 8> ExitingBlocks;
4162 L->getExitingBlocks(ExitingBlocks);
4164 // Examine all exits and pick the most conservative values.
4165 const SCEV *MaxBECount = getCouldNotCompute();
4166 bool CouldComputeBECount = true;
4167 SmallVector<std::pair<BasicBlock *, const SCEV *>, 4> ExitCounts;
4168 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
4169 ExitLimit EL = ComputeExitLimit(L, ExitingBlocks[i]);
4170 if (EL.Exact == getCouldNotCompute())
4171 // We couldn't compute an exact value for this exit, so
4172 // we won't be able to compute an exact value for the loop.
4173 CouldComputeBECount = false;
4175 ExitCounts.push_back(std::make_pair(ExitingBlocks[i], EL.Exact));
4177 if (MaxBECount == getCouldNotCompute())
4178 MaxBECount = EL.Max;
4179 else if (EL.Max != getCouldNotCompute())
4180 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, EL.Max);
4183 return BackedgeTakenInfo(ExitCounts, CouldComputeBECount, MaxBECount);
4186 /// ComputeExitLimit - Compute the number of times the backedge of the specified
4187 /// loop will execute if it exits via the specified block.
4188 ScalarEvolution::ExitLimit
4189 ScalarEvolution::ComputeExitLimit(const Loop *L, BasicBlock *ExitingBlock) {
4191 // Okay, we've chosen an exiting block. See what condition causes us to
4192 // exit at this block.
4194 // FIXME: we should be able to handle switch instructions (with a single exit)
4195 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
4196 if (ExitBr == 0) return getCouldNotCompute();
4197 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
4199 // At this point, we know we have a conditional branch that determines whether
4200 // the loop is exited. However, we don't know if the branch is executed each
4201 // time through the loop. If not, then the execution count of the branch will
4202 // not be equal to the trip count of the loop.
4204 // Currently we check for this by checking to see if the Exit branch goes to
4205 // the loop header. If so, we know it will always execute the same number of
4206 // times as the loop. We also handle the case where the exit block *is* the
4207 // loop header. This is common for un-rotated loops.
4209 // If both of those tests fail, walk up the unique predecessor chain to the
4210 // header, stopping if there is an edge that doesn't exit the loop. If the
4211 // header is reached, the execution count of the branch will be equal to the
4212 // trip count of the loop.
4214 // More extensive analysis could be done to handle more cases here.
4216 if (ExitBr->getSuccessor(0) != L->getHeader() &&
4217 ExitBr->getSuccessor(1) != L->getHeader() &&
4218 ExitBr->getParent() != L->getHeader()) {
4219 // The simple checks failed, try climbing the unique predecessor chain
4220 // up to the header.
4222 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
4223 BasicBlock *Pred = BB->getUniquePredecessor();
4225 return getCouldNotCompute();
4226 TerminatorInst *PredTerm = Pred->getTerminator();
4227 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
4228 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
4231 // If the predecessor has a successor that isn't BB and isn't
4232 // outside the loop, assume the worst.
4233 if (L->contains(PredSucc))
4234 return getCouldNotCompute();
4236 if (Pred == L->getHeader()) {
4243 return getCouldNotCompute();
4246 // Proceed to the next level to examine the exit condition expression.
4247 return ComputeExitLimitFromCond(L, ExitBr->getCondition(),
4248 ExitBr->getSuccessor(0),
4249 ExitBr->getSuccessor(1));
4252 /// ComputeExitLimitFromCond - Compute the number of times the
4253 /// backedge of the specified loop will execute if its exit condition
4254 /// were a conditional branch of ExitCond, TBB, and FBB.
4255 ScalarEvolution::ExitLimit
4256 ScalarEvolution::ComputeExitLimitFromCond(const Loop *L,
4260 // Check if the controlling expression for this loop is an And or Or.
4261 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
4262 if (BO->getOpcode() == Instruction::And) {
4263 // Recurse on the operands of the and.
4264 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4265 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4266 const SCEV *BECount = getCouldNotCompute();
4267 const SCEV *MaxBECount = getCouldNotCompute();
4268 if (L->contains(TBB)) {
4269 // Both conditions must be true for the loop to continue executing.
4270 // Choose the less conservative count.
4271 if (EL0.Exact == getCouldNotCompute() ||
4272 EL1.Exact == getCouldNotCompute())
4273 BECount = getCouldNotCompute();
4275 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4276 if (EL0.Max == getCouldNotCompute())
4277 MaxBECount = EL1.Max;
4278 else if (EL1.Max == getCouldNotCompute())
4279 MaxBECount = EL0.Max;
4281 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4283 // Both conditions must be true at the same time for the loop to exit.
4284 // For now, be conservative.
4285 assert(L->contains(FBB) && "Loop block has no successor in loop!");
4286 if (EL0.Max == EL1.Max)
4287 MaxBECount = EL0.Max;
4288 if (EL0.Exact == EL1.Exact)
4289 BECount = EL0.Exact;
4292 return ExitLimit(BECount, MaxBECount);
4294 if (BO->getOpcode() == Instruction::Or) {
4295 // Recurse on the operands of the or.
4296 ExitLimit EL0 = ComputeExitLimitFromCond(L, BO->getOperand(0), TBB, FBB);
4297 ExitLimit EL1 = ComputeExitLimitFromCond(L, BO->getOperand(1), TBB, FBB);
4298 const SCEV *BECount = getCouldNotCompute();
4299 const SCEV *MaxBECount = getCouldNotCompute();
4300 if (L->contains(FBB)) {
4301 // Both conditions must be false for the loop to continue executing.
4302 // Choose the less conservative count.
4303 if (EL0.Exact == getCouldNotCompute() ||
4304 EL1.Exact == getCouldNotCompute())
4305 BECount = getCouldNotCompute();
4307 BECount = getUMinFromMismatchedTypes(EL0.Exact, EL1.Exact);
4308 if (EL0.Max == getCouldNotCompute())
4309 MaxBECount = EL1.Max;
4310 else if (EL1.Max == getCouldNotCompute())
4311 MaxBECount = EL0.Max;
4313 MaxBECount = getUMinFromMismatchedTypes(EL0.Max, EL1.Max);
4315 // Both conditions must be false at the same time for the loop to exit.
4316 // For now, be conservative.
4317 assert(L->contains(TBB) && "Loop block has no successor in loop!");
4318 if (EL0.Max == EL1.Max)
4319 MaxBECount = EL0.Max;
4320 if (EL0.Exact == EL1.Exact)
4321 BECount = EL0.Exact;
4324 return ExitLimit(BECount, MaxBECount);
4328 // With an icmp, it may be feasible to compute an exact backedge-taken count.
4329 // Proceed to the next level to examine the icmp.
4330 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
4331 return ComputeExitLimitFromICmp(L, ExitCondICmp, TBB, FBB);
4333 // Check for a constant condition. These are normally stripped out by
4334 // SimplifyCFG, but ScalarEvolution may be used by a pass which wishes to
4335 // preserve the CFG and is temporarily leaving constant conditions
4337 if (ConstantInt *CI = dyn_cast<ConstantInt>(ExitCond)) {
4338 if (L->contains(FBB) == !CI->getZExtValue())
4339 // The backedge is always taken.
4340 return getCouldNotCompute();
4342 // The backedge is never taken.
4343 return getConstant(CI->getType(), 0);
4346 // If it's not an integer or pointer comparison then compute it the hard way.
4347 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4350 /// ComputeExitLimitFromICmp - Compute the number of times the
4351 /// backedge of the specified loop will execute if its exit condition
4352 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
4353 ScalarEvolution::ExitLimit
4354 ScalarEvolution::ComputeExitLimitFromICmp(const Loop *L,
4359 // If the condition was exit on true, convert the condition to exit on false
4360 ICmpInst::Predicate Cond;
4361 if (!L->contains(FBB))
4362 Cond = ExitCond->getPredicate();
4364 Cond = ExitCond->getInversePredicate();
4366 // Handle common loops like: for (X = "string"; *X; ++X)
4367 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
4368 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
4370 ComputeLoadConstantCompareExitLimit(LI, RHS, L, Cond);
4371 if (ItCnt.hasAnyInfo())
4375 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
4376 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
4378 // Try to evaluate any dependencies out of the loop.
4379 LHS = getSCEVAtScope(LHS, L);
4380 RHS = getSCEVAtScope(RHS, L);
4382 // At this point, we would like to compute how many iterations of the
4383 // loop the predicate will return true for these inputs.
4384 if (isLoopInvariant(LHS, L) && !isLoopInvariant(RHS, L)) {
4385 // If there is a loop-invariant, force it into the RHS.
4386 std::swap(LHS, RHS);
4387 Cond = ICmpInst::getSwappedPredicate(Cond);
4390 // Simplify the operands before analyzing them.
4391 (void)SimplifyICmpOperands(Cond, LHS, RHS);
4393 // If we have a comparison of a chrec against a constant, try to use value
4394 // ranges to answer this query.
4395 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
4396 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
4397 if (AddRec->getLoop() == L) {
4398 // Form the constant range.
4399 ConstantRange CompRange(
4400 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
4402 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
4403 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
4407 case ICmpInst::ICMP_NE: { // while (X != Y)
4408 // Convert to: while (X-Y != 0)
4409 ExitLimit EL = HowFarToZero(getMinusSCEV(LHS, RHS), L);
4410 if (EL.hasAnyInfo()) return EL;
4413 case ICmpInst::ICMP_EQ: { // while (X == Y)
4414 // Convert to: while (X-Y == 0)
4415 ExitLimit EL = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
4416 if (EL.hasAnyInfo()) return EL;
4419 case ICmpInst::ICMP_SLT: {
4420 ExitLimit EL = HowManyLessThans(LHS, RHS, L, true);
4421 if (EL.hasAnyInfo()) return EL;
4424 case ICmpInst::ICMP_SGT: {
4425 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4426 getNotSCEV(RHS), L, true);
4427 if (EL.hasAnyInfo()) return EL;
4430 case ICmpInst::ICMP_ULT: {
4431 ExitLimit EL = HowManyLessThans(LHS, RHS, L, false);
4432 if (EL.hasAnyInfo()) return EL;
4435 case ICmpInst::ICMP_UGT: {
4436 ExitLimit EL = HowManyLessThans(getNotSCEV(LHS),
4437 getNotSCEV(RHS), L, false);
4438 if (EL.hasAnyInfo()) return EL;
4443 dbgs() << "ComputeBackedgeTakenCount ";
4444 if (ExitCond->getOperand(0)->getType()->isUnsigned())
4445 dbgs() << "[unsigned] ";
4446 dbgs() << *LHS << " "
4447 << Instruction::getOpcodeName(Instruction::ICmp)
4448 << " " << *RHS << "\n";
4452 return ComputeExitCountExhaustively(L, ExitCond, !L->contains(TBB));
4455 static ConstantInt *
4456 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
4457 ScalarEvolution &SE) {
4458 const SCEV *InVal = SE.getConstant(C);
4459 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
4460 assert(isa<SCEVConstant>(Val) &&
4461 "Evaluation of SCEV at constant didn't fold correctly?");
4462 return cast<SCEVConstant>(Val)->getValue();
4465 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
4466 /// and a GEP expression (missing the pointer index) indexing into it, return
4467 /// the addressed element of the initializer or null if the index expression is
4470 GetAddressedElementFromGlobal(GlobalVariable *GV,
4471 const std::vector<ConstantInt*> &Indices) {
4472 Constant *Init = GV->getInitializer();
4473 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
4474 uint64_t Idx = Indices[i]->getZExtValue();
4475 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
4476 assert(Idx < CS->getNumOperands() && "Bad struct index!");
4477 Init = cast<Constant>(CS->getOperand(Idx));
4478 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
4479 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
4480 Init = cast<Constant>(CA->getOperand(Idx));
4481 } else if (isa<ConstantAggregateZero>(Init)) {
4482 if (StructType *STy = dyn_cast<StructType>(Init->getType())) {
4483 assert(Idx < STy->getNumElements() && "Bad struct index!");
4484 Init = Constant::getNullValue(STy->getElementType(Idx));
4485 } else if (ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
4486 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
4487 Init = Constant::getNullValue(ATy->getElementType());
4489 llvm_unreachable("Unknown constant aggregate type!");
4493 return 0; // Unknown initializer type
4499 /// ComputeLoadConstantCompareExitLimit - Given an exit condition of
4500 /// 'icmp op load X, cst', try to see if we can compute the backedge
4501 /// execution count.
4502 ScalarEvolution::ExitLimit
4503 ScalarEvolution::ComputeLoadConstantCompareExitLimit(
4507 ICmpInst::Predicate predicate) {
4509 if (LI->isVolatile()) return getCouldNotCompute();
4511 // Check to see if the loaded pointer is a getelementptr of a global.
4512 // TODO: Use SCEV instead of manually grubbing with GEPs.
4513 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
4514 if (!GEP) return getCouldNotCompute();
4516 // Make sure that it is really a constant global we are gepping, with an
4517 // initializer, and make sure the first IDX is really 0.
4518 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
4519 if (!GV || !GV->isConstant() || !GV->hasDefinitiveInitializer() ||
4520 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
4521 !cast<Constant>(GEP->getOperand(1))->isNullValue())
4522 return getCouldNotCompute();
4524 // Okay, we allow one non-constant index into the GEP instruction.
4526 std::vector<ConstantInt*> Indexes;
4527 unsigned VarIdxNum = 0;
4528 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
4529 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
4530 Indexes.push_back(CI);
4531 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
4532 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
4533 VarIdx = GEP->getOperand(i);
4535 Indexes.push_back(0);
4538 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
4539 // Check to see if X is a loop variant variable value now.
4540 const SCEV *Idx = getSCEV(VarIdx);
4541 Idx = getSCEVAtScope(Idx, L);
4543 // We can only recognize very limited forms of loop index expressions, in
4544 // particular, only affine AddRec's like {C1,+,C2}.
4545 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
4546 if (!IdxExpr || !IdxExpr->isAffine() || isLoopInvariant(IdxExpr, L) ||
4547 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
4548 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
4549 return getCouldNotCompute();
4551 unsigned MaxSteps = MaxBruteForceIterations;
4552 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
4553 ConstantInt *ItCst = ConstantInt::get(
4554 cast<IntegerType>(IdxExpr->getType()), IterationNum);
4555 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
4557 // Form the GEP offset.
4558 Indexes[VarIdxNum] = Val;
4560 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
4561 if (Result == 0) break; // Cannot compute!
4563 // Evaluate the condition for this iteration.
4564 Result = ConstantExpr::getICmp(predicate, Result, RHS);
4565 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
4566 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
4568 dbgs() << "\n***\n*** Computed loop count " << *ItCst
4569 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
4572 ++NumArrayLenItCounts;
4573 return getConstant(ItCst); // Found terminating iteration!
4576 return getCouldNotCompute();
4580 /// CanConstantFold - Return true if we can constant fold an instruction of the
4581 /// specified type, assuming that all operands were constants.
4582 static bool CanConstantFold(const Instruction *I) {
4583 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
4584 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
4587 if (const CallInst *CI = dyn_cast<CallInst>(I))
4588 if (const Function *F = CI->getCalledFunction())
4589 return canConstantFoldCallTo(F);
4593 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
4594 /// in the loop that V is derived from. We allow arbitrary operations along the
4595 /// way, but the operands of an operation must either be constants or a value
4596 /// derived from a constant PHI. If this expression does not fit with these
4597 /// constraints, return null.
4598 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
4599 // If this is not an instruction, or if this is an instruction outside of the
4600 // loop, it can't be derived from a loop PHI.
4601 Instruction *I = dyn_cast<Instruction>(V);
4602 if (I == 0 || !L->contains(I)) return 0;
4604 if (PHINode *PN = dyn_cast<PHINode>(I)) {
4605 if (L->getHeader() == I->getParent())
4608 // We don't currently keep track of the control flow needed to evaluate
4609 // PHIs, so we cannot handle PHIs inside of loops.
4613 // If we won't be able to constant fold this expression even if the operands
4614 // are constants, return early.
4615 if (!CanConstantFold(I)) return 0;
4617 // Otherwise, we can evaluate this instruction if all of its operands are
4618 // constant or derived from a PHI node themselves.
4620 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
4621 if (!isa<Constant>(I->getOperand(Op))) {
4622 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
4623 if (P == 0) return 0; // Not evolving from PHI
4627 return 0; // Evolving from multiple different PHIs.
4630 // This is a expression evolving from a constant PHI!
4634 /// EvaluateExpression - Given an expression that passes the
4635 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
4636 /// in the loop has the value PHIVal. If we can't fold this expression for some
4637 /// reason, return null.
4638 static Constant *EvaluateExpression(Value *V, Constant *PHIVal,
4639 const TargetData *TD) {
4640 if (isa<PHINode>(V)) return PHIVal;
4641 if (Constant *C = dyn_cast<Constant>(V)) return C;
4642 Instruction *I = cast<Instruction>(V);
4644 std::vector<Constant*> Operands(I->getNumOperands());
4646 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4647 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal, TD);
4648 if (Operands[i] == 0) return 0;
4651 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4652 return ConstantFoldCompareInstOperands(CI->getPredicate(), Operands[0],
4654 return ConstantFoldInstOperands(I->getOpcode(), I->getType(), Operands, TD);
4657 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
4658 /// in the header of its containing loop, we know the loop executes a
4659 /// constant number of times, and the PHI node is just a recurrence
4660 /// involving constants, fold it.
4662 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
4665 DenseMap<PHINode*, Constant*>::const_iterator I =
4666 ConstantEvolutionLoopExitValue.find(PN);
4667 if (I != ConstantEvolutionLoopExitValue.end())
4670 if (BEs.ugt(MaxBruteForceIterations))
4671 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
4673 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
4675 // Since the loop is canonicalized, the PHI node must have two entries. One
4676 // entry must be a constant (coming in from outside of the loop), and the
4677 // second must be derived from the same PHI.
4678 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4679 Constant *StartCST =
4680 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4682 return RetVal = 0; // Must be a constant.
4684 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4685 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4686 !isa<Constant>(BEValue))
4687 return RetVal = 0; // Not derived from same PHI.
4689 // Execute the loop symbolically to determine the exit value.
4690 if (BEs.getActiveBits() >= 32)
4691 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
4693 unsigned NumIterations = BEs.getZExtValue(); // must be in range
4694 unsigned IterationNum = 0;
4695 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
4696 if (IterationNum == NumIterations)
4697 return RetVal = PHIVal; // Got exit value!
4699 // Compute the value of the PHI node for the next iteration.
4700 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4701 if (NextPHI == PHIVal)
4702 return RetVal = NextPHI; // Stopped evolving!
4704 return 0; // Couldn't evaluate!
4709 /// ComputeExitCountExhaustively - If the loop is known to execute a
4710 /// constant number of times (the condition evolves only from constants),
4711 /// try to evaluate a few iterations of the loop until we get the exit
4712 /// condition gets a value of ExitWhen (true or false). If we cannot
4713 /// evaluate the trip count of the loop, return getCouldNotCompute().
4714 const SCEV * ScalarEvolution::ComputeExitCountExhaustively(const Loop *L,
4717 PHINode *PN = getConstantEvolvingPHI(Cond, L);
4718 if (PN == 0) return getCouldNotCompute();
4720 // If the loop is canonicalized, the PHI will have exactly two entries.
4721 // That's the only form we support here.
4722 if (PN->getNumIncomingValues() != 2) return getCouldNotCompute();
4724 // One entry must be a constant (coming in from outside of the loop), and the
4725 // second must be derived from the same PHI.
4726 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
4727 Constant *StartCST =
4728 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
4729 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
4731 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
4732 if (getConstantEvolvingPHI(BEValue, L) != PN &&
4733 !isa<Constant>(BEValue))
4734 return getCouldNotCompute(); // Not derived from same PHI.
4736 // Okay, we find a PHI node that defines the trip count of this loop. Execute
4737 // the loop symbolically to determine when the condition gets a value of
4739 unsigned IterationNum = 0;
4740 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
4741 for (Constant *PHIVal = StartCST;
4742 IterationNum != MaxIterations; ++IterationNum) {
4743 ConstantInt *CondVal =
4744 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal, TD));
4746 // Couldn't symbolically evaluate.
4747 if (!CondVal) return getCouldNotCompute();
4749 if (CondVal->getValue() == uint64_t(ExitWhen)) {
4750 ++NumBruteForceTripCountsComputed;
4751 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
4754 // Compute the value of the PHI node for the next iteration.
4755 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal, TD);
4756 if (NextPHI == 0 || NextPHI == PHIVal)
4757 return getCouldNotCompute();// Couldn't evaluate or not making progress...
4761 // Too many iterations were needed to evaluate.
4762 return getCouldNotCompute();
4765 /// getSCEVAtScope - Return a SCEV expression for the specified value
4766 /// at the specified scope in the program. The L value specifies a loop
4767 /// nest to evaluate the expression at, where null is the top-level or a
4768 /// specified loop is immediately inside of the loop.
4770 /// This method can be used to compute the exit value for a variable defined
4771 /// in a loop by querying what the value will hold in the parent loop.
4773 /// In the case that a relevant loop exit value cannot be computed, the
4774 /// original value V is returned.
4775 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
4776 // Check to see if we've folded this expression at this loop before.
4777 std::map<const Loop *, const SCEV *> &Values = ValuesAtScopes[V];
4778 std::pair<std::map<const Loop *, const SCEV *>::iterator, bool> Pair =
4779 Values.insert(std::make_pair(L, static_cast<const SCEV *>(0)));
4781 return Pair.first->second ? Pair.first->second : V;
4783 // Otherwise compute it.
4784 const SCEV *C = computeSCEVAtScope(V, L);
4785 ValuesAtScopes[V][L] = C;
4789 const SCEV *ScalarEvolution::computeSCEVAtScope(const SCEV *V, const Loop *L) {
4790 if (isa<SCEVConstant>(V)) return V;
4792 // If this instruction is evolved from a constant-evolving PHI, compute the
4793 // exit value from the loop without using SCEVs.
4794 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
4795 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
4796 const Loop *LI = (*this->LI)[I->getParent()];
4797 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
4798 if (PHINode *PN = dyn_cast<PHINode>(I))
4799 if (PN->getParent() == LI->getHeader()) {
4800 // Okay, there is no closed form solution for the PHI node. Check
4801 // to see if the loop that contains it has a known backedge-taken
4802 // count. If so, we may be able to force computation of the exit
4804 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
4805 if (const SCEVConstant *BTCC =
4806 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
4807 // Okay, we know how many times the containing loop executes. If
4808 // this is a constant evolving PHI node, get the final value at
4809 // the specified iteration number.
4810 Constant *RV = getConstantEvolutionLoopExitValue(PN,
4811 BTCC->getValue()->getValue(),
4813 if (RV) return getSCEV(RV);
4817 // Okay, this is an expression that we cannot symbolically evaluate
4818 // into a SCEV. Check to see if it's possible to symbolically evaluate
4819 // the arguments into constants, and if so, try to constant propagate the
4820 // result. This is particularly useful for computing loop exit values.
4821 if (CanConstantFold(I)) {
4822 SmallVector<Constant *, 4> Operands;
4823 bool MadeImprovement = false;
4824 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
4825 Value *Op = I->getOperand(i);
4826 if (Constant *C = dyn_cast<Constant>(Op)) {
4827 Operands.push_back(C);
4831 // If any of the operands is non-constant and if they are
4832 // non-integer and non-pointer, don't even try to analyze them
4833 // with scev techniques.
4834 if (!isSCEVable(Op->getType()))
4837 const SCEV *OrigV = getSCEV(Op);
4838 const SCEV *OpV = getSCEVAtScope(OrigV, L);
4839 MadeImprovement |= OrigV != OpV;
4842 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
4844 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV))
4845 C = dyn_cast<Constant>(SU->getValue());
4847 if (C->getType() != Op->getType())
4848 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
4852 Operands.push_back(C);
4855 // Check to see if getSCEVAtScope actually made an improvement.
4856 if (MadeImprovement) {
4858 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
4859 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
4860 Operands[0], Operands[1], TD);
4862 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
4870 // This is some other type of SCEVUnknown, just return it.
4874 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
4875 // Avoid performing the look-up in the common case where the specified
4876 // expression has no loop-variant portions.
4877 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
4878 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4879 if (OpAtScope != Comm->getOperand(i)) {
4880 // Okay, at least one of these operands is loop variant but might be
4881 // foldable. Build a new instance of the folded commutative expression.
4882 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
4883 Comm->op_begin()+i);
4884 NewOps.push_back(OpAtScope);
4886 for (++i; i != e; ++i) {
4887 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
4888 NewOps.push_back(OpAtScope);
4890 if (isa<SCEVAddExpr>(Comm))
4891 return getAddExpr(NewOps);
4892 if (isa<SCEVMulExpr>(Comm))
4893 return getMulExpr(NewOps);
4894 if (isa<SCEVSMaxExpr>(Comm))
4895 return getSMaxExpr(NewOps);
4896 if (isa<SCEVUMaxExpr>(Comm))
4897 return getUMaxExpr(NewOps);
4898 llvm_unreachable("Unknown commutative SCEV type!");
4901 // If we got here, all operands are loop invariant.
4905 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
4906 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
4907 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
4908 if (LHS == Div->getLHS() && RHS == Div->getRHS())
4909 return Div; // must be loop invariant
4910 return getUDivExpr(LHS, RHS);
4913 // If this is a loop recurrence for a loop that does not contain L, then we
4914 // are dealing with the final value computed by the loop.
4915 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
4916 // First, attempt to evaluate each operand.
4917 // Avoid performing the look-up in the common case where the specified
4918 // expression has no loop-variant portions.
4919 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
4920 const SCEV *OpAtScope = getSCEVAtScope(AddRec->getOperand(i), L);
4921 if (OpAtScope == AddRec->getOperand(i))
4924 // Okay, at least one of these operands is loop variant but might be
4925 // foldable. Build a new instance of the folded commutative expression.
4926 SmallVector<const SCEV *, 8> NewOps(AddRec->op_begin(),
4927 AddRec->op_begin()+i);
4928 NewOps.push_back(OpAtScope);
4929 for (++i; i != e; ++i)
4930 NewOps.push_back(getSCEVAtScope(AddRec->getOperand(i), L));
4932 const SCEV *FoldedRec =
4933 getAddRecExpr(NewOps, AddRec->getLoop(),
4934 AddRec->getNoWrapFlags(SCEV::FlagNW));
4935 AddRec = dyn_cast<SCEVAddRecExpr>(FoldedRec);
4936 // The addrec may be folded to a nonrecurrence, for example, if the
4937 // induction variable is multiplied by zero after constant folding. Go
4938 // ahead and return the folded value.
4944 // If the scope is outside the addrec's loop, evaluate it by using the
4945 // loop exit value of the addrec.
4946 if (!AddRec->getLoop()->contains(L)) {
4947 // To evaluate this recurrence, we need to know how many times the AddRec
4948 // loop iterates. Compute this now.
4949 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
4950 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
4952 // Then, evaluate the AddRec.
4953 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
4959 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
4960 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4961 if (Op == Cast->getOperand())
4962 return Cast; // must be loop invariant
4963 return getZeroExtendExpr(Op, Cast->getType());
4966 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
4967 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4968 if (Op == Cast->getOperand())
4969 return Cast; // must be loop invariant
4970 return getSignExtendExpr(Op, Cast->getType());
4973 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
4974 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
4975 if (Op == Cast->getOperand())
4976 return Cast; // must be loop invariant
4977 return getTruncateExpr(Op, Cast->getType());
4980 llvm_unreachable("Unknown SCEV type!");
4984 /// getSCEVAtScope - This is a convenience function which does
4985 /// getSCEVAtScope(getSCEV(V), L).
4986 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
4987 return getSCEVAtScope(getSCEV(V), L);
4990 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
4991 /// following equation:
4993 /// A * X = B (mod N)
4995 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
4996 /// A and B isn't important.
4998 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
4999 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
5000 ScalarEvolution &SE) {
5001 uint32_t BW = A.getBitWidth();
5002 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
5003 assert(A != 0 && "A must be non-zero.");
5007 // The gcd of A and N may have only one prime factor: 2. The number of
5008 // trailing zeros in A is its multiplicity
5009 uint32_t Mult2 = A.countTrailingZeros();
5012 // 2. Check if B is divisible by D.
5014 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
5015 // is not less than multiplicity of this prime factor for D.
5016 if (B.countTrailingZeros() < Mult2)
5017 return SE.getCouldNotCompute();
5019 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
5022 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
5023 // bit width during computations.
5024 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
5025 APInt Mod(BW + 1, 0);
5026 Mod.setBit(BW - Mult2); // Mod = N / D
5027 APInt I = AD.multiplicativeInverse(Mod);
5029 // 4. Compute the minimum unsigned root of the equation:
5030 // I * (B / D) mod (N / D)
5031 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
5033 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
5035 return SE.getConstant(Result.trunc(BW));
5038 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
5039 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
5040 /// might be the same) or two SCEVCouldNotCompute objects.
5042 static std::pair<const SCEV *,const SCEV *>
5043 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
5044 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
5045 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
5046 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
5047 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
5049 // We currently can only solve this if the coefficients are constants.
5050 if (!LC || !MC || !NC) {
5051 const SCEV *CNC = SE.getCouldNotCompute();
5052 return std::make_pair(CNC, CNC);
5055 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
5056 const APInt &L = LC->getValue()->getValue();
5057 const APInt &M = MC->getValue()->getValue();
5058 const APInt &N = NC->getValue()->getValue();
5059 APInt Two(BitWidth, 2);
5060 APInt Four(BitWidth, 4);
5063 using namespace APIntOps;
5065 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
5066 // The B coefficient is M-N/2
5070 // The A coefficient is N/2
5071 APInt A(N.sdiv(Two));
5073 // Compute the B^2-4ac term.
5076 SqrtTerm -= Four * (A * C);
5078 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
5079 // integer value or else APInt::sqrt() will assert.
5080 APInt SqrtVal(SqrtTerm.sqrt());
5082 // Compute the two solutions for the quadratic formula.
5083 // The divisions must be performed as signed divisions.
5085 APInt TwoA( A << 1 );
5086 if (TwoA.isMinValue()) {
5087 const SCEV *CNC = SE.getCouldNotCompute();
5088 return std::make_pair(CNC, CNC);
5091 LLVMContext &Context = SE.getContext();
5093 ConstantInt *Solution1 =
5094 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
5095 ConstantInt *Solution2 =
5096 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
5098 return std::make_pair(SE.getConstant(Solution1),
5099 SE.getConstant(Solution2));
5100 } // end APIntOps namespace
5103 /// HowFarToZero - Return the number of times a backedge comparing the specified
5104 /// value to zero will execute. If not computable, return CouldNotCompute.
5106 /// This is only used for loops with a "x != y" exit test. The exit condition is
5107 /// now expressed as a single expression, V = x-y. So the exit test is
5108 /// effectively V != 0. We know and take advantage of the fact that this
5109 /// expression only being used in a comparison by zero context.
5110 ScalarEvolution::ExitLimit
5111 ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
5112 // If the value is a constant
5113 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5114 // If the value is already zero, the branch will execute zero times.
5115 if (C->getValue()->isZero()) return C;
5116 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5119 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
5120 if (!AddRec || AddRec->getLoop() != L)
5121 return getCouldNotCompute();
5123 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
5124 // the quadratic equation to solve it.
5125 if (AddRec->isQuadratic() && AddRec->getType()->isIntegerTy()) {
5126 std::pair<const SCEV *,const SCEV *> Roots =
5127 SolveQuadraticEquation(AddRec, *this);
5128 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
5129 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
5132 dbgs() << "HFTZ: " << *V << " - sol#1: " << *R1
5133 << " sol#2: " << *R2 << "\n";
5135 // Pick the smallest positive root value.
5136 if (ConstantInt *CB =
5137 dyn_cast<ConstantInt>(ConstantExpr::getICmp(CmpInst::ICMP_ULT,
5140 if (CB->getZExtValue() == false)
5141 std::swap(R1, R2); // R1 is the minimum root now.
5143 // We can only use this value if the chrec ends up with an exact zero
5144 // value at this index. When solving for "X*X != 5", for example, we
5145 // should not accept a root of 2.
5146 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
5148 return R1; // We found a quadratic root!
5151 return getCouldNotCompute();
5154 // Otherwise we can only handle this if it is affine.
5155 if (!AddRec->isAffine())
5156 return getCouldNotCompute();
5158 // If this is an affine expression, the execution count of this branch is
5159 // the minimum unsigned root of the following equation:
5161 // Start + Step*N = 0 (mod 2^BW)
5165 // Step*N = -Start (mod 2^BW)
5167 // where BW is the common bit width of Start and Step.
5169 // Get the initial value for the loop.
5170 const SCEV *Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
5171 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
5173 // For now we handle only constant steps.
5175 // TODO: Handle a nonconstant Step given AddRec<NUW>. If the
5176 // AddRec is NUW, then (in an unsigned sense) it cannot be counting up to wrap
5177 // to 0, it must be counting down to equal 0. Consequently, N = Start / -Step.
5178 // We have not yet seen any such cases.
5179 const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step);
5181 return getCouldNotCompute();
5183 // For positive steps (counting up until unsigned overflow):
5184 // N = -Start/Step (as unsigned)
5185 // For negative steps (counting down to zero):
5187 // First compute the unsigned distance from zero in the direction of Step.
5188 bool CountDown = StepC->getValue()->getValue().isNegative();
5189 const SCEV *Distance = CountDown ? Start : getNegativeSCEV(Start);
5191 // Handle unitary steps, which cannot wraparound.
5192 // 1*N = -Start; -1*N = Start (mod 2^BW), so:
5193 // N = Distance (as unsigned)
5194 if (StepC->getValue()->equalsInt(1) || StepC->getValue()->isAllOnesValue())
5197 // If the recurrence is known not to wraparound, unsigned divide computes the
5198 // back edge count. We know that the value will either become zero (and thus
5199 // the loop terminates), that the loop will terminate through some other exit
5200 // condition first, or that the loop has undefined behavior. This means
5201 // we can't "miss" the exit value, even with nonunit stride.
5203 // FIXME: Prove that loops always exhibits *acceptable* undefined
5204 // behavior. Loops must exhibit defined behavior until a wrapped value is
5205 // actually used. So the trip count computed by udiv could be smaller than the
5206 // number of well-defined iterations.
5207 if (AddRec->getNoWrapFlags(SCEV::FlagNW))
5208 // FIXME: We really want an "isexact" bit for udiv.
5209 return getUDivExpr(Distance, CountDown ? getNegativeSCEV(Step) : Step);
5211 // Then, try to solve the above equation provided that Start is constant.
5212 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
5213 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
5214 -StartC->getValue()->getValue(),
5216 return getCouldNotCompute();
5219 /// HowFarToNonZero - Return the number of times a backedge checking the
5220 /// specified value for nonzero will execute. If not computable, return
5222 ScalarEvolution::ExitLimit
5223 ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
5224 // Loops that look like: while (X == 0) are very strange indeed. We don't
5225 // handle them yet except for the trivial case. This could be expanded in the
5226 // future as needed.
5228 // If the value is a constant, check to see if it is known to be non-zero
5229 // already. If so, the backedge will execute zero times.
5230 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
5231 if (!C->getValue()->isNullValue())
5232 return getConstant(C->getType(), 0);
5233 return getCouldNotCompute(); // Otherwise it will loop infinitely.
5236 // We could implement others, but I really doubt anyone writes loops like
5237 // this, and if they did, they would already be constant folded.
5238 return getCouldNotCompute();
5241 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
5242 /// (which may not be an immediate predecessor) which has exactly one
5243 /// successor from which BB is reachable, or null if no such block is
5246 std::pair<BasicBlock *, BasicBlock *>
5247 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
5248 // If the block has a unique predecessor, then there is no path from the
5249 // predecessor to the block that does not go through the direct edge
5250 // from the predecessor to the block.
5251 if (BasicBlock *Pred = BB->getSinglePredecessor())
5252 return std::make_pair(Pred, BB);
5254 // A loop's header is defined to be a block that dominates the loop.
5255 // If the header has a unique predecessor outside the loop, it must be
5256 // a block that has exactly one successor that can reach the loop.
5257 if (Loop *L = LI->getLoopFor(BB))
5258 return std::make_pair(L->getLoopPredecessor(), L->getHeader());
5260 return std::pair<BasicBlock *, BasicBlock *>();
5263 /// HasSameValue - SCEV structural equivalence is usually sufficient for
5264 /// testing whether two expressions are equal, however for the purposes of
5265 /// looking for a condition guarding a loop, it can be useful to be a little
5266 /// more general, since a front-end may have replicated the controlling
5269 static bool HasSameValue(const SCEV *A, const SCEV *B) {
5270 // Quick check to see if they are the same SCEV.
5271 if (A == B) return true;
5273 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
5274 // two different instructions with the same value. Check for this case.
5275 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
5276 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
5277 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
5278 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
5279 if (AI->isIdenticalTo(BI) && !AI->mayReadFromMemory())
5282 // Otherwise assume they may have a different value.
5286 /// SimplifyICmpOperands - Simplify LHS and RHS in a comparison with
5287 /// predicate Pred. Return true iff any changes were made.
5289 bool ScalarEvolution::SimplifyICmpOperands(ICmpInst::Predicate &Pred,
5290 const SCEV *&LHS, const SCEV *&RHS) {
5291 bool Changed = false;
5293 // Canonicalize a constant to the right side.
5294 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
5295 // Check for both operands constant.
5296 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
5297 if (ConstantExpr::getICmp(Pred,
5299 RHSC->getValue())->isNullValue())
5300 goto trivially_false;
5302 goto trivially_true;
5304 // Otherwise swap the operands to put the constant on the right.
5305 std::swap(LHS, RHS);
5306 Pred = ICmpInst::getSwappedPredicate(Pred);
5310 // If we're comparing an addrec with a value which is loop-invariant in the
5311 // addrec's loop, put the addrec on the left. Also make a dominance check,
5312 // as both operands could be addrecs loop-invariant in each other's loop.
5313 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS)) {
5314 const Loop *L = AR->getLoop();
5315 if (isLoopInvariant(LHS, L) && properlyDominates(LHS, L->getHeader())) {
5316 std::swap(LHS, RHS);
5317 Pred = ICmpInst::getSwappedPredicate(Pred);
5322 // If there's a constant operand, canonicalize comparisons with boundary
5323 // cases, and canonicalize *-or-equal comparisons to regular comparisons.
5324 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
5325 const APInt &RA = RC->getValue()->getValue();
5327 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5328 case ICmpInst::ICMP_EQ:
5329 case ICmpInst::ICMP_NE:
5331 case ICmpInst::ICMP_UGE:
5332 if ((RA - 1).isMinValue()) {
5333 Pred = ICmpInst::ICMP_NE;
5334 RHS = getConstant(RA - 1);
5338 if (RA.isMaxValue()) {
5339 Pred = ICmpInst::ICMP_EQ;
5343 if (RA.isMinValue()) goto trivially_true;
5345 Pred = ICmpInst::ICMP_UGT;
5346 RHS = getConstant(RA - 1);
5349 case ICmpInst::ICMP_ULE:
5350 if ((RA + 1).isMaxValue()) {
5351 Pred = ICmpInst::ICMP_NE;
5352 RHS = getConstant(RA + 1);
5356 if (RA.isMinValue()) {
5357 Pred = ICmpInst::ICMP_EQ;
5361 if (RA.isMaxValue()) goto trivially_true;
5363 Pred = ICmpInst::ICMP_ULT;
5364 RHS = getConstant(RA + 1);
5367 case ICmpInst::ICMP_SGE:
5368 if ((RA - 1).isMinSignedValue()) {
5369 Pred = ICmpInst::ICMP_NE;
5370 RHS = getConstant(RA - 1);
5374 if (RA.isMaxSignedValue()) {
5375 Pred = ICmpInst::ICMP_EQ;
5379 if (RA.isMinSignedValue()) goto trivially_true;
5381 Pred = ICmpInst::ICMP_SGT;
5382 RHS = getConstant(RA - 1);
5385 case ICmpInst::ICMP_SLE:
5386 if ((RA + 1).isMaxSignedValue()) {
5387 Pred = ICmpInst::ICMP_NE;
5388 RHS = getConstant(RA + 1);
5392 if (RA.isMinSignedValue()) {
5393 Pred = ICmpInst::ICMP_EQ;
5397 if (RA.isMaxSignedValue()) goto trivially_true;
5399 Pred = ICmpInst::ICMP_SLT;
5400 RHS = getConstant(RA + 1);
5403 case ICmpInst::ICMP_UGT:
5404 if (RA.isMinValue()) {
5405 Pred = ICmpInst::ICMP_NE;
5409 if ((RA + 1).isMaxValue()) {
5410 Pred = ICmpInst::ICMP_EQ;
5411 RHS = getConstant(RA + 1);
5415 if (RA.isMaxValue()) goto trivially_false;
5417 case ICmpInst::ICMP_ULT:
5418 if (RA.isMaxValue()) {
5419 Pred = ICmpInst::ICMP_NE;
5423 if ((RA - 1).isMinValue()) {
5424 Pred = ICmpInst::ICMP_EQ;
5425 RHS = getConstant(RA - 1);
5429 if (RA.isMinValue()) goto trivially_false;
5431 case ICmpInst::ICMP_SGT:
5432 if (RA.isMinSignedValue()) {
5433 Pred = ICmpInst::ICMP_NE;
5437 if ((RA + 1).isMaxSignedValue()) {
5438 Pred = ICmpInst::ICMP_EQ;
5439 RHS = getConstant(RA + 1);
5443 if (RA.isMaxSignedValue()) goto trivially_false;
5445 case ICmpInst::ICMP_SLT:
5446 if (RA.isMaxSignedValue()) {
5447 Pred = ICmpInst::ICMP_NE;
5451 if ((RA - 1).isMinSignedValue()) {
5452 Pred = ICmpInst::ICMP_EQ;
5453 RHS = getConstant(RA - 1);
5457 if (RA.isMinSignedValue()) goto trivially_false;
5462 // Check for obvious equality.
5463 if (HasSameValue(LHS, RHS)) {
5464 if (ICmpInst::isTrueWhenEqual(Pred))
5465 goto trivially_true;
5466 if (ICmpInst::isFalseWhenEqual(Pred))
5467 goto trivially_false;
5470 // If possible, canonicalize GE/LE comparisons to GT/LT comparisons, by
5471 // adding or subtracting 1 from one of the operands.
5473 case ICmpInst::ICMP_SLE:
5474 if (!getSignedRange(RHS).getSignedMax().isMaxSignedValue()) {
5475 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5477 Pred = ICmpInst::ICMP_SLT;
5479 } else if (!getSignedRange(LHS).getSignedMin().isMinSignedValue()) {
5480 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5482 Pred = ICmpInst::ICMP_SLT;
5486 case ICmpInst::ICMP_SGE:
5487 if (!getSignedRange(RHS).getSignedMin().isMinSignedValue()) {
5488 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5490 Pred = ICmpInst::ICMP_SGT;
5492 } else if (!getSignedRange(LHS).getSignedMax().isMaxSignedValue()) {
5493 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5495 Pred = ICmpInst::ICMP_SGT;
5499 case ICmpInst::ICMP_ULE:
5500 if (!getUnsignedRange(RHS).getUnsignedMax().isMaxValue()) {
5501 RHS = getAddExpr(getConstant(RHS->getType(), 1, true), RHS,
5503 Pred = ICmpInst::ICMP_ULT;
5505 } else if (!getUnsignedRange(LHS).getUnsignedMin().isMinValue()) {
5506 LHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), LHS,
5508 Pred = ICmpInst::ICMP_ULT;
5512 case ICmpInst::ICMP_UGE:
5513 if (!getUnsignedRange(RHS).getUnsignedMin().isMinValue()) {
5514 RHS = getAddExpr(getConstant(RHS->getType(), (uint64_t)-1, true), RHS,
5516 Pred = ICmpInst::ICMP_UGT;
5518 } else if (!getUnsignedRange(LHS).getUnsignedMax().isMaxValue()) {
5519 LHS = getAddExpr(getConstant(RHS->getType(), 1, true), LHS,
5521 Pred = ICmpInst::ICMP_UGT;
5529 // TODO: More simplifications are possible here.
5535 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5536 Pred = ICmpInst::ICMP_EQ;
5541 LHS = RHS = getConstant(ConstantInt::getFalse(getContext()));
5542 Pred = ICmpInst::ICMP_NE;
5546 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
5547 return getSignedRange(S).getSignedMax().isNegative();
5550 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
5551 return getSignedRange(S).getSignedMin().isStrictlyPositive();
5554 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
5555 return !getSignedRange(S).getSignedMin().isNegative();
5558 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
5559 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
5562 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
5563 return isKnownNegative(S) || isKnownPositive(S);
5566 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
5567 const SCEV *LHS, const SCEV *RHS) {
5568 // Canonicalize the inputs first.
5569 (void)SimplifyICmpOperands(Pred, LHS, RHS);
5571 // If LHS or RHS is an addrec, check to see if the condition is true in
5572 // every iteration of the loop.
5573 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
5574 if (isLoopEntryGuardedByCond(
5575 AR->getLoop(), Pred, AR->getStart(), RHS) &&
5576 isLoopBackedgeGuardedByCond(
5577 AR->getLoop(), Pred, AR->getPostIncExpr(*this), RHS))
5579 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(RHS))
5580 if (isLoopEntryGuardedByCond(
5581 AR->getLoop(), Pred, LHS, AR->getStart()) &&
5582 isLoopBackedgeGuardedByCond(
5583 AR->getLoop(), Pred, LHS, AR->getPostIncExpr(*this)))
5586 // Otherwise see what can be done with known constant ranges.
5587 return isKnownPredicateWithRanges(Pred, LHS, RHS);
5591 ScalarEvolution::isKnownPredicateWithRanges(ICmpInst::Predicate Pred,
5592 const SCEV *LHS, const SCEV *RHS) {
5593 if (HasSameValue(LHS, RHS))
5594 return ICmpInst::isTrueWhenEqual(Pred);
5596 // This code is split out from isKnownPredicate because it is called from
5597 // within isLoopEntryGuardedByCond.
5600 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5602 case ICmpInst::ICMP_SGT:
5603 Pred = ICmpInst::ICMP_SLT;
5604 std::swap(LHS, RHS);
5605 case ICmpInst::ICMP_SLT: {
5606 ConstantRange LHSRange = getSignedRange(LHS);
5607 ConstantRange RHSRange = getSignedRange(RHS);
5608 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
5610 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
5614 case ICmpInst::ICMP_SGE:
5615 Pred = ICmpInst::ICMP_SLE;
5616 std::swap(LHS, RHS);
5617 case ICmpInst::ICMP_SLE: {
5618 ConstantRange LHSRange = getSignedRange(LHS);
5619 ConstantRange RHSRange = getSignedRange(RHS);
5620 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
5622 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
5626 case ICmpInst::ICMP_UGT:
5627 Pred = ICmpInst::ICMP_ULT;
5628 std::swap(LHS, RHS);
5629 case ICmpInst::ICMP_ULT: {
5630 ConstantRange LHSRange = getUnsignedRange(LHS);
5631 ConstantRange RHSRange = getUnsignedRange(RHS);
5632 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
5634 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
5638 case ICmpInst::ICMP_UGE:
5639 Pred = ICmpInst::ICMP_ULE;
5640 std::swap(LHS, RHS);
5641 case ICmpInst::ICMP_ULE: {
5642 ConstantRange LHSRange = getUnsignedRange(LHS);
5643 ConstantRange RHSRange = getUnsignedRange(RHS);
5644 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
5646 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
5650 case ICmpInst::ICMP_NE: {
5651 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
5653 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
5656 const SCEV *Diff = getMinusSCEV(LHS, RHS);
5657 if (isKnownNonZero(Diff))
5661 case ICmpInst::ICMP_EQ:
5662 // The check at the top of the function catches the case where
5663 // the values are known to be equal.
5669 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
5670 /// protected by a conditional between LHS and RHS. This is used to
5671 /// to eliminate casts.
5673 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
5674 ICmpInst::Predicate Pred,
5675 const SCEV *LHS, const SCEV *RHS) {
5676 // Interpret a null as meaning no loop, where there is obviously no guard
5677 // (interprocedural conditions notwithstanding).
5678 if (!L) return true;
5680 BasicBlock *Latch = L->getLoopLatch();
5684 BranchInst *LoopContinuePredicate =
5685 dyn_cast<BranchInst>(Latch->getTerminator());
5686 if (!LoopContinuePredicate ||
5687 LoopContinuePredicate->isUnconditional())
5690 return isImpliedCond(Pred, LHS, RHS,
5691 LoopContinuePredicate->getCondition(),
5692 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
5695 /// isLoopEntryGuardedByCond - Test whether entry to the loop is protected
5696 /// by a conditional between LHS and RHS. This is used to help avoid max
5697 /// expressions in loop trip counts, and to eliminate casts.
5699 ScalarEvolution::isLoopEntryGuardedByCond(const Loop *L,
5700 ICmpInst::Predicate Pred,
5701 const SCEV *LHS, const SCEV *RHS) {
5702 // Interpret a null as meaning no loop, where there is obviously no guard
5703 // (interprocedural conditions notwithstanding).
5704 if (!L) return false;
5706 // Starting at the loop predecessor, climb up the predecessor chain, as long
5707 // as there are predecessors that can be found that have unique successors
5708 // leading to the original header.
5709 for (std::pair<BasicBlock *, BasicBlock *>
5710 Pair(L->getLoopPredecessor(), L->getHeader());
5712 Pair = getPredecessorWithUniqueSuccessorForBB(Pair.first)) {
5714 BranchInst *LoopEntryPredicate =
5715 dyn_cast<BranchInst>(Pair.first->getTerminator());
5716 if (!LoopEntryPredicate ||
5717 LoopEntryPredicate->isUnconditional())
5720 if (isImpliedCond(Pred, LHS, RHS,
5721 LoopEntryPredicate->getCondition(),
5722 LoopEntryPredicate->getSuccessor(0) != Pair.second))
5729 /// isImpliedCond - Test whether the condition described by Pred, LHS,
5730 /// and RHS is true whenever the given Cond value evaluates to true.
5731 bool ScalarEvolution::isImpliedCond(ICmpInst::Predicate Pred,
5732 const SCEV *LHS, const SCEV *RHS,
5733 Value *FoundCondValue,
5735 // Recursively handle And and Or conditions.
5736 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(FoundCondValue)) {
5737 if (BO->getOpcode() == Instruction::And) {
5739 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5740 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5741 } else if (BO->getOpcode() == Instruction::Or) {
5743 return isImpliedCond(Pred, LHS, RHS, BO->getOperand(0), Inverse) ||
5744 isImpliedCond(Pred, LHS, RHS, BO->getOperand(1), Inverse);
5748 ICmpInst *ICI = dyn_cast<ICmpInst>(FoundCondValue);
5749 if (!ICI) return false;
5751 // Bail if the ICmp's operands' types are wider than the needed type
5752 // before attempting to call getSCEV on them. This avoids infinite
5753 // recursion, since the analysis of widening casts can require loop
5754 // exit condition information for overflow checking, which would
5756 if (getTypeSizeInBits(LHS->getType()) <
5757 getTypeSizeInBits(ICI->getOperand(0)->getType()))
5760 // Now that we found a conditional branch that dominates the loop, check to
5761 // see if it is the comparison we are looking for.
5762 ICmpInst::Predicate FoundPred;
5764 FoundPred = ICI->getInversePredicate();
5766 FoundPred = ICI->getPredicate();
5768 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
5769 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
5771 // Balance the types. The case where FoundLHS' type is wider than
5772 // LHS' type is checked for above.
5773 if (getTypeSizeInBits(LHS->getType()) >
5774 getTypeSizeInBits(FoundLHS->getType())) {
5775 if (CmpInst::isSigned(Pred)) {
5776 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
5777 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
5779 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
5780 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
5784 // Canonicalize the query to match the way instcombine will have
5785 // canonicalized the comparison.
5786 if (SimplifyICmpOperands(Pred, LHS, RHS))
5788 return CmpInst::isTrueWhenEqual(Pred);
5789 if (SimplifyICmpOperands(FoundPred, FoundLHS, FoundRHS))
5790 if (FoundLHS == FoundRHS)
5791 return CmpInst::isFalseWhenEqual(Pred);
5793 // Check to see if we can make the LHS or RHS match.
5794 if (LHS == FoundRHS || RHS == FoundLHS) {
5795 if (isa<SCEVConstant>(RHS)) {
5796 std::swap(FoundLHS, FoundRHS);
5797 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
5799 std::swap(LHS, RHS);
5800 Pred = ICmpInst::getSwappedPredicate(Pred);
5804 // Check whether the found predicate is the same as the desired predicate.
5805 if (FoundPred == Pred)
5806 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
5808 // Check whether swapping the found predicate makes it the same as the
5809 // desired predicate.
5810 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
5811 if (isa<SCEVConstant>(RHS))
5812 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
5814 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
5815 RHS, LHS, FoundLHS, FoundRHS);
5818 // Check whether the actual condition is beyond sufficient.
5819 if (FoundPred == ICmpInst::ICMP_EQ)
5820 if (ICmpInst::isTrueWhenEqual(Pred))
5821 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
5823 if (Pred == ICmpInst::ICMP_NE)
5824 if (!ICmpInst::isTrueWhenEqual(FoundPred))
5825 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
5828 // Otherwise assume the worst.
5832 /// isImpliedCondOperands - Test whether the condition described by Pred,
5833 /// LHS, and RHS is true whenever the condition described by Pred, FoundLHS,
5834 /// and FoundRHS is true.
5835 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
5836 const SCEV *LHS, const SCEV *RHS,
5837 const SCEV *FoundLHS,
5838 const SCEV *FoundRHS) {
5839 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
5840 FoundLHS, FoundRHS) ||
5841 // ~x < ~y --> x > y
5842 isImpliedCondOperandsHelper(Pred, LHS, RHS,
5843 getNotSCEV(FoundRHS),
5844 getNotSCEV(FoundLHS));
5847 /// isImpliedCondOperandsHelper - Test whether the condition described by
5848 /// Pred, LHS, and RHS is true whenever the condition described by Pred,
5849 /// FoundLHS, and FoundRHS is true.
5851 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
5852 const SCEV *LHS, const SCEV *RHS,
5853 const SCEV *FoundLHS,
5854 const SCEV *FoundRHS) {
5856 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
5857 case ICmpInst::ICMP_EQ:
5858 case ICmpInst::ICMP_NE:
5859 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
5862 case ICmpInst::ICMP_SLT:
5863 case ICmpInst::ICMP_SLE:
5864 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
5865 isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, RHS, FoundRHS))
5868 case ICmpInst::ICMP_SGT:
5869 case ICmpInst::ICMP_SGE:
5870 if (isKnownPredicateWithRanges(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
5871 isKnownPredicateWithRanges(ICmpInst::ICMP_SLE, RHS, FoundRHS))
5874 case ICmpInst::ICMP_ULT:
5875 case ICmpInst::ICMP_ULE:
5876 if (isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
5877 isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, RHS, FoundRHS))
5880 case ICmpInst::ICMP_UGT:
5881 case ICmpInst::ICMP_UGE:
5882 if (isKnownPredicateWithRanges(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
5883 isKnownPredicateWithRanges(ICmpInst::ICMP_ULE, RHS, FoundRHS))
5891 /// getBECount - Subtract the end and start values and divide by the step,
5892 /// rounding up, to get the number of times the backedge is executed. Return
5893 /// CouldNotCompute if an intermediate computation overflows.
5894 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
5898 assert(!isKnownNegative(Step) &&
5899 "This code doesn't handle negative strides yet!");
5901 Type *Ty = Start->getType();
5903 // When Start == End, we have an exact BECount == 0. Short-circuit this case
5904 // here because SCEV may not be able to determine that the unsigned division
5905 // after rounding is zero.
5907 return getConstant(Ty, 0);
5909 const SCEV *NegOne = getConstant(Ty, (uint64_t)-1);
5910 const SCEV *Diff = getMinusSCEV(End, Start);
5911 const SCEV *RoundUp = getAddExpr(Step, NegOne);
5913 // Add an adjustment to the difference between End and Start so that
5914 // the division will effectively round up.
5915 const SCEV *Add = getAddExpr(Diff, RoundUp);
5918 // Check Add for unsigned overflow.
5919 // TODO: More sophisticated things could be done here.
5920 Type *WideTy = IntegerType::get(getContext(),
5921 getTypeSizeInBits(Ty) + 1);
5922 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
5923 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
5924 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
5925 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
5926 return getCouldNotCompute();
5929 return getUDivExpr(Add, Step);
5932 /// HowManyLessThans - Return the number of times a backedge containing the
5933 /// specified less-than comparison will execute. If not computable, return
5934 /// CouldNotCompute.
5935 ScalarEvolution::ExitLimit
5936 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
5937 const Loop *L, bool isSigned) {
5938 // Only handle: "ADDREC < LoopInvariant".
5939 if (!isLoopInvariant(RHS, L)) return getCouldNotCompute();
5941 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
5942 if (!AddRec || AddRec->getLoop() != L)
5943 return getCouldNotCompute();
5945 // Check to see if we have a flag which makes analysis easy.
5946 bool NoWrap = isSigned ? AddRec->getNoWrapFlags(SCEV::FlagNSW) :
5947 AddRec->getNoWrapFlags(SCEV::FlagNUW);
5949 if (AddRec->isAffine()) {
5950 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
5951 const SCEV *Step = AddRec->getStepRecurrence(*this);
5954 return getCouldNotCompute();
5955 if (Step->isOne()) {
5956 // With unit stride, the iteration never steps past the limit value.
5957 } else if (isKnownPositive(Step)) {
5958 // Test whether a positive iteration can step past the limit
5959 // value and past the maximum value for its type in a single step.
5960 // Note that it's not sufficient to check NoWrap here, because even
5961 // though the value after a wrap is undefined, it's not undefined
5962 // behavior, so if wrap does occur, the loop could either terminate or
5963 // loop infinitely, but in either case, the loop is guaranteed to
5964 // iterate at least until the iteration where the wrapping occurs.
5965 const SCEV *One = getConstant(Step->getType(), 1);
5967 APInt Max = APInt::getSignedMaxValue(BitWidth);
5968 if ((Max - getSignedRange(getMinusSCEV(Step, One)).getSignedMax())
5969 .slt(getSignedRange(RHS).getSignedMax()))
5970 return getCouldNotCompute();
5972 APInt Max = APInt::getMaxValue(BitWidth);
5973 if ((Max - getUnsignedRange(getMinusSCEV(Step, One)).getUnsignedMax())
5974 .ult(getUnsignedRange(RHS).getUnsignedMax()))
5975 return getCouldNotCompute();
5978 // TODO: Handle negative strides here and below.
5979 return getCouldNotCompute();
5981 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
5982 // m. So, we count the number of iterations in which {n,+,s} < m is true.
5983 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
5984 // treat m-n as signed nor unsigned due to overflow possibility.
5986 // First, we get the value of the LHS in the first iteration: n
5987 const SCEV *Start = AddRec->getOperand(0);
5989 // Determine the minimum constant start value.
5990 const SCEV *MinStart = getConstant(isSigned ?
5991 getSignedRange(Start).getSignedMin() :
5992 getUnsignedRange(Start).getUnsignedMin());
5994 // If we know that the condition is true in order to enter the loop,
5995 // then we know that it will run exactly (m-n)/s times. Otherwise, we
5996 // only know that it will execute (max(m,n)-n)/s times. In both cases,
5997 // the division must round up.
5998 const SCEV *End = RHS;
5999 if (!isLoopEntryGuardedByCond(L,
6000 isSigned ? ICmpInst::ICMP_SLT :
6002 getMinusSCEV(Start, Step), RHS))
6003 End = isSigned ? getSMaxExpr(RHS, Start)
6004 : getUMaxExpr(RHS, Start);
6006 // Determine the maximum constant end value.
6007 const SCEV *MaxEnd = getConstant(isSigned ?
6008 getSignedRange(End).getSignedMax() :
6009 getUnsignedRange(End).getUnsignedMax());
6011 // If MaxEnd is within a step of the maximum integer value in its type,
6012 // adjust it down to the minimum value which would produce the same effect.
6013 // This allows the subsequent ceiling division of (N+(step-1))/step to
6014 // compute the correct value.
6015 const SCEV *StepMinusOne = getMinusSCEV(Step,
6016 getConstant(Step->getType(), 1));
6019 getMinusSCEV(getConstant(APInt::getSignedMaxValue(BitWidth)),
6022 getMinusSCEV(getConstant(APInt::getMaxValue(BitWidth)),
6025 // Finally, we subtract these two values and divide, rounding up, to get
6026 // the number of times the backedge is executed.
6027 const SCEV *BECount = getBECount(Start, End, Step, NoWrap);
6029 // The maximum backedge count is similar, except using the minimum start
6030 // value and the maximum end value.
6031 // If we already have an exact constant BECount, use it instead.
6032 const SCEV *MaxBECount = isa<SCEVConstant>(BECount) ? BECount
6033 : getBECount(MinStart, MaxEnd, Step, NoWrap);
6035 // If the stride is nonconstant, and NoWrap == true, then
6036 // getBECount(MinStart, MaxEnd) may not compute. This would result in an
6037 // exact BECount and invalid MaxBECount, which should be avoided to catch
6038 // more optimization opportunities.
6039 if (isa<SCEVCouldNotCompute>(MaxBECount))
6040 MaxBECount = BECount;
6042 return ExitLimit(BECount, MaxBECount);
6045 return getCouldNotCompute();
6048 /// getNumIterationsInRange - Return the number of iterations of this loop that
6049 /// produce values in the specified constant range. Another way of looking at
6050 /// this is that it returns the first iteration number where the value is not in
6051 /// the condition, thus computing the exit count. If the iteration count can't
6052 /// be computed, an instance of SCEVCouldNotCompute is returned.
6053 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
6054 ScalarEvolution &SE) const {
6055 if (Range.isFullSet()) // Infinite loop.
6056 return SE.getCouldNotCompute();
6058 // If the start is a non-zero constant, shift the range to simplify things.
6059 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
6060 if (!SC->getValue()->isZero()) {
6061 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
6062 Operands[0] = SE.getConstant(SC->getType(), 0);
6063 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop(),
6064 getNoWrapFlags(FlagNW));
6065 if (const SCEVAddRecExpr *ShiftedAddRec =
6066 dyn_cast<SCEVAddRecExpr>(Shifted))
6067 return ShiftedAddRec->getNumIterationsInRange(
6068 Range.subtract(SC->getValue()->getValue()), SE);
6069 // This is strange and shouldn't happen.
6070 return SE.getCouldNotCompute();
6073 // The only time we can solve this is when we have all constant indices.
6074 // Otherwise, we cannot determine the overflow conditions.
6075 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
6076 if (!isa<SCEVConstant>(getOperand(i)))
6077 return SE.getCouldNotCompute();
6080 // Okay at this point we know that all elements of the chrec are constants and
6081 // that the start element is zero.
6083 // First check to see if the range contains zero. If not, the first
6085 unsigned BitWidth = SE.getTypeSizeInBits(getType());
6086 if (!Range.contains(APInt(BitWidth, 0)))
6087 return SE.getConstant(getType(), 0);
6090 // If this is an affine expression then we have this situation:
6091 // Solve {0,+,A} in Range === Ax in Range
6093 // We know that zero is in the range. If A is positive then we know that
6094 // the upper value of the range must be the first possible exit value.
6095 // If A is negative then the lower of the range is the last possible loop
6096 // value. Also note that we already checked for a full range.
6097 APInt One(BitWidth,1);
6098 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
6099 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
6101 // The exit value should be (End+A)/A.
6102 APInt ExitVal = (End + A).udiv(A);
6103 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
6105 // Evaluate at the exit value. If we really did fall out of the valid
6106 // range, then we computed our trip count, otherwise wrap around or other
6107 // things must have happened.
6108 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
6109 if (Range.contains(Val->getValue()))
6110 return SE.getCouldNotCompute(); // Something strange happened
6112 // Ensure that the previous value is in the range. This is a sanity check.
6113 assert(Range.contains(
6114 EvaluateConstantChrecAtConstant(this,
6115 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
6116 "Linear scev computation is off in a bad way!");
6117 return SE.getConstant(ExitValue);
6118 } else if (isQuadratic()) {
6119 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
6120 // quadratic equation to solve it. To do this, we must frame our problem in
6121 // terms of figuring out when zero is crossed, instead of when
6122 // Range.getUpper() is crossed.
6123 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
6124 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
6125 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop(),
6126 // getNoWrapFlags(FlagNW)
6129 // Next, solve the constructed addrec
6130 std::pair<const SCEV *,const SCEV *> Roots =
6131 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
6132 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
6133 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
6135 // Pick the smallest positive root value.
6136 if (ConstantInt *CB =
6137 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
6138 R1->getValue(), R2->getValue()))) {
6139 if (CB->getZExtValue() == false)
6140 std::swap(R1, R2); // R1 is the minimum root now.
6142 // Make sure the root is not off by one. The returned iteration should
6143 // not be in the range, but the previous one should be. When solving
6144 // for "X*X < 5", for example, we should not return a root of 2.
6145 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
6148 if (Range.contains(R1Val->getValue())) {
6149 // The next iteration must be out of the range...
6150 ConstantInt *NextVal =
6151 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
6153 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6154 if (!Range.contains(R1Val->getValue()))
6155 return SE.getConstant(NextVal);
6156 return SE.getCouldNotCompute(); // Something strange happened
6159 // If R1 was not in the range, then it is a good return value. Make
6160 // sure that R1-1 WAS in the range though, just in case.
6161 ConstantInt *NextVal =
6162 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
6163 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
6164 if (Range.contains(R1Val->getValue()))
6166 return SE.getCouldNotCompute(); // Something strange happened
6171 return SE.getCouldNotCompute();
6176 //===----------------------------------------------------------------------===//
6177 // SCEVCallbackVH Class Implementation
6178 //===----------------------------------------------------------------------===//
6180 void ScalarEvolution::SCEVCallbackVH::deleted() {
6181 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6182 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
6183 SE->ConstantEvolutionLoopExitValue.erase(PN);
6184 SE->ValueExprMap.erase(getValPtr());
6185 // this now dangles!
6188 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *V) {
6189 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
6191 // Forget all the expressions associated with users of the old value,
6192 // so that future queries will recompute the expressions using the new
6194 Value *Old = getValPtr();
6195 SmallVector<User *, 16> Worklist;
6196 SmallPtrSet<User *, 8> Visited;
6197 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
6199 Worklist.push_back(*UI);
6200 while (!Worklist.empty()) {
6201 User *U = Worklist.pop_back_val();
6202 // Deleting the Old value will cause this to dangle. Postpone
6203 // that until everything else is done.
6206 if (!Visited.insert(U))
6208 if (PHINode *PN = dyn_cast<PHINode>(U))
6209 SE->ConstantEvolutionLoopExitValue.erase(PN);
6210 SE->ValueExprMap.erase(U);
6211 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
6213 Worklist.push_back(*UI);
6215 // Delete the Old value.
6216 if (PHINode *PN = dyn_cast<PHINode>(Old))
6217 SE->ConstantEvolutionLoopExitValue.erase(PN);
6218 SE->ValueExprMap.erase(Old);
6219 // this now dangles!
6222 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
6223 : CallbackVH(V), SE(se) {}
6225 //===----------------------------------------------------------------------===//
6226 // ScalarEvolution Class Implementation
6227 //===----------------------------------------------------------------------===//
6229 ScalarEvolution::ScalarEvolution()
6230 : FunctionPass(ID), FirstUnknown(0) {
6231 initializeScalarEvolutionPass(*PassRegistry::getPassRegistry());
6234 bool ScalarEvolution::runOnFunction(Function &F) {
6236 LI = &getAnalysis<LoopInfo>();
6237 TD = getAnalysisIfAvailable<TargetData>();
6238 DT = &getAnalysis<DominatorTree>();
6242 void ScalarEvolution::releaseMemory() {
6243 // Iterate through all the SCEVUnknown instances and call their
6244 // destructors, so that they release their references to their values.
6245 for (SCEVUnknown *U = FirstUnknown; U; U = U->Next)
6249 ValueExprMap.clear();
6251 // Free any extra memory created for ExitNotTakenInfo in the unlikely event
6252 // that a loop had multiple computable exits.
6253 for (DenseMap<const Loop*, BackedgeTakenInfo>::iterator I =
6254 BackedgeTakenCounts.begin(), E = BackedgeTakenCounts.end();
6259 BackedgeTakenCounts.clear();
6260 ConstantEvolutionLoopExitValue.clear();
6261 ValuesAtScopes.clear();
6262 LoopDispositions.clear();
6263 BlockDispositions.clear();
6264 UnsignedRanges.clear();
6265 SignedRanges.clear();
6266 UniqueSCEVs.clear();
6267 SCEVAllocator.Reset();
6270 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
6271 AU.setPreservesAll();
6272 AU.addRequiredTransitive<LoopInfo>();
6273 AU.addRequiredTransitive<DominatorTree>();
6276 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
6277 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
6280 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
6282 // Print all inner loops first
6283 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
6284 PrintLoopInfo(OS, SE, *I);
6287 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6290 SmallVector<BasicBlock *, 8> ExitBlocks;
6291 L->getExitBlocks(ExitBlocks);
6292 if (ExitBlocks.size() != 1)
6293 OS << "<multiple exits> ";
6295 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
6296 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
6298 OS << "Unpredictable backedge-taken count. ";
6303 WriteAsOperand(OS, L->getHeader(), /*PrintType=*/false);
6306 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
6307 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
6309 OS << "Unpredictable max backedge-taken count. ";
6315 void ScalarEvolution::print(raw_ostream &OS, const Module *) const {
6316 // ScalarEvolution's implementation of the print method is to print
6317 // out SCEV values of all instructions that are interesting. Doing
6318 // this potentially causes it to create new SCEV objects though,
6319 // which technically conflicts with the const qualifier. This isn't
6320 // observable from outside the class though, so casting away the
6321 // const isn't dangerous.
6322 ScalarEvolution &SE = *const_cast<ScalarEvolution *>(this);
6324 OS << "Classifying expressions for: ";
6325 WriteAsOperand(OS, F, /*PrintType=*/false);
6327 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
6328 if (isSCEVable(I->getType()) && !isa<CmpInst>(*I)) {
6331 const SCEV *SV = SE.getSCEV(&*I);
6334 const Loop *L = LI->getLoopFor((*I).getParent());
6336 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
6343 OS << "\t\t" "Exits: ";
6344 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
6345 if (!SE.isLoopInvariant(ExitValue, L)) {
6346 OS << "<<Unknown>>";
6355 OS << "Determining loop execution counts for: ";
6356 WriteAsOperand(OS, F, /*PrintType=*/false);
6358 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
6359 PrintLoopInfo(OS, &SE, *I);
6362 ScalarEvolution::LoopDisposition
6363 ScalarEvolution::getLoopDisposition(const SCEV *S, const Loop *L) {
6364 std::map<const Loop *, LoopDisposition> &Values = LoopDispositions[S];
6365 std::pair<std::map<const Loop *, LoopDisposition>::iterator, bool> Pair =
6366 Values.insert(std::make_pair(L, LoopVariant));
6368 return Pair.first->second;
6370 LoopDisposition D = computeLoopDisposition(S, L);
6371 return LoopDispositions[S][L] = D;
6374 ScalarEvolution::LoopDisposition
6375 ScalarEvolution::computeLoopDisposition(const SCEV *S, const Loop *L) {
6376 switch (S->getSCEVType()) {
6378 return LoopInvariant;
6382 return getLoopDisposition(cast<SCEVCastExpr>(S)->getOperand(), L);
6383 case scAddRecExpr: {
6384 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6386 // If L is the addrec's loop, it's computable.
6387 if (AR->getLoop() == L)
6388 return LoopComputable;
6390 // Add recurrences are never invariant in the function-body (null loop).
6394 // This recurrence is variant w.r.t. L if L contains AR's loop.
6395 if (L->contains(AR->getLoop()))
6398 // This recurrence is invariant w.r.t. L if AR's loop contains L.
6399 if (AR->getLoop()->contains(L))
6400 return LoopInvariant;
6402 // This recurrence is variant w.r.t. L if any of its operands
6404 for (SCEVAddRecExpr::op_iterator I = AR->op_begin(), E = AR->op_end();
6406 if (!isLoopInvariant(*I, L))
6409 // Otherwise it's loop-invariant.
6410 return LoopInvariant;
6416 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6417 bool HasVarying = false;
6418 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6420 LoopDisposition D = getLoopDisposition(*I, L);
6421 if (D == LoopVariant)
6423 if (D == LoopComputable)
6426 return HasVarying ? LoopComputable : LoopInvariant;
6429 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6430 LoopDisposition LD = getLoopDisposition(UDiv->getLHS(), L);
6431 if (LD == LoopVariant)
6433 LoopDisposition RD = getLoopDisposition(UDiv->getRHS(), L);
6434 if (RD == LoopVariant)
6436 return (LD == LoopInvariant && RD == LoopInvariant) ?
6437 LoopInvariant : LoopComputable;
6440 // All non-instruction values are loop invariant. All instructions are loop
6441 // invariant if they are not contained in the specified loop.
6442 // Instructions are never considered invariant in the function body
6443 // (null loop) because they are defined within the "loop".
6444 if (Instruction *I = dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue()))
6445 return (L && !L->contains(I)) ? LoopInvariant : LoopVariant;
6446 return LoopInvariant;
6447 case scCouldNotCompute:
6448 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6452 llvm_unreachable("Unknown SCEV kind!");
6456 bool ScalarEvolution::isLoopInvariant(const SCEV *S, const Loop *L) {
6457 return getLoopDisposition(S, L) == LoopInvariant;
6460 bool ScalarEvolution::hasComputableLoopEvolution(const SCEV *S, const Loop *L) {
6461 return getLoopDisposition(S, L) == LoopComputable;
6464 ScalarEvolution::BlockDisposition
6465 ScalarEvolution::getBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6466 std::map<const BasicBlock *, BlockDisposition> &Values = BlockDispositions[S];
6467 std::pair<std::map<const BasicBlock *, BlockDisposition>::iterator, bool>
6468 Pair = Values.insert(std::make_pair(BB, DoesNotDominateBlock));
6470 return Pair.first->second;
6472 BlockDisposition D = computeBlockDisposition(S, BB);
6473 return BlockDispositions[S][BB] = D;
6476 ScalarEvolution::BlockDisposition
6477 ScalarEvolution::computeBlockDisposition(const SCEV *S, const BasicBlock *BB) {
6478 switch (S->getSCEVType()) {
6480 return ProperlyDominatesBlock;
6484 return getBlockDisposition(cast<SCEVCastExpr>(S)->getOperand(), BB);
6485 case scAddRecExpr: {
6486 // This uses a "dominates" query instead of "properly dominates" query
6487 // to test for proper dominance too, because the instruction which
6488 // produces the addrec's value is a PHI, and a PHI effectively properly
6489 // dominates its entire containing block.
6490 const SCEVAddRecExpr *AR = cast<SCEVAddRecExpr>(S);
6491 if (!DT->dominates(AR->getLoop()->getHeader(), BB))
6492 return DoesNotDominateBlock;
6494 // FALL THROUGH into SCEVNAryExpr handling.
6499 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6501 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6503 BlockDisposition D = getBlockDisposition(*I, BB);
6504 if (D == DoesNotDominateBlock)
6505 return DoesNotDominateBlock;
6506 if (D == DominatesBlock)
6509 return Proper ? ProperlyDominatesBlock : DominatesBlock;
6512 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6513 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6514 BlockDisposition LD = getBlockDisposition(LHS, BB);
6515 if (LD == DoesNotDominateBlock)
6516 return DoesNotDominateBlock;
6517 BlockDisposition RD = getBlockDisposition(RHS, BB);
6518 if (RD == DoesNotDominateBlock)
6519 return DoesNotDominateBlock;
6520 return (LD == ProperlyDominatesBlock && RD == ProperlyDominatesBlock) ?
6521 ProperlyDominatesBlock : DominatesBlock;
6524 if (Instruction *I =
6525 dyn_cast<Instruction>(cast<SCEVUnknown>(S)->getValue())) {
6526 if (I->getParent() == BB)
6527 return DominatesBlock;
6528 if (DT->properlyDominates(I->getParent(), BB))
6529 return ProperlyDominatesBlock;
6530 return DoesNotDominateBlock;
6532 return ProperlyDominatesBlock;
6533 case scCouldNotCompute:
6534 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6535 return DoesNotDominateBlock;
6538 llvm_unreachable("Unknown SCEV kind!");
6539 return DoesNotDominateBlock;
6542 bool ScalarEvolution::dominates(const SCEV *S, const BasicBlock *BB) {
6543 return getBlockDisposition(S, BB) >= DominatesBlock;
6546 bool ScalarEvolution::properlyDominates(const SCEV *S, const BasicBlock *BB) {
6547 return getBlockDisposition(S, BB) == ProperlyDominatesBlock;
6550 bool ScalarEvolution::hasOperand(const SCEV *S, const SCEV *Op) const {
6551 switch (S->getSCEVType()) {
6556 case scSignExtend: {
6557 const SCEVCastExpr *Cast = cast<SCEVCastExpr>(S);
6558 const SCEV *CastOp = Cast->getOperand();
6559 return Op == CastOp || hasOperand(CastOp, Op);
6566 const SCEVNAryExpr *NAry = cast<SCEVNAryExpr>(S);
6567 for (SCEVNAryExpr::op_iterator I = NAry->op_begin(), E = NAry->op_end();
6569 const SCEV *NAryOp = *I;
6570 if (NAryOp == Op || hasOperand(NAryOp, Op))
6576 const SCEVUDivExpr *UDiv = cast<SCEVUDivExpr>(S);
6577 const SCEV *LHS = UDiv->getLHS(), *RHS = UDiv->getRHS();
6578 return LHS == Op || hasOperand(LHS, Op) ||
6579 RHS == Op || hasOperand(RHS, Op);
6583 case scCouldNotCompute:
6584 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
6588 llvm_unreachable("Unknown SCEV kind!");
6592 void ScalarEvolution::forgetMemoizedResults(const SCEV *S) {
6593 ValuesAtScopes.erase(S);
6594 LoopDispositions.erase(S);
6595 BlockDispositions.erase(S);
6596 UnsignedRanges.erase(S);
6597 SignedRanges.erase(S);