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. These classes are reference counted, managed by the const SCEV *
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.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/LoopInfo.h"
73 #include "llvm/Analysis/ValueTracking.h"
74 #include "llvm/Assembly/Writer.h"
75 #include "llvm/Target/TargetData.h"
76 #include "llvm/Support/CommandLine.h"
77 #include "llvm/Support/Compiler.h"
78 #include "llvm/Support/ConstantRange.h"
79 #include "llvm/Support/ErrorHandling.h"
80 #include "llvm/Support/GetElementPtrTypeIterator.h"
81 #include "llvm/Support/InstIterator.h"
82 #include "llvm/Support/MathExtras.h"
83 #include "llvm/Support/raw_ostream.h"
84 #include "llvm/ADT/Statistic.h"
85 #include "llvm/ADT/STLExtras.h"
86 #include "llvm/ADT/SmallPtrSet.h"
90 STATISTIC(NumArrayLenItCounts,
91 "Number of trip counts computed with array length");
92 STATISTIC(NumTripCountsComputed,
93 "Number of loops with predictable loop counts");
94 STATISTIC(NumTripCountsNotComputed,
95 "Number of loops without predictable loop counts");
96 STATISTIC(NumBruteForceTripCountsComputed,
97 "Number of loops with trip counts computed by force");
99 static cl::opt<unsigned>
100 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
101 cl::desc("Maximum number of iterations SCEV will "
102 "symbolically execute a constant "
106 static RegisterPass<ScalarEvolution>
107 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
108 char ScalarEvolution::ID = 0;
110 //===----------------------------------------------------------------------===//
111 // SCEV class definitions
112 //===----------------------------------------------------------------------===//
114 //===----------------------------------------------------------------------===//
115 // Implementation of the SCEV class.
120 void SCEV::dump() const {
125 void SCEV::print(std::ostream &o) const {
126 raw_os_ostream OS(o);
130 bool SCEV::isZero() const {
131 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
132 return SC->getValue()->isZero();
136 bool SCEV::isOne() const {
137 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
138 return SC->getValue()->isOne();
142 bool SCEV::isAllOnesValue() const {
143 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
144 return SC->getValue()->isAllOnesValue();
148 SCEVCouldNotCompute::SCEVCouldNotCompute() :
149 SCEV(FoldingSetNodeID(), scCouldNotCompute) {}
151 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
152 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
156 const Type *SCEVCouldNotCompute::getType() const {
157 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
161 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
162 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
167 SCEVCouldNotCompute::replaceSymbolicValuesWithConcrete(
170 ScalarEvolution &SE) const {
174 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
175 OS << "***COULDNOTCOMPUTE***";
178 bool SCEVCouldNotCompute::classof(const SCEV *S) {
179 return S->getSCEVType() == scCouldNotCompute;
182 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
184 ID.AddInteger(scConstant);
187 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
188 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>();
189 new (S) SCEVConstant(ID, V);
190 UniqueSCEVs.InsertNode(S, IP);
194 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
195 return getConstant(Context->getConstantInt(Val));
199 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
201 Context->getConstantInt(cast<IntegerType>(Ty), V, isSigned));
204 const Type *SCEVConstant::getType() const { return V->getType(); }
206 void SCEVConstant::print(raw_ostream &OS) const {
207 WriteAsOperand(OS, V, false);
210 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID,
211 unsigned SCEVTy, const SCEV *op, const Type *ty)
212 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
214 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
215 return Op->dominates(BB, DT);
218 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID,
219 const SCEV *op, const Type *ty)
220 : SCEVCastExpr(ID, scTruncate, op, ty) {
221 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
222 (Ty->isInteger() || isa<PointerType>(Ty)) &&
223 "Cannot truncate non-integer value!");
226 void SCEVTruncateExpr::print(raw_ostream &OS) const {
227 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
230 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID,
231 const SCEV *op, const Type *ty)
232 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
233 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
234 (Ty->isInteger() || isa<PointerType>(Ty)) &&
235 "Cannot zero extend non-integer value!");
238 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
239 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
242 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID,
243 const SCEV *op, const Type *ty)
244 : SCEVCastExpr(ID, scSignExtend, op, ty) {
245 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
246 (Ty->isInteger() || isa<PointerType>(Ty)) &&
247 "Cannot sign extend non-integer value!");
250 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
251 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
254 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
255 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
256 const char *OpStr = getOperationStr();
257 OS << "(" << *Operands[0];
258 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
259 OS << OpStr << *Operands[i];
264 SCEVCommutativeExpr::replaceSymbolicValuesWithConcrete(
267 ScalarEvolution &SE) const {
268 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
270 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
271 if (H != getOperand(i)) {
272 SmallVector<const SCEV *, 8> NewOps;
273 NewOps.reserve(getNumOperands());
274 for (unsigned j = 0; j != i; ++j)
275 NewOps.push_back(getOperand(j));
277 for (++i; i != e; ++i)
278 NewOps.push_back(getOperand(i)->
279 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
281 if (isa<SCEVAddExpr>(this))
282 return SE.getAddExpr(NewOps);
283 else if (isa<SCEVMulExpr>(this))
284 return SE.getMulExpr(NewOps);
285 else if (isa<SCEVSMaxExpr>(this))
286 return SE.getSMaxExpr(NewOps);
287 else if (isa<SCEVUMaxExpr>(this))
288 return SE.getUMaxExpr(NewOps);
290 llvm_unreachable("Unknown commutative expr!");
296 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
297 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
298 if (!getOperand(i)->dominates(BB, DT))
304 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
305 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
308 void SCEVUDivExpr::print(raw_ostream &OS) const {
309 OS << "(" << *LHS << " /u " << *RHS << ")";
312 const Type *SCEVUDivExpr::getType() const {
313 // In most cases the types of LHS and RHS will be the same, but in some
314 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
315 // depend on the type for correctness, but handling types carefully can
316 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
317 // a pointer type than the RHS, so use the RHS' type here.
318 return RHS->getType();
322 SCEVAddRecExpr::replaceSymbolicValuesWithConcrete(const SCEV *Sym,
324 ScalarEvolution &SE) const {
325 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
327 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
328 if (H != getOperand(i)) {
329 SmallVector<const SCEV *, 8> NewOps;
330 NewOps.reserve(getNumOperands());
331 for (unsigned j = 0; j != i; ++j)
332 NewOps.push_back(getOperand(j));
334 for (++i; i != e; ++i)
335 NewOps.push_back(getOperand(i)->
336 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
338 return SE.getAddRecExpr(NewOps, L);
345 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
346 // Add recurrences are never invariant in the function-body (null loop).
350 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
351 if (QueryLoop->contains(L->getHeader()))
354 // This recurrence is variant w.r.t. QueryLoop if any of its operands
356 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
357 if (!getOperand(i)->isLoopInvariant(QueryLoop))
360 // Otherwise it's loop-invariant.
364 void SCEVAddRecExpr::print(raw_ostream &OS) const {
365 OS << "{" << *Operands[0];
366 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
367 OS << ",+," << *Operands[i];
368 OS << "}<" << L->getHeader()->getName() + ">";
371 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
372 // All non-instruction values are loop invariant. All instructions are loop
373 // invariant if they are not contained in the specified loop.
374 // Instructions are never considered invariant in the function body
375 // (null loop) because they are defined within the "loop".
376 if (Instruction *I = dyn_cast<Instruction>(V))
377 return L && !L->contains(I->getParent());
381 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
382 if (Instruction *I = dyn_cast<Instruction>(getValue()))
383 return DT->dominates(I->getParent(), BB);
387 const Type *SCEVUnknown::getType() const {
391 void SCEVUnknown::print(raw_ostream &OS) const {
392 WriteAsOperand(OS, V, false);
395 //===----------------------------------------------------------------------===//
397 //===----------------------------------------------------------------------===//
400 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
401 /// than the complexity of the RHS. This comparator is used to canonicalize
403 class VISIBILITY_HIDDEN SCEVComplexityCompare {
406 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
408 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
409 // Primarily, sort the SCEVs by their getSCEVType().
410 if (LHS->getSCEVType() != RHS->getSCEVType())
411 return LHS->getSCEVType() < RHS->getSCEVType();
413 // Aside from the getSCEVType() ordering, the particular ordering
414 // isn't very important except that it's beneficial to be consistent,
415 // so that (a + b) and (b + a) don't end up as different expressions.
417 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
418 // not as complete as it could be.
419 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
420 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
422 // Order pointer values after integer values. This helps SCEVExpander
424 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
426 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
429 // Compare getValueID values.
430 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
431 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
433 // Sort arguments by their position.
434 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
435 const Argument *RA = cast<Argument>(RU->getValue());
436 return LA->getArgNo() < RA->getArgNo();
439 // For instructions, compare their loop depth, and their opcode.
440 // This is pretty loose.
441 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
442 Instruction *RV = cast<Instruction>(RU->getValue());
444 // Compare loop depths.
445 if (LI->getLoopDepth(LV->getParent()) !=
446 LI->getLoopDepth(RV->getParent()))
447 return LI->getLoopDepth(LV->getParent()) <
448 LI->getLoopDepth(RV->getParent());
451 if (LV->getOpcode() != RV->getOpcode())
452 return LV->getOpcode() < RV->getOpcode();
454 // Compare the number of operands.
455 if (LV->getNumOperands() != RV->getNumOperands())
456 return LV->getNumOperands() < RV->getNumOperands();
462 // Compare constant values.
463 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
464 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
465 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
466 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
467 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
470 // Compare addrec loop depths.
471 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
472 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
473 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
474 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
477 // Lexicographically compare n-ary expressions.
478 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
479 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
480 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
481 if (i >= RC->getNumOperands())
483 if (operator()(LC->getOperand(i), RC->getOperand(i)))
485 if (operator()(RC->getOperand(i), LC->getOperand(i)))
488 return LC->getNumOperands() < RC->getNumOperands();
491 // Lexicographically compare udiv expressions.
492 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
493 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
494 if (operator()(LC->getLHS(), RC->getLHS()))
496 if (operator()(RC->getLHS(), LC->getLHS()))
498 if (operator()(LC->getRHS(), RC->getRHS()))
500 if (operator()(RC->getRHS(), LC->getRHS()))
505 // Compare cast expressions by operand.
506 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
507 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
508 return operator()(LC->getOperand(), RC->getOperand());
511 llvm_unreachable("Unknown SCEV kind!");
517 /// GroupByComplexity - Given a list of SCEV objects, order them by their
518 /// complexity, and group objects of the same complexity together by value.
519 /// When this routine is finished, we know that any duplicates in the vector are
520 /// consecutive and that complexity is monotonically increasing.
522 /// Note that we go take special precautions to ensure that we get determinstic
523 /// results from this routine. In other words, we don't want the results of
524 /// this to depend on where the addresses of various SCEV objects happened to
527 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
529 if (Ops.size() < 2) return; // Noop
530 if (Ops.size() == 2) {
531 // This is the common case, which also happens to be trivially simple.
533 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
534 std::swap(Ops[0], Ops[1]);
538 // Do the rough sort by complexity.
539 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
541 // Now that we are sorted by complexity, group elements of the same
542 // complexity. Note that this is, at worst, N^2, but the vector is likely to
543 // be extremely short in practice. Note that we take this approach because we
544 // do not want to depend on the addresses of the objects we are grouping.
545 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
546 const SCEV *S = Ops[i];
547 unsigned Complexity = S->getSCEVType();
549 // If there are any objects of the same complexity and same value as this
551 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
552 if (Ops[j] == S) { // Found a duplicate.
553 // Move it to immediately after i'th element.
554 std::swap(Ops[i+1], Ops[j]);
555 ++i; // no need to rescan it.
556 if (i == e-2) return; // Done!
564 //===----------------------------------------------------------------------===//
565 // Simple SCEV method implementations
566 //===----------------------------------------------------------------------===//
568 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
570 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
572 const Type* ResultTy) {
573 // Handle the simplest case efficiently.
575 return SE.getTruncateOrZeroExtend(It, ResultTy);
577 // We are using the following formula for BC(It, K):
579 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
581 // Suppose, W is the bitwidth of the return value. We must be prepared for
582 // overflow. Hence, we must assure that the result of our computation is
583 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
584 // safe in modular arithmetic.
586 // However, this code doesn't use exactly that formula; the formula it uses
587 // is something like the following, where T is the number of factors of 2 in
588 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
591 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
593 // This formula is trivially equivalent to the previous formula. However,
594 // this formula can be implemented much more efficiently. The trick is that
595 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
596 // arithmetic. To do exact division in modular arithmetic, all we have
597 // to do is multiply by the inverse. Therefore, this step can be done at
600 // The next issue is how to safely do the division by 2^T. The way this
601 // is done is by doing the multiplication step at a width of at least W + T
602 // bits. This way, the bottom W+T bits of the product are accurate. Then,
603 // when we perform the division by 2^T (which is equivalent to a right shift
604 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
605 // truncated out after the division by 2^T.
607 // In comparison to just directly using the first formula, this technique
608 // is much more efficient; using the first formula requires W * K bits,
609 // but this formula less than W + K bits. Also, the first formula requires
610 // a division step, whereas this formula only requires multiplies and shifts.
612 // It doesn't matter whether the subtraction step is done in the calculation
613 // width or the input iteration count's width; if the subtraction overflows,
614 // the result must be zero anyway. We prefer here to do it in the width of
615 // the induction variable because it helps a lot for certain cases; CodeGen
616 // isn't smart enough to ignore the overflow, which leads to much less
617 // efficient code if the width of the subtraction is wider than the native
620 // (It's possible to not widen at all by pulling out factors of 2 before
621 // the multiplication; for example, K=2 can be calculated as
622 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
623 // extra arithmetic, so it's not an obvious win, and it gets
624 // much more complicated for K > 3.)
626 // Protection from insane SCEVs; this bound is conservative,
627 // but it probably doesn't matter.
629 return SE.getCouldNotCompute();
631 unsigned W = SE.getTypeSizeInBits(ResultTy);
633 // Calculate K! / 2^T and T; we divide out the factors of two before
634 // multiplying for calculating K! / 2^T to avoid overflow.
635 // Other overflow doesn't matter because we only care about the bottom
636 // W bits of the result.
637 APInt OddFactorial(W, 1);
639 for (unsigned i = 3; i <= K; ++i) {
641 unsigned TwoFactors = Mult.countTrailingZeros();
643 Mult = Mult.lshr(TwoFactors);
644 OddFactorial *= Mult;
647 // We need at least W + T bits for the multiplication step
648 unsigned CalculationBits = W + T;
650 // Calcuate 2^T, at width T+W.
651 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
653 // Calculate the multiplicative inverse of K! / 2^T;
654 // this multiplication factor will perform the exact division by
656 APInt Mod = APInt::getSignedMinValue(W+1);
657 APInt MultiplyFactor = OddFactorial.zext(W+1);
658 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
659 MultiplyFactor = MultiplyFactor.trunc(W);
661 // Calculate the product, at width T+W
662 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
663 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
664 for (unsigned i = 1; i != K; ++i) {
665 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
666 Dividend = SE.getMulExpr(Dividend,
667 SE.getTruncateOrZeroExtend(S, CalculationTy));
671 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
673 // Truncate the result, and divide by K! / 2^T.
675 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
676 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
679 /// evaluateAtIteration - Return the value of this chain of recurrences at
680 /// the specified iteration number. We can evaluate this recurrence by
681 /// multiplying each element in the chain by the binomial coefficient
682 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
684 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
686 /// where BC(It, k) stands for binomial coefficient.
688 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
689 ScalarEvolution &SE) const {
690 const SCEV *Result = getStart();
691 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
692 // The computation is correct in the face of overflow provided that the
693 // multiplication is performed _after_ the evaluation of the binomial
695 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
696 if (isa<SCEVCouldNotCompute>(Coeff))
699 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
704 //===----------------------------------------------------------------------===//
705 // SCEV Expression folder implementations
706 //===----------------------------------------------------------------------===//
708 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
710 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
711 "This is not a truncating conversion!");
712 assert(isSCEVable(Ty) &&
713 "This is not a conversion to a SCEVable type!");
714 Ty = getEffectiveSCEVType(Ty);
717 ID.AddInteger(scTruncate);
721 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
723 // Fold if the operand is constant.
724 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
726 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
728 // trunc(trunc(x)) --> trunc(x)
729 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
730 return getTruncateExpr(ST->getOperand(), Ty);
732 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
733 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
734 return getTruncateOrSignExtend(SS->getOperand(), Ty);
736 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
737 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
738 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
740 // If the input value is a chrec scev, truncate the chrec's operands.
741 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
742 SmallVector<const SCEV *, 4> Operands;
743 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
744 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
745 return getAddRecExpr(Operands, AddRec->getLoop());
748 // The cast wasn't folded; create an explicit cast node.
749 // Recompute the insert position, as it may have been invalidated.
750 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
751 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>();
752 new (S) SCEVTruncateExpr(ID, Op, Ty);
753 UniqueSCEVs.InsertNode(S, IP);
757 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
759 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
760 "This is not an extending conversion!");
761 assert(isSCEVable(Ty) &&
762 "This is not a conversion to a SCEVable type!");
763 Ty = getEffectiveSCEVType(Ty);
765 // Fold if the operand is constant.
766 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
767 const Type *IntTy = getEffectiveSCEVType(Ty);
768 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
769 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
770 return getConstant(cast<ConstantInt>(C));
773 // zext(zext(x)) --> zext(x)
774 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
775 return getZeroExtendExpr(SZ->getOperand(), Ty);
777 // Before doing any expensive analysis, check to see if we've already
778 // computed a SCEV for this Op and Ty.
780 ID.AddInteger(scZeroExtend);
784 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
786 // If the input value is a chrec scev, and we can prove that the value
787 // did not overflow the old, smaller, value, we can zero extend all of the
788 // operands (often constants). This allows analysis of something like
789 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
790 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
791 if (AR->isAffine()) {
792 const SCEV *Start = AR->getStart();
793 const SCEV *Step = AR->getStepRecurrence(*this);
794 unsigned BitWidth = getTypeSizeInBits(AR->getType());
795 const Loop *L = AR->getLoop();
797 // Check whether the backedge-taken count is SCEVCouldNotCompute.
798 // Note that this serves two purposes: It filters out loops that are
799 // simply not analyzable, and it covers the case where this code is
800 // being called from within backedge-taken count analysis, such that
801 // attempting to ask for the backedge-taken count would likely result
802 // in infinite recursion. In the later case, the analysis code will
803 // cope with a conservative value, and it will take care to purge
804 // that value once it has finished.
805 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
806 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
807 // Manually compute the final value for AR, checking for
810 // Check whether the backedge-taken count can be losslessly casted to
811 // the addrec's type. The count is always unsigned.
812 const SCEV *CastedMaxBECount =
813 getTruncateOrZeroExtend(MaxBECount, Start->getType());
814 const SCEV *RecastedMaxBECount =
815 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
816 if (MaxBECount == RecastedMaxBECount) {
817 const Type *WideTy = IntegerType::get(BitWidth * 2);
818 // Check whether Start+Step*MaxBECount has no unsigned overflow.
820 getMulExpr(CastedMaxBECount,
821 getTruncateOrZeroExtend(Step, Start->getType()));
822 const SCEV *Add = getAddExpr(Start, ZMul);
823 const SCEV *OperandExtendedAdd =
824 getAddExpr(getZeroExtendExpr(Start, WideTy),
825 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
826 getZeroExtendExpr(Step, WideTy)));
827 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
828 // Return the expression with the addrec on the outside.
829 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
830 getZeroExtendExpr(Step, Ty),
833 // Similar to above, only this time treat the step value as signed.
834 // This covers loops that count down.
836 getMulExpr(CastedMaxBECount,
837 getTruncateOrSignExtend(Step, Start->getType()));
838 Add = getAddExpr(Start, SMul);
840 getAddExpr(getZeroExtendExpr(Start, WideTy),
841 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
842 getSignExtendExpr(Step, WideTy)));
843 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
844 // Return the expression with the addrec on the outside.
845 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
846 getSignExtendExpr(Step, Ty),
850 // If the backedge is guarded by a comparison with the pre-inc value
851 // the addrec is safe. Also, if the entry is guarded by a comparison
852 // with the start value and the backedge is guarded by a comparison
853 // with the post-inc value, the addrec is safe.
854 if (isKnownPositive(Step)) {
855 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
856 getUnsignedRange(Step).getUnsignedMax());
857 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
858 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
859 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
860 AR->getPostIncExpr(*this), N)))
861 // Return the expression with the addrec on the outside.
862 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
863 getZeroExtendExpr(Step, Ty),
865 } else if (isKnownNegative(Step)) {
866 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
867 getSignedRange(Step).getSignedMin());
868 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) &&
869 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) ||
870 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
871 AR->getPostIncExpr(*this), N)))
872 // Return the expression with the addrec on the outside.
873 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
874 getSignExtendExpr(Step, Ty),
880 // The cast wasn't folded; create an explicit cast node.
881 // Recompute the insert position, as it may have been invalidated.
882 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
883 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>();
884 new (S) SCEVZeroExtendExpr(ID, Op, Ty);
885 UniqueSCEVs.InsertNode(S, IP);
889 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
891 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
892 "This is not an extending conversion!");
893 assert(isSCEVable(Ty) &&
894 "This is not a conversion to a SCEVable type!");
895 Ty = getEffectiveSCEVType(Ty);
897 // Fold if the operand is constant.
898 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
899 const Type *IntTy = getEffectiveSCEVType(Ty);
900 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
901 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
902 return getConstant(cast<ConstantInt>(C));
905 // sext(sext(x)) --> sext(x)
906 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
907 return getSignExtendExpr(SS->getOperand(), Ty);
909 // Before doing any expensive analysis, check to see if we've already
910 // computed a SCEV for this Op and Ty.
912 ID.AddInteger(scSignExtend);
916 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
918 // If the input value is a chrec scev, and we can prove that the value
919 // did not overflow the old, smaller, value, we can sign extend all of the
920 // operands (often constants). This allows analysis of something like
921 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
922 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
923 if (AR->isAffine()) {
924 const SCEV *Start = AR->getStart();
925 const SCEV *Step = AR->getStepRecurrence(*this);
926 unsigned BitWidth = getTypeSizeInBits(AR->getType());
927 const Loop *L = AR->getLoop();
929 // Check whether the backedge-taken count is SCEVCouldNotCompute.
930 // Note that this serves two purposes: It filters out loops that are
931 // simply not analyzable, and it covers the case where this code is
932 // being called from within backedge-taken count analysis, such that
933 // attempting to ask for the backedge-taken count would likely result
934 // in infinite recursion. In the later case, the analysis code will
935 // cope with a conservative value, and it will take care to purge
936 // that value once it has finished.
937 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
938 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
939 // Manually compute the final value for AR, checking for
942 // Check whether the backedge-taken count can be losslessly casted to
943 // the addrec's type. The count is always unsigned.
944 const SCEV *CastedMaxBECount =
945 getTruncateOrZeroExtend(MaxBECount, Start->getType());
946 const SCEV *RecastedMaxBECount =
947 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
948 if (MaxBECount == RecastedMaxBECount) {
949 const Type *WideTy = IntegerType::get(BitWidth * 2);
950 // Check whether Start+Step*MaxBECount has no signed overflow.
952 getMulExpr(CastedMaxBECount,
953 getTruncateOrSignExtend(Step, Start->getType()));
954 const SCEV *Add = getAddExpr(Start, SMul);
955 const SCEV *OperandExtendedAdd =
956 getAddExpr(getSignExtendExpr(Start, WideTy),
957 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
958 getSignExtendExpr(Step, WideTy)));
959 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
960 // Return the expression with the addrec on the outside.
961 return getAddRecExpr(getSignExtendExpr(Start, Ty),
962 getSignExtendExpr(Step, Ty),
965 // Similar to above, only this time treat the step value as unsigned.
966 // This covers loops that count up with an unsigned step.
968 getMulExpr(CastedMaxBECount,
969 getTruncateOrZeroExtend(Step, Start->getType()));
970 Add = getAddExpr(Start, UMul);
972 getAddExpr(getZeroExtendExpr(Start, WideTy),
973 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
974 getZeroExtendExpr(Step, WideTy)));
975 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
976 // Return the expression with the addrec on the outside.
977 return getAddRecExpr(getSignExtendExpr(Start, Ty),
978 getZeroExtendExpr(Step, Ty),
982 // If the backedge is guarded by a comparison with the pre-inc value
983 // the addrec is safe. Also, if the entry is guarded by a comparison
984 // with the start value and the backedge is guarded by a comparison
985 // with the post-inc value, the addrec is safe.
986 if (isKnownPositive(Step)) {
987 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
988 getSignedRange(Step).getSignedMax());
989 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
990 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
991 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
992 AR->getPostIncExpr(*this), N)))
993 // Return the expression with the addrec on the outside.
994 return getAddRecExpr(getSignExtendExpr(Start, Ty),
995 getSignExtendExpr(Step, Ty),
997 } else if (isKnownNegative(Step)) {
998 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
999 getSignedRange(Step).getSignedMin());
1000 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
1001 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
1002 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
1003 AR->getPostIncExpr(*this), N)))
1004 // Return the expression with the addrec on the outside.
1005 return getAddRecExpr(getSignExtendExpr(Start, Ty),
1006 getSignExtendExpr(Step, Ty),
1012 // The cast wasn't folded; create an explicit cast node.
1013 // Recompute the insert position, as it may have been invalidated.
1014 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1015 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>();
1016 new (S) SCEVSignExtendExpr(ID, Op, Ty);
1017 UniqueSCEVs.InsertNode(S, IP);
1021 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
1022 /// unspecified bits out to the given type.
1024 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
1026 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
1027 "This is not an extending conversion!");
1028 assert(isSCEVable(Ty) &&
1029 "This is not a conversion to a SCEVable type!");
1030 Ty = getEffectiveSCEVType(Ty);
1032 // Sign-extend negative constants.
1033 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
1034 if (SC->getValue()->getValue().isNegative())
1035 return getSignExtendExpr(Op, Ty);
1037 // Peel off a truncate cast.
1038 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
1039 const SCEV *NewOp = T->getOperand();
1040 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
1041 return getAnyExtendExpr(NewOp, Ty);
1042 return getTruncateOrNoop(NewOp, Ty);
1045 // Next try a zext cast. If the cast is folded, use it.
1046 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1047 if (!isa<SCEVZeroExtendExpr>(ZExt))
1050 // Next try a sext cast. If the cast is folded, use it.
1051 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1052 if (!isa<SCEVSignExtendExpr>(SExt))
1055 // If the expression is obviously signed, use the sext cast value.
1056 if (isa<SCEVSMaxExpr>(Op))
1059 // Absent any other information, use the zext cast value.
1063 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1064 /// a list of operands to be added under the given scale, update the given
1065 /// map. This is a helper function for getAddRecExpr. As an example of
1066 /// what it does, given a sequence of operands that would form an add
1067 /// expression like this:
1069 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1071 /// where A and B are constants, update the map with these values:
1073 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1075 /// and add 13 + A*B*29 to AccumulatedConstant.
1076 /// This will allow getAddRecExpr to produce this:
1078 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1080 /// This form often exposes folding opportunities that are hidden in
1081 /// the original operand list.
1083 /// Return true iff it appears that any interesting folding opportunities
1084 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1085 /// the common case where no interesting opportunities are present, and
1086 /// is also used as a check to avoid infinite recursion.
1089 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1090 SmallVector<const SCEV *, 8> &NewOps,
1091 APInt &AccumulatedConstant,
1092 const SmallVectorImpl<const SCEV *> &Ops,
1094 ScalarEvolution &SE) {
1095 bool Interesting = false;
1097 // Iterate over the add operands.
1098 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1099 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1100 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1102 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1103 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1104 // A multiplication of a constant with another add; recurse.
1106 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1107 cast<SCEVAddExpr>(Mul->getOperand(1))
1111 // A multiplication of a constant with some other value. Update
1113 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1114 const SCEV *Key = SE.getMulExpr(MulOps);
1115 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1116 M.insert(std::make_pair(Key, NewScale));
1118 NewOps.push_back(Pair.first->first);
1120 Pair.first->second += NewScale;
1121 // The map already had an entry for this value, which may indicate
1122 // a folding opportunity.
1126 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1127 // Pull a buried constant out to the outside.
1128 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
1130 AccumulatedConstant += Scale * C->getValue()->getValue();
1132 // An ordinary operand. Update the map.
1133 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1134 M.insert(std::make_pair(Ops[i], Scale));
1136 NewOps.push_back(Pair.first->first);
1138 Pair.first->second += Scale;
1139 // The map already had an entry for this value, which may indicate
1140 // a folding opportunity.
1150 struct APIntCompare {
1151 bool operator()(const APInt &LHS, const APInt &RHS) const {
1152 return LHS.ult(RHS);
1157 /// getAddExpr - Get a canonical add expression, or something simpler if
1159 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops) {
1160 assert(!Ops.empty() && "Cannot get empty add!");
1161 if (Ops.size() == 1) return Ops[0];
1163 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1164 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1165 getEffectiveSCEVType(Ops[0]->getType()) &&
1166 "SCEVAddExpr operand types don't match!");
1169 // Sort by complexity, this groups all similar expression types together.
1170 GroupByComplexity(Ops, LI);
1172 // If there are any constants, fold them together.
1174 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1176 assert(Idx < Ops.size());
1177 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1178 // We found two constants, fold them together!
1179 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1180 RHSC->getValue()->getValue());
1181 if (Ops.size() == 2) return Ops[0];
1182 Ops.erase(Ops.begin()+1); // Erase the folded element
1183 LHSC = cast<SCEVConstant>(Ops[0]);
1186 // If we are left with a constant zero being added, strip it off.
1187 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1188 Ops.erase(Ops.begin());
1193 if (Ops.size() == 1) return Ops[0];
1195 // Okay, check to see if the same value occurs in the operand list twice. If
1196 // so, merge them together into an multiply expression. Since we sorted the
1197 // list, these values are required to be adjacent.
1198 const Type *Ty = Ops[0]->getType();
1199 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1200 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1201 // Found a match, merge the two values into a multiply, and add any
1202 // remaining values to the result.
1203 const SCEV *Two = getIntegerSCEV(2, Ty);
1204 const SCEV *Mul = getMulExpr(Ops[i], Two);
1205 if (Ops.size() == 2)
1207 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1209 return getAddExpr(Ops);
1212 // Check for truncates. If all the operands are truncated from the same
1213 // type, see if factoring out the truncate would permit the result to be
1214 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1215 // if the contents of the resulting outer trunc fold to something simple.
1216 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1217 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1218 const Type *DstType = Trunc->getType();
1219 const Type *SrcType = Trunc->getOperand()->getType();
1220 SmallVector<const SCEV *, 8> LargeOps;
1222 // Check all the operands to see if they can be represented in the
1223 // source type of the truncate.
1224 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1225 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1226 if (T->getOperand()->getType() != SrcType) {
1230 LargeOps.push_back(T->getOperand());
1231 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1232 // This could be either sign or zero extension, but sign extension
1233 // is much more likely to be foldable here.
1234 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1235 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1236 SmallVector<const SCEV *, 8> LargeMulOps;
1237 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1238 if (const SCEVTruncateExpr *T =
1239 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1240 if (T->getOperand()->getType() != SrcType) {
1244 LargeMulOps.push_back(T->getOperand());
1245 } else if (const SCEVConstant *C =
1246 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1247 // This could be either sign or zero extension, but sign extension
1248 // is much more likely to be foldable here.
1249 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1256 LargeOps.push_back(getMulExpr(LargeMulOps));
1263 // Evaluate the expression in the larger type.
1264 const SCEV *Fold = getAddExpr(LargeOps);
1265 // If it folds to something simple, use it. Otherwise, don't.
1266 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1267 return getTruncateExpr(Fold, DstType);
1271 // Skip past any other cast SCEVs.
1272 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1275 // If there are add operands they would be next.
1276 if (Idx < Ops.size()) {
1277 bool DeletedAdd = false;
1278 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1279 // If we have an add, expand the add operands onto the end of the operands
1281 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1282 Ops.erase(Ops.begin()+Idx);
1286 // If we deleted at least one add, we added operands to the end of the list,
1287 // and they are not necessarily sorted. Recurse to resort and resimplify
1288 // any operands we just aquired.
1290 return getAddExpr(Ops);
1293 // Skip over the add expression until we get to a multiply.
1294 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1297 // Check to see if there are any folding opportunities present with
1298 // operands multiplied by constant values.
1299 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1300 uint64_t BitWidth = getTypeSizeInBits(Ty);
1301 DenseMap<const SCEV *, APInt> M;
1302 SmallVector<const SCEV *, 8> NewOps;
1303 APInt AccumulatedConstant(BitWidth, 0);
1304 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1305 Ops, APInt(BitWidth, 1), *this)) {
1306 // Some interesting folding opportunity is present, so its worthwhile to
1307 // re-generate the operands list. Group the operands by constant scale,
1308 // to avoid multiplying by the same constant scale multiple times.
1309 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1310 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1311 E = NewOps.end(); I != E; ++I)
1312 MulOpLists[M.find(*I)->second].push_back(*I);
1313 // Re-generate the operands list.
1315 if (AccumulatedConstant != 0)
1316 Ops.push_back(getConstant(AccumulatedConstant));
1317 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1318 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1320 Ops.push_back(getMulExpr(getConstant(I->first),
1321 getAddExpr(I->second)));
1323 return getIntegerSCEV(0, Ty);
1324 if (Ops.size() == 1)
1326 return getAddExpr(Ops);
1330 // If we are adding something to a multiply expression, make sure the
1331 // something is not already an operand of the multiply. If so, merge it into
1333 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1334 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1335 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1336 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1337 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1338 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1339 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1340 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1341 if (Mul->getNumOperands() != 2) {
1342 // If the multiply has more than two operands, we must get the
1344 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1345 MulOps.erase(MulOps.begin()+MulOp);
1346 InnerMul = getMulExpr(MulOps);
1348 const SCEV *One = getIntegerSCEV(1, Ty);
1349 const SCEV *AddOne = getAddExpr(InnerMul, One);
1350 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1351 if (Ops.size() == 2) return OuterMul;
1353 Ops.erase(Ops.begin()+AddOp);
1354 Ops.erase(Ops.begin()+Idx-1);
1356 Ops.erase(Ops.begin()+Idx);
1357 Ops.erase(Ops.begin()+AddOp-1);
1359 Ops.push_back(OuterMul);
1360 return getAddExpr(Ops);
1363 // Check this multiply against other multiplies being added together.
1364 for (unsigned OtherMulIdx = Idx+1;
1365 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1367 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1368 // If MulOp occurs in OtherMul, we can fold the two multiplies
1370 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1371 OMulOp != e; ++OMulOp)
1372 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1373 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1374 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1375 if (Mul->getNumOperands() != 2) {
1376 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1378 MulOps.erase(MulOps.begin()+MulOp);
1379 InnerMul1 = getMulExpr(MulOps);
1381 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1382 if (OtherMul->getNumOperands() != 2) {
1383 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1384 OtherMul->op_end());
1385 MulOps.erase(MulOps.begin()+OMulOp);
1386 InnerMul2 = getMulExpr(MulOps);
1388 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1389 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1390 if (Ops.size() == 2) return OuterMul;
1391 Ops.erase(Ops.begin()+Idx);
1392 Ops.erase(Ops.begin()+OtherMulIdx-1);
1393 Ops.push_back(OuterMul);
1394 return getAddExpr(Ops);
1400 // If there are any add recurrences in the operands list, see if any other
1401 // added values are loop invariant. If so, we can fold them into the
1403 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1406 // Scan over all recurrences, trying to fold loop invariants into them.
1407 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1408 // Scan all of the other operands to this add and add them to the vector if
1409 // they are loop invariant w.r.t. the recurrence.
1410 SmallVector<const SCEV *, 8> LIOps;
1411 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1412 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1413 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1414 LIOps.push_back(Ops[i]);
1415 Ops.erase(Ops.begin()+i);
1419 // If we found some loop invariants, fold them into the recurrence.
1420 if (!LIOps.empty()) {
1421 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1422 LIOps.push_back(AddRec->getStart());
1424 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1426 AddRecOps[0] = getAddExpr(LIOps);
1428 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1429 // If all of the other operands were loop invariant, we are done.
1430 if (Ops.size() == 1) return NewRec;
1432 // Otherwise, add the folded AddRec by the non-liv parts.
1433 for (unsigned i = 0;; ++i)
1434 if (Ops[i] == AddRec) {
1438 return getAddExpr(Ops);
1441 // Okay, if there weren't any loop invariants to be folded, check to see if
1442 // there are multiple AddRec's with the same loop induction variable being
1443 // added together. If so, we can fold them.
1444 for (unsigned OtherIdx = Idx+1;
1445 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1446 if (OtherIdx != Idx) {
1447 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1448 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1449 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1450 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1452 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1453 if (i >= NewOps.size()) {
1454 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1455 OtherAddRec->op_end());
1458 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1460 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1462 if (Ops.size() == 2) return NewAddRec;
1464 Ops.erase(Ops.begin()+Idx);
1465 Ops.erase(Ops.begin()+OtherIdx-1);
1466 Ops.push_back(NewAddRec);
1467 return getAddExpr(Ops);
1471 // Otherwise couldn't fold anything into this recurrence. Move onto the
1475 // Okay, it looks like we really DO need an add expr. Check to see if we
1476 // already have one, otherwise create a new one.
1477 FoldingSetNodeID ID;
1478 ID.AddInteger(scAddExpr);
1479 ID.AddInteger(Ops.size());
1480 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1481 ID.AddPointer(Ops[i]);
1483 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1484 SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>();
1485 new (S) SCEVAddExpr(ID, Ops);
1486 UniqueSCEVs.InsertNode(S, IP);
1491 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1493 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops) {
1494 assert(!Ops.empty() && "Cannot get empty mul!");
1496 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1497 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1498 getEffectiveSCEVType(Ops[0]->getType()) &&
1499 "SCEVMulExpr operand types don't match!");
1502 // Sort by complexity, this groups all similar expression types together.
1503 GroupByComplexity(Ops, LI);
1505 // If there are any constants, fold them together.
1507 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1509 // C1*(C2+V) -> C1*C2 + C1*V
1510 if (Ops.size() == 2)
1511 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1512 if (Add->getNumOperands() == 2 &&
1513 isa<SCEVConstant>(Add->getOperand(0)))
1514 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1515 getMulExpr(LHSC, Add->getOperand(1)));
1519 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1520 // We found two constants, fold them together!
1521 ConstantInt *Fold = Context->getConstantInt(LHSC->getValue()->getValue() *
1522 RHSC->getValue()->getValue());
1523 Ops[0] = getConstant(Fold);
1524 Ops.erase(Ops.begin()+1); // Erase the folded element
1525 if (Ops.size() == 1) return Ops[0];
1526 LHSC = cast<SCEVConstant>(Ops[0]);
1529 // If we are left with a constant one being multiplied, strip it off.
1530 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1531 Ops.erase(Ops.begin());
1533 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1534 // If we have a multiply of zero, it will always be zero.
1539 // Skip over the add expression until we get to a multiply.
1540 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1543 if (Ops.size() == 1)
1546 // If there are mul operands inline them all into this expression.
1547 if (Idx < Ops.size()) {
1548 bool DeletedMul = false;
1549 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1550 // If we have an mul, expand the mul operands onto the end of the operands
1552 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1553 Ops.erase(Ops.begin()+Idx);
1557 // If we deleted at least one mul, we added operands to the end of the list,
1558 // and they are not necessarily sorted. Recurse to resort and resimplify
1559 // any operands we just aquired.
1561 return getMulExpr(Ops);
1564 // If there are any add recurrences in the operands list, see if any other
1565 // added values are loop invariant. If so, we can fold them into the
1567 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1570 // Scan over all recurrences, trying to fold loop invariants into them.
1571 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1572 // Scan all of the other operands to this mul and add them to the vector if
1573 // they are loop invariant w.r.t. the recurrence.
1574 SmallVector<const SCEV *, 8> LIOps;
1575 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1576 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1577 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1578 LIOps.push_back(Ops[i]);
1579 Ops.erase(Ops.begin()+i);
1583 // If we found some loop invariants, fold them into the recurrence.
1584 if (!LIOps.empty()) {
1585 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1586 SmallVector<const SCEV *, 4> NewOps;
1587 NewOps.reserve(AddRec->getNumOperands());
1588 if (LIOps.size() == 1) {
1589 const SCEV *Scale = LIOps[0];
1590 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1591 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1593 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1594 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
1595 MulOps.push_back(AddRec->getOperand(i));
1596 NewOps.push_back(getMulExpr(MulOps));
1600 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1602 // If all of the other operands were loop invariant, we are done.
1603 if (Ops.size() == 1) return NewRec;
1605 // Otherwise, multiply the folded AddRec by the non-liv parts.
1606 for (unsigned i = 0;; ++i)
1607 if (Ops[i] == AddRec) {
1611 return getMulExpr(Ops);
1614 // Okay, if there weren't any loop invariants to be folded, check to see if
1615 // there are multiple AddRec's with the same loop induction variable being
1616 // multiplied together. If so, we can fold them.
1617 for (unsigned OtherIdx = Idx+1;
1618 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1619 if (OtherIdx != Idx) {
1620 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1621 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1622 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1623 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1624 const SCEV *NewStart = getMulExpr(F->getStart(),
1626 const SCEV *B = F->getStepRecurrence(*this);
1627 const SCEV *D = G->getStepRecurrence(*this);
1628 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1631 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1633 if (Ops.size() == 2) return NewAddRec;
1635 Ops.erase(Ops.begin()+Idx);
1636 Ops.erase(Ops.begin()+OtherIdx-1);
1637 Ops.push_back(NewAddRec);
1638 return getMulExpr(Ops);
1642 // Otherwise couldn't fold anything into this recurrence. Move onto the
1646 // Okay, it looks like we really DO need an mul expr. Check to see if we
1647 // already have one, otherwise create a new one.
1648 FoldingSetNodeID ID;
1649 ID.AddInteger(scMulExpr);
1650 ID.AddInteger(Ops.size());
1651 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1652 ID.AddPointer(Ops[i]);
1654 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1655 SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>();
1656 new (S) SCEVMulExpr(ID, Ops);
1657 UniqueSCEVs.InsertNode(S, IP);
1661 /// getUDivExpr - Get a canonical multiply expression, or something simpler if
1663 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1665 assert(getEffectiveSCEVType(LHS->getType()) ==
1666 getEffectiveSCEVType(RHS->getType()) &&
1667 "SCEVUDivExpr operand types don't match!");
1669 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1670 if (RHSC->getValue()->equalsInt(1))
1671 return LHS; // X udiv 1 --> x
1673 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1675 // Determine if the division can be folded into the operands of
1677 // TODO: Generalize this to non-constants by using known-bits information.
1678 const Type *Ty = LHS->getType();
1679 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1680 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1681 // For non-power-of-two values, effectively round the value up to the
1682 // nearest power of two.
1683 if (!RHSC->getValue()->getValue().isPowerOf2())
1685 const IntegerType *ExtTy =
1686 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1687 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1688 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1689 if (const SCEVConstant *Step =
1690 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1691 if (!Step->getValue()->getValue()
1692 .urem(RHSC->getValue()->getValue()) &&
1693 getZeroExtendExpr(AR, ExtTy) ==
1694 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1695 getZeroExtendExpr(Step, ExtTy),
1697 SmallVector<const SCEV *, 4> Operands;
1698 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1699 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1700 return getAddRecExpr(Operands, AR->getLoop());
1702 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1703 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1704 SmallVector<const SCEV *, 4> Operands;
1705 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1706 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1707 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1708 // Find an operand that's safely divisible.
1709 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1710 const SCEV *Op = M->getOperand(i);
1711 const SCEV *Div = getUDivExpr(Op, RHSC);
1712 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1713 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands();
1714 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(),
1717 return getMulExpr(Operands);
1721 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1722 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1723 SmallVector<const SCEV *, 4> Operands;
1724 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1725 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1726 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1728 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1729 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1730 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1732 Operands.push_back(Op);
1734 if (Operands.size() == A->getNumOperands())
1735 return getAddExpr(Operands);
1739 // Fold if both operands are constant.
1740 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1741 Constant *LHSCV = LHSC->getValue();
1742 Constant *RHSCV = RHSC->getValue();
1743 return getConstant(cast<ConstantInt>(Context->getConstantExprUDiv(LHSCV,
1748 FoldingSetNodeID ID;
1749 ID.AddInteger(scUDivExpr);
1753 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1754 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>();
1755 new (S) SCEVUDivExpr(ID, LHS, RHS);
1756 UniqueSCEVs.InsertNode(S, IP);
1761 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1762 /// Simplify the expression as much as possible.
1763 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1764 const SCEV *Step, const Loop *L) {
1765 SmallVector<const SCEV *, 4> Operands;
1766 Operands.push_back(Start);
1767 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1768 if (StepChrec->getLoop() == L) {
1769 Operands.insert(Operands.end(), StepChrec->op_begin(),
1770 StepChrec->op_end());
1771 return getAddRecExpr(Operands, L);
1774 Operands.push_back(Step);
1775 return getAddRecExpr(Operands, L);
1778 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1779 /// Simplify the expression as much as possible.
1781 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1783 if (Operands.size() == 1) return Operands[0];
1785 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1786 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1787 getEffectiveSCEVType(Operands[0]->getType()) &&
1788 "SCEVAddRecExpr operand types don't match!");
1791 if (Operands.back()->isZero()) {
1792 Operands.pop_back();
1793 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1796 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1797 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1798 const Loop* NestedLoop = NestedAR->getLoop();
1799 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1800 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
1801 NestedAR->op_end());
1802 Operands[0] = NestedAR->getStart();
1803 // AddRecs require their operands be loop-invariant with respect to their
1804 // loops. Don't perform this transformation if it would break this
1806 bool AllInvariant = true;
1807 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1808 if (!Operands[i]->isLoopInvariant(L)) {
1809 AllInvariant = false;
1813 NestedOperands[0] = getAddRecExpr(Operands, L);
1814 AllInvariant = true;
1815 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
1816 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
1817 AllInvariant = false;
1821 // Ok, both add recurrences are valid after the transformation.
1822 return getAddRecExpr(NestedOperands, NestedLoop);
1824 // Reset Operands to its original state.
1825 Operands[0] = NestedAR;
1829 FoldingSetNodeID ID;
1830 ID.AddInteger(scAddRecExpr);
1831 ID.AddInteger(Operands.size());
1832 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1833 ID.AddPointer(Operands[i]);
1836 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1837 SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>();
1838 new (S) SCEVAddRecExpr(ID, Operands, L);
1839 UniqueSCEVs.InsertNode(S, IP);
1843 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
1845 SmallVector<const SCEV *, 2> Ops;
1848 return getSMaxExpr(Ops);
1852 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1853 assert(!Ops.empty() && "Cannot get empty smax!");
1854 if (Ops.size() == 1) return Ops[0];
1856 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1857 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1858 getEffectiveSCEVType(Ops[0]->getType()) &&
1859 "SCEVSMaxExpr operand types don't match!");
1862 // Sort by complexity, this groups all similar expression types together.
1863 GroupByComplexity(Ops, LI);
1865 // If there are any constants, fold them together.
1867 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1869 assert(Idx < Ops.size());
1870 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1871 // We found two constants, fold them together!
1872 ConstantInt *Fold = Context->getConstantInt(
1873 APIntOps::smax(LHSC->getValue()->getValue(),
1874 RHSC->getValue()->getValue()));
1875 Ops[0] = getConstant(Fold);
1876 Ops.erase(Ops.begin()+1); // Erase the folded element
1877 if (Ops.size() == 1) return Ops[0];
1878 LHSC = cast<SCEVConstant>(Ops[0]);
1881 // If we are left with a constant minimum-int, strip it off.
1882 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1883 Ops.erase(Ops.begin());
1885 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
1886 // If we have an smax with a constant maximum-int, it will always be
1892 if (Ops.size() == 1) return Ops[0];
1894 // Find the first SMax
1895 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1898 // Check to see if one of the operands is an SMax. If so, expand its operands
1899 // onto our operand list, and recurse to simplify.
1900 if (Idx < Ops.size()) {
1901 bool DeletedSMax = false;
1902 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1903 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1904 Ops.erase(Ops.begin()+Idx);
1909 return getSMaxExpr(Ops);
1912 // Okay, check to see if the same value occurs in the operand list twice. If
1913 // so, delete one. Since we sorted the list, these values are required to
1915 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1916 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1917 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1921 if (Ops.size() == 1) return Ops[0];
1923 assert(!Ops.empty() && "Reduced smax down to nothing!");
1925 // Okay, it looks like we really DO need an smax expr. Check to see if we
1926 // already have one, otherwise create a new one.
1927 FoldingSetNodeID ID;
1928 ID.AddInteger(scSMaxExpr);
1929 ID.AddInteger(Ops.size());
1930 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1931 ID.AddPointer(Ops[i]);
1933 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1934 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>();
1935 new (S) SCEVSMaxExpr(ID, Ops);
1936 UniqueSCEVs.InsertNode(S, IP);
1940 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
1942 SmallVector<const SCEV *, 2> Ops;
1945 return getUMaxExpr(Ops);
1949 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1950 assert(!Ops.empty() && "Cannot get empty umax!");
1951 if (Ops.size() == 1) return Ops[0];
1953 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1954 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1955 getEffectiveSCEVType(Ops[0]->getType()) &&
1956 "SCEVUMaxExpr operand types don't match!");
1959 // Sort by complexity, this groups all similar expression types together.
1960 GroupByComplexity(Ops, LI);
1962 // If there are any constants, fold them together.
1964 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1966 assert(Idx < Ops.size());
1967 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1968 // We found two constants, fold them together!
1969 ConstantInt *Fold = Context->getConstantInt(
1970 APIntOps::umax(LHSC->getValue()->getValue(),
1971 RHSC->getValue()->getValue()));
1972 Ops[0] = getConstant(Fold);
1973 Ops.erase(Ops.begin()+1); // Erase the folded element
1974 if (Ops.size() == 1) return Ops[0];
1975 LHSC = cast<SCEVConstant>(Ops[0]);
1978 // If we are left with a constant minimum-int, strip it off.
1979 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1980 Ops.erase(Ops.begin());
1982 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
1983 // If we have an umax with a constant maximum-int, it will always be
1989 if (Ops.size() == 1) return Ops[0];
1991 // Find the first UMax
1992 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1995 // Check to see if one of the operands is a UMax. If so, expand its operands
1996 // onto our operand list, and recurse to simplify.
1997 if (Idx < Ops.size()) {
1998 bool DeletedUMax = false;
1999 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
2000 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
2001 Ops.erase(Ops.begin()+Idx);
2006 return getUMaxExpr(Ops);
2009 // Okay, check to see if the same value occurs in the operand list twice. If
2010 // so, delete one. Since we sorted the list, these values are required to
2012 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
2013 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
2014 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
2018 if (Ops.size() == 1) return Ops[0];
2020 assert(!Ops.empty() && "Reduced umax down to nothing!");
2022 // Okay, it looks like we really DO need a umax expr. Check to see if we
2023 // already have one, otherwise create a new one.
2024 FoldingSetNodeID ID;
2025 ID.AddInteger(scUMaxExpr);
2026 ID.AddInteger(Ops.size());
2027 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
2028 ID.AddPointer(Ops[i]);
2030 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2031 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>();
2032 new (S) SCEVUMaxExpr(ID, Ops);
2033 UniqueSCEVs.InsertNode(S, IP);
2037 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
2039 // ~smax(~x, ~y) == smin(x, y).
2040 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2043 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2045 // ~umax(~x, ~y) == umin(x, y)
2046 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2049 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2050 // Don't attempt to do anything other than create a SCEVUnknown object
2051 // here. createSCEV only calls getUnknown after checking for all other
2052 // interesting possibilities, and any other code that calls getUnknown
2053 // is doing so in order to hide a value from SCEV canonicalization.
2055 FoldingSetNodeID ID;
2056 ID.AddInteger(scUnknown);
2059 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2060 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>();
2061 new (S) SCEVUnknown(ID, V);
2062 UniqueSCEVs.InsertNode(S, IP);
2066 //===----------------------------------------------------------------------===//
2067 // Basic SCEV Analysis and PHI Idiom Recognition Code
2070 /// isSCEVable - Test if values of the given type are analyzable within
2071 /// the SCEV framework. This primarily includes integer types, and it
2072 /// can optionally include pointer types if the ScalarEvolution class
2073 /// has access to target-specific information.
2074 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2075 // Integers are always SCEVable.
2076 if (Ty->isInteger())
2079 // Pointers are SCEVable if TargetData information is available
2080 // to provide pointer size information.
2081 if (isa<PointerType>(Ty))
2084 // Otherwise it's not SCEVable.
2088 /// getTypeSizeInBits - Return the size in bits of the specified type,
2089 /// for which isSCEVable must return true.
2090 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2091 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2093 // If we have a TargetData, use it!
2095 return TD->getTypeSizeInBits(Ty);
2097 // Otherwise, we support only integer types.
2098 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
2099 return Ty->getPrimitiveSizeInBits();
2102 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2103 /// the given type and which represents how SCEV will treat the given
2104 /// type, for which isSCEVable must return true. For pointer types,
2105 /// this is the pointer-sized integer type.
2106 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2107 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2109 if (Ty->isInteger())
2112 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
2113 return TD->getIntPtrType();
2116 const SCEV *ScalarEvolution::getCouldNotCompute() {
2117 return &CouldNotCompute;
2120 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2121 /// expression and create a new one.
2122 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2123 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2125 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2126 if (I != Scalars.end()) return I->second;
2127 const SCEV *S = createSCEV(V);
2128 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2132 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
2133 /// specified signed integer value and return a SCEV for the constant.
2134 const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
2135 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2136 return getConstant(Context->getConstantInt(ITy, Val));
2139 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2141 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2142 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2144 cast<ConstantInt>(Context->getConstantExprNeg(VC->getValue())));
2146 const Type *Ty = V->getType();
2147 Ty = getEffectiveSCEVType(Ty);
2148 return getMulExpr(V,
2149 getConstant(cast<ConstantInt>(Context->getAllOnesValue(Ty))));
2152 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2153 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2154 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2156 cast<ConstantInt>(Context->getConstantExprNot(VC->getValue())));
2158 const Type *Ty = V->getType();
2159 Ty = getEffectiveSCEVType(Ty);
2160 const SCEV *AllOnes =
2161 getConstant(cast<ConstantInt>(Context->getAllOnesValue(Ty)));
2162 return getMinusSCEV(AllOnes, V);
2165 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2167 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2170 return getAddExpr(LHS, getNegativeSCEV(RHS));
2173 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2174 /// input value to the specified type. If the type must be extended, it is zero
2177 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2179 const Type *SrcTy = V->getType();
2180 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2181 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2182 "Cannot truncate or zero extend with non-integer arguments!");
2183 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2184 return V; // No conversion
2185 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2186 return getTruncateExpr(V, Ty);
2187 return getZeroExtendExpr(V, Ty);
2190 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2191 /// input value to the specified type. If the type must be extended, it is sign
2194 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2196 const Type *SrcTy = V->getType();
2197 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2198 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2199 "Cannot truncate or zero extend with non-integer arguments!");
2200 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2201 return V; // No conversion
2202 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2203 return getTruncateExpr(V, Ty);
2204 return getSignExtendExpr(V, Ty);
2207 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2208 /// input value to the specified type. If the type must be extended, it is zero
2209 /// extended. The conversion must not be narrowing.
2211 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2212 const Type *SrcTy = V->getType();
2213 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2214 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2215 "Cannot noop or zero extend with non-integer arguments!");
2216 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2217 "getNoopOrZeroExtend cannot truncate!");
2218 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2219 return V; // No conversion
2220 return getZeroExtendExpr(V, Ty);
2223 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2224 /// input value to the specified type. If the type must be extended, it is sign
2225 /// extended. The conversion must not be narrowing.
2227 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2228 const Type *SrcTy = V->getType();
2229 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2230 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2231 "Cannot noop or sign extend with non-integer arguments!");
2232 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2233 "getNoopOrSignExtend cannot truncate!");
2234 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2235 return V; // No conversion
2236 return getSignExtendExpr(V, Ty);
2239 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2240 /// the input value to the specified type. If the type must be extended,
2241 /// it is extended with unspecified bits. The conversion must not be
2244 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2245 const Type *SrcTy = V->getType();
2246 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2247 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2248 "Cannot noop or any extend with non-integer arguments!");
2249 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2250 "getNoopOrAnyExtend cannot truncate!");
2251 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2252 return V; // No conversion
2253 return getAnyExtendExpr(V, Ty);
2256 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2257 /// input value to the specified type. The conversion must not be widening.
2259 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2260 const Type *SrcTy = V->getType();
2261 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2262 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2263 "Cannot truncate or noop with non-integer arguments!");
2264 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2265 "getTruncateOrNoop cannot extend!");
2266 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2267 return V; // No conversion
2268 return getTruncateExpr(V, Ty);
2271 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2272 /// the types using zero-extension, and then perform a umax operation
2274 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2276 const SCEV *PromotedLHS = LHS;
2277 const SCEV *PromotedRHS = RHS;
2279 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2280 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2282 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2284 return getUMaxExpr(PromotedLHS, PromotedRHS);
2287 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2288 /// the types using zero-extension, and then perform a umin operation
2290 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2292 const SCEV *PromotedLHS = LHS;
2293 const SCEV *PromotedRHS = RHS;
2295 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2296 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2298 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2300 return getUMinExpr(PromotedLHS, PromotedRHS);
2303 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
2304 /// the specified instruction and replaces any references to the symbolic value
2305 /// SymName with the specified value. This is used during PHI resolution.
2307 ScalarEvolution::ReplaceSymbolicValueWithConcrete(Instruction *I,
2308 const SCEV *SymName,
2309 const SCEV *NewVal) {
2310 std::map<SCEVCallbackVH, const SCEV *>::iterator SI =
2311 Scalars.find(SCEVCallbackVH(I, this));
2312 if (SI == Scalars.end()) return;
2315 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
2316 if (NV == SI->second) return; // No change.
2318 SI->second = NV; // Update the scalars map!
2320 // Any instruction values that use this instruction might also need to be
2322 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
2324 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
2327 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2328 /// a loop header, making it a potential recurrence, or it doesn't.
2330 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2331 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2332 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2333 if (L->getHeader() == PN->getParent()) {
2334 // If it lives in the loop header, it has two incoming values, one
2335 // from outside the loop, and one from inside.
2336 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2337 unsigned BackEdge = IncomingEdge^1;
2339 // While we are analyzing this PHI node, handle its value symbolically.
2340 const SCEV *SymbolicName = getUnknown(PN);
2341 assert(Scalars.find(PN) == Scalars.end() &&
2342 "PHI node already processed?");
2343 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2345 // Using this symbolic name for the PHI, analyze the value coming around
2347 const SCEV *BEValue = getSCEV(PN->getIncomingValue(BackEdge));
2349 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2350 // has a special value for the first iteration of the loop.
2352 // If the value coming around the backedge is an add with the symbolic
2353 // value we just inserted, then we found a simple induction variable!
2354 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2355 // If there is a single occurrence of the symbolic value, replace it
2356 // with a recurrence.
2357 unsigned FoundIndex = Add->getNumOperands();
2358 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2359 if (Add->getOperand(i) == SymbolicName)
2360 if (FoundIndex == e) {
2365 if (FoundIndex != Add->getNumOperands()) {
2366 // Create an add with everything but the specified operand.
2367 SmallVector<const SCEV *, 8> Ops;
2368 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2369 if (i != FoundIndex)
2370 Ops.push_back(Add->getOperand(i));
2371 const SCEV *Accum = getAddExpr(Ops);
2373 // This is not a valid addrec if the step amount is varying each
2374 // loop iteration, but is not itself an addrec in this loop.
2375 if (Accum->isLoopInvariant(L) ||
2376 (isa<SCEVAddRecExpr>(Accum) &&
2377 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2378 const SCEV *StartVal =
2379 getSCEV(PN->getIncomingValue(IncomingEdge));
2380 const SCEV *PHISCEV =
2381 getAddRecExpr(StartVal, Accum, L);
2383 // Okay, for the entire analysis of this edge we assumed the PHI
2384 // to be symbolic. We now need to go back and update all of the
2385 // entries for the scalars that use the PHI (except for the PHI
2386 // itself) to use the new analyzed value instead of the "symbolic"
2388 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2392 } else if (const SCEVAddRecExpr *AddRec =
2393 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2394 // Otherwise, this could be a loop like this:
2395 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2396 // In this case, j = {1,+,1} and BEValue is j.
2397 // Because the other in-value of i (0) fits the evolution of BEValue
2398 // i really is an addrec evolution.
2399 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2400 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2402 // If StartVal = j.start - j.stride, we can use StartVal as the
2403 // initial step of the addrec evolution.
2404 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2405 AddRec->getOperand(1))) {
2406 const SCEV *PHISCEV =
2407 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2409 // Okay, for the entire analysis of this edge we assumed the PHI
2410 // to be symbolic. We now need to go back and update all of the
2411 // entries for the scalars that use the PHI (except for the PHI
2412 // itself) to use the new analyzed value instead of the "symbolic"
2414 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2420 return SymbolicName;
2423 // It's tempting to recognize PHIs with a unique incoming value, however
2424 // this leads passes like indvars to break LCSSA form. Fortunately, such
2425 // PHIs are rare, as instcombine zaps them.
2427 // If it's not a loop phi, we can't handle it yet.
2428 return getUnknown(PN);
2431 /// createNodeForGEP - Expand GEP instructions into add and multiply
2432 /// operations. This allows them to be analyzed by regular SCEV code.
2434 const SCEV *ScalarEvolution::createNodeForGEP(Operator *GEP) {
2436 const Type *IntPtrTy = TD->getIntPtrType();
2437 Value *Base = GEP->getOperand(0);
2438 // Don't attempt to analyze GEPs over unsized objects.
2439 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2440 return getUnknown(GEP);
2441 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
2442 gep_type_iterator GTI = gep_type_begin(GEP);
2443 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2447 // Compute the (potentially symbolic) offset in bytes for this index.
2448 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2449 // For a struct, add the member offset.
2450 const StructLayout &SL = *TD->getStructLayout(STy);
2451 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2452 uint64_t Offset = SL.getElementOffset(FieldNo);
2453 TotalOffset = getAddExpr(TotalOffset, getIntegerSCEV(Offset, IntPtrTy));
2455 // For an array, add the element offset, explicitly scaled.
2456 const SCEV *LocalOffset = getSCEV(Index);
2457 if (!isa<PointerType>(LocalOffset->getType()))
2458 // Getelementptr indicies are signed.
2459 LocalOffset = getTruncateOrSignExtend(LocalOffset, IntPtrTy);
2461 getMulExpr(LocalOffset,
2462 getIntegerSCEV(TD->getTypeAllocSize(*GTI), IntPtrTy));
2463 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2466 return getAddExpr(getSCEV(Base), TotalOffset);
2469 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2470 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2471 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2472 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2474 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2475 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2476 return C->getValue()->getValue().countTrailingZeros();
2478 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2479 return std::min(GetMinTrailingZeros(T->getOperand()),
2480 (uint32_t)getTypeSizeInBits(T->getType()));
2482 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2483 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2484 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2485 getTypeSizeInBits(E->getType()) : OpRes;
2488 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2489 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2490 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2491 getTypeSizeInBits(E->getType()) : OpRes;
2494 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2495 // The result is the min of all operands results.
2496 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2497 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2498 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2502 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2503 // The result is the sum of all operands results.
2504 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2505 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2506 for (unsigned i = 1, e = M->getNumOperands();
2507 SumOpRes != BitWidth && i != e; ++i)
2508 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2513 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2514 // The result is the min of all operands results.
2515 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2516 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2517 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2521 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2522 // The result is the min of all operands results.
2523 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2524 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2525 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2529 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2530 // The result is the min of all operands results.
2531 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2532 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2533 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2537 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2538 // For a SCEVUnknown, ask ValueTracking.
2539 unsigned BitWidth = getTypeSizeInBits(U->getType());
2540 APInt Mask = APInt::getAllOnesValue(BitWidth);
2541 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2542 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2543 return Zeros.countTrailingOnes();
2550 /// getUnsignedRange - Determine the unsigned range for a particular SCEV.
2553 ScalarEvolution::getUnsignedRange(const SCEV *S) {
2555 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2556 return ConstantRange(C->getValue()->getValue());
2558 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2559 ConstantRange X = getUnsignedRange(Add->getOperand(0));
2560 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2561 X = X.add(getUnsignedRange(Add->getOperand(i)));
2565 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2566 ConstantRange X = getUnsignedRange(Mul->getOperand(0));
2567 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2568 X = X.multiply(getUnsignedRange(Mul->getOperand(i)));
2572 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2573 ConstantRange X = getUnsignedRange(SMax->getOperand(0));
2574 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2575 X = X.smax(getUnsignedRange(SMax->getOperand(i)));
2579 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2580 ConstantRange X = getUnsignedRange(UMax->getOperand(0));
2581 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2582 X = X.umax(getUnsignedRange(UMax->getOperand(i)));
2586 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2587 ConstantRange X = getUnsignedRange(UDiv->getLHS());
2588 ConstantRange Y = getUnsignedRange(UDiv->getRHS());
2592 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2593 ConstantRange X = getUnsignedRange(ZExt->getOperand());
2594 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
2597 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2598 ConstantRange X = getUnsignedRange(SExt->getOperand());
2599 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
2602 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2603 ConstantRange X = getUnsignedRange(Trunc->getOperand());
2604 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
2607 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
2609 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2610 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
2611 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
2612 if (!Trip) return FullSet;
2614 // TODO: non-affine addrec
2615 if (AddRec->isAffine()) {
2616 const Type *Ty = AddRec->getType();
2617 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2618 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
2619 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2621 const SCEV *Start = AddRec->getStart();
2622 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2624 // Check for overflow.
2625 if (!isKnownPredicate(ICmpInst::ICMP_ULE, Start, End))
2628 ConstantRange StartRange = getUnsignedRange(Start);
2629 ConstantRange EndRange = getUnsignedRange(End);
2630 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
2631 EndRange.getUnsignedMin());
2632 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
2633 EndRange.getUnsignedMax());
2634 if (Min.isMinValue() && Max.isMaxValue())
2636 return ConstantRange(Min, Max+1);
2641 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2642 // For a SCEVUnknown, ask ValueTracking.
2643 unsigned BitWidth = getTypeSizeInBits(U->getType());
2644 APInt Mask = APInt::getAllOnesValue(BitWidth);
2645 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2646 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
2647 if (Ones == ~Zeros + 1)
2649 return ConstantRange(Ones, ~Zeros + 1);
2655 /// getSignedRange - Determine the signed range for a particular SCEV.
2658 ScalarEvolution::getSignedRange(const SCEV *S) {
2660 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2661 return ConstantRange(C->getValue()->getValue());
2663 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2664 ConstantRange X = getSignedRange(Add->getOperand(0));
2665 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2666 X = X.add(getSignedRange(Add->getOperand(i)));
2670 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2671 ConstantRange X = getSignedRange(Mul->getOperand(0));
2672 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2673 X = X.multiply(getSignedRange(Mul->getOperand(i)));
2677 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2678 ConstantRange X = getSignedRange(SMax->getOperand(0));
2679 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2680 X = X.smax(getSignedRange(SMax->getOperand(i)));
2684 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2685 ConstantRange X = getSignedRange(UMax->getOperand(0));
2686 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2687 X = X.umax(getSignedRange(UMax->getOperand(i)));
2691 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2692 ConstantRange X = getSignedRange(UDiv->getLHS());
2693 ConstantRange Y = getSignedRange(UDiv->getRHS());
2697 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2698 ConstantRange X = getSignedRange(ZExt->getOperand());
2699 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
2702 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2703 ConstantRange X = getSignedRange(SExt->getOperand());
2704 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
2707 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2708 ConstantRange X = getSignedRange(Trunc->getOperand());
2709 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
2712 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
2714 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2715 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
2716 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
2717 if (!Trip) return FullSet;
2719 // TODO: non-affine addrec
2720 if (AddRec->isAffine()) {
2721 const Type *Ty = AddRec->getType();
2722 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2723 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
2724 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2726 const SCEV *Start = AddRec->getStart();
2727 const SCEV *Step = AddRec->getStepRecurrence(*this);
2728 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2730 // Check for overflow.
2731 if (!(isKnownPositive(Step) &&
2732 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) &&
2733 !(isKnownNegative(Step) &&
2734 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End)))
2737 ConstantRange StartRange = getSignedRange(Start);
2738 ConstantRange EndRange = getSignedRange(End);
2739 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
2740 EndRange.getSignedMin());
2741 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
2742 EndRange.getSignedMax());
2743 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
2745 return ConstantRange(Min, Max+1);
2750 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2751 // For a SCEVUnknown, ask ValueTracking.
2752 unsigned BitWidth = getTypeSizeInBits(U->getType());
2753 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
2757 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
2758 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1);
2764 /// createSCEV - We know that there is no SCEV for the specified value.
2765 /// Analyze the expression.
2767 const SCEV *ScalarEvolution::createSCEV(Value *V) {
2768 if (!isSCEVable(V->getType()))
2769 return getUnknown(V);
2771 unsigned Opcode = Instruction::UserOp1;
2772 if (Instruction *I = dyn_cast<Instruction>(V))
2773 Opcode = I->getOpcode();
2774 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2775 Opcode = CE->getOpcode();
2776 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
2777 return getConstant(CI);
2778 else if (isa<ConstantPointerNull>(V))
2779 return getIntegerSCEV(0, V->getType());
2780 else if (isa<UndefValue>(V))
2781 return getIntegerSCEV(0, V->getType());
2783 return getUnknown(V);
2785 Operator *U = cast<Operator>(V);
2787 case Instruction::Add:
2788 return getAddExpr(getSCEV(U->getOperand(0)),
2789 getSCEV(U->getOperand(1)));
2790 case Instruction::Mul:
2791 return getMulExpr(getSCEV(U->getOperand(0)),
2792 getSCEV(U->getOperand(1)));
2793 case Instruction::UDiv:
2794 return getUDivExpr(getSCEV(U->getOperand(0)),
2795 getSCEV(U->getOperand(1)));
2796 case Instruction::Sub:
2797 return getMinusSCEV(getSCEV(U->getOperand(0)),
2798 getSCEV(U->getOperand(1)));
2799 case Instruction::And:
2800 // For an expression like x&255 that merely masks off the high bits,
2801 // use zext(trunc(x)) as the SCEV expression.
2802 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2803 if (CI->isNullValue())
2804 return getSCEV(U->getOperand(1));
2805 if (CI->isAllOnesValue())
2806 return getSCEV(U->getOperand(0));
2807 const APInt &A = CI->getValue();
2809 // Instcombine's ShrinkDemandedConstant may strip bits out of
2810 // constants, obscuring what would otherwise be a low-bits mask.
2811 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
2812 // knew about to reconstruct a low-bits mask value.
2813 unsigned LZ = A.countLeadingZeros();
2814 unsigned BitWidth = A.getBitWidth();
2815 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
2816 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
2817 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
2819 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
2821 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
2823 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2824 IntegerType::get(BitWidth - LZ)),
2829 case Instruction::Or:
2830 // If the RHS of the Or is a constant, we may have something like:
2831 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2832 // optimizations will transparently handle this case.
2834 // In order for this transformation to be safe, the LHS must be of the
2835 // form X*(2^n) and the Or constant must be less than 2^n.
2836 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2837 const SCEV *LHS = getSCEV(U->getOperand(0));
2838 const APInt &CIVal = CI->getValue();
2839 if (GetMinTrailingZeros(LHS) >=
2840 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2841 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2844 case Instruction::Xor:
2845 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2846 // If the RHS of the xor is a signbit, then this is just an add.
2847 // Instcombine turns add of signbit into xor as a strength reduction step.
2848 if (CI->getValue().isSignBit())
2849 return getAddExpr(getSCEV(U->getOperand(0)),
2850 getSCEV(U->getOperand(1)));
2852 // If the RHS of xor is -1, then this is a not operation.
2853 if (CI->isAllOnesValue())
2854 return getNotSCEV(getSCEV(U->getOperand(0)));
2856 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2857 // This is a variant of the check for xor with -1, and it handles
2858 // the case where instcombine has trimmed non-demanded bits out
2859 // of an xor with -1.
2860 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2861 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2862 if (BO->getOpcode() == Instruction::And &&
2863 LCI->getValue() == CI->getValue())
2864 if (const SCEVZeroExtendExpr *Z =
2865 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
2866 const Type *UTy = U->getType();
2867 const SCEV *Z0 = Z->getOperand();
2868 const Type *Z0Ty = Z0->getType();
2869 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
2871 // If C is a low-bits mask, the zero extend is zerving to
2872 // mask off the high bits. Complement the operand and
2873 // re-apply the zext.
2874 if (APIntOps::isMask(Z0TySize, CI->getValue()))
2875 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
2877 // If C is a single bit, it may be in the sign-bit position
2878 // before the zero-extend. In this case, represent the xor
2879 // using an add, which is equivalent, and re-apply the zext.
2880 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
2881 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
2883 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
2889 case Instruction::Shl:
2890 // Turn shift left of a constant amount into a multiply.
2891 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2892 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2893 Constant *X = Context->getConstantInt(
2894 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2895 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2899 case Instruction::LShr:
2900 // Turn logical shift right of a constant into a unsigned divide.
2901 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2902 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2903 Constant *X = Context->getConstantInt(
2904 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2905 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2909 case Instruction::AShr:
2910 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2911 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2912 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2913 if (L->getOpcode() == Instruction::Shl &&
2914 L->getOperand(1) == U->getOperand(1)) {
2915 unsigned BitWidth = getTypeSizeInBits(U->getType());
2916 uint64_t Amt = BitWidth - CI->getZExtValue();
2917 if (Amt == BitWidth)
2918 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2920 return getIntegerSCEV(0, U->getType()); // value is undefined
2922 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2923 IntegerType::get(Amt)),
2928 case Instruction::Trunc:
2929 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2931 case Instruction::ZExt:
2932 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2934 case Instruction::SExt:
2935 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2937 case Instruction::BitCast:
2938 // BitCasts are no-op casts so we just eliminate the cast.
2939 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2940 return getSCEV(U->getOperand(0));
2943 // It's tempting to handle inttoptr and ptrtoint, however this can
2944 // lead to pointer expressions which cannot be expanded to GEPs
2945 // (because they may overflow). For now, the only pointer-typed
2946 // expressions we handle are GEPs and address literals.
2948 case Instruction::GetElementPtr:
2949 if (!TD) break; // Without TD we can't analyze pointers.
2950 return createNodeForGEP(U);
2952 case Instruction::PHI:
2953 return createNodeForPHI(cast<PHINode>(U));
2955 case Instruction::Select:
2956 // This could be a smax or umax that was lowered earlier.
2957 // Try to recover it.
2958 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2959 Value *LHS = ICI->getOperand(0);
2960 Value *RHS = ICI->getOperand(1);
2961 switch (ICI->getPredicate()) {
2962 case ICmpInst::ICMP_SLT:
2963 case ICmpInst::ICMP_SLE:
2964 std::swap(LHS, RHS);
2966 case ICmpInst::ICMP_SGT:
2967 case ICmpInst::ICMP_SGE:
2968 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2969 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2970 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2971 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
2973 case ICmpInst::ICMP_ULT:
2974 case ICmpInst::ICMP_ULE:
2975 std::swap(LHS, RHS);
2977 case ICmpInst::ICMP_UGT:
2978 case ICmpInst::ICMP_UGE:
2979 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2980 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2981 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2982 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
2984 case ICmpInst::ICMP_NE:
2985 // n != 0 ? n : 1 -> umax(n, 1)
2986 if (LHS == U->getOperand(1) &&
2987 isa<ConstantInt>(U->getOperand(2)) &&
2988 cast<ConstantInt>(U->getOperand(2))->isOne() &&
2989 isa<ConstantInt>(RHS) &&
2990 cast<ConstantInt>(RHS)->isZero())
2991 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
2993 case ICmpInst::ICMP_EQ:
2994 // n == 0 ? 1 : n -> umax(n, 1)
2995 if (LHS == U->getOperand(2) &&
2996 isa<ConstantInt>(U->getOperand(1)) &&
2997 cast<ConstantInt>(U->getOperand(1))->isOne() &&
2998 isa<ConstantInt>(RHS) &&
2999 cast<ConstantInt>(RHS)->isZero())
3000 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
3007 default: // We cannot analyze this expression.
3011 return getUnknown(V);
3016 //===----------------------------------------------------------------------===//
3017 // Iteration Count Computation Code
3020 /// getBackedgeTakenCount - If the specified loop has a predictable
3021 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3022 /// object. The backedge-taken count is the number of times the loop header
3023 /// will be branched to from within the loop. This is one less than the
3024 /// trip count of the loop, since it doesn't count the first iteration,
3025 /// when the header is branched to from outside the loop.
3027 /// Note that it is not valid to call this method on a loop without a
3028 /// loop-invariant backedge-taken count (see
3029 /// hasLoopInvariantBackedgeTakenCount).
3031 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3032 return getBackedgeTakenInfo(L).Exact;
3035 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3036 /// return the least SCEV value that is known never to be less than the
3037 /// actual backedge taken count.
3038 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3039 return getBackedgeTakenInfo(L).Max;
3042 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3043 /// onto the given Worklist.
3045 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3046 BasicBlock *Header = L->getHeader();
3048 // Push all Loop-header PHIs onto the Worklist stack.
3049 for (BasicBlock::iterator I = Header->begin();
3050 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3051 Worklist.push_back(PN);
3054 /// PushDefUseChildren - Push users of the given Instruction
3055 /// onto the given Worklist.
3057 PushDefUseChildren(Instruction *I,
3058 SmallVectorImpl<Instruction *> &Worklist) {
3059 // Push the def-use children onto the Worklist stack.
3060 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
3062 Worklist.push_back(cast<Instruction>(UI));
3065 const ScalarEvolution::BackedgeTakenInfo &
3066 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3067 // Initially insert a CouldNotCompute for this loop. If the insertion
3068 // succeeds, procede to actually compute a backedge-taken count and
3069 // update the value. The temporary CouldNotCompute value tells SCEV
3070 // code elsewhere that it shouldn't attempt to request a new
3071 // backedge-taken count, which could result in infinite recursion.
3072 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
3073 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3075 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
3076 if (ItCount.Exact != getCouldNotCompute()) {
3077 assert(ItCount.Exact->isLoopInvariant(L) &&
3078 ItCount.Max->isLoopInvariant(L) &&
3079 "Computed trip count isn't loop invariant for loop!");
3080 ++NumTripCountsComputed;
3082 // Update the value in the map.
3083 Pair.first->second = ItCount;
3085 if (ItCount.Max != getCouldNotCompute())
3086 // Update the value in the map.
3087 Pair.first->second = ItCount;
3088 if (isa<PHINode>(L->getHeader()->begin()))
3089 // Only count loops that have phi nodes as not being computable.
3090 ++NumTripCountsNotComputed;
3093 // Now that we know more about the trip count for this loop, forget any
3094 // existing SCEV values for PHI nodes in this loop since they are only
3095 // conservative estimates made without the benefit of trip count
3096 // information. This is similar to the code in
3097 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI
3099 if (ItCount.hasAnyInfo()) {
3100 SmallVector<Instruction *, 16> Worklist;
3101 PushLoopPHIs(L, Worklist);
3103 SmallPtrSet<Instruction *, 8> Visited;
3104 while (!Worklist.empty()) {
3105 Instruction *I = Worklist.pop_back_val();
3106 if (!Visited.insert(I)) continue;
3108 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
3109 Scalars.find(static_cast<Value *>(I));
3110 if (It != Scalars.end()) {
3111 // SCEVUnknown for a PHI either means that it has an unrecognized
3112 // structure, or it's a PHI that's in the progress of being computed
3113 // by createNodeForPHI. In the former case, additional loop trip
3114 // count information isn't going to change anything. In the later
3115 // case, createNodeForPHI will perform the necessary updates on its
3116 // own when it gets to that point.
3117 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second))
3119 ValuesAtScopes.erase(I);
3120 if (PHINode *PN = dyn_cast<PHINode>(I))
3121 ConstantEvolutionLoopExitValue.erase(PN);
3124 PushDefUseChildren(I, Worklist);
3128 return Pair.first->second;
3131 /// forgetLoopBackedgeTakenCount - This method should be called by the
3132 /// client when it has changed a loop in a way that may effect
3133 /// ScalarEvolution's ability to compute a trip count, or if the loop
3135 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
3136 BackedgeTakenCounts.erase(L);
3138 SmallVector<Instruction *, 16> Worklist;
3139 PushLoopPHIs(L, Worklist);
3141 SmallPtrSet<Instruction *, 8> Visited;
3142 while (!Worklist.empty()) {
3143 Instruction *I = Worklist.pop_back_val();
3144 if (!Visited.insert(I)) continue;
3146 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
3147 Scalars.find(static_cast<Value *>(I));
3148 if (It != Scalars.end()) {
3150 ValuesAtScopes.erase(I);
3151 if (PHINode *PN = dyn_cast<PHINode>(I))
3152 ConstantEvolutionLoopExitValue.erase(PN);
3155 PushDefUseChildren(I, Worklist);
3159 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3160 /// of the specified loop will execute.
3161 ScalarEvolution::BackedgeTakenInfo
3162 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3163 SmallVector<BasicBlock*, 8> ExitingBlocks;
3164 L->getExitingBlocks(ExitingBlocks);
3166 // Examine all exits and pick the most conservative values.
3167 const SCEV *BECount = getCouldNotCompute();
3168 const SCEV *MaxBECount = getCouldNotCompute();
3169 bool CouldNotComputeBECount = false;
3170 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3171 BackedgeTakenInfo NewBTI =
3172 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3174 if (NewBTI.Exact == getCouldNotCompute()) {
3175 // We couldn't compute an exact value for this exit, so
3176 // we won't be able to compute an exact value for the loop.
3177 CouldNotComputeBECount = true;
3178 BECount = getCouldNotCompute();
3179 } else if (!CouldNotComputeBECount) {
3180 if (BECount == getCouldNotCompute())
3181 BECount = NewBTI.Exact;
3183 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3185 if (MaxBECount == getCouldNotCompute())
3186 MaxBECount = NewBTI.Max;
3187 else if (NewBTI.Max != getCouldNotCompute())
3188 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3191 return BackedgeTakenInfo(BECount, MaxBECount);
3194 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3195 /// of the specified loop will execute if it exits via the specified block.
3196 ScalarEvolution::BackedgeTakenInfo
3197 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3198 BasicBlock *ExitingBlock) {
3200 // Okay, we've chosen an exiting block. See what condition causes us to
3201 // exit at this block.
3203 // FIXME: we should be able to handle switch instructions (with a single exit)
3204 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3205 if (ExitBr == 0) return getCouldNotCompute();
3206 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3208 // At this point, we know we have a conditional branch that determines whether
3209 // the loop is exited. However, we don't know if the branch is executed each
3210 // time through the loop. If not, then the execution count of the branch will
3211 // not be equal to the trip count of the loop.
3213 // Currently we check for this by checking to see if the Exit branch goes to
3214 // the loop header. If so, we know it will always execute the same number of
3215 // times as the loop. We also handle the case where the exit block *is* the
3216 // loop header. This is common for un-rotated loops.
3218 // If both of those tests fail, walk up the unique predecessor chain to the
3219 // header, stopping if there is an edge that doesn't exit the loop. If the
3220 // header is reached, the execution count of the branch will be equal to the
3221 // trip count of the loop.
3223 // More extensive analysis could be done to handle more cases here.
3225 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3226 ExitBr->getSuccessor(1) != L->getHeader() &&
3227 ExitBr->getParent() != L->getHeader()) {
3228 // The simple checks failed, try climbing the unique predecessor chain
3229 // up to the header.
3231 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3232 BasicBlock *Pred = BB->getUniquePredecessor();
3234 return getCouldNotCompute();
3235 TerminatorInst *PredTerm = Pred->getTerminator();
3236 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3237 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3240 // If the predecessor has a successor that isn't BB and isn't
3241 // outside the loop, assume the worst.
3242 if (L->contains(PredSucc))
3243 return getCouldNotCompute();
3245 if (Pred == L->getHeader()) {
3252 return getCouldNotCompute();
3255 // Procede to the next level to examine the exit condition expression.
3256 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3257 ExitBr->getSuccessor(0),
3258 ExitBr->getSuccessor(1));
3261 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3262 /// backedge of the specified loop will execute if its exit condition
3263 /// were a conditional branch of ExitCond, TBB, and FBB.
3264 ScalarEvolution::BackedgeTakenInfo
3265 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3269 // Check if the controlling expression for this loop is an And or Or.
3270 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3271 if (BO->getOpcode() == Instruction::And) {
3272 // Recurse on the operands of the and.
3273 BackedgeTakenInfo BTI0 =
3274 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3275 BackedgeTakenInfo BTI1 =
3276 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3277 const SCEV *BECount = getCouldNotCompute();
3278 const SCEV *MaxBECount = getCouldNotCompute();
3279 if (L->contains(TBB)) {
3280 // Both conditions must be true for the loop to continue executing.
3281 // Choose the less conservative count.
3282 if (BTI0.Exact == getCouldNotCompute() ||
3283 BTI1.Exact == getCouldNotCompute())
3284 BECount = getCouldNotCompute();
3286 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3287 if (BTI0.Max == getCouldNotCompute())
3288 MaxBECount = BTI1.Max;
3289 else if (BTI1.Max == getCouldNotCompute())
3290 MaxBECount = BTI0.Max;
3292 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3294 // Both conditions must be true for the loop to exit.
3295 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3296 if (BTI0.Exact != getCouldNotCompute() &&
3297 BTI1.Exact != getCouldNotCompute())
3298 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3299 if (BTI0.Max != getCouldNotCompute() &&
3300 BTI1.Max != getCouldNotCompute())
3301 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3304 return BackedgeTakenInfo(BECount, MaxBECount);
3306 if (BO->getOpcode() == Instruction::Or) {
3307 // Recurse on the operands of the or.
3308 BackedgeTakenInfo BTI0 =
3309 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3310 BackedgeTakenInfo BTI1 =
3311 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3312 const SCEV *BECount = getCouldNotCompute();
3313 const SCEV *MaxBECount = getCouldNotCompute();
3314 if (L->contains(FBB)) {
3315 // Both conditions must be false for the loop to continue executing.
3316 // Choose the less conservative count.
3317 if (BTI0.Exact == getCouldNotCompute() ||
3318 BTI1.Exact == getCouldNotCompute())
3319 BECount = getCouldNotCompute();
3321 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3322 if (BTI0.Max == getCouldNotCompute())
3323 MaxBECount = BTI1.Max;
3324 else if (BTI1.Max == getCouldNotCompute())
3325 MaxBECount = BTI0.Max;
3327 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3329 // Both conditions must be false for the loop to exit.
3330 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3331 if (BTI0.Exact != getCouldNotCompute() &&
3332 BTI1.Exact != getCouldNotCompute())
3333 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3334 if (BTI0.Max != getCouldNotCompute() &&
3335 BTI1.Max != getCouldNotCompute())
3336 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3339 return BackedgeTakenInfo(BECount, MaxBECount);
3343 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3344 // Procede to the next level to examine the icmp.
3345 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3346 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3348 // If it's not an integer or pointer comparison then compute it the hard way.
3349 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3352 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3353 /// backedge of the specified loop will execute if its exit condition
3354 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3355 ScalarEvolution::BackedgeTakenInfo
3356 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3361 // If the condition was exit on true, convert the condition to exit on false
3362 ICmpInst::Predicate Cond;
3363 if (!L->contains(FBB))
3364 Cond = ExitCond->getPredicate();
3366 Cond = ExitCond->getInversePredicate();
3368 // Handle common loops like: for (X = "string"; *X; ++X)
3369 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3370 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3372 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3373 if (!isa<SCEVCouldNotCompute>(ItCnt)) {
3374 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType());
3375 return BackedgeTakenInfo(ItCnt,
3376 isa<SCEVConstant>(ItCnt) ? ItCnt :
3377 getConstant(APInt::getMaxValue(BitWidth)-1));
3381 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3382 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3384 // Try to evaluate any dependencies out of the loop.
3385 LHS = getSCEVAtScope(LHS, L);
3386 RHS = getSCEVAtScope(RHS, L);
3388 // At this point, we would like to compute how many iterations of the
3389 // loop the predicate will return true for these inputs.
3390 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3391 // If there is a loop-invariant, force it into the RHS.
3392 std::swap(LHS, RHS);
3393 Cond = ICmpInst::getSwappedPredicate(Cond);
3396 // If we have a comparison of a chrec against a constant, try to use value
3397 // ranges to answer this query.
3398 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3399 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3400 if (AddRec->getLoop() == L) {
3401 // Form the constant range.
3402 ConstantRange CompRange(
3403 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3405 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3406 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3410 case ICmpInst::ICMP_NE: { // while (X != Y)
3411 // Convert to: while (X-Y != 0)
3412 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3413 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3416 case ICmpInst::ICMP_EQ: {
3417 // Convert to: while (X-Y == 0) // while (X == Y)
3418 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3419 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3422 case ICmpInst::ICMP_SLT: {
3423 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3424 if (BTI.hasAnyInfo()) return BTI;
3427 case ICmpInst::ICMP_SGT: {
3428 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3429 getNotSCEV(RHS), L, true);
3430 if (BTI.hasAnyInfo()) return BTI;
3433 case ICmpInst::ICMP_ULT: {
3434 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3435 if (BTI.hasAnyInfo()) return BTI;
3438 case ICmpInst::ICMP_UGT: {
3439 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3440 getNotSCEV(RHS), L, false);
3441 if (BTI.hasAnyInfo()) return BTI;
3446 errs() << "ComputeBackedgeTakenCount ";
3447 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3448 errs() << "[unsigned] ";
3449 errs() << *LHS << " "
3450 << Instruction::getOpcodeName(Instruction::ICmp)
3451 << " " << *RHS << "\n";
3456 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3459 static ConstantInt *
3460 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3461 ScalarEvolution &SE) {
3462 const SCEV *InVal = SE.getConstant(C);
3463 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3464 assert(isa<SCEVConstant>(Val) &&
3465 "Evaluation of SCEV at constant didn't fold correctly?");
3466 return cast<SCEVConstant>(Val)->getValue();
3469 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3470 /// and a GEP expression (missing the pointer index) indexing into it, return
3471 /// the addressed element of the initializer or null if the index expression is
3474 GetAddressedElementFromGlobal(LLVMContext *Context, GlobalVariable *GV,
3475 const std::vector<ConstantInt*> &Indices) {
3476 Constant *Init = GV->getInitializer();
3477 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3478 uint64_t Idx = Indices[i]->getZExtValue();
3479 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3480 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3481 Init = cast<Constant>(CS->getOperand(Idx));
3482 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3483 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3484 Init = cast<Constant>(CA->getOperand(Idx));
3485 } else if (isa<ConstantAggregateZero>(Init)) {
3486 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3487 assert(Idx < STy->getNumElements() && "Bad struct index!");
3488 Init = Context->getNullValue(STy->getElementType(Idx));
3489 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3490 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3491 Init = Context->getNullValue(ATy->getElementType());
3493 llvm_unreachable("Unknown constant aggregate type!");
3497 return 0; // Unknown initializer type
3503 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3504 /// 'icmp op load X, cst', try to see if we can compute the backedge
3505 /// execution count.
3507 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3511 ICmpInst::Predicate predicate) {
3512 if (LI->isVolatile()) return getCouldNotCompute();
3514 // Check to see if the loaded pointer is a getelementptr of a global.
3515 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3516 if (!GEP) return getCouldNotCompute();
3518 // Make sure that it is really a constant global we are gepping, with an
3519 // initializer, and make sure the first IDX is really 0.
3520 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3521 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
3522 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3523 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3524 return getCouldNotCompute();
3526 // Okay, we allow one non-constant index into the GEP instruction.
3528 std::vector<ConstantInt*> Indexes;
3529 unsigned VarIdxNum = 0;
3530 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3531 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3532 Indexes.push_back(CI);
3533 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3534 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3535 VarIdx = GEP->getOperand(i);
3537 Indexes.push_back(0);
3540 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3541 // Check to see if X is a loop variant variable value now.
3542 const SCEV *Idx = getSCEV(VarIdx);
3543 Idx = getSCEVAtScope(Idx, L);
3545 // We can only recognize very limited forms of loop index expressions, in
3546 // particular, only affine AddRec's like {C1,+,C2}.
3547 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3548 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3549 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3550 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
3551 return getCouldNotCompute();
3553 unsigned MaxSteps = MaxBruteForceIterations;
3554 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3555 ConstantInt *ItCst = Context->getConstantInt(
3556 cast<IntegerType>(IdxExpr->getType()), IterationNum);
3557 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
3559 // Form the GEP offset.
3560 Indexes[VarIdxNum] = Val;
3562 Constant *Result = GetAddressedElementFromGlobal(Context, GV, Indexes);
3563 if (Result == 0) break; // Cannot compute!
3565 // Evaluate the condition for this iteration.
3566 Result = ConstantExpr::getICmp(predicate, Result, RHS);
3567 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
3568 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
3570 errs() << "\n***\n*** Computed loop count " << *ItCst
3571 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
3574 ++NumArrayLenItCounts;
3575 return getConstant(ItCst); // Found terminating iteration!
3578 return getCouldNotCompute();
3582 /// CanConstantFold - Return true if we can constant fold an instruction of the
3583 /// specified type, assuming that all operands were constants.
3584 static bool CanConstantFold(const Instruction *I) {
3585 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
3586 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
3589 if (const CallInst *CI = dyn_cast<CallInst>(I))
3590 if (const Function *F = CI->getCalledFunction())
3591 return canConstantFoldCallTo(F);
3595 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
3596 /// in the loop that V is derived from. We allow arbitrary operations along the
3597 /// way, but the operands of an operation must either be constants or a value
3598 /// derived from a constant PHI. If this expression does not fit with these
3599 /// constraints, return null.
3600 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
3601 // If this is not an instruction, or if this is an instruction outside of the
3602 // loop, it can't be derived from a loop PHI.
3603 Instruction *I = dyn_cast<Instruction>(V);
3604 if (I == 0 || !L->contains(I->getParent())) return 0;
3606 if (PHINode *PN = dyn_cast<PHINode>(I)) {
3607 if (L->getHeader() == I->getParent())
3610 // We don't currently keep track of the control flow needed to evaluate
3611 // PHIs, so we cannot handle PHIs inside of loops.
3615 // If we won't be able to constant fold this expression even if the operands
3616 // are constants, return early.
3617 if (!CanConstantFold(I)) return 0;
3619 // Otherwise, we can evaluate this instruction if all of its operands are
3620 // constant or derived from a PHI node themselves.
3622 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
3623 if (!(isa<Constant>(I->getOperand(Op)) ||
3624 isa<GlobalValue>(I->getOperand(Op)))) {
3625 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
3626 if (P == 0) return 0; // Not evolving from PHI
3630 return 0; // Evolving from multiple different PHIs.
3633 // This is a expression evolving from a constant PHI!
3637 /// EvaluateExpression - Given an expression that passes the
3638 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
3639 /// in the loop has the value PHIVal. If we can't fold this expression for some
3640 /// reason, return null.
3641 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
3642 if (isa<PHINode>(V)) return PHIVal;
3643 if (Constant *C = dyn_cast<Constant>(V)) return C;
3644 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
3645 Instruction *I = cast<Instruction>(V);
3646 LLVMContext *Context = I->getParent()->getContext();
3648 std::vector<Constant*> Operands;
3649 Operands.resize(I->getNumOperands());
3651 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3652 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
3653 if (Operands[i] == 0) return 0;
3656 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3657 return ConstantFoldCompareInstOperands(CI->getPredicate(),
3658 &Operands[0], Operands.size(),
3661 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3662 &Operands[0], Operands.size(),
3666 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
3667 /// in the header of its containing loop, we know the loop executes a
3668 /// constant number of times, and the PHI node is just a recurrence
3669 /// involving constants, fold it.
3671 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
3674 std::map<PHINode*, Constant*>::iterator I =
3675 ConstantEvolutionLoopExitValue.find(PN);
3676 if (I != ConstantEvolutionLoopExitValue.end())
3679 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
3680 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
3682 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
3684 // Since the loop is canonicalized, the PHI node must have two entries. One
3685 // entry must be a constant (coming in from outside of the loop), and the
3686 // second must be derived from the same PHI.
3687 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3688 Constant *StartCST =
3689 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3691 return RetVal = 0; // Must be a constant.
3693 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3694 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3696 return RetVal = 0; // Not derived from same PHI.
3698 // Execute the loop symbolically to determine the exit value.
3699 if (BEs.getActiveBits() >= 32)
3700 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
3702 unsigned NumIterations = BEs.getZExtValue(); // must be in range
3703 unsigned IterationNum = 0;
3704 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
3705 if (IterationNum == NumIterations)
3706 return RetVal = PHIVal; // Got exit value!
3708 // Compute the value of the PHI node for the next iteration.
3709 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3710 if (NextPHI == PHIVal)
3711 return RetVal = NextPHI; // Stopped evolving!
3713 return 0; // Couldn't evaluate!
3718 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
3719 /// constant number of times (the condition evolves only from constants),
3720 /// try to evaluate a few iterations of the loop until we get the exit
3721 /// condition gets a value of ExitWhen (true or false). If we cannot
3722 /// evaluate the trip count of the loop, return getCouldNotCompute().
3724 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
3727 PHINode *PN = getConstantEvolvingPHI(Cond, L);
3728 if (PN == 0) return getCouldNotCompute();
3730 // Since the loop is canonicalized, the PHI node must have two entries. One
3731 // entry must be a constant (coming in from outside of the loop), and the
3732 // second must be derived from the same PHI.
3733 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3734 Constant *StartCST =
3735 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3736 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
3738 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3739 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3740 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
3742 // Okay, we find a PHI node that defines the trip count of this loop. Execute
3743 // the loop symbolically to determine when the condition gets a value of
3745 unsigned IterationNum = 0;
3746 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
3747 for (Constant *PHIVal = StartCST;
3748 IterationNum != MaxIterations; ++IterationNum) {
3749 ConstantInt *CondVal =
3750 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
3752 // Couldn't symbolically evaluate.
3753 if (!CondVal) return getCouldNotCompute();
3755 if (CondVal->getValue() == uint64_t(ExitWhen)) {
3756 ++NumBruteForceTripCountsComputed;
3757 return getConstant(Type::Int32Ty, IterationNum);
3760 // Compute the value of the PHI node for the next iteration.
3761 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3762 if (NextPHI == 0 || NextPHI == PHIVal)
3763 return getCouldNotCompute();// Couldn't evaluate or not making progress...
3767 // Too many iterations were needed to evaluate.
3768 return getCouldNotCompute();
3771 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
3772 /// at the specified scope in the program. The L value specifies a loop
3773 /// nest to evaluate the expression at, where null is the top-level or a
3774 /// specified loop is immediately inside of the loop.
3776 /// This method can be used to compute the exit value for a variable defined
3777 /// in a loop by querying what the value will hold in the parent loop.
3779 /// In the case that a relevant loop exit value cannot be computed, the
3780 /// original value V is returned.
3781 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
3782 // FIXME: this should be turned into a virtual method on SCEV!
3784 if (isa<SCEVConstant>(V)) return V;
3786 // If this instruction is evolved from a constant-evolving PHI, compute the
3787 // exit value from the loop without using SCEVs.
3788 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
3789 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
3790 const Loop *LI = (*this->LI)[I->getParent()];
3791 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
3792 if (PHINode *PN = dyn_cast<PHINode>(I))
3793 if (PN->getParent() == LI->getHeader()) {
3794 // Okay, there is no closed form solution for the PHI node. Check
3795 // to see if the loop that contains it has a known backedge-taken
3796 // count. If so, we may be able to force computation of the exit
3798 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
3799 if (const SCEVConstant *BTCC =
3800 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
3801 // Okay, we know how many times the containing loop executes. If
3802 // this is a constant evolving PHI node, get the final value at
3803 // the specified iteration number.
3804 Constant *RV = getConstantEvolutionLoopExitValue(PN,
3805 BTCC->getValue()->getValue(),
3807 if (RV) return getSCEV(RV);
3811 // Okay, this is an expression that we cannot symbolically evaluate
3812 // into a SCEV. Check to see if it's possible to symbolically evaluate
3813 // the arguments into constants, and if so, try to constant propagate the
3814 // result. This is particularly useful for computing loop exit values.
3815 if (CanConstantFold(I)) {
3816 // Check to see if we've folded this instruction at this loop before.
3817 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
3818 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
3819 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
3821 return Pair.first->second ? &*getSCEV(Pair.first->second) : V;
3823 std::vector<Constant*> Operands;
3824 Operands.reserve(I->getNumOperands());
3825 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3826 Value *Op = I->getOperand(i);
3827 if (Constant *C = dyn_cast<Constant>(Op)) {
3828 Operands.push_back(C);
3830 // If any of the operands is non-constant and if they are
3831 // non-integer and non-pointer, don't even try to analyze them
3832 // with scev techniques.
3833 if (!isSCEVable(Op->getType()))
3836 const SCEV* OpV = getSCEVAtScope(Op, L);
3837 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
3838 Constant *C = SC->getValue();
3839 if (C->getType() != Op->getType())
3840 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3844 Operands.push_back(C);
3845 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
3846 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
3847 if (C->getType() != Op->getType())
3849 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3853 Operands.push_back(C);
3863 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3864 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
3865 &Operands[0], Operands.size(),
3868 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3869 &Operands[0], Operands.size(), Context);
3870 Pair.first->second = C;
3875 // This is some other type of SCEVUnknown, just return it.
3879 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3880 // Avoid performing the look-up in the common case where the specified
3881 // expression has no loop-variant portions.
3882 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3883 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3884 if (OpAtScope != Comm->getOperand(i)) {
3885 // Okay, at least one of these operands is loop variant but might be
3886 // foldable. Build a new instance of the folded commutative expression.
3887 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
3888 Comm->op_begin()+i);
3889 NewOps.push_back(OpAtScope);
3891 for (++i; i != e; ++i) {
3892 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3893 NewOps.push_back(OpAtScope);
3895 if (isa<SCEVAddExpr>(Comm))
3896 return getAddExpr(NewOps);
3897 if (isa<SCEVMulExpr>(Comm))
3898 return getMulExpr(NewOps);
3899 if (isa<SCEVSMaxExpr>(Comm))
3900 return getSMaxExpr(NewOps);
3901 if (isa<SCEVUMaxExpr>(Comm))
3902 return getUMaxExpr(NewOps);
3903 llvm_unreachable("Unknown commutative SCEV type!");
3906 // If we got here, all operands are loop invariant.
3910 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3911 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
3912 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
3913 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3914 return Div; // must be loop invariant
3915 return getUDivExpr(LHS, RHS);
3918 // If this is a loop recurrence for a loop that does not contain L, then we
3919 // are dealing with the final value computed by the loop.
3920 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3921 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3922 // To evaluate this recurrence, we need to know how many times the AddRec
3923 // loop iterates. Compute this now.
3924 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3925 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
3927 // Then, evaluate the AddRec.
3928 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3933 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3934 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3935 if (Op == Cast->getOperand())
3936 return Cast; // must be loop invariant
3937 return getZeroExtendExpr(Op, Cast->getType());
3940 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3941 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3942 if (Op == Cast->getOperand())
3943 return Cast; // must be loop invariant
3944 return getSignExtendExpr(Op, Cast->getType());
3947 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3948 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3949 if (Op == Cast->getOperand())
3950 return Cast; // must be loop invariant
3951 return getTruncateExpr(Op, Cast->getType());
3954 llvm_unreachable("Unknown SCEV type!");
3958 /// getSCEVAtScope - This is a convenience function which does
3959 /// getSCEVAtScope(getSCEV(V), L).
3960 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3961 return getSCEVAtScope(getSCEV(V), L);
3964 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3965 /// following equation:
3967 /// A * X = B (mod N)
3969 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3970 /// A and B isn't important.
3972 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3973 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3974 ScalarEvolution &SE) {
3975 uint32_t BW = A.getBitWidth();
3976 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3977 assert(A != 0 && "A must be non-zero.");
3981 // The gcd of A and N may have only one prime factor: 2. The number of
3982 // trailing zeros in A is its multiplicity
3983 uint32_t Mult2 = A.countTrailingZeros();
3986 // 2. Check if B is divisible by D.
3988 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3989 // is not less than multiplicity of this prime factor for D.
3990 if (B.countTrailingZeros() < Mult2)
3991 return SE.getCouldNotCompute();
3993 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3996 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3997 // bit width during computations.
3998 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3999 APInt Mod(BW + 1, 0);
4000 Mod.set(BW - Mult2); // Mod = N / D
4001 APInt I = AD.multiplicativeInverse(Mod);
4003 // 4. Compute the minimum unsigned root of the equation:
4004 // I * (B / D) mod (N / D)
4005 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4007 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4009 return SE.getConstant(Result.trunc(BW));
4012 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4013 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4014 /// might be the same) or two SCEVCouldNotCompute objects.
4016 static std::pair<const SCEV *,const SCEV *>
4017 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4018 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4019 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4020 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4021 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4023 // We currently can only solve this if the coefficients are constants.
4024 if (!LC || !MC || !NC) {
4025 const SCEV *CNC = SE.getCouldNotCompute();
4026 return std::make_pair(CNC, CNC);
4029 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4030 const APInt &L = LC->getValue()->getValue();
4031 const APInt &M = MC->getValue()->getValue();
4032 const APInt &N = NC->getValue()->getValue();
4033 APInt Two(BitWidth, 2);
4034 APInt Four(BitWidth, 4);
4037 using namespace APIntOps;
4039 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4040 // The B coefficient is M-N/2
4044 // The A coefficient is N/2
4045 APInt A(N.sdiv(Two));
4047 // Compute the B^2-4ac term.
4050 SqrtTerm -= Four * (A * C);
4052 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4053 // integer value or else APInt::sqrt() will assert.
4054 APInt SqrtVal(SqrtTerm.sqrt());
4056 // Compute the two solutions for the quadratic formula.
4057 // The divisions must be performed as signed divisions.
4059 APInt TwoA( A << 1 );
4060 if (TwoA.isMinValue()) {
4061 const SCEV *CNC = SE.getCouldNotCompute();
4062 return std::make_pair(CNC, CNC);
4065 LLVMContext *Context = SE.getContext();
4067 ConstantInt *Solution1 =
4068 Context->getConstantInt((NegB + SqrtVal).sdiv(TwoA));
4069 ConstantInt *Solution2 =
4070 Context->getConstantInt((NegB - SqrtVal).sdiv(TwoA));
4072 return std::make_pair(SE.getConstant(Solution1),
4073 SE.getConstant(Solution2));
4074 } // end APIntOps namespace
4077 /// HowFarToZero - Return the number of times a backedge comparing the specified
4078 /// value to zero will execute. If not computable, return CouldNotCompute.
4079 const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4080 // If the value is a constant
4081 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4082 // If the value is already zero, the branch will execute zero times.
4083 if (C->getValue()->isZero()) return C;
4084 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4087 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4088 if (!AddRec || AddRec->getLoop() != L)
4089 return getCouldNotCompute();
4091 if (AddRec->isAffine()) {
4092 // If this is an affine expression, the execution count of this branch is
4093 // the minimum unsigned root of the following equation:
4095 // Start + Step*N = 0 (mod 2^BW)
4099 // Step*N = -Start (mod 2^BW)
4101 // where BW is the common bit width of Start and Step.
4103 // Get the initial value for the loop.
4104 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4105 L->getParentLoop());
4106 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4107 L->getParentLoop());
4109 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4110 // For now we handle only constant steps.
4112 // First, handle unitary steps.
4113 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4114 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4115 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4116 return Start; // N = Start (as unsigned)
4118 // Then, try to solve the above equation provided that Start is constant.
4119 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4120 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4121 -StartC->getValue()->getValue(),
4124 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
4125 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4126 // the quadratic equation to solve it.
4127 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4129 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4130 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4133 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
4134 << " sol#2: " << *R2 << "\n";
4136 // Pick the smallest positive root value.
4137 if (ConstantInt *CB =
4138 dyn_cast<ConstantInt>(Context->getConstantExprICmp(ICmpInst::ICMP_ULT,
4139 R1->getValue(), R2->getValue()))) {
4140 if (CB->getZExtValue() == false)
4141 std::swap(R1, R2); // R1 is the minimum root now.
4143 // We can only use this value if the chrec ends up with an exact zero
4144 // value at this index. When solving for "X*X != 5", for example, we
4145 // should not accept a root of 2.
4146 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4148 return R1; // We found a quadratic root!
4153 return getCouldNotCompute();
4156 /// HowFarToNonZero - Return the number of times a backedge checking the
4157 /// specified value for nonzero will execute. If not computable, return
4159 const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4160 // Loops that look like: while (X == 0) are very strange indeed. We don't
4161 // handle them yet except for the trivial case. This could be expanded in the
4162 // future as needed.
4164 // If the value is a constant, check to see if it is known to be non-zero
4165 // already. If so, the backedge will execute zero times.
4166 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4167 if (!C->getValue()->isNullValue())
4168 return getIntegerSCEV(0, C->getType());
4169 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4172 // We could implement others, but I really doubt anyone writes loops like
4173 // this, and if they did, they would already be constant folded.
4174 return getCouldNotCompute();
4177 /// getLoopPredecessor - If the given loop's header has exactly one unique
4178 /// predecessor outside the loop, return it. Otherwise return null.
4180 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
4181 BasicBlock *Header = L->getHeader();
4182 BasicBlock *Pred = 0;
4183 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
4185 if (!L->contains(*PI)) {
4186 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
4192 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4193 /// (which may not be an immediate predecessor) which has exactly one
4194 /// successor from which BB is reachable, or null if no such block is
4198 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4199 // If the block has a unique predecessor, then there is no path from the
4200 // predecessor to the block that does not go through the direct edge
4201 // from the predecessor to the block.
4202 if (BasicBlock *Pred = BB->getSinglePredecessor())
4205 // A loop's header is defined to be a block that dominates the loop.
4206 // If the header has a unique predecessor outside the loop, it must be
4207 // a block that has exactly one successor that can reach the loop.
4208 if (Loop *L = LI->getLoopFor(BB))
4209 return getLoopPredecessor(L);
4214 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4215 /// testing whether two expressions are equal, however for the purposes of
4216 /// looking for a condition guarding a loop, it can be useful to be a little
4217 /// more general, since a front-end may have replicated the controlling
4220 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4221 // Quick check to see if they are the same SCEV.
4222 if (A == B) return true;
4224 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4225 // two different instructions with the same value. Check for this case.
4226 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4227 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4228 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4229 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4230 if (AI->isIdenticalTo(BI))
4233 // Otherwise assume they may have a different value.
4237 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
4238 return getSignedRange(S).getSignedMax().isNegative();
4241 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
4242 return getSignedRange(S).getSignedMin().isStrictlyPositive();
4245 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
4246 return !getSignedRange(S).getSignedMin().isNegative();
4249 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
4250 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
4253 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
4254 return isKnownNegative(S) || isKnownPositive(S);
4257 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
4258 const SCEV *LHS, const SCEV *RHS) {
4260 if (HasSameValue(LHS, RHS))
4261 return ICmpInst::isTrueWhenEqual(Pred);
4265 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4267 case ICmpInst::ICMP_SGT:
4268 Pred = ICmpInst::ICMP_SLT;
4269 std::swap(LHS, RHS);
4270 case ICmpInst::ICMP_SLT: {
4271 ConstantRange LHSRange = getSignedRange(LHS);
4272 ConstantRange RHSRange = getSignedRange(RHS);
4273 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
4275 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
4279 case ICmpInst::ICMP_SGE:
4280 Pred = ICmpInst::ICMP_SLE;
4281 std::swap(LHS, RHS);
4282 case ICmpInst::ICMP_SLE: {
4283 ConstantRange LHSRange = getSignedRange(LHS);
4284 ConstantRange RHSRange = getSignedRange(RHS);
4285 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
4287 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
4291 case ICmpInst::ICMP_UGT:
4292 Pred = ICmpInst::ICMP_ULT;
4293 std::swap(LHS, RHS);
4294 case ICmpInst::ICMP_ULT: {
4295 ConstantRange LHSRange = getUnsignedRange(LHS);
4296 ConstantRange RHSRange = getUnsignedRange(RHS);
4297 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
4299 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
4303 case ICmpInst::ICMP_UGE:
4304 Pred = ICmpInst::ICMP_ULE;
4305 std::swap(LHS, RHS);
4306 case ICmpInst::ICMP_ULE: {
4307 ConstantRange LHSRange = getUnsignedRange(LHS);
4308 ConstantRange RHSRange = getUnsignedRange(RHS);
4309 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
4311 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
4315 case ICmpInst::ICMP_NE: {
4316 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
4318 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
4321 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4322 if (isKnownNonZero(Diff))
4326 case ICmpInst::ICMP_EQ:
4327 // The check at the top of the function catches the case where
4328 // the values are known to be equal.
4334 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
4335 /// protected by a conditional between LHS and RHS. This is used to
4336 /// to eliminate casts.
4338 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
4339 ICmpInst::Predicate Pred,
4340 const SCEV *LHS, const SCEV *RHS) {
4341 // Interpret a null as meaning no loop, where there is obviously no guard
4342 // (interprocedural conditions notwithstanding).
4343 if (!L) return true;
4345 BasicBlock *Latch = L->getLoopLatch();
4349 BranchInst *LoopContinuePredicate =
4350 dyn_cast<BranchInst>(Latch->getTerminator());
4351 if (!LoopContinuePredicate ||
4352 LoopContinuePredicate->isUnconditional())
4356 isNecessaryCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
4357 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
4360 /// isLoopGuardedByCond - Test whether entry to the loop is protected
4361 /// by a conditional between LHS and RHS. This is used to help avoid max
4362 /// expressions in loop trip counts, and to eliminate casts.
4364 ScalarEvolution::isLoopGuardedByCond(const Loop *L,
4365 ICmpInst::Predicate Pred,
4366 const SCEV *LHS, const SCEV *RHS) {
4367 // Interpret a null as meaning no loop, where there is obviously no guard
4368 // (interprocedural conditions notwithstanding).
4369 if (!L) return false;
4371 BasicBlock *Predecessor = getLoopPredecessor(L);
4372 BasicBlock *PredecessorDest = L->getHeader();
4374 // Starting at the loop predecessor, climb up the predecessor chain, as long
4375 // as there are predecessors that can be found that have unique successors
4376 // leading to the original header.
4378 PredecessorDest = Predecessor,
4379 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4381 BranchInst *LoopEntryPredicate =
4382 dyn_cast<BranchInst>(Predecessor->getTerminator());
4383 if (!LoopEntryPredicate ||
4384 LoopEntryPredicate->isUnconditional())
4387 if (isNecessaryCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4388 LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4395 /// isNecessaryCond - Test whether the condition described by Pred, LHS,
4396 /// and RHS is a necessary condition for the given Cond value to evaluate
4398 bool ScalarEvolution::isNecessaryCond(Value *CondValue,
4399 ICmpInst::Predicate Pred,
4400 const SCEV *LHS, const SCEV *RHS,
4402 // Recursivly handle And and Or conditions.
4403 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4404 if (BO->getOpcode() == Instruction::And) {
4406 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4407 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4408 } else if (BO->getOpcode() == Instruction::Or) {
4410 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4411 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4415 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4416 if (!ICI) return false;
4418 // Now that we found a conditional branch that dominates the loop, check to
4419 // see if it is the comparison we are looking for.
4420 Value *PreCondLHS = ICI->getOperand(0);
4421 Value *PreCondRHS = ICI->getOperand(1);
4422 ICmpInst::Predicate FoundPred;
4424 FoundPred = ICI->getInversePredicate();
4426 FoundPred = ICI->getPredicate();
4428 if (FoundPred == Pred)
4429 ; // An exact match.
4430 else if (!ICmpInst::isTrueWhenEqual(FoundPred) && Pred == ICmpInst::ICMP_NE) {
4431 // The actual condition is beyond sufficient.
4432 FoundPred = ICmpInst::ICMP_NE;
4433 // NE is symmetric but the original comparison may not be. Swap
4434 // the operands if necessary so that they match below.
4435 if (isa<SCEVConstant>(LHS))
4436 std::swap(PreCondLHS, PreCondRHS);
4438 // Check a few special cases.
4439 switch (FoundPred) {
4440 case ICmpInst::ICMP_UGT:
4441 if (Pred == ICmpInst::ICMP_ULT) {
4442 std::swap(PreCondLHS, PreCondRHS);
4443 FoundPred = ICmpInst::ICMP_ULT;
4447 case ICmpInst::ICMP_SGT:
4448 if (Pred == ICmpInst::ICMP_SLT) {
4449 std::swap(PreCondLHS, PreCondRHS);
4450 FoundPred = ICmpInst::ICMP_SLT;
4454 case ICmpInst::ICMP_NE:
4455 // Expressions like (x >u 0) are often canonicalized to (x != 0),
4456 // so check for this case by checking if the NE is comparing against
4457 // a minimum or maximum constant.
4458 if (!ICmpInst::isTrueWhenEqual(Pred))
4459 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(RHS)) {
4460 const APInt &A = C->getValue()->getValue();
4462 case ICmpInst::ICMP_SLT:
4463 if (A.isMaxSignedValue()) break;
4465 case ICmpInst::ICMP_SGT:
4466 if (A.isMinSignedValue()) break;
4468 case ICmpInst::ICMP_ULT:
4469 if (A.isMaxValue()) break;
4471 case ICmpInst::ICMP_UGT:
4472 if (A.isMinValue()) break;
4478 // NE is symmetric but the original comparison may not be. Swap
4479 // the operands if necessary so that they match below.
4480 if (isa<SCEVConstant>(LHS))
4481 std::swap(PreCondLHS, PreCondRHS);
4486 // We weren't able to reconcile the condition.
4490 assert(Pred == FoundPred && "Conditions were not reconciled!");
4492 // Bail if the ICmp's operands' types are wider than the needed type
4493 // before attempting to call getSCEV on them. This avoids infinite
4494 // recursion, since the analysis of widening casts can require loop
4495 // exit condition information for overflow checking, which would
4497 if (getTypeSizeInBits(LHS->getType()) <
4498 getTypeSizeInBits(PreCondLHS->getType()))
4501 const SCEV *FoundLHS = getSCEV(PreCondLHS);
4502 const SCEV *FoundRHS = getSCEV(PreCondRHS);
4504 // Balance the types. The case where FoundLHS' type is wider than
4505 // LHS' type is checked for above.
4506 if (getTypeSizeInBits(LHS->getType()) >
4507 getTypeSizeInBits(FoundLHS->getType())) {
4508 if (CmpInst::isSigned(Pred)) {
4509 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
4510 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
4512 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
4513 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
4517 return isNecessaryCondOperands(Pred, LHS, RHS,
4518 FoundLHS, FoundRHS) ||
4519 // ~x < ~y --> x > y
4520 isNecessaryCondOperands(Pred, LHS, RHS,
4521 getNotSCEV(FoundRHS), getNotSCEV(FoundLHS));
4524 /// isNecessaryCondOperands - Test whether the condition described by Pred,
4525 /// LHS, and RHS is a necessary condition for the condition described by
4526 /// Pred, FoundLHS, and FoundRHS to evaluate to true.
4528 ScalarEvolution::isNecessaryCondOperands(ICmpInst::Predicate Pred,
4529 const SCEV *LHS, const SCEV *RHS,
4530 const SCEV *FoundLHS,
4531 const SCEV *FoundRHS) {
4533 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4534 case ICmpInst::ICMP_EQ:
4535 case ICmpInst::ICMP_NE:
4536 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
4539 case ICmpInst::ICMP_SLT:
4540 case ICmpInst::ICMP_SLE:
4541 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
4542 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS))
4545 case ICmpInst::ICMP_SGT:
4546 case ICmpInst::ICMP_SGE:
4547 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
4548 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS))
4551 case ICmpInst::ICMP_ULT:
4552 case ICmpInst::ICMP_ULE:
4553 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
4554 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS))
4557 case ICmpInst::ICMP_UGT:
4558 case ICmpInst::ICMP_UGE:
4559 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
4560 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS))
4568 /// getBECount - Subtract the end and start values and divide by the step,
4569 /// rounding up, to get the number of times the backedge is executed. Return
4570 /// CouldNotCompute if an intermediate computation overflows.
4571 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
4574 const Type *Ty = Start->getType();
4575 const SCEV *NegOne = getIntegerSCEV(-1, Ty);
4576 const SCEV *Diff = getMinusSCEV(End, Start);
4577 const SCEV *RoundUp = getAddExpr(Step, NegOne);
4579 // Add an adjustment to the difference between End and Start so that
4580 // the division will effectively round up.
4581 const SCEV *Add = getAddExpr(Diff, RoundUp);
4583 // Check Add for unsigned overflow.
4584 // TODO: More sophisticated things could be done here.
4585 const Type *WideTy = Context->getIntegerType(getTypeSizeInBits(Ty) + 1);
4586 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
4587 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
4588 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
4589 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
4590 return getCouldNotCompute();
4592 return getUDivExpr(Add, Step);
4595 /// HowManyLessThans - Return the number of times a backedge containing the
4596 /// specified less-than comparison will execute. If not computable, return
4597 /// CouldNotCompute.
4598 ScalarEvolution::BackedgeTakenInfo
4599 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
4600 const Loop *L, bool isSigned) {
4601 // Only handle: "ADDREC < LoopInvariant".
4602 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
4604 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
4605 if (!AddRec || AddRec->getLoop() != L)
4606 return getCouldNotCompute();
4608 if (AddRec->isAffine()) {
4609 // FORNOW: We only support unit strides.
4610 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
4611 const SCEV *Step = AddRec->getStepRecurrence(*this);
4613 // TODO: handle non-constant strides.
4614 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
4615 if (!CStep || CStep->isZero())
4616 return getCouldNotCompute();
4617 if (CStep->isOne()) {
4618 // With unit stride, the iteration never steps past the limit value.
4619 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
4620 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
4621 // Test whether a positive iteration iteration can step past the limit
4622 // value and past the maximum value for its type in a single step.
4624 APInt Max = APInt::getSignedMaxValue(BitWidth);
4625 if ((Max - CStep->getValue()->getValue())
4626 .slt(CLimit->getValue()->getValue()))
4627 return getCouldNotCompute();
4629 APInt Max = APInt::getMaxValue(BitWidth);
4630 if ((Max - CStep->getValue()->getValue())
4631 .ult(CLimit->getValue()->getValue()))
4632 return getCouldNotCompute();
4635 // TODO: handle non-constant limit values below.
4636 return getCouldNotCompute();
4638 // TODO: handle negative strides below.
4639 return getCouldNotCompute();
4641 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
4642 // m. So, we count the number of iterations in which {n,+,s} < m is true.
4643 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
4644 // treat m-n as signed nor unsigned due to overflow possibility.
4646 // First, we get the value of the LHS in the first iteration: n
4647 const SCEV *Start = AddRec->getOperand(0);
4649 // Determine the minimum constant start value.
4650 const SCEV *MinStart = getConstant(isSigned ?
4651 getSignedRange(Start).getSignedMin() :
4652 getUnsignedRange(Start).getUnsignedMin());
4654 // If we know that the condition is true in order to enter the loop,
4655 // then we know that it will run exactly (m-n)/s times. Otherwise, we
4656 // only know that it will execute (max(m,n)-n)/s times. In both cases,
4657 // the division must round up.
4658 const SCEV *End = RHS;
4659 if (!isLoopGuardedByCond(L,
4660 isSigned ? ICmpInst::ICMP_SLT :
4662 getMinusSCEV(Start, Step), RHS))
4663 End = isSigned ? getSMaxExpr(RHS, Start)
4664 : getUMaxExpr(RHS, Start);
4666 // Determine the maximum constant end value.
4667 const SCEV *MaxEnd = getConstant(isSigned ?
4668 getSignedRange(End).getSignedMax() :
4669 getUnsignedRange(End).getUnsignedMax());
4671 // Finally, we subtract these two values and divide, rounding up, to get
4672 // the number of times the backedge is executed.
4673 const SCEV *BECount = getBECount(Start, End, Step);
4675 // The maximum backedge count is similar, except using the minimum start
4676 // value and the maximum end value.
4677 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step);
4679 return BackedgeTakenInfo(BECount, MaxBECount);
4682 return getCouldNotCompute();
4685 /// getNumIterationsInRange - Return the number of iterations of this loop that
4686 /// produce values in the specified constant range. Another way of looking at
4687 /// this is that it returns the first iteration number where the value is not in
4688 /// the condition, thus computing the exit count. If the iteration count can't
4689 /// be computed, an instance of SCEVCouldNotCompute is returned.
4690 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
4691 ScalarEvolution &SE) const {
4692 if (Range.isFullSet()) // Infinite loop.
4693 return SE.getCouldNotCompute();
4695 // If the start is a non-zero constant, shift the range to simplify things.
4696 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
4697 if (!SC->getValue()->isZero()) {
4698 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
4699 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
4700 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
4701 if (const SCEVAddRecExpr *ShiftedAddRec =
4702 dyn_cast<SCEVAddRecExpr>(Shifted))
4703 return ShiftedAddRec->getNumIterationsInRange(
4704 Range.subtract(SC->getValue()->getValue()), SE);
4705 // This is strange and shouldn't happen.
4706 return SE.getCouldNotCompute();
4709 // The only time we can solve this is when we have all constant indices.
4710 // Otherwise, we cannot determine the overflow conditions.
4711 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
4712 if (!isa<SCEVConstant>(getOperand(i)))
4713 return SE.getCouldNotCompute();
4716 // Okay at this point we know that all elements of the chrec are constants and
4717 // that the start element is zero.
4719 // First check to see if the range contains zero. If not, the first
4721 unsigned BitWidth = SE.getTypeSizeInBits(getType());
4722 if (!Range.contains(APInt(BitWidth, 0)))
4723 return SE.getIntegerSCEV(0, getType());
4726 // If this is an affine expression then we have this situation:
4727 // Solve {0,+,A} in Range === Ax in Range
4729 // We know that zero is in the range. If A is positive then we know that
4730 // the upper value of the range must be the first possible exit value.
4731 // If A is negative then the lower of the range is the last possible loop
4732 // value. Also note that we already checked for a full range.
4733 APInt One(BitWidth,1);
4734 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
4735 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
4737 // The exit value should be (End+A)/A.
4738 APInt ExitVal = (End + A).udiv(A);
4739 ConstantInt *ExitValue = SE.getContext()->getConstantInt(ExitVal);
4741 // Evaluate at the exit value. If we really did fall out of the valid
4742 // range, then we computed our trip count, otherwise wrap around or other
4743 // things must have happened.
4744 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
4745 if (Range.contains(Val->getValue()))
4746 return SE.getCouldNotCompute(); // Something strange happened
4748 // Ensure that the previous value is in the range. This is a sanity check.
4749 assert(Range.contains(
4750 EvaluateConstantChrecAtConstant(this,
4751 SE.getContext()->getConstantInt(ExitVal - One), SE)->getValue()) &&
4752 "Linear scev computation is off in a bad way!");
4753 return SE.getConstant(ExitValue);
4754 } else if (isQuadratic()) {
4755 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
4756 // quadratic equation to solve it. To do this, we must frame our problem in
4757 // terms of figuring out when zero is crossed, instead of when
4758 // Range.getUpper() is crossed.
4759 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
4760 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
4761 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
4763 // Next, solve the constructed addrec
4764 std::pair<const SCEV *,const SCEV *> Roots =
4765 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
4766 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4767 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4769 // Pick the smallest positive root value.
4770 if (ConstantInt *CB =
4771 dyn_cast<ConstantInt>(
4772 SE.getContext()->getConstantExprICmp(ICmpInst::ICMP_ULT,
4773 R1->getValue(), R2->getValue()))) {
4774 if (CB->getZExtValue() == false)
4775 std::swap(R1, R2); // R1 is the minimum root now.
4777 // Make sure the root is not off by one. The returned iteration should
4778 // not be in the range, but the previous one should be. When solving
4779 // for "X*X < 5", for example, we should not return a root of 2.
4780 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
4783 if (Range.contains(R1Val->getValue())) {
4784 // The next iteration must be out of the range...
4785 ConstantInt *NextVal =
4786 SE.getContext()->getConstantInt(R1->getValue()->getValue()+1);
4788 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4789 if (!Range.contains(R1Val->getValue()))
4790 return SE.getConstant(NextVal);
4791 return SE.getCouldNotCompute(); // Something strange happened
4794 // If R1 was not in the range, then it is a good return value. Make
4795 // sure that R1-1 WAS in the range though, just in case.
4796 ConstantInt *NextVal =
4797 SE.getContext()->getConstantInt(R1->getValue()->getValue()-1);
4798 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4799 if (Range.contains(R1Val->getValue()))
4801 return SE.getCouldNotCompute(); // Something strange happened
4806 return SE.getCouldNotCompute();
4811 //===----------------------------------------------------------------------===//
4812 // SCEVCallbackVH Class Implementation
4813 //===----------------------------------------------------------------------===//
4815 void ScalarEvolution::SCEVCallbackVH::deleted() {
4816 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
4817 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
4818 SE->ConstantEvolutionLoopExitValue.erase(PN);
4819 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
4820 SE->ValuesAtScopes.erase(I);
4821 SE->Scalars.erase(getValPtr());
4822 // this now dangles!
4825 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
4826 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
4828 // Forget all the expressions associated with users of the old value,
4829 // so that future queries will recompute the expressions using the new
4831 SmallVector<User *, 16> Worklist;
4832 SmallPtrSet<User *, 8> Visited;
4833 Value *Old = getValPtr();
4834 bool DeleteOld = false;
4835 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
4837 Worklist.push_back(*UI);
4838 while (!Worklist.empty()) {
4839 User *U = Worklist.pop_back_val();
4840 // Deleting the Old value will cause this to dangle. Postpone
4841 // that until everything else is done.
4846 if (!Visited.insert(U))
4848 if (PHINode *PN = dyn_cast<PHINode>(U))
4849 SE->ConstantEvolutionLoopExitValue.erase(PN);
4850 if (Instruction *I = dyn_cast<Instruction>(U))
4851 SE->ValuesAtScopes.erase(I);
4852 SE->Scalars.erase(U);
4853 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
4855 Worklist.push_back(*UI);
4857 // Delete the Old value if it (indirectly) references itself.
4859 if (PHINode *PN = dyn_cast<PHINode>(Old))
4860 SE->ConstantEvolutionLoopExitValue.erase(PN);
4861 if (Instruction *I = dyn_cast<Instruction>(Old))
4862 SE->ValuesAtScopes.erase(I);
4863 SE->Scalars.erase(Old);
4864 // this now dangles!
4869 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
4870 : CallbackVH(V), SE(se) {}
4872 //===----------------------------------------------------------------------===//
4873 // ScalarEvolution Class Implementation
4874 //===----------------------------------------------------------------------===//
4876 ScalarEvolution::ScalarEvolution()
4877 : FunctionPass(&ID) {
4880 bool ScalarEvolution::runOnFunction(Function &F) {
4882 LI = &getAnalysis<LoopInfo>();
4883 TD = getAnalysisIfAvailable<TargetData>();
4887 void ScalarEvolution::releaseMemory() {
4889 BackedgeTakenCounts.clear();
4890 ConstantEvolutionLoopExitValue.clear();
4891 ValuesAtScopes.clear();
4892 UniqueSCEVs.clear();
4893 SCEVAllocator.Reset();
4896 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
4897 AU.setPreservesAll();
4898 AU.addRequiredTransitive<LoopInfo>();
4901 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
4902 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
4905 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
4907 // Print all inner loops first
4908 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4909 PrintLoopInfo(OS, SE, *I);
4911 OS << "Loop " << L->getHeader()->getName() << ": ";
4913 SmallVector<BasicBlock*, 8> ExitBlocks;
4914 L->getExitBlocks(ExitBlocks);
4915 if (ExitBlocks.size() != 1)
4916 OS << "<multiple exits> ";
4918 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
4919 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
4921 OS << "Unpredictable backedge-taken count. ";
4925 OS << "Loop " << L->getHeader()->getName() << ": ";
4927 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
4928 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
4930 OS << "Unpredictable max backedge-taken count. ";
4936 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
4937 // ScalarEvolution's implementaiton of the print method is to print
4938 // out SCEV values of all instructions that are interesting. Doing
4939 // this potentially causes it to create new SCEV objects though,
4940 // which technically conflicts with the const qualifier. This isn't
4941 // observable from outside the class though, so casting away the
4942 // const isn't dangerous.
4943 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
4945 OS << "Classifying expressions for: " << F->getName() << "\n";
4946 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
4947 if (isSCEVable(I->getType())) {
4950 const SCEV *SV = SE.getSCEV(&*I);
4953 const Loop *L = LI->getLoopFor((*I).getParent());
4955 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
4962 OS << "\t\t" "Exits: ";
4963 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
4964 if (!ExitValue->isLoopInvariant(L)) {
4965 OS << "<<Unknown>>";
4974 OS << "Determining loop execution counts for: " << F->getName() << "\n";
4975 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
4976 PrintLoopInfo(OS, &SE, *I);
4979 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
4980 raw_os_ostream OS(o);