1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. We only create one SCEV of a particular shape, so
18 // pointer-comparisons for equality are legal.
20 // One important aspect of the SCEV objects is that they are never cyclic, even
21 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
22 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
23 // recurrence) then we represent it directly as a recurrence node, otherwise we
24 // represent it as a SCEVUnknown node.
26 // In addition to being able to represent expressions of various types, we also
27 // have folders that are used to build the *canonical* representation for a
28 // particular expression. These folders are capable of using a variety of
29 // rewrite rules to simplify the expressions.
31 // Once the folders are defined, we can implement the more interesting
32 // higher-level code, such as the code that recognizes PHI nodes of various
33 // types, computes the execution count of a loop, etc.
35 // TODO: We should use these routines and value representations to implement
36 // dependence analysis!
38 //===----------------------------------------------------------------------===//
40 // There are several good references for the techniques used in this analysis.
42 // Chains of recurrences -- a method to expedite the evaluation
43 // of closed-form functions
44 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46 // On computational properties of chains of recurrences
49 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
50 // Robert A. van Engelen
52 // Efficient Symbolic Analysis for Optimizing Compilers
53 // Robert A. van Engelen
55 // Using the chains of recurrences algebra for data dependence testing and
56 // induction variable substitution
57 // MS Thesis, Johnie Birch
59 //===----------------------------------------------------------------------===//
61 #define DEBUG_TYPE "scalar-evolution"
62 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
63 #include "llvm/Constants.h"
64 #include "llvm/DerivedTypes.h"
65 #include "llvm/GlobalVariable.h"
66 #include "llvm/Instructions.h"
67 #include "llvm/LLVMContext.h"
68 #include "llvm/Operator.h"
69 #include "llvm/Analysis/ConstantFolding.h"
70 #include "llvm/Analysis/Dominators.h"
71 #include "llvm/Analysis/LoopInfo.h"
72 #include "llvm/Analysis/ValueTracking.h"
73 #include "llvm/Assembly/Writer.h"
74 #include "llvm/Target/TargetData.h"
75 #include "llvm/Support/CommandLine.h"
76 #include "llvm/Support/Compiler.h"
77 #include "llvm/Support/ConstantRange.h"
78 #include "llvm/Support/ErrorHandling.h"
79 #include "llvm/Support/GetElementPtrTypeIterator.h"
80 #include "llvm/Support/InstIterator.h"
81 #include "llvm/Support/MathExtras.h"
82 #include "llvm/Support/raw_ostream.h"
83 #include "llvm/ADT/Statistic.h"
84 #include "llvm/ADT/STLExtras.h"
85 #include "llvm/ADT/SmallPtrSet.h"
89 STATISTIC(NumArrayLenItCounts,
90 "Number of trip counts computed with array length");
91 STATISTIC(NumTripCountsComputed,
92 "Number of loops with predictable loop counts");
93 STATISTIC(NumTripCountsNotComputed,
94 "Number of loops without predictable loop counts");
95 STATISTIC(NumBruteForceTripCountsComputed,
96 "Number of loops with trip counts computed by force");
98 static cl::opt<unsigned>
99 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
100 cl::desc("Maximum number of iterations SCEV will "
101 "symbolically execute a constant "
105 static RegisterPass<ScalarEvolution>
106 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
107 char ScalarEvolution::ID = 0;
109 //===----------------------------------------------------------------------===//
110 // SCEV class definitions
111 //===----------------------------------------------------------------------===//
113 //===----------------------------------------------------------------------===//
114 // Implementation of the SCEV class.
119 void SCEV::dump() const {
124 void SCEV::print(std::ostream &o) const {
125 raw_os_ostream OS(o);
129 bool SCEV::isZero() const {
130 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
131 return SC->getValue()->isZero();
135 bool SCEV::isOne() const {
136 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
137 return SC->getValue()->isOne();
141 bool SCEV::isAllOnesValue() const {
142 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
143 return SC->getValue()->isAllOnesValue();
147 SCEVCouldNotCompute::SCEVCouldNotCompute() :
148 SCEV(FoldingSetNodeID(), scCouldNotCompute) {}
150 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
151 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
155 const Type *SCEVCouldNotCompute::getType() const {
156 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
160 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
161 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
165 bool SCEVCouldNotCompute::hasOperand(const SCEV *) const {
166 llvm_unreachable("Attempt to use a SCEVCouldNotCompute object!");
170 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
171 OS << "***COULDNOTCOMPUTE***";
174 bool SCEVCouldNotCompute::classof(const SCEV *S) {
175 return S->getSCEVType() == scCouldNotCompute;
178 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
180 ID.AddInteger(scConstant);
183 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
184 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>();
185 new (S) SCEVConstant(ID, V);
186 UniqueSCEVs.InsertNode(S, IP);
190 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
191 return getConstant(ConstantInt::get(getContext(), Val));
195 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
197 ConstantInt::get(cast<IntegerType>(Ty), V, isSigned));
200 const Type *SCEVConstant::getType() const { return V->getType(); }
202 void SCEVConstant::print(raw_ostream &OS) const {
203 WriteAsOperand(OS, V, false);
206 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID,
207 unsigned SCEVTy, const SCEV *op, const Type *ty)
208 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
210 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
211 return Op->dominates(BB, DT);
214 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID,
215 const SCEV *op, const Type *ty)
216 : SCEVCastExpr(ID, scTruncate, op, ty) {
217 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
218 (Ty->isInteger() || isa<PointerType>(Ty)) &&
219 "Cannot truncate non-integer value!");
222 void SCEVTruncateExpr::print(raw_ostream &OS) const {
223 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
226 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID,
227 const SCEV *op, const Type *ty)
228 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
229 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
230 (Ty->isInteger() || isa<PointerType>(Ty)) &&
231 "Cannot zero extend non-integer value!");
234 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
235 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
238 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID,
239 const SCEV *op, const Type *ty)
240 : SCEVCastExpr(ID, scSignExtend, op, ty) {
241 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
242 (Ty->isInteger() || isa<PointerType>(Ty)) &&
243 "Cannot sign extend non-integer value!");
246 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
247 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
250 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
251 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
252 const char *OpStr = getOperationStr();
253 OS << "(" << *Operands[0];
254 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
255 OS << OpStr << *Operands[i];
259 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
260 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
261 if (!getOperand(i)->dominates(BB, DT))
267 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
268 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
271 void SCEVUDivExpr::print(raw_ostream &OS) const {
272 OS << "(" << *LHS << " /u " << *RHS << ")";
275 const Type *SCEVUDivExpr::getType() const {
276 // In most cases the types of LHS and RHS will be the same, but in some
277 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
278 // depend on the type for correctness, but handling types carefully can
279 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
280 // a pointer type than the RHS, so use the RHS' type here.
281 return RHS->getType();
284 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
285 // Add recurrences are never invariant in the function-body (null loop).
289 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
290 if (QueryLoop->contains(L->getHeader()))
293 // This recurrence is variant w.r.t. QueryLoop if any of its operands
295 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
296 if (!getOperand(i)->isLoopInvariant(QueryLoop))
299 // Otherwise it's loop-invariant.
303 void SCEVAddRecExpr::print(raw_ostream &OS) const {
304 OS << "{" << *Operands[0];
305 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
306 OS << ",+," << *Operands[i];
307 OS << "}<" << L->getHeader()->getName() + ">";
310 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
311 // All non-instruction values are loop invariant. All instructions are loop
312 // invariant if they are not contained in the specified loop.
313 // Instructions are never considered invariant in the function body
314 // (null loop) because they are defined within the "loop".
315 if (Instruction *I = dyn_cast<Instruction>(V))
316 return L && !L->contains(I->getParent());
320 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
321 if (Instruction *I = dyn_cast<Instruction>(getValue()))
322 return DT->dominates(I->getParent(), BB);
326 const Type *SCEVUnknown::getType() const {
330 void SCEVUnknown::print(raw_ostream &OS) const {
331 WriteAsOperand(OS, V, false);
334 //===----------------------------------------------------------------------===//
336 //===----------------------------------------------------------------------===//
339 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
340 /// than the complexity of the RHS. This comparator is used to canonicalize
342 class VISIBILITY_HIDDEN SCEVComplexityCompare {
345 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
347 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
348 // Primarily, sort the SCEVs by their getSCEVType().
349 if (LHS->getSCEVType() != RHS->getSCEVType())
350 return LHS->getSCEVType() < RHS->getSCEVType();
352 // Aside from the getSCEVType() ordering, the particular ordering
353 // isn't very important except that it's beneficial to be consistent,
354 // so that (a + b) and (b + a) don't end up as different expressions.
356 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
357 // not as complete as it could be.
358 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
359 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
361 // Order pointer values after integer values. This helps SCEVExpander
363 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
365 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
368 // Compare getValueID values.
369 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
370 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
372 // Sort arguments by their position.
373 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
374 const Argument *RA = cast<Argument>(RU->getValue());
375 return LA->getArgNo() < RA->getArgNo();
378 // For instructions, compare their loop depth, and their opcode.
379 // This is pretty loose.
380 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
381 Instruction *RV = cast<Instruction>(RU->getValue());
383 // Compare loop depths.
384 if (LI->getLoopDepth(LV->getParent()) !=
385 LI->getLoopDepth(RV->getParent()))
386 return LI->getLoopDepth(LV->getParent()) <
387 LI->getLoopDepth(RV->getParent());
390 if (LV->getOpcode() != RV->getOpcode())
391 return LV->getOpcode() < RV->getOpcode();
393 // Compare the number of operands.
394 if (LV->getNumOperands() != RV->getNumOperands())
395 return LV->getNumOperands() < RV->getNumOperands();
401 // Compare constant values.
402 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
403 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
404 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
405 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
406 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
409 // Compare addrec loop depths.
410 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
411 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
412 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
413 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
416 // Lexicographically compare n-ary expressions.
417 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
418 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
419 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
420 if (i >= RC->getNumOperands())
422 if (operator()(LC->getOperand(i), RC->getOperand(i)))
424 if (operator()(RC->getOperand(i), LC->getOperand(i)))
427 return LC->getNumOperands() < RC->getNumOperands();
430 // Lexicographically compare udiv expressions.
431 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
432 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
433 if (operator()(LC->getLHS(), RC->getLHS()))
435 if (operator()(RC->getLHS(), LC->getLHS()))
437 if (operator()(LC->getRHS(), RC->getRHS()))
439 if (operator()(RC->getRHS(), LC->getRHS()))
444 // Compare cast expressions by operand.
445 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
446 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
447 return operator()(LC->getOperand(), RC->getOperand());
450 llvm_unreachable("Unknown SCEV kind!");
456 /// GroupByComplexity - Given a list of SCEV objects, order them by their
457 /// complexity, and group objects of the same complexity together by value.
458 /// When this routine is finished, we know that any duplicates in the vector are
459 /// consecutive and that complexity is monotonically increasing.
461 /// Note that we go take special precautions to ensure that we get determinstic
462 /// results from this routine. In other words, we don't want the results of
463 /// this to depend on where the addresses of various SCEV objects happened to
466 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
468 if (Ops.size() < 2) return; // Noop
469 if (Ops.size() == 2) {
470 // This is the common case, which also happens to be trivially simple.
472 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
473 std::swap(Ops[0], Ops[1]);
477 // Do the rough sort by complexity.
478 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
480 // Now that we are sorted by complexity, group elements of the same
481 // complexity. Note that this is, at worst, N^2, but the vector is likely to
482 // be extremely short in practice. Note that we take this approach because we
483 // do not want to depend on the addresses of the objects we are grouping.
484 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
485 const SCEV *S = Ops[i];
486 unsigned Complexity = S->getSCEVType();
488 // If there are any objects of the same complexity and same value as this
490 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
491 if (Ops[j] == S) { // Found a duplicate.
492 // Move it to immediately after i'th element.
493 std::swap(Ops[i+1], Ops[j]);
494 ++i; // no need to rescan it.
495 if (i == e-2) return; // Done!
503 //===----------------------------------------------------------------------===//
504 // Simple SCEV method implementations
505 //===----------------------------------------------------------------------===//
507 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
509 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
511 const Type* ResultTy) {
512 // Handle the simplest case efficiently.
514 return SE.getTruncateOrZeroExtend(It, ResultTy);
516 // We are using the following formula for BC(It, K):
518 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
520 // Suppose, W is the bitwidth of the return value. We must be prepared for
521 // overflow. Hence, we must assure that the result of our computation is
522 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
523 // safe in modular arithmetic.
525 // However, this code doesn't use exactly that formula; the formula it uses
526 // is something like the following, where T is the number of factors of 2 in
527 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
530 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
532 // This formula is trivially equivalent to the previous formula. However,
533 // this formula can be implemented much more efficiently. The trick is that
534 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
535 // arithmetic. To do exact division in modular arithmetic, all we have
536 // to do is multiply by the inverse. Therefore, this step can be done at
539 // The next issue is how to safely do the division by 2^T. The way this
540 // is done is by doing the multiplication step at a width of at least W + T
541 // bits. This way, the bottom W+T bits of the product are accurate. Then,
542 // when we perform the division by 2^T (which is equivalent to a right shift
543 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
544 // truncated out after the division by 2^T.
546 // In comparison to just directly using the first formula, this technique
547 // is much more efficient; using the first formula requires W * K bits,
548 // but this formula less than W + K bits. Also, the first formula requires
549 // a division step, whereas this formula only requires multiplies and shifts.
551 // It doesn't matter whether the subtraction step is done in the calculation
552 // width or the input iteration count's width; if the subtraction overflows,
553 // the result must be zero anyway. We prefer here to do it in the width of
554 // the induction variable because it helps a lot for certain cases; CodeGen
555 // isn't smart enough to ignore the overflow, which leads to much less
556 // efficient code if the width of the subtraction is wider than the native
559 // (It's possible to not widen at all by pulling out factors of 2 before
560 // the multiplication; for example, K=2 can be calculated as
561 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
562 // extra arithmetic, so it's not an obvious win, and it gets
563 // much more complicated for K > 3.)
565 // Protection from insane SCEVs; this bound is conservative,
566 // but it probably doesn't matter.
568 return SE.getCouldNotCompute();
570 unsigned W = SE.getTypeSizeInBits(ResultTy);
572 // Calculate K! / 2^T and T; we divide out the factors of two before
573 // multiplying for calculating K! / 2^T to avoid overflow.
574 // Other overflow doesn't matter because we only care about the bottom
575 // W bits of the result.
576 APInt OddFactorial(W, 1);
578 for (unsigned i = 3; i <= K; ++i) {
580 unsigned TwoFactors = Mult.countTrailingZeros();
582 Mult = Mult.lshr(TwoFactors);
583 OddFactorial *= Mult;
586 // We need at least W + T bits for the multiplication step
587 unsigned CalculationBits = W + T;
589 // Calcuate 2^T, at width T+W.
590 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
592 // Calculate the multiplicative inverse of K! / 2^T;
593 // this multiplication factor will perform the exact division by
595 APInt Mod = APInt::getSignedMinValue(W+1);
596 APInt MultiplyFactor = OddFactorial.zext(W+1);
597 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
598 MultiplyFactor = MultiplyFactor.trunc(W);
600 // Calculate the product, at width T+W
601 const IntegerType *CalculationTy = IntegerType::get(SE.getContext(),
603 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
604 for (unsigned i = 1; i != K; ++i) {
605 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
606 Dividend = SE.getMulExpr(Dividend,
607 SE.getTruncateOrZeroExtend(S, CalculationTy));
611 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
613 // Truncate the result, and divide by K! / 2^T.
615 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
616 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
619 /// evaluateAtIteration - Return the value of this chain of recurrences at
620 /// the specified iteration number. We can evaluate this recurrence by
621 /// multiplying each element in the chain by the binomial coefficient
622 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
624 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
626 /// where BC(It, k) stands for binomial coefficient.
628 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
629 ScalarEvolution &SE) const {
630 const SCEV *Result = getStart();
631 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
632 // The computation is correct in the face of overflow provided that the
633 // multiplication is performed _after_ the evaluation of the binomial
635 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
636 if (isa<SCEVCouldNotCompute>(Coeff))
639 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
644 //===----------------------------------------------------------------------===//
645 // SCEV Expression folder implementations
646 //===----------------------------------------------------------------------===//
648 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
650 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
651 "This is not a truncating conversion!");
652 assert(isSCEVable(Ty) &&
653 "This is not a conversion to a SCEVable type!");
654 Ty = getEffectiveSCEVType(Ty);
657 ID.AddInteger(scTruncate);
661 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
663 // Fold if the operand is constant.
664 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
666 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
668 // trunc(trunc(x)) --> trunc(x)
669 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
670 return getTruncateExpr(ST->getOperand(), Ty);
672 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
673 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
674 return getTruncateOrSignExtend(SS->getOperand(), Ty);
676 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
677 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
678 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
680 // If the input value is a chrec scev, truncate the chrec's operands.
681 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
682 SmallVector<const SCEV *, 4> Operands;
683 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
684 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
685 return getAddRecExpr(Operands, AddRec->getLoop());
688 // The cast wasn't folded; create an explicit cast node.
689 // Recompute the insert position, as it may have been invalidated.
690 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
691 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>();
692 new (S) SCEVTruncateExpr(ID, Op, Ty);
693 UniqueSCEVs.InsertNode(S, IP);
697 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
699 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
700 "This is not an extending conversion!");
701 assert(isSCEVable(Ty) &&
702 "This is not a conversion to a SCEVable type!");
703 Ty = getEffectiveSCEVType(Ty);
705 // Fold if the operand is constant.
706 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
707 const Type *IntTy = getEffectiveSCEVType(Ty);
708 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
709 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
710 return getConstant(cast<ConstantInt>(C));
713 // zext(zext(x)) --> zext(x)
714 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
715 return getZeroExtendExpr(SZ->getOperand(), Ty);
717 // Before doing any expensive analysis, check to see if we've already
718 // computed a SCEV for this Op and Ty.
720 ID.AddInteger(scZeroExtend);
724 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
726 // If the input value is a chrec scev, and we can prove that the value
727 // did not overflow the old, smaller, value, we can zero extend all of the
728 // operands (often constants). This allows analysis of something like
729 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
730 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
731 if (AR->isAffine()) {
732 const SCEV *Start = AR->getStart();
733 const SCEV *Step = AR->getStepRecurrence(*this);
734 unsigned BitWidth = getTypeSizeInBits(AR->getType());
735 const Loop *L = AR->getLoop();
737 // If we have special knowledge that this addrec won't overflow,
738 // we don't need to do any further analysis.
739 if (AR->hasNoUnsignedOverflow())
740 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
741 getZeroExtendExpr(Step, Ty),
744 // Check whether the backedge-taken count is SCEVCouldNotCompute.
745 // Note that this serves two purposes: It filters out loops that are
746 // simply not analyzable, and it covers the case where this code is
747 // being called from within backedge-taken count analysis, such that
748 // attempting to ask for the backedge-taken count would likely result
749 // in infinite recursion. In the later case, the analysis code will
750 // cope with a conservative value, and it will take care to purge
751 // that value once it has finished.
752 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
753 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
754 // Manually compute the final value for AR, checking for
757 // Check whether the backedge-taken count can be losslessly casted to
758 // the addrec's type. The count is always unsigned.
759 const SCEV *CastedMaxBECount =
760 getTruncateOrZeroExtend(MaxBECount, Start->getType());
761 const SCEV *RecastedMaxBECount =
762 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
763 if (MaxBECount == RecastedMaxBECount) {
764 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
765 // Check whether Start+Step*MaxBECount has no unsigned overflow.
767 getMulExpr(CastedMaxBECount,
768 getTruncateOrZeroExtend(Step, Start->getType()));
769 const SCEV *Add = getAddExpr(Start, ZMul);
770 const SCEV *OperandExtendedAdd =
771 getAddExpr(getZeroExtendExpr(Start, WideTy),
772 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
773 getZeroExtendExpr(Step, WideTy)));
774 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
775 // Return the expression with the addrec on the outside.
776 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
777 getZeroExtendExpr(Step, Ty),
780 // Similar to above, only this time treat the step value as signed.
781 // This covers loops that count down.
783 getMulExpr(CastedMaxBECount,
784 getTruncateOrSignExtend(Step, Start->getType()));
785 Add = getAddExpr(Start, SMul);
787 getAddExpr(getZeroExtendExpr(Start, WideTy),
788 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
789 getSignExtendExpr(Step, WideTy)));
790 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
791 // Return the expression with the addrec on the outside.
792 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
793 getSignExtendExpr(Step, Ty),
797 // If the backedge is guarded by a comparison with the pre-inc value
798 // the addrec is safe. Also, if the entry is guarded by a comparison
799 // with the start value and the backedge is guarded by a comparison
800 // with the post-inc value, the addrec is safe.
801 if (isKnownPositive(Step)) {
802 const SCEV *N = getConstant(APInt::getMinValue(BitWidth) -
803 getUnsignedRange(Step).getUnsignedMax());
804 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT, AR, N) ||
805 (isLoopGuardedByCond(L, ICmpInst::ICMP_ULT, Start, N) &&
806 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_ULT,
807 AR->getPostIncExpr(*this), N)))
808 // Return the expression with the addrec on the outside.
809 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
810 getZeroExtendExpr(Step, Ty),
812 } else if (isKnownNegative(Step)) {
813 const SCEV *N = getConstant(APInt::getMaxValue(BitWidth) -
814 getSignedRange(Step).getSignedMin());
815 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT, AR, N) &&
816 (isLoopGuardedByCond(L, ICmpInst::ICMP_UGT, Start, N) ||
817 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_UGT,
818 AR->getPostIncExpr(*this), N)))
819 // Return the expression with the addrec on the outside.
820 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
821 getSignExtendExpr(Step, Ty),
827 // The cast wasn't folded; create an explicit cast node.
828 // Recompute the insert position, as it may have been invalidated.
829 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
830 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>();
831 new (S) SCEVZeroExtendExpr(ID, Op, Ty);
832 UniqueSCEVs.InsertNode(S, IP);
836 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
838 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
839 "This is not an extending conversion!");
840 assert(isSCEVable(Ty) &&
841 "This is not a conversion to a SCEVable type!");
842 Ty = getEffectiveSCEVType(Ty);
844 // Fold if the operand is constant.
845 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
846 const Type *IntTy = getEffectiveSCEVType(Ty);
847 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
848 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
849 return getConstant(cast<ConstantInt>(C));
852 // sext(sext(x)) --> sext(x)
853 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
854 return getSignExtendExpr(SS->getOperand(), Ty);
856 // Before doing any expensive analysis, check to see if we've already
857 // computed a SCEV for this Op and Ty.
859 ID.AddInteger(scSignExtend);
863 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
865 // If the input value is a chrec scev, and we can prove that the value
866 // did not overflow the old, smaller, value, we can sign extend all of the
867 // operands (often constants). This allows analysis of something like
868 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
869 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
870 if (AR->isAffine()) {
871 const SCEV *Start = AR->getStart();
872 const SCEV *Step = AR->getStepRecurrence(*this);
873 unsigned BitWidth = getTypeSizeInBits(AR->getType());
874 const Loop *L = AR->getLoop();
876 // If we have special knowledge that this addrec won't overflow,
877 // we don't need to do any further analysis.
878 if (AR->hasNoSignedOverflow())
879 return getAddRecExpr(getSignExtendExpr(Start, Ty),
880 getSignExtendExpr(Step, Ty),
883 // Check whether the backedge-taken count is SCEVCouldNotCompute.
884 // Note that this serves two purposes: It filters out loops that are
885 // simply not analyzable, and it covers the case where this code is
886 // being called from within backedge-taken count analysis, such that
887 // attempting to ask for the backedge-taken count would likely result
888 // in infinite recursion. In the later case, the analysis code will
889 // cope with a conservative value, and it will take care to purge
890 // that value once it has finished.
891 const SCEV *MaxBECount = getMaxBackedgeTakenCount(L);
892 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
893 // Manually compute the final value for AR, checking for
896 // Check whether the backedge-taken count can be losslessly casted to
897 // the addrec's type. The count is always unsigned.
898 const SCEV *CastedMaxBECount =
899 getTruncateOrZeroExtend(MaxBECount, Start->getType());
900 const SCEV *RecastedMaxBECount =
901 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
902 if (MaxBECount == RecastedMaxBECount) {
903 const Type *WideTy = IntegerType::get(getContext(), BitWidth * 2);
904 // Check whether Start+Step*MaxBECount has no signed overflow.
906 getMulExpr(CastedMaxBECount,
907 getTruncateOrSignExtend(Step, Start->getType()));
908 const SCEV *Add = getAddExpr(Start, SMul);
909 const SCEV *OperandExtendedAdd =
910 getAddExpr(getSignExtendExpr(Start, WideTy),
911 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
912 getSignExtendExpr(Step, WideTy)));
913 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
914 // Return the expression with the addrec on the outside.
915 return getAddRecExpr(getSignExtendExpr(Start, Ty),
916 getSignExtendExpr(Step, Ty),
919 // Similar to above, only this time treat the step value as unsigned.
920 // This covers loops that count up with an unsigned step.
922 getMulExpr(CastedMaxBECount,
923 getTruncateOrZeroExtend(Step, Start->getType()));
924 Add = getAddExpr(Start, UMul);
926 getAddExpr(getSignExtendExpr(Start, WideTy),
927 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
928 getZeroExtendExpr(Step, WideTy)));
929 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
930 // Return the expression with the addrec on the outside.
931 return getAddRecExpr(getSignExtendExpr(Start, Ty),
932 getZeroExtendExpr(Step, Ty),
936 // If the backedge is guarded by a comparison with the pre-inc value
937 // the addrec is safe. Also, if the entry is guarded by a comparison
938 // with the start value and the backedge is guarded by a comparison
939 // with the post-inc value, the addrec is safe.
940 if (isKnownPositive(Step)) {
941 const SCEV *N = getConstant(APInt::getSignedMinValue(BitWidth) -
942 getSignedRange(Step).getSignedMax());
943 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT, AR, N) ||
944 (isLoopGuardedByCond(L, ICmpInst::ICMP_SLT, Start, N) &&
945 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SLT,
946 AR->getPostIncExpr(*this), N)))
947 // Return the expression with the addrec on the outside.
948 return getAddRecExpr(getSignExtendExpr(Start, Ty),
949 getSignExtendExpr(Step, Ty),
951 } else if (isKnownNegative(Step)) {
952 const SCEV *N = getConstant(APInt::getSignedMaxValue(BitWidth) -
953 getSignedRange(Step).getSignedMin());
954 if (isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT, AR, N) ||
955 (isLoopGuardedByCond(L, ICmpInst::ICMP_SGT, Start, N) &&
956 isLoopBackedgeGuardedByCond(L, ICmpInst::ICMP_SGT,
957 AR->getPostIncExpr(*this), N)))
958 // Return the expression with the addrec on the outside.
959 return getAddRecExpr(getSignExtendExpr(Start, Ty),
960 getSignExtendExpr(Step, Ty),
966 // The cast wasn't folded; create an explicit cast node.
967 // Recompute the insert position, as it may have been invalidated.
968 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
969 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>();
970 new (S) SCEVSignExtendExpr(ID, Op, Ty);
971 UniqueSCEVs.InsertNode(S, IP);
975 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
976 /// unspecified bits out to the given type.
978 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
980 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
981 "This is not an extending conversion!");
982 assert(isSCEVable(Ty) &&
983 "This is not a conversion to a SCEVable type!");
984 Ty = getEffectiveSCEVType(Ty);
986 // Sign-extend negative constants.
987 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
988 if (SC->getValue()->getValue().isNegative())
989 return getSignExtendExpr(Op, Ty);
991 // Peel off a truncate cast.
992 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
993 const SCEV *NewOp = T->getOperand();
994 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
995 return getAnyExtendExpr(NewOp, Ty);
996 return getTruncateOrNoop(NewOp, Ty);
999 // Next try a zext cast. If the cast is folded, use it.
1000 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
1001 if (!isa<SCEVZeroExtendExpr>(ZExt))
1004 // Next try a sext cast. If the cast is folded, use it.
1005 const SCEV *SExt = getSignExtendExpr(Op, Ty);
1006 if (!isa<SCEVSignExtendExpr>(SExt))
1009 // If the expression is obviously signed, use the sext cast value.
1010 if (isa<SCEVSMaxExpr>(Op))
1013 // Absent any other information, use the zext cast value.
1017 /// CollectAddOperandsWithScales - Process the given Ops list, which is
1018 /// a list of operands to be added under the given scale, update the given
1019 /// map. This is a helper function for getAddRecExpr. As an example of
1020 /// what it does, given a sequence of operands that would form an add
1021 /// expression like this:
1023 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1025 /// where A and B are constants, update the map with these values:
1027 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1029 /// and add 13 + A*B*29 to AccumulatedConstant.
1030 /// This will allow getAddRecExpr to produce this:
1032 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1034 /// This form often exposes folding opportunities that are hidden in
1035 /// the original operand list.
1037 /// Return true iff it appears that any interesting folding opportunities
1038 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
1039 /// the common case where no interesting opportunities are present, and
1040 /// is also used as a check to avoid infinite recursion.
1043 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1044 SmallVector<const SCEV *, 8> &NewOps,
1045 APInt &AccumulatedConstant,
1046 const SmallVectorImpl<const SCEV *> &Ops,
1048 ScalarEvolution &SE) {
1049 bool Interesting = false;
1051 // Iterate over the add operands.
1052 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1053 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1054 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1056 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1057 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1058 // A multiplication of a constant with another add; recurse.
1060 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1061 cast<SCEVAddExpr>(Mul->getOperand(1))
1065 // A multiplication of a constant with some other value. Update
1067 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1068 const SCEV *Key = SE.getMulExpr(MulOps);
1069 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1070 M.insert(std::make_pair(Key, NewScale));
1072 NewOps.push_back(Pair.first->first);
1074 Pair.first->second += NewScale;
1075 // The map already had an entry for this value, which may indicate
1076 // a folding opportunity.
1080 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1081 // Pull a buried constant out to the outside.
1082 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
1084 AccumulatedConstant += Scale * C->getValue()->getValue();
1086 // An ordinary operand. Update the map.
1087 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1088 M.insert(std::make_pair(Ops[i], Scale));
1090 NewOps.push_back(Pair.first->first);
1092 Pair.first->second += Scale;
1093 // The map already had an entry for this value, which may indicate
1094 // a folding opportunity.
1104 struct APIntCompare {
1105 bool operator()(const APInt &LHS, const APInt &RHS) const {
1106 return LHS.ult(RHS);
1111 /// getAddExpr - Get a canonical add expression, or something simpler if
1113 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops) {
1114 assert(!Ops.empty() && "Cannot get empty add!");
1115 if (Ops.size() == 1) return Ops[0];
1117 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1118 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1119 getEffectiveSCEVType(Ops[0]->getType()) &&
1120 "SCEVAddExpr operand types don't match!");
1123 // Sort by complexity, this groups all similar expression types together.
1124 GroupByComplexity(Ops, LI);
1126 // If there are any constants, fold them together.
1128 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1130 assert(Idx < Ops.size());
1131 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1132 // We found two constants, fold them together!
1133 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1134 RHSC->getValue()->getValue());
1135 if (Ops.size() == 2) return Ops[0];
1136 Ops.erase(Ops.begin()+1); // Erase the folded element
1137 LHSC = cast<SCEVConstant>(Ops[0]);
1140 // If we are left with a constant zero being added, strip it off.
1141 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1142 Ops.erase(Ops.begin());
1147 if (Ops.size() == 1) return Ops[0];
1149 // Okay, check to see if the same value occurs in the operand list twice. If
1150 // so, merge them together into an multiply expression. Since we sorted the
1151 // list, these values are required to be adjacent.
1152 const Type *Ty = Ops[0]->getType();
1153 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1154 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1155 // Found a match, merge the two values into a multiply, and add any
1156 // remaining values to the result.
1157 const SCEV *Two = getIntegerSCEV(2, Ty);
1158 const SCEV *Mul = getMulExpr(Ops[i], Two);
1159 if (Ops.size() == 2)
1161 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1163 return getAddExpr(Ops);
1166 // Check for truncates. If all the operands are truncated from the same
1167 // type, see if factoring out the truncate would permit the result to be
1168 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1169 // if the contents of the resulting outer trunc fold to something simple.
1170 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1171 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1172 const Type *DstType = Trunc->getType();
1173 const Type *SrcType = Trunc->getOperand()->getType();
1174 SmallVector<const SCEV *, 8> LargeOps;
1176 // Check all the operands to see if they can be represented in the
1177 // source type of the truncate.
1178 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1179 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1180 if (T->getOperand()->getType() != SrcType) {
1184 LargeOps.push_back(T->getOperand());
1185 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1186 // This could be either sign or zero extension, but sign extension
1187 // is much more likely to be foldable here.
1188 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1189 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1190 SmallVector<const SCEV *, 8> LargeMulOps;
1191 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1192 if (const SCEVTruncateExpr *T =
1193 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1194 if (T->getOperand()->getType() != SrcType) {
1198 LargeMulOps.push_back(T->getOperand());
1199 } else if (const SCEVConstant *C =
1200 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1201 // This could be either sign or zero extension, but sign extension
1202 // is much more likely to be foldable here.
1203 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1210 LargeOps.push_back(getMulExpr(LargeMulOps));
1217 // Evaluate the expression in the larger type.
1218 const SCEV *Fold = getAddExpr(LargeOps);
1219 // If it folds to something simple, use it. Otherwise, don't.
1220 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1221 return getTruncateExpr(Fold, DstType);
1225 // Skip past any other cast SCEVs.
1226 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1229 // If there are add operands they would be next.
1230 if (Idx < Ops.size()) {
1231 bool DeletedAdd = false;
1232 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1233 // If we have an add, expand the add operands onto the end of the operands
1235 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1236 Ops.erase(Ops.begin()+Idx);
1240 // If we deleted at least one add, we added operands to the end of the list,
1241 // and they are not necessarily sorted. Recurse to resort and resimplify
1242 // any operands we just aquired.
1244 return getAddExpr(Ops);
1247 // Skip over the add expression until we get to a multiply.
1248 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1251 // Check to see if there are any folding opportunities present with
1252 // operands multiplied by constant values.
1253 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1254 uint64_t BitWidth = getTypeSizeInBits(Ty);
1255 DenseMap<const SCEV *, APInt> M;
1256 SmallVector<const SCEV *, 8> NewOps;
1257 APInt AccumulatedConstant(BitWidth, 0);
1258 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1259 Ops, APInt(BitWidth, 1), *this)) {
1260 // Some interesting folding opportunity is present, so its worthwhile to
1261 // re-generate the operands list. Group the operands by constant scale,
1262 // to avoid multiplying by the same constant scale multiple times.
1263 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1264 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1265 E = NewOps.end(); I != E; ++I)
1266 MulOpLists[M.find(*I)->second].push_back(*I);
1267 // Re-generate the operands list.
1269 if (AccumulatedConstant != 0)
1270 Ops.push_back(getConstant(AccumulatedConstant));
1271 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1272 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1274 Ops.push_back(getMulExpr(getConstant(I->first),
1275 getAddExpr(I->second)));
1277 return getIntegerSCEV(0, Ty);
1278 if (Ops.size() == 1)
1280 return getAddExpr(Ops);
1284 // If we are adding something to a multiply expression, make sure the
1285 // something is not already an operand of the multiply. If so, merge it into
1287 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1288 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1289 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1290 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1291 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1292 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1293 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1294 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1295 if (Mul->getNumOperands() != 2) {
1296 // If the multiply has more than two operands, we must get the
1298 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1299 MulOps.erase(MulOps.begin()+MulOp);
1300 InnerMul = getMulExpr(MulOps);
1302 const SCEV *One = getIntegerSCEV(1, Ty);
1303 const SCEV *AddOne = getAddExpr(InnerMul, One);
1304 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1305 if (Ops.size() == 2) return OuterMul;
1307 Ops.erase(Ops.begin()+AddOp);
1308 Ops.erase(Ops.begin()+Idx-1);
1310 Ops.erase(Ops.begin()+Idx);
1311 Ops.erase(Ops.begin()+AddOp-1);
1313 Ops.push_back(OuterMul);
1314 return getAddExpr(Ops);
1317 // Check this multiply against other multiplies being added together.
1318 for (unsigned OtherMulIdx = Idx+1;
1319 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1321 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1322 // If MulOp occurs in OtherMul, we can fold the two multiplies
1324 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1325 OMulOp != e; ++OMulOp)
1326 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1327 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1328 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1329 if (Mul->getNumOperands() != 2) {
1330 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1332 MulOps.erase(MulOps.begin()+MulOp);
1333 InnerMul1 = getMulExpr(MulOps);
1335 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1336 if (OtherMul->getNumOperands() != 2) {
1337 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1338 OtherMul->op_end());
1339 MulOps.erase(MulOps.begin()+OMulOp);
1340 InnerMul2 = getMulExpr(MulOps);
1342 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1343 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1344 if (Ops.size() == 2) return OuterMul;
1345 Ops.erase(Ops.begin()+Idx);
1346 Ops.erase(Ops.begin()+OtherMulIdx-1);
1347 Ops.push_back(OuterMul);
1348 return getAddExpr(Ops);
1354 // If there are any add recurrences in the operands list, see if any other
1355 // added values are loop invariant. If so, we can fold them into the
1357 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1360 // Scan over all recurrences, trying to fold loop invariants into them.
1361 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1362 // Scan all of the other operands to this add and add them to the vector if
1363 // they are loop invariant w.r.t. the recurrence.
1364 SmallVector<const SCEV *, 8> LIOps;
1365 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1366 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1367 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1368 LIOps.push_back(Ops[i]);
1369 Ops.erase(Ops.begin()+i);
1373 // If we found some loop invariants, fold them into the recurrence.
1374 if (!LIOps.empty()) {
1375 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1376 LIOps.push_back(AddRec->getStart());
1378 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1380 AddRecOps[0] = getAddExpr(LIOps);
1382 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1383 // If all of the other operands were loop invariant, we are done.
1384 if (Ops.size() == 1) return NewRec;
1386 // Otherwise, add the folded AddRec by the non-liv parts.
1387 for (unsigned i = 0;; ++i)
1388 if (Ops[i] == AddRec) {
1392 return getAddExpr(Ops);
1395 // Okay, if there weren't any loop invariants to be folded, check to see if
1396 // there are multiple AddRec's with the same loop induction variable being
1397 // added together. If so, we can fold them.
1398 for (unsigned OtherIdx = Idx+1;
1399 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1400 if (OtherIdx != Idx) {
1401 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1402 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1403 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1404 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1406 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1407 if (i >= NewOps.size()) {
1408 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1409 OtherAddRec->op_end());
1412 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1414 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1416 if (Ops.size() == 2) return NewAddRec;
1418 Ops.erase(Ops.begin()+Idx);
1419 Ops.erase(Ops.begin()+OtherIdx-1);
1420 Ops.push_back(NewAddRec);
1421 return getAddExpr(Ops);
1425 // Otherwise couldn't fold anything into this recurrence. Move onto the
1429 // Okay, it looks like we really DO need an add expr. Check to see if we
1430 // already have one, otherwise create a new one.
1431 FoldingSetNodeID ID;
1432 ID.AddInteger(scAddExpr);
1433 ID.AddInteger(Ops.size());
1434 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1435 ID.AddPointer(Ops[i]);
1437 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1438 SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>();
1439 new (S) SCEVAddExpr(ID, Ops);
1440 UniqueSCEVs.InsertNode(S, IP);
1445 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1447 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops) {
1448 assert(!Ops.empty() && "Cannot get empty mul!");
1450 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1451 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1452 getEffectiveSCEVType(Ops[0]->getType()) &&
1453 "SCEVMulExpr operand types don't match!");
1456 // Sort by complexity, this groups all similar expression types together.
1457 GroupByComplexity(Ops, LI);
1459 // If there are any constants, fold them together.
1461 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1463 // C1*(C2+V) -> C1*C2 + C1*V
1464 if (Ops.size() == 2)
1465 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1466 if (Add->getNumOperands() == 2 &&
1467 isa<SCEVConstant>(Add->getOperand(0)))
1468 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1469 getMulExpr(LHSC, Add->getOperand(1)));
1473 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1474 // We found two constants, fold them together!
1475 ConstantInt *Fold = ConstantInt::get(getContext(),
1476 LHSC->getValue()->getValue() *
1477 RHSC->getValue()->getValue());
1478 Ops[0] = getConstant(Fold);
1479 Ops.erase(Ops.begin()+1); // Erase the folded element
1480 if (Ops.size() == 1) return Ops[0];
1481 LHSC = cast<SCEVConstant>(Ops[0]);
1484 // If we are left with a constant one being multiplied, strip it off.
1485 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1486 Ops.erase(Ops.begin());
1488 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1489 // If we have a multiply of zero, it will always be zero.
1494 // Skip over the add expression until we get to a multiply.
1495 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1498 if (Ops.size() == 1)
1501 // If there are mul operands inline them all into this expression.
1502 if (Idx < Ops.size()) {
1503 bool DeletedMul = false;
1504 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1505 // If we have an mul, expand the mul operands onto the end of the operands
1507 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1508 Ops.erase(Ops.begin()+Idx);
1512 // If we deleted at least one mul, we added operands to the end of the list,
1513 // and they are not necessarily sorted. Recurse to resort and resimplify
1514 // any operands we just aquired.
1516 return getMulExpr(Ops);
1519 // If there are any add recurrences in the operands list, see if any other
1520 // added values are loop invariant. If so, we can fold them into the
1522 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1525 // Scan over all recurrences, trying to fold loop invariants into them.
1526 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1527 // Scan all of the other operands to this mul and add them to the vector if
1528 // they are loop invariant w.r.t. the recurrence.
1529 SmallVector<const SCEV *, 8> LIOps;
1530 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1531 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1532 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1533 LIOps.push_back(Ops[i]);
1534 Ops.erase(Ops.begin()+i);
1538 // If we found some loop invariants, fold them into the recurrence.
1539 if (!LIOps.empty()) {
1540 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1541 SmallVector<const SCEV *, 4> NewOps;
1542 NewOps.reserve(AddRec->getNumOperands());
1543 if (LIOps.size() == 1) {
1544 const SCEV *Scale = LIOps[0];
1545 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1546 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1548 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1549 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
1550 MulOps.push_back(AddRec->getOperand(i));
1551 NewOps.push_back(getMulExpr(MulOps));
1555 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1557 // If all of the other operands were loop invariant, we are done.
1558 if (Ops.size() == 1) return NewRec;
1560 // Otherwise, multiply the folded AddRec by the non-liv parts.
1561 for (unsigned i = 0;; ++i)
1562 if (Ops[i] == AddRec) {
1566 return getMulExpr(Ops);
1569 // Okay, if there weren't any loop invariants to be folded, check to see if
1570 // there are multiple AddRec's with the same loop induction variable being
1571 // multiplied together. If so, we can fold them.
1572 for (unsigned OtherIdx = Idx+1;
1573 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1574 if (OtherIdx != Idx) {
1575 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1576 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1577 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1578 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1579 const SCEV *NewStart = getMulExpr(F->getStart(),
1581 const SCEV *B = F->getStepRecurrence(*this);
1582 const SCEV *D = G->getStepRecurrence(*this);
1583 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1586 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1588 if (Ops.size() == 2) return NewAddRec;
1590 Ops.erase(Ops.begin()+Idx);
1591 Ops.erase(Ops.begin()+OtherIdx-1);
1592 Ops.push_back(NewAddRec);
1593 return getMulExpr(Ops);
1597 // Otherwise couldn't fold anything into this recurrence. Move onto the
1601 // Okay, it looks like we really DO need an mul expr. Check to see if we
1602 // already have one, otherwise create a new one.
1603 FoldingSetNodeID ID;
1604 ID.AddInteger(scMulExpr);
1605 ID.AddInteger(Ops.size());
1606 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1607 ID.AddPointer(Ops[i]);
1609 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1610 SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>();
1611 new (S) SCEVMulExpr(ID, Ops);
1612 UniqueSCEVs.InsertNode(S, IP);
1616 /// getUDivExpr - Get a canonical unsigned division expression, or something
1617 /// simpler if possible.
1618 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1620 assert(getEffectiveSCEVType(LHS->getType()) ==
1621 getEffectiveSCEVType(RHS->getType()) &&
1622 "SCEVUDivExpr operand types don't match!");
1624 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1625 if (RHSC->getValue()->equalsInt(1))
1626 return LHS; // X udiv 1 --> x
1628 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1630 // Determine if the division can be folded into the operands of
1632 // TODO: Generalize this to non-constants by using known-bits information.
1633 const Type *Ty = LHS->getType();
1634 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1635 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1636 // For non-power-of-two values, effectively round the value up to the
1637 // nearest power of two.
1638 if (!RHSC->getValue()->getValue().isPowerOf2())
1640 const IntegerType *ExtTy =
1641 IntegerType::get(getContext(), getTypeSizeInBits(Ty) + MaxShiftAmt);
1642 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1643 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1644 if (const SCEVConstant *Step =
1645 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1646 if (!Step->getValue()->getValue()
1647 .urem(RHSC->getValue()->getValue()) &&
1648 getZeroExtendExpr(AR, ExtTy) ==
1649 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1650 getZeroExtendExpr(Step, ExtTy),
1652 SmallVector<const SCEV *, 4> Operands;
1653 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1654 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1655 return getAddRecExpr(Operands, AR->getLoop());
1657 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1658 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1659 SmallVector<const SCEV *, 4> Operands;
1660 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1661 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1662 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1663 // Find an operand that's safely divisible.
1664 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1665 const SCEV *Op = M->getOperand(i);
1666 const SCEV *Div = getUDivExpr(Op, RHSC);
1667 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1668 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands();
1669 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(),
1672 return getMulExpr(Operands);
1676 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1677 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1678 SmallVector<const SCEV *, 4> Operands;
1679 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1680 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1681 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1683 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1684 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1685 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1687 Operands.push_back(Op);
1689 if (Operands.size() == A->getNumOperands())
1690 return getAddExpr(Operands);
1694 // Fold if both operands are constant.
1695 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1696 Constant *LHSCV = LHSC->getValue();
1697 Constant *RHSCV = RHSC->getValue();
1698 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1703 FoldingSetNodeID ID;
1704 ID.AddInteger(scUDivExpr);
1708 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1709 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>();
1710 new (S) SCEVUDivExpr(ID, LHS, RHS);
1711 UniqueSCEVs.InsertNode(S, IP);
1716 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1717 /// Simplify the expression as much as possible.
1718 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1719 const SCEV *Step, const Loop *L) {
1720 SmallVector<const SCEV *, 4> Operands;
1721 Operands.push_back(Start);
1722 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1723 if (StepChrec->getLoop() == L) {
1724 Operands.insert(Operands.end(), StepChrec->op_begin(),
1725 StepChrec->op_end());
1726 return getAddRecExpr(Operands, L);
1729 Operands.push_back(Step);
1730 return getAddRecExpr(Operands, L);
1733 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1734 /// Simplify the expression as much as possible.
1736 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1738 if (Operands.size() == 1) return Operands[0];
1740 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1741 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1742 getEffectiveSCEVType(Operands[0]->getType()) &&
1743 "SCEVAddRecExpr operand types don't match!");
1746 if (Operands.back()->isZero()) {
1747 Operands.pop_back();
1748 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1751 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1752 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1753 const Loop* NestedLoop = NestedAR->getLoop();
1754 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1755 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
1756 NestedAR->op_end());
1757 Operands[0] = NestedAR->getStart();
1758 // AddRecs require their operands be loop-invariant with respect to their
1759 // loops. Don't perform this transformation if it would break this
1761 bool AllInvariant = true;
1762 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1763 if (!Operands[i]->isLoopInvariant(L)) {
1764 AllInvariant = false;
1768 NestedOperands[0] = getAddRecExpr(Operands, L);
1769 AllInvariant = true;
1770 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
1771 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
1772 AllInvariant = false;
1776 // Ok, both add recurrences are valid after the transformation.
1777 return getAddRecExpr(NestedOperands, NestedLoop);
1779 // Reset Operands to its original state.
1780 Operands[0] = NestedAR;
1784 FoldingSetNodeID ID;
1785 ID.AddInteger(scAddRecExpr);
1786 ID.AddInteger(Operands.size());
1787 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1788 ID.AddPointer(Operands[i]);
1791 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1792 SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>();
1793 new (S) SCEVAddRecExpr(ID, Operands, L);
1794 UniqueSCEVs.InsertNode(S, IP);
1798 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
1800 SmallVector<const SCEV *, 2> Ops;
1803 return getSMaxExpr(Ops);
1807 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1808 assert(!Ops.empty() && "Cannot get empty smax!");
1809 if (Ops.size() == 1) return Ops[0];
1811 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1812 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1813 getEffectiveSCEVType(Ops[0]->getType()) &&
1814 "SCEVSMaxExpr operand types don't match!");
1817 // Sort by complexity, this groups all similar expression types together.
1818 GroupByComplexity(Ops, LI);
1820 // If there are any constants, fold them together.
1822 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1824 assert(Idx < Ops.size());
1825 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1826 // We found two constants, fold them together!
1827 ConstantInt *Fold = ConstantInt::get(getContext(),
1828 APIntOps::smax(LHSC->getValue()->getValue(),
1829 RHSC->getValue()->getValue()));
1830 Ops[0] = getConstant(Fold);
1831 Ops.erase(Ops.begin()+1); // Erase the folded element
1832 if (Ops.size() == 1) return Ops[0];
1833 LHSC = cast<SCEVConstant>(Ops[0]);
1836 // If we are left with a constant minimum-int, strip it off.
1837 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1838 Ops.erase(Ops.begin());
1840 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
1841 // If we have an smax with a constant maximum-int, it will always be
1847 if (Ops.size() == 1) return Ops[0];
1849 // Find the first SMax
1850 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1853 // Check to see if one of the operands is an SMax. If so, expand its operands
1854 // onto our operand list, and recurse to simplify.
1855 if (Idx < Ops.size()) {
1856 bool DeletedSMax = false;
1857 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1858 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1859 Ops.erase(Ops.begin()+Idx);
1864 return getSMaxExpr(Ops);
1867 // Okay, check to see if the same value occurs in the operand list twice. If
1868 // so, delete one. Since we sorted the list, these values are required to
1870 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1871 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1872 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1876 if (Ops.size() == 1) return Ops[0];
1878 assert(!Ops.empty() && "Reduced smax down to nothing!");
1880 // Okay, it looks like we really DO need an smax expr. Check to see if we
1881 // already have one, otherwise create a new one.
1882 FoldingSetNodeID ID;
1883 ID.AddInteger(scSMaxExpr);
1884 ID.AddInteger(Ops.size());
1885 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1886 ID.AddPointer(Ops[i]);
1888 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1889 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>();
1890 new (S) SCEVSMaxExpr(ID, Ops);
1891 UniqueSCEVs.InsertNode(S, IP);
1895 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
1897 SmallVector<const SCEV *, 2> Ops;
1900 return getUMaxExpr(Ops);
1904 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1905 assert(!Ops.empty() && "Cannot get empty umax!");
1906 if (Ops.size() == 1) return Ops[0];
1908 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1909 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1910 getEffectiveSCEVType(Ops[0]->getType()) &&
1911 "SCEVUMaxExpr operand types don't match!");
1914 // Sort by complexity, this groups all similar expression types together.
1915 GroupByComplexity(Ops, LI);
1917 // If there are any constants, fold them together.
1919 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1921 assert(Idx < Ops.size());
1922 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1923 // We found two constants, fold them together!
1924 ConstantInt *Fold = ConstantInt::get(getContext(),
1925 APIntOps::umax(LHSC->getValue()->getValue(),
1926 RHSC->getValue()->getValue()));
1927 Ops[0] = getConstant(Fold);
1928 Ops.erase(Ops.begin()+1); // Erase the folded element
1929 if (Ops.size() == 1) return Ops[0];
1930 LHSC = cast<SCEVConstant>(Ops[0]);
1933 // If we are left with a constant minimum-int, strip it off.
1934 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1935 Ops.erase(Ops.begin());
1937 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
1938 // If we have an umax with a constant maximum-int, it will always be
1944 if (Ops.size() == 1) return Ops[0];
1946 // Find the first UMax
1947 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1950 // Check to see if one of the operands is a UMax. If so, expand its operands
1951 // onto our operand list, and recurse to simplify.
1952 if (Idx < Ops.size()) {
1953 bool DeletedUMax = false;
1954 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1955 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1956 Ops.erase(Ops.begin()+Idx);
1961 return getUMaxExpr(Ops);
1964 // Okay, check to see if the same value occurs in the operand list twice. If
1965 // so, delete one. Since we sorted the list, these values are required to
1967 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1968 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1969 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1973 if (Ops.size() == 1) return Ops[0];
1975 assert(!Ops.empty() && "Reduced umax down to nothing!");
1977 // Okay, it looks like we really DO need a umax expr. Check to see if we
1978 // already have one, otherwise create a new one.
1979 FoldingSetNodeID ID;
1980 ID.AddInteger(scUMaxExpr);
1981 ID.AddInteger(Ops.size());
1982 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1983 ID.AddPointer(Ops[i]);
1985 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1986 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>();
1987 new (S) SCEVUMaxExpr(ID, Ops);
1988 UniqueSCEVs.InsertNode(S, IP);
1992 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
1994 // ~smax(~x, ~y) == smin(x, y).
1995 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
1998 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
2000 // ~umax(~x, ~y) == umin(x, y)
2001 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
2004 const SCEV *ScalarEvolution::getUnknown(Value *V) {
2005 // Don't attempt to do anything other than create a SCEVUnknown object
2006 // here. createSCEV only calls getUnknown after checking for all other
2007 // interesting possibilities, and any other code that calls getUnknown
2008 // is doing so in order to hide a value from SCEV canonicalization.
2010 FoldingSetNodeID ID;
2011 ID.AddInteger(scUnknown);
2014 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
2015 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>();
2016 new (S) SCEVUnknown(ID, V);
2017 UniqueSCEVs.InsertNode(S, IP);
2021 //===----------------------------------------------------------------------===//
2022 // Basic SCEV Analysis and PHI Idiom Recognition Code
2025 /// isSCEVable - Test if values of the given type are analyzable within
2026 /// the SCEV framework. This primarily includes integer types, and it
2027 /// can optionally include pointer types if the ScalarEvolution class
2028 /// has access to target-specific information.
2029 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2030 // Integers are always SCEVable.
2031 if (Ty->isInteger())
2034 // Pointers are SCEVable if TargetData information is available
2035 // to provide pointer size information.
2036 if (isa<PointerType>(Ty))
2039 // Otherwise it's not SCEVable.
2043 /// getTypeSizeInBits - Return the size in bits of the specified type,
2044 /// for which isSCEVable must return true.
2045 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2046 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2048 // If we have a TargetData, use it!
2050 return TD->getTypeSizeInBits(Ty);
2052 // Otherwise, we support only integer types.
2053 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
2054 return Ty->getPrimitiveSizeInBits();
2057 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2058 /// the given type and which represents how SCEV will treat the given
2059 /// type, for which isSCEVable must return true. For pointer types,
2060 /// this is the pointer-sized integer type.
2061 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2062 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2064 if (Ty->isInteger())
2067 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
2068 return TD->getIntPtrType(getContext());
2071 const SCEV *ScalarEvolution::getCouldNotCompute() {
2072 return &CouldNotCompute;
2075 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2076 /// expression and create a new one.
2077 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2078 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2080 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2081 if (I != Scalars.end()) return I->second;
2082 const SCEV *S = createSCEV(V);
2083 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2087 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
2088 /// specified signed integer value and return a SCEV for the constant.
2089 const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
2090 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2091 return getConstant(ConstantInt::get(ITy, Val));
2094 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2096 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2097 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2099 cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2101 const Type *Ty = V->getType();
2102 Ty = getEffectiveSCEVType(Ty);
2103 return getMulExpr(V,
2104 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty))));
2107 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2108 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2109 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2111 cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2113 const Type *Ty = V->getType();
2114 Ty = getEffectiveSCEVType(Ty);
2115 const SCEV *AllOnes =
2116 getConstant(cast<ConstantInt>(Constant::getAllOnesValue(Ty)));
2117 return getMinusSCEV(AllOnes, V);
2120 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2122 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2125 return getAddExpr(LHS, getNegativeSCEV(RHS));
2128 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2129 /// input value to the specified type. If the type must be extended, it is zero
2132 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2134 const Type *SrcTy = V->getType();
2135 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2136 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2137 "Cannot truncate or zero extend with non-integer arguments!");
2138 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2139 return V; // No conversion
2140 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2141 return getTruncateExpr(V, Ty);
2142 return getZeroExtendExpr(V, Ty);
2145 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2146 /// input value to the specified type. If the type must be extended, it is sign
2149 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2151 const Type *SrcTy = V->getType();
2152 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2153 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2154 "Cannot truncate or zero extend with non-integer arguments!");
2155 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2156 return V; // No conversion
2157 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2158 return getTruncateExpr(V, Ty);
2159 return getSignExtendExpr(V, Ty);
2162 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2163 /// input value to the specified type. If the type must be extended, it is zero
2164 /// extended. The conversion must not be narrowing.
2166 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2167 const Type *SrcTy = V->getType();
2168 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2169 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2170 "Cannot noop or zero extend with non-integer arguments!");
2171 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2172 "getNoopOrZeroExtend cannot truncate!");
2173 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2174 return V; // No conversion
2175 return getZeroExtendExpr(V, Ty);
2178 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2179 /// input value to the specified type. If the type must be extended, it is sign
2180 /// extended. The conversion must not be narrowing.
2182 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2183 const Type *SrcTy = V->getType();
2184 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2185 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2186 "Cannot noop or sign extend with non-integer arguments!");
2187 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2188 "getNoopOrSignExtend cannot truncate!");
2189 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2190 return V; // No conversion
2191 return getSignExtendExpr(V, Ty);
2194 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2195 /// the input value to the specified type. If the type must be extended,
2196 /// it is extended with unspecified bits. The conversion must not be
2199 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2200 const Type *SrcTy = V->getType();
2201 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2202 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2203 "Cannot noop or any extend with non-integer arguments!");
2204 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2205 "getNoopOrAnyExtend cannot truncate!");
2206 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2207 return V; // No conversion
2208 return getAnyExtendExpr(V, Ty);
2211 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2212 /// input value to the specified type. The conversion must not be widening.
2214 ScalarEvolution::getTruncateOrNoop(const SCEV *V, const Type *Ty) {
2215 const Type *SrcTy = V->getType();
2216 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2217 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2218 "Cannot truncate or noop with non-integer arguments!");
2219 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2220 "getTruncateOrNoop cannot extend!");
2221 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2222 return V; // No conversion
2223 return getTruncateExpr(V, Ty);
2226 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2227 /// the types using zero-extension, and then perform a umax operation
2229 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2231 const SCEV *PromotedLHS = LHS;
2232 const SCEV *PromotedRHS = RHS;
2234 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2235 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2237 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2239 return getUMaxExpr(PromotedLHS, PromotedRHS);
2242 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2243 /// the types using zero-extension, and then perform a umin operation
2245 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2247 const SCEV *PromotedLHS = LHS;
2248 const SCEV *PromotedRHS = RHS;
2250 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2251 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2253 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2255 return getUMinExpr(PromotedLHS, PromotedRHS);
2258 /// PushDefUseChildren - Push users of the given Instruction
2259 /// onto the given Worklist.
2261 PushDefUseChildren(Instruction *I,
2262 SmallVectorImpl<Instruction *> &Worklist) {
2263 // Push the def-use children onto the Worklist stack.
2264 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2266 Worklist.push_back(cast<Instruction>(UI));
2269 /// ForgetSymbolicValue - This looks up computed SCEV values for all
2270 /// instructions that depend on the given instruction and removes them from
2271 /// the Scalars map if they reference SymName. This is used during PHI
2274 ScalarEvolution::ForgetSymbolicName(Instruction *I, const SCEV *SymName) {
2275 SmallVector<Instruction *, 16> Worklist;
2276 PushDefUseChildren(I, Worklist);
2278 SmallPtrSet<Instruction *, 8> Visited;
2280 while (!Worklist.empty()) {
2281 Instruction *I = Worklist.pop_back_val();
2282 if (!Visited.insert(I)) continue;
2284 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
2285 Scalars.find(static_cast<Value *>(I));
2286 if (It != Scalars.end()) {
2287 // Short-circuit the def-use traversal if the symbolic name
2288 // ceases to appear in expressions.
2289 if (!It->second->hasOperand(SymName))
2292 // SCEVUnknown for a PHI either means that it has an unrecognized
2293 // structure, or it's a PHI that's in the progress of being computed
2294 // by createNodeForPHI. In the former case, additional loop trip
2295 // count information isn't going to change anything. In the later
2296 // case, createNodeForPHI will perform the necessary updates on its
2297 // own when it gets to that point.
2298 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second))
2300 ValuesAtScopes.erase(I);
2303 PushDefUseChildren(I, Worklist);
2307 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2308 /// a loop header, making it a potential recurrence, or it doesn't.
2310 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2311 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2312 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2313 if (L->getHeader() == PN->getParent()) {
2314 // If it lives in the loop header, it has two incoming values, one
2315 // from outside the loop, and one from inside.
2316 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2317 unsigned BackEdge = IncomingEdge^1;
2319 // While we are analyzing this PHI node, handle its value symbolically.
2320 const SCEV *SymbolicName = getUnknown(PN);
2321 assert(Scalars.find(PN) == Scalars.end() &&
2322 "PHI node already processed?");
2323 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2325 // Using this symbolic name for the PHI, analyze the value coming around
2327 Value *BEValueV = PN->getIncomingValue(BackEdge);
2328 const SCEV *BEValue = getSCEV(BEValueV);
2330 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2331 // has a special value for the first iteration of the loop.
2333 // If the value coming around the backedge is an add with the symbolic
2334 // value we just inserted, then we found a simple induction variable!
2335 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2336 // If there is a single occurrence of the symbolic value, replace it
2337 // with a recurrence.
2338 unsigned FoundIndex = Add->getNumOperands();
2339 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2340 if (Add->getOperand(i) == SymbolicName)
2341 if (FoundIndex == e) {
2346 if (FoundIndex != Add->getNumOperands()) {
2347 // Create an add with everything but the specified operand.
2348 SmallVector<const SCEV *, 8> Ops;
2349 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2350 if (i != FoundIndex)
2351 Ops.push_back(Add->getOperand(i));
2352 const SCEV *Accum = getAddExpr(Ops);
2354 // This is not a valid addrec if the step amount is varying each
2355 // loop iteration, but is not itself an addrec in this loop.
2356 if (Accum->isLoopInvariant(L) ||
2357 (isa<SCEVAddRecExpr>(Accum) &&
2358 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2359 const SCEV *StartVal =
2360 getSCEV(PN->getIncomingValue(IncomingEdge));
2361 const SCEVAddRecExpr *PHISCEV =
2362 cast<SCEVAddRecExpr>(getAddRecExpr(StartVal, Accum, L));
2364 // If the increment doesn't overflow, then neither the addrec nor the
2365 // post-increment will overflow.
2366 if (const AddOperator *OBO = dyn_cast<AddOperator>(BEValueV))
2367 if (OBO->getOperand(0) == PN &&
2368 getSCEV(OBO->getOperand(1)) ==
2369 PHISCEV->getStepRecurrence(*this)) {
2370 const SCEVAddRecExpr *PostInc = PHISCEV->getPostIncExpr(*this);
2371 if (OBO->hasNoUnsignedOverflow()) {
2372 const_cast<SCEVAddRecExpr *>(PHISCEV)
2373 ->setHasNoUnsignedOverflow(true);
2374 const_cast<SCEVAddRecExpr *>(PostInc)
2375 ->setHasNoUnsignedOverflow(true);
2377 if (OBO->hasNoSignedOverflow()) {
2378 const_cast<SCEVAddRecExpr *>(PHISCEV)
2379 ->setHasNoSignedOverflow(true);
2380 const_cast<SCEVAddRecExpr *>(PostInc)
2381 ->setHasNoSignedOverflow(true);
2385 // Okay, for the entire analysis of this edge we assumed the PHI
2386 // to be symbolic. We now need to go back and purge all of the
2387 // entries for the scalars that use the symbolic expression.
2388 ForgetSymbolicName(PN, SymbolicName);
2389 Scalars[SCEVCallbackVH(PN, this)] = PHISCEV;
2393 } else if (const SCEVAddRecExpr *AddRec =
2394 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2395 // Otherwise, this could be a loop like this:
2396 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2397 // In this case, j = {1,+,1} and BEValue is j.
2398 // Because the other in-value of i (0) fits the evolution of BEValue
2399 // i really is an addrec evolution.
2400 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2401 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2403 // If StartVal = j.start - j.stride, we can use StartVal as the
2404 // initial step of the addrec evolution.
2405 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2406 AddRec->getOperand(1))) {
2407 const SCEV *PHISCEV =
2408 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2410 // Okay, for the entire analysis of this edge we assumed the PHI
2411 // to be symbolic. We now need to go back and purge all of the
2412 // entries for the scalars that use the symbolic expression.
2413 ForgetSymbolicName(PN, SymbolicName);
2414 Scalars[SCEVCallbackVH(PN, this)] = 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(getContext());
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 *Step = AddRec->getStepRecurrence(*this);
2623 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2625 // Check for overflow.
2626 // TODO: This is very conservative.
2627 if (!(Step->isOne() &&
2628 isKnownPredicate(ICmpInst::ICMP_ULT, Start, End)) &&
2629 !(Step->isAllOnesValue() &&
2630 isKnownPredicate(ICmpInst::ICMP_UGT, Start, End)))
2633 ConstantRange StartRange = getUnsignedRange(Start);
2634 ConstantRange EndRange = getUnsignedRange(End);
2635 APInt Min = APIntOps::umin(StartRange.getUnsignedMin(),
2636 EndRange.getUnsignedMin());
2637 APInt Max = APIntOps::umax(StartRange.getUnsignedMax(),
2638 EndRange.getUnsignedMax());
2639 if (Min.isMinValue() && Max.isMaxValue())
2641 return ConstantRange(Min, Max+1);
2646 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2647 // For a SCEVUnknown, ask ValueTracking.
2648 unsigned BitWidth = getTypeSizeInBits(U->getType());
2649 APInt Mask = APInt::getAllOnesValue(BitWidth);
2650 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2651 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
2652 if (Ones == ~Zeros + 1)
2654 return ConstantRange(Ones, ~Zeros + 1);
2660 /// getSignedRange - Determine the signed range for a particular SCEV.
2663 ScalarEvolution::getSignedRange(const SCEV *S) {
2665 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2666 return ConstantRange(C->getValue()->getValue());
2668 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
2669 ConstantRange X = getSignedRange(Add->getOperand(0));
2670 for (unsigned i = 1, e = Add->getNumOperands(); i != e; ++i)
2671 X = X.add(getSignedRange(Add->getOperand(i)));
2675 if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
2676 ConstantRange X = getSignedRange(Mul->getOperand(0));
2677 for (unsigned i = 1, e = Mul->getNumOperands(); i != e; ++i)
2678 X = X.multiply(getSignedRange(Mul->getOperand(i)));
2682 if (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(S)) {
2683 ConstantRange X = getSignedRange(SMax->getOperand(0));
2684 for (unsigned i = 1, e = SMax->getNumOperands(); i != e; ++i)
2685 X = X.smax(getSignedRange(SMax->getOperand(i)));
2689 if (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(S)) {
2690 ConstantRange X = getSignedRange(UMax->getOperand(0));
2691 for (unsigned i = 1, e = UMax->getNumOperands(); i != e; ++i)
2692 X = X.umax(getSignedRange(UMax->getOperand(i)));
2696 if (const SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(S)) {
2697 ConstantRange X = getSignedRange(UDiv->getLHS());
2698 ConstantRange Y = getSignedRange(UDiv->getRHS());
2702 if (const SCEVZeroExtendExpr *ZExt = dyn_cast<SCEVZeroExtendExpr>(S)) {
2703 ConstantRange X = getSignedRange(ZExt->getOperand());
2704 return X.zeroExtend(cast<IntegerType>(ZExt->getType())->getBitWidth());
2707 if (const SCEVSignExtendExpr *SExt = dyn_cast<SCEVSignExtendExpr>(S)) {
2708 ConstantRange X = getSignedRange(SExt->getOperand());
2709 return X.signExtend(cast<IntegerType>(SExt->getType())->getBitWidth());
2712 if (const SCEVTruncateExpr *Trunc = dyn_cast<SCEVTruncateExpr>(S)) {
2713 ConstantRange X = getSignedRange(Trunc->getOperand());
2714 return X.truncate(cast<IntegerType>(Trunc->getType())->getBitWidth());
2717 ConstantRange FullSet(getTypeSizeInBits(S->getType()), true);
2719 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S)) {
2720 const SCEV *T = getBackedgeTakenCount(AddRec->getLoop());
2721 const SCEVConstant *Trip = dyn_cast<SCEVConstant>(T);
2722 if (!Trip) return FullSet;
2724 // TODO: non-affine addrec
2725 if (AddRec->isAffine()) {
2726 const Type *Ty = AddRec->getType();
2727 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AddRec->getLoop());
2728 if (getTypeSizeInBits(MaxBECount->getType()) <= getTypeSizeInBits(Ty)) {
2729 MaxBECount = getNoopOrZeroExtend(MaxBECount, Ty);
2731 const SCEV *Start = AddRec->getStart();
2732 const SCEV *Step = AddRec->getStepRecurrence(*this);
2733 const SCEV *End = AddRec->evaluateAtIteration(MaxBECount, *this);
2735 // Check for overflow.
2736 // TODO: This is very conservative.
2737 if (!(Step->isOne() &&
2738 isKnownPredicate(ICmpInst::ICMP_SLT, Start, End)) &&
2739 !(Step->isAllOnesValue() &&
2740 isKnownPredicate(ICmpInst::ICMP_SGT, Start, End)))
2743 ConstantRange StartRange = getSignedRange(Start);
2744 ConstantRange EndRange = getSignedRange(End);
2745 APInt Min = APIntOps::smin(StartRange.getSignedMin(),
2746 EndRange.getSignedMin());
2747 APInt Max = APIntOps::smax(StartRange.getSignedMax(),
2748 EndRange.getSignedMax());
2749 if (Min.isMinSignedValue() && Max.isMaxSignedValue())
2751 return ConstantRange(Min, Max+1);
2756 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2757 // For a SCEVUnknown, ask ValueTracking.
2758 unsigned BitWidth = getTypeSizeInBits(U->getType());
2759 unsigned NS = ComputeNumSignBits(U->getValue(), TD);
2763 ConstantRange(APInt::getSignedMinValue(BitWidth).ashr(NS - 1),
2764 APInt::getSignedMaxValue(BitWidth).ashr(NS - 1)+1);
2770 /// createSCEV - We know that there is no SCEV for the specified value.
2771 /// Analyze the expression.
2773 const SCEV *ScalarEvolution::createSCEV(Value *V) {
2774 if (!isSCEVable(V->getType()))
2775 return getUnknown(V);
2777 unsigned Opcode = Instruction::UserOp1;
2778 if (Instruction *I = dyn_cast<Instruction>(V))
2779 Opcode = I->getOpcode();
2780 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2781 Opcode = CE->getOpcode();
2782 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
2783 return getConstant(CI);
2784 else if (isa<ConstantPointerNull>(V))
2785 return getIntegerSCEV(0, V->getType());
2786 else if (isa<UndefValue>(V))
2787 return getIntegerSCEV(0, V->getType());
2789 return getUnknown(V);
2791 Operator *U = cast<Operator>(V);
2793 case Instruction::Add:
2794 return getAddExpr(getSCEV(U->getOperand(0)),
2795 getSCEV(U->getOperand(1)));
2796 case Instruction::Mul:
2797 return getMulExpr(getSCEV(U->getOperand(0)),
2798 getSCEV(U->getOperand(1)));
2799 case Instruction::UDiv:
2800 return getUDivExpr(getSCEV(U->getOperand(0)),
2801 getSCEV(U->getOperand(1)));
2802 case Instruction::Sub:
2803 return getMinusSCEV(getSCEV(U->getOperand(0)),
2804 getSCEV(U->getOperand(1)));
2805 case Instruction::And:
2806 // For an expression like x&255 that merely masks off the high bits,
2807 // use zext(trunc(x)) as the SCEV expression.
2808 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2809 if (CI->isNullValue())
2810 return getSCEV(U->getOperand(1));
2811 if (CI->isAllOnesValue())
2812 return getSCEV(U->getOperand(0));
2813 const APInt &A = CI->getValue();
2815 // Instcombine's ShrinkDemandedConstant may strip bits out of
2816 // constants, obscuring what would otherwise be a low-bits mask.
2817 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
2818 // knew about to reconstruct a low-bits mask value.
2819 unsigned LZ = A.countLeadingZeros();
2820 unsigned BitWidth = A.getBitWidth();
2821 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
2822 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
2823 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
2825 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
2827 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
2829 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2830 IntegerType::get(getContext(), BitWidth - LZ)),
2835 case Instruction::Or:
2836 // If the RHS of the Or is a constant, we may have something like:
2837 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2838 // optimizations will transparently handle this case.
2840 // In order for this transformation to be safe, the LHS must be of the
2841 // form X*(2^n) and the Or constant must be less than 2^n.
2842 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2843 const SCEV *LHS = getSCEV(U->getOperand(0));
2844 const APInt &CIVal = CI->getValue();
2845 if (GetMinTrailingZeros(LHS) >=
2846 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2847 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2850 case Instruction::Xor:
2851 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2852 // If the RHS of the xor is a signbit, then this is just an add.
2853 // Instcombine turns add of signbit into xor as a strength reduction step.
2854 if (CI->getValue().isSignBit())
2855 return getAddExpr(getSCEV(U->getOperand(0)),
2856 getSCEV(U->getOperand(1)));
2858 // If the RHS of xor is -1, then this is a not operation.
2859 if (CI->isAllOnesValue())
2860 return getNotSCEV(getSCEV(U->getOperand(0)));
2862 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2863 // This is a variant of the check for xor with -1, and it handles
2864 // the case where instcombine has trimmed non-demanded bits out
2865 // of an xor with -1.
2866 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2867 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2868 if (BO->getOpcode() == Instruction::And &&
2869 LCI->getValue() == CI->getValue())
2870 if (const SCEVZeroExtendExpr *Z =
2871 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
2872 const Type *UTy = U->getType();
2873 const SCEV *Z0 = Z->getOperand();
2874 const Type *Z0Ty = Z0->getType();
2875 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
2877 // If C is a low-bits mask, the zero extend is zerving to
2878 // mask off the high bits. Complement the operand and
2879 // re-apply the zext.
2880 if (APIntOps::isMask(Z0TySize, CI->getValue()))
2881 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
2883 // If C is a single bit, it may be in the sign-bit position
2884 // before the zero-extend. In this case, represent the xor
2885 // using an add, which is equivalent, and re-apply the zext.
2886 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
2887 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
2889 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
2895 case Instruction::Shl:
2896 // Turn shift left of a constant amount into a multiply.
2897 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2898 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2899 Constant *X = ConstantInt::get(getContext(),
2900 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2901 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2905 case Instruction::LShr:
2906 // Turn logical shift right of a constant into a unsigned divide.
2907 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2908 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2909 Constant *X = ConstantInt::get(getContext(),
2910 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2911 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2915 case Instruction::AShr:
2916 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2917 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2918 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2919 if (L->getOpcode() == Instruction::Shl &&
2920 L->getOperand(1) == U->getOperand(1)) {
2921 unsigned BitWidth = getTypeSizeInBits(U->getType());
2922 uint64_t Amt = BitWidth - CI->getZExtValue();
2923 if (Amt == BitWidth)
2924 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2926 return getIntegerSCEV(0, U->getType()); // value is undefined
2928 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2929 IntegerType::get(getContext(), Amt)),
2934 case Instruction::Trunc:
2935 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2937 case Instruction::ZExt:
2938 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2940 case Instruction::SExt:
2941 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2943 case Instruction::BitCast:
2944 // BitCasts are no-op casts so we just eliminate the cast.
2945 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2946 return getSCEV(U->getOperand(0));
2949 // It's tempting to handle inttoptr and ptrtoint, however this can
2950 // lead to pointer expressions which cannot be expanded to GEPs
2951 // (because they may overflow). For now, the only pointer-typed
2952 // expressions we handle are GEPs and address literals.
2954 case Instruction::GetElementPtr:
2955 if (!TD) break; // Without TD we can't analyze pointers.
2956 return createNodeForGEP(U);
2958 case Instruction::PHI:
2959 return createNodeForPHI(cast<PHINode>(U));
2961 case Instruction::Select:
2962 // This could be a smax or umax that was lowered earlier.
2963 // Try to recover it.
2964 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2965 Value *LHS = ICI->getOperand(0);
2966 Value *RHS = ICI->getOperand(1);
2967 switch (ICI->getPredicate()) {
2968 case ICmpInst::ICMP_SLT:
2969 case ICmpInst::ICMP_SLE:
2970 std::swap(LHS, RHS);
2972 case ICmpInst::ICMP_SGT:
2973 case ICmpInst::ICMP_SGE:
2974 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2975 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2976 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2977 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
2979 case ICmpInst::ICMP_ULT:
2980 case ICmpInst::ICMP_ULE:
2981 std::swap(LHS, RHS);
2983 case ICmpInst::ICMP_UGT:
2984 case ICmpInst::ICMP_UGE:
2985 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2986 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2987 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2988 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
2990 case ICmpInst::ICMP_NE:
2991 // n != 0 ? n : 1 -> umax(n, 1)
2992 if (LHS == U->getOperand(1) &&
2993 isa<ConstantInt>(U->getOperand(2)) &&
2994 cast<ConstantInt>(U->getOperand(2))->isOne() &&
2995 isa<ConstantInt>(RHS) &&
2996 cast<ConstantInt>(RHS)->isZero())
2997 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
2999 case ICmpInst::ICMP_EQ:
3000 // n == 0 ? 1 : n -> umax(n, 1)
3001 if (LHS == U->getOperand(2) &&
3002 isa<ConstantInt>(U->getOperand(1)) &&
3003 cast<ConstantInt>(U->getOperand(1))->isOne() &&
3004 isa<ConstantInt>(RHS) &&
3005 cast<ConstantInt>(RHS)->isZero())
3006 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
3013 default: // We cannot analyze this expression.
3017 return getUnknown(V);
3022 //===----------------------------------------------------------------------===//
3023 // Iteration Count Computation Code
3026 /// getBackedgeTakenCount - If the specified loop has a predictable
3027 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
3028 /// object. The backedge-taken count is the number of times the loop header
3029 /// will be branched to from within the loop. This is one less than the
3030 /// trip count of the loop, since it doesn't count the first iteration,
3031 /// when the header is branched to from outside the loop.
3033 /// Note that it is not valid to call this method on a loop without a
3034 /// loop-invariant backedge-taken count (see
3035 /// hasLoopInvariantBackedgeTakenCount).
3037 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
3038 return getBackedgeTakenInfo(L).Exact;
3041 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
3042 /// return the least SCEV value that is known never to be less than the
3043 /// actual backedge taken count.
3044 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
3045 return getBackedgeTakenInfo(L).Max;
3048 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
3049 /// onto the given Worklist.
3051 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
3052 BasicBlock *Header = L->getHeader();
3054 // Push all Loop-header PHIs onto the Worklist stack.
3055 for (BasicBlock::iterator I = Header->begin();
3056 PHINode *PN = dyn_cast<PHINode>(I); ++I)
3057 Worklist.push_back(PN);
3060 const ScalarEvolution::BackedgeTakenInfo &
3061 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
3062 // Initially insert a CouldNotCompute for this loop. If the insertion
3063 // succeeds, procede to actually compute a backedge-taken count and
3064 // update the value. The temporary CouldNotCompute value tells SCEV
3065 // code elsewhere that it shouldn't attempt to request a new
3066 // backedge-taken count, which could result in infinite recursion.
3067 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
3068 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
3070 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
3071 if (ItCount.Exact != getCouldNotCompute()) {
3072 assert(ItCount.Exact->isLoopInvariant(L) &&
3073 ItCount.Max->isLoopInvariant(L) &&
3074 "Computed trip count isn't loop invariant for loop!");
3075 ++NumTripCountsComputed;
3077 // Update the value in the map.
3078 Pair.first->second = ItCount;
3080 if (ItCount.Max != getCouldNotCompute())
3081 // Update the value in the map.
3082 Pair.first->second = ItCount;
3083 if (isa<PHINode>(L->getHeader()->begin()))
3084 // Only count loops that have phi nodes as not being computable.
3085 ++NumTripCountsNotComputed;
3088 // Now that we know more about the trip count for this loop, forget any
3089 // existing SCEV values for PHI nodes in this loop since they are only
3090 // conservative estimates made without the benefit of trip count
3091 // information. This is similar to the code in
3092 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI
3094 if (ItCount.hasAnyInfo()) {
3095 SmallVector<Instruction *, 16> Worklist;
3096 PushLoopPHIs(L, Worklist);
3098 SmallPtrSet<Instruction *, 8> Visited;
3099 while (!Worklist.empty()) {
3100 Instruction *I = Worklist.pop_back_val();
3101 if (!Visited.insert(I)) continue;
3103 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
3104 Scalars.find(static_cast<Value *>(I));
3105 if (It != Scalars.end()) {
3106 // SCEVUnknown for a PHI either means that it has an unrecognized
3107 // structure, or it's a PHI that's in the progress of being computed
3108 // by createNodeForPHI. In the former case, additional loop trip
3109 // count information isn't going to change anything. In the later
3110 // case, createNodeForPHI will perform the necessary updates on its
3111 // own when it gets to that point.
3112 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second))
3114 ValuesAtScopes.erase(I);
3115 if (PHINode *PN = dyn_cast<PHINode>(I))
3116 ConstantEvolutionLoopExitValue.erase(PN);
3119 PushDefUseChildren(I, Worklist);
3123 return Pair.first->second;
3126 /// forgetLoopBackedgeTakenCount - This method should be called by the
3127 /// client when it has changed a loop in a way that may effect
3128 /// ScalarEvolution's ability to compute a trip count, or if the loop
3130 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
3131 BackedgeTakenCounts.erase(L);
3133 SmallVector<Instruction *, 16> Worklist;
3134 PushLoopPHIs(L, Worklist);
3136 SmallPtrSet<Instruction *, 8> Visited;
3137 while (!Worklist.empty()) {
3138 Instruction *I = Worklist.pop_back_val();
3139 if (!Visited.insert(I)) continue;
3141 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
3142 Scalars.find(static_cast<Value *>(I));
3143 if (It != Scalars.end()) {
3145 ValuesAtScopes.erase(I);
3146 if (PHINode *PN = dyn_cast<PHINode>(I))
3147 ConstantEvolutionLoopExitValue.erase(PN);
3150 PushDefUseChildren(I, Worklist);
3154 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
3155 /// of the specified loop will execute.
3156 ScalarEvolution::BackedgeTakenInfo
3157 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
3158 SmallVector<BasicBlock*, 8> ExitingBlocks;
3159 L->getExitingBlocks(ExitingBlocks);
3161 // Examine all exits and pick the most conservative values.
3162 const SCEV *BECount = getCouldNotCompute();
3163 const SCEV *MaxBECount = getCouldNotCompute();
3164 bool CouldNotComputeBECount = false;
3165 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
3166 BackedgeTakenInfo NewBTI =
3167 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
3169 if (NewBTI.Exact == getCouldNotCompute()) {
3170 // We couldn't compute an exact value for this exit, so
3171 // we won't be able to compute an exact value for the loop.
3172 CouldNotComputeBECount = true;
3173 BECount = getCouldNotCompute();
3174 } else if (!CouldNotComputeBECount) {
3175 if (BECount == getCouldNotCompute())
3176 BECount = NewBTI.Exact;
3178 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
3180 if (MaxBECount == getCouldNotCompute())
3181 MaxBECount = NewBTI.Max;
3182 else if (NewBTI.Max != getCouldNotCompute())
3183 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
3186 return BackedgeTakenInfo(BECount, MaxBECount);
3189 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
3190 /// of the specified loop will execute if it exits via the specified block.
3191 ScalarEvolution::BackedgeTakenInfo
3192 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
3193 BasicBlock *ExitingBlock) {
3195 // Okay, we've chosen an exiting block. See what condition causes us to
3196 // exit at this block.
3198 // FIXME: we should be able to handle switch instructions (with a single exit)
3199 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
3200 if (ExitBr == 0) return getCouldNotCompute();
3201 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
3203 // At this point, we know we have a conditional branch that determines whether
3204 // the loop is exited. However, we don't know if the branch is executed each
3205 // time through the loop. If not, then the execution count of the branch will
3206 // not be equal to the trip count of the loop.
3208 // Currently we check for this by checking to see if the Exit branch goes to
3209 // the loop header. If so, we know it will always execute the same number of
3210 // times as the loop. We also handle the case where the exit block *is* the
3211 // loop header. This is common for un-rotated loops.
3213 // If both of those tests fail, walk up the unique predecessor chain to the
3214 // header, stopping if there is an edge that doesn't exit the loop. If the
3215 // header is reached, the execution count of the branch will be equal to the
3216 // trip count of the loop.
3218 // More extensive analysis could be done to handle more cases here.
3220 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3221 ExitBr->getSuccessor(1) != L->getHeader() &&
3222 ExitBr->getParent() != L->getHeader()) {
3223 // The simple checks failed, try climbing the unique predecessor chain
3224 // up to the header.
3226 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3227 BasicBlock *Pred = BB->getUniquePredecessor();
3229 return getCouldNotCompute();
3230 TerminatorInst *PredTerm = Pred->getTerminator();
3231 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3232 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3235 // If the predecessor has a successor that isn't BB and isn't
3236 // outside the loop, assume the worst.
3237 if (L->contains(PredSucc))
3238 return getCouldNotCompute();
3240 if (Pred == L->getHeader()) {
3247 return getCouldNotCompute();
3250 // Procede to the next level to examine the exit condition expression.
3251 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3252 ExitBr->getSuccessor(0),
3253 ExitBr->getSuccessor(1));
3256 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3257 /// backedge of the specified loop will execute if its exit condition
3258 /// were a conditional branch of ExitCond, TBB, and FBB.
3259 ScalarEvolution::BackedgeTakenInfo
3260 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3264 // Check if the controlling expression for this loop is an And or Or.
3265 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3266 if (BO->getOpcode() == Instruction::And) {
3267 // Recurse on the operands of the and.
3268 BackedgeTakenInfo BTI0 =
3269 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3270 BackedgeTakenInfo BTI1 =
3271 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3272 const SCEV *BECount = getCouldNotCompute();
3273 const SCEV *MaxBECount = getCouldNotCompute();
3274 if (L->contains(TBB)) {
3275 // Both conditions must be true for the loop to continue executing.
3276 // Choose the less conservative count.
3277 if (BTI0.Exact == getCouldNotCompute() ||
3278 BTI1.Exact == getCouldNotCompute())
3279 BECount = getCouldNotCompute();
3281 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3282 if (BTI0.Max == getCouldNotCompute())
3283 MaxBECount = BTI1.Max;
3284 else if (BTI1.Max == getCouldNotCompute())
3285 MaxBECount = BTI0.Max;
3287 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3289 // Both conditions must be true for the loop to exit.
3290 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3291 if (BTI0.Exact != getCouldNotCompute() &&
3292 BTI1.Exact != getCouldNotCompute())
3293 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3294 if (BTI0.Max != getCouldNotCompute() &&
3295 BTI1.Max != getCouldNotCompute())
3296 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3299 return BackedgeTakenInfo(BECount, MaxBECount);
3301 if (BO->getOpcode() == Instruction::Or) {
3302 // Recurse on the operands of the or.
3303 BackedgeTakenInfo BTI0 =
3304 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3305 BackedgeTakenInfo BTI1 =
3306 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3307 const SCEV *BECount = getCouldNotCompute();
3308 const SCEV *MaxBECount = getCouldNotCompute();
3309 if (L->contains(FBB)) {
3310 // Both conditions must be false for the loop to continue executing.
3311 // Choose the less conservative count.
3312 if (BTI0.Exact == getCouldNotCompute() ||
3313 BTI1.Exact == getCouldNotCompute())
3314 BECount = getCouldNotCompute();
3316 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3317 if (BTI0.Max == getCouldNotCompute())
3318 MaxBECount = BTI1.Max;
3319 else if (BTI1.Max == getCouldNotCompute())
3320 MaxBECount = BTI0.Max;
3322 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3324 // Both conditions must be false for the loop to exit.
3325 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3326 if (BTI0.Exact != getCouldNotCompute() &&
3327 BTI1.Exact != getCouldNotCompute())
3328 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3329 if (BTI0.Max != getCouldNotCompute() &&
3330 BTI1.Max != getCouldNotCompute())
3331 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3334 return BackedgeTakenInfo(BECount, MaxBECount);
3338 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3339 // Procede to the next level to examine the icmp.
3340 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3341 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3343 // If it's not an integer or pointer comparison then compute it the hard way.
3344 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3347 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3348 /// backedge of the specified loop will execute if its exit condition
3349 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3350 ScalarEvolution::BackedgeTakenInfo
3351 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3356 // If the condition was exit on true, convert the condition to exit on false
3357 ICmpInst::Predicate Cond;
3358 if (!L->contains(FBB))
3359 Cond = ExitCond->getPredicate();
3361 Cond = ExitCond->getInversePredicate();
3363 // Handle common loops like: for (X = "string"; *X; ++X)
3364 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3365 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3367 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3368 if (!isa<SCEVCouldNotCompute>(ItCnt)) {
3369 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType());
3370 return BackedgeTakenInfo(ItCnt,
3371 isa<SCEVConstant>(ItCnt) ? ItCnt :
3372 getConstant(APInt::getMaxValue(BitWidth)-1));
3376 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3377 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3379 // Try to evaluate any dependencies out of the loop.
3380 LHS = getSCEVAtScope(LHS, L);
3381 RHS = getSCEVAtScope(RHS, L);
3383 // At this point, we would like to compute how many iterations of the
3384 // loop the predicate will return true for these inputs.
3385 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3386 // If there is a loop-invariant, force it into the RHS.
3387 std::swap(LHS, RHS);
3388 Cond = ICmpInst::getSwappedPredicate(Cond);
3391 // If we have a comparison of a chrec against a constant, try to use value
3392 // ranges to answer this query.
3393 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3394 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3395 if (AddRec->getLoop() == L) {
3396 // Form the constant range.
3397 ConstantRange CompRange(
3398 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3400 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3401 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3405 case ICmpInst::ICMP_NE: { // while (X != Y)
3406 // Convert to: while (X-Y != 0)
3407 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3408 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3411 case ICmpInst::ICMP_EQ: {
3412 // Convert to: while (X-Y == 0) // while (X == Y)
3413 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3414 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3417 case ICmpInst::ICMP_SLT: {
3418 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3419 if (BTI.hasAnyInfo()) return BTI;
3422 case ICmpInst::ICMP_SGT: {
3423 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3424 getNotSCEV(RHS), L, true);
3425 if (BTI.hasAnyInfo()) return BTI;
3428 case ICmpInst::ICMP_ULT: {
3429 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3430 if (BTI.hasAnyInfo()) return BTI;
3433 case ICmpInst::ICMP_UGT: {
3434 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3435 getNotSCEV(RHS), L, false);
3436 if (BTI.hasAnyInfo()) return BTI;
3441 errs() << "ComputeBackedgeTakenCount ";
3442 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3443 errs() << "[unsigned] ";
3444 errs() << *LHS << " "
3445 << Instruction::getOpcodeName(Instruction::ICmp)
3446 << " " << *RHS << "\n";
3451 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3454 static ConstantInt *
3455 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3456 ScalarEvolution &SE) {
3457 const SCEV *InVal = SE.getConstant(C);
3458 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3459 assert(isa<SCEVConstant>(Val) &&
3460 "Evaluation of SCEV at constant didn't fold correctly?");
3461 return cast<SCEVConstant>(Val)->getValue();
3464 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3465 /// and a GEP expression (missing the pointer index) indexing into it, return
3466 /// the addressed element of the initializer or null if the index expression is
3469 GetAddressedElementFromGlobal(LLVMContext &Context, GlobalVariable *GV,
3470 const std::vector<ConstantInt*> &Indices) {
3471 Constant *Init = GV->getInitializer();
3472 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3473 uint64_t Idx = Indices[i]->getZExtValue();
3474 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3475 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3476 Init = cast<Constant>(CS->getOperand(Idx));
3477 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3478 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3479 Init = cast<Constant>(CA->getOperand(Idx));
3480 } else if (isa<ConstantAggregateZero>(Init)) {
3481 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3482 assert(Idx < STy->getNumElements() && "Bad struct index!");
3483 Init = Constant::getNullValue(STy->getElementType(Idx));
3484 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3485 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3486 Init = Constant::getNullValue(ATy->getElementType());
3488 llvm_unreachable("Unknown constant aggregate type!");
3492 return 0; // Unknown initializer type
3498 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3499 /// 'icmp op load X, cst', try to see if we can compute the backedge
3500 /// execution count.
3502 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3506 ICmpInst::Predicate predicate) {
3507 if (LI->isVolatile()) return getCouldNotCompute();
3509 // Check to see if the loaded pointer is a getelementptr of a global.
3510 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3511 if (!GEP) return getCouldNotCompute();
3513 // Make sure that it is really a constant global we are gepping, with an
3514 // initializer, and make sure the first IDX is really 0.
3515 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3516 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
3517 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3518 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3519 return getCouldNotCompute();
3521 // Okay, we allow one non-constant index into the GEP instruction.
3523 std::vector<ConstantInt*> Indexes;
3524 unsigned VarIdxNum = 0;
3525 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3526 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3527 Indexes.push_back(CI);
3528 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3529 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3530 VarIdx = GEP->getOperand(i);
3532 Indexes.push_back(0);
3535 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3536 // Check to see if X is a loop variant variable value now.
3537 const SCEV *Idx = getSCEV(VarIdx);
3538 Idx = getSCEVAtScope(Idx, L);
3540 // We can only recognize very limited forms of loop index expressions, in
3541 // particular, only affine AddRec's like {C1,+,C2}.
3542 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3543 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3544 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3545 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
3546 return getCouldNotCompute();
3548 unsigned MaxSteps = MaxBruteForceIterations;
3549 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3550 ConstantInt *ItCst = ConstantInt::get(
3551 cast<IntegerType>(IdxExpr->getType()), IterationNum);
3552 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
3554 // Form the GEP offset.
3555 Indexes[VarIdxNum] = Val;
3557 Constant *Result = GetAddressedElementFromGlobal(getContext(), GV, Indexes);
3558 if (Result == 0) break; // Cannot compute!
3560 // Evaluate the condition for this iteration.
3561 Result = ConstantExpr::getICmp(predicate, Result, RHS);
3562 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
3563 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
3565 errs() << "\n***\n*** Computed loop count " << *ItCst
3566 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
3569 ++NumArrayLenItCounts;
3570 return getConstant(ItCst); // Found terminating iteration!
3573 return getCouldNotCompute();
3577 /// CanConstantFold - Return true if we can constant fold an instruction of the
3578 /// specified type, assuming that all operands were constants.
3579 static bool CanConstantFold(const Instruction *I) {
3580 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
3581 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
3584 if (const CallInst *CI = dyn_cast<CallInst>(I))
3585 if (const Function *F = CI->getCalledFunction())
3586 return canConstantFoldCallTo(F);
3590 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
3591 /// in the loop that V is derived from. We allow arbitrary operations along the
3592 /// way, but the operands of an operation must either be constants or a value
3593 /// derived from a constant PHI. If this expression does not fit with these
3594 /// constraints, return null.
3595 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
3596 // If this is not an instruction, or if this is an instruction outside of the
3597 // loop, it can't be derived from a loop PHI.
3598 Instruction *I = dyn_cast<Instruction>(V);
3599 if (I == 0 || !L->contains(I->getParent())) return 0;
3601 if (PHINode *PN = dyn_cast<PHINode>(I)) {
3602 if (L->getHeader() == I->getParent())
3605 // We don't currently keep track of the control flow needed to evaluate
3606 // PHIs, so we cannot handle PHIs inside of loops.
3610 // If we won't be able to constant fold this expression even if the operands
3611 // are constants, return early.
3612 if (!CanConstantFold(I)) return 0;
3614 // Otherwise, we can evaluate this instruction if all of its operands are
3615 // constant or derived from a PHI node themselves.
3617 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
3618 if (!(isa<Constant>(I->getOperand(Op)) ||
3619 isa<GlobalValue>(I->getOperand(Op)))) {
3620 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
3621 if (P == 0) return 0; // Not evolving from PHI
3625 return 0; // Evolving from multiple different PHIs.
3628 // This is a expression evolving from a constant PHI!
3632 /// EvaluateExpression - Given an expression that passes the
3633 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
3634 /// in the loop has the value PHIVal. If we can't fold this expression for some
3635 /// reason, return null.
3636 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
3637 if (isa<PHINode>(V)) return PHIVal;
3638 if (Constant *C = dyn_cast<Constant>(V)) return C;
3639 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
3640 Instruction *I = cast<Instruction>(V);
3641 LLVMContext &Context = I->getParent()->getContext();
3643 std::vector<Constant*> Operands;
3644 Operands.resize(I->getNumOperands());
3646 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3647 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
3648 if (Operands[i] == 0) return 0;
3651 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3652 return ConstantFoldCompareInstOperands(CI->getPredicate(),
3653 &Operands[0], Operands.size(),
3656 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3657 &Operands[0], Operands.size(),
3661 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
3662 /// in the header of its containing loop, we know the loop executes a
3663 /// constant number of times, and the PHI node is just a recurrence
3664 /// involving constants, fold it.
3666 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
3669 std::map<PHINode*, Constant*>::iterator I =
3670 ConstantEvolutionLoopExitValue.find(PN);
3671 if (I != ConstantEvolutionLoopExitValue.end())
3674 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
3675 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
3677 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
3679 // Since the loop is canonicalized, the PHI node must have two entries. One
3680 // entry must be a constant (coming in from outside of the loop), and the
3681 // second must be derived from the same PHI.
3682 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3683 Constant *StartCST =
3684 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3686 return RetVal = 0; // Must be a constant.
3688 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3689 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3691 return RetVal = 0; // Not derived from same PHI.
3693 // Execute the loop symbolically to determine the exit value.
3694 if (BEs.getActiveBits() >= 32)
3695 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
3697 unsigned NumIterations = BEs.getZExtValue(); // must be in range
3698 unsigned IterationNum = 0;
3699 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
3700 if (IterationNum == NumIterations)
3701 return RetVal = PHIVal; // Got exit value!
3703 // Compute the value of the PHI node for the next iteration.
3704 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3705 if (NextPHI == PHIVal)
3706 return RetVal = NextPHI; // Stopped evolving!
3708 return 0; // Couldn't evaluate!
3713 /// ComputeBackedgeTakenCountExhaustively - If the loop is known to execute a
3714 /// constant number of times (the condition evolves only from constants),
3715 /// try to evaluate a few iterations of the loop until we get the exit
3716 /// condition gets a value of ExitWhen (true or false). If we cannot
3717 /// evaluate the trip count of the loop, return getCouldNotCompute().
3719 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
3722 PHINode *PN = getConstantEvolvingPHI(Cond, L);
3723 if (PN == 0) return getCouldNotCompute();
3725 // Since the loop is canonicalized, the PHI node must have two entries. One
3726 // entry must be a constant (coming in from outside of the loop), and the
3727 // second must be derived from the same PHI.
3728 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3729 Constant *StartCST =
3730 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3731 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
3733 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3734 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3735 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
3737 // Okay, we find a PHI node that defines the trip count of this loop. Execute
3738 // the loop symbolically to determine when the condition gets a value of
3740 unsigned IterationNum = 0;
3741 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
3742 for (Constant *PHIVal = StartCST;
3743 IterationNum != MaxIterations; ++IterationNum) {
3744 ConstantInt *CondVal =
3745 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
3747 // Couldn't symbolically evaluate.
3748 if (!CondVal) return getCouldNotCompute();
3750 if (CondVal->getValue() == uint64_t(ExitWhen)) {
3751 ++NumBruteForceTripCountsComputed;
3752 return getConstant(Type::getInt32Ty(getContext()), IterationNum);
3755 // Compute the value of the PHI node for the next iteration.
3756 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3757 if (NextPHI == 0 || NextPHI == PHIVal)
3758 return getCouldNotCompute();// Couldn't evaluate or not making progress...
3762 // Too many iterations were needed to evaluate.
3763 return getCouldNotCompute();
3766 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
3767 /// at the specified scope in the program. The L value specifies a loop
3768 /// nest to evaluate the expression at, where null is the top-level or a
3769 /// specified loop is immediately inside of the loop.
3771 /// This method can be used to compute the exit value for a variable defined
3772 /// in a loop by querying what the value will hold in the parent loop.
3774 /// In the case that a relevant loop exit value cannot be computed, the
3775 /// original value V is returned.
3776 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
3777 // FIXME: this should be turned into a virtual method on SCEV!
3779 if (isa<SCEVConstant>(V)) return V;
3781 // If this instruction is evolved from a constant-evolving PHI, compute the
3782 // exit value from the loop without using SCEVs.
3783 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
3784 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
3785 const Loop *LI = (*this->LI)[I->getParent()];
3786 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
3787 if (PHINode *PN = dyn_cast<PHINode>(I))
3788 if (PN->getParent() == LI->getHeader()) {
3789 // Okay, there is no closed form solution for the PHI node. Check
3790 // to see if the loop that contains it has a known backedge-taken
3791 // count. If so, we may be able to force computation of the exit
3793 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
3794 if (const SCEVConstant *BTCC =
3795 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
3796 // Okay, we know how many times the containing loop executes. If
3797 // this is a constant evolving PHI node, get the final value at
3798 // the specified iteration number.
3799 Constant *RV = getConstantEvolutionLoopExitValue(PN,
3800 BTCC->getValue()->getValue(),
3802 if (RV) return getSCEV(RV);
3806 // Okay, this is an expression that we cannot symbolically evaluate
3807 // into a SCEV. Check to see if it's possible to symbolically evaluate
3808 // the arguments into constants, and if so, try to constant propagate the
3809 // result. This is particularly useful for computing loop exit values.
3810 if (CanConstantFold(I)) {
3811 // Check to see if we've folded this instruction at this loop before.
3812 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
3813 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
3814 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
3816 return Pair.first->second ? &*getSCEV(Pair.first->second) : V;
3818 std::vector<Constant*> Operands;
3819 Operands.reserve(I->getNumOperands());
3820 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3821 Value *Op = I->getOperand(i);
3822 if (Constant *C = dyn_cast<Constant>(Op)) {
3823 Operands.push_back(C);
3825 // If any of the operands is non-constant and if they are
3826 // non-integer and non-pointer, don't even try to analyze them
3827 // with scev techniques.
3828 if (!isSCEVable(Op->getType()))
3831 const SCEV* OpV = getSCEVAtScope(Op, L);
3832 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
3833 Constant *C = SC->getValue();
3834 if (C->getType() != Op->getType())
3835 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3839 Operands.push_back(C);
3840 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
3841 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
3842 if (C->getType() != Op->getType())
3844 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3848 Operands.push_back(C);
3858 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3859 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
3860 &Operands[0], Operands.size(),
3863 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3864 &Operands[0], Operands.size(),
3866 Pair.first->second = C;
3871 // This is some other type of SCEVUnknown, just return it.
3875 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3876 // Avoid performing the look-up in the common case where the specified
3877 // expression has no loop-variant portions.
3878 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3879 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3880 if (OpAtScope != Comm->getOperand(i)) {
3881 // Okay, at least one of these operands is loop variant but might be
3882 // foldable. Build a new instance of the folded commutative expression.
3883 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
3884 Comm->op_begin()+i);
3885 NewOps.push_back(OpAtScope);
3887 for (++i; i != e; ++i) {
3888 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3889 NewOps.push_back(OpAtScope);
3891 if (isa<SCEVAddExpr>(Comm))
3892 return getAddExpr(NewOps);
3893 if (isa<SCEVMulExpr>(Comm))
3894 return getMulExpr(NewOps);
3895 if (isa<SCEVSMaxExpr>(Comm))
3896 return getSMaxExpr(NewOps);
3897 if (isa<SCEVUMaxExpr>(Comm))
3898 return getUMaxExpr(NewOps);
3899 llvm_unreachable("Unknown commutative SCEV type!");
3902 // If we got here, all operands are loop invariant.
3906 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3907 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
3908 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
3909 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3910 return Div; // must be loop invariant
3911 return getUDivExpr(LHS, RHS);
3914 // If this is a loop recurrence for a loop that does not contain L, then we
3915 // are dealing with the final value computed by the loop.
3916 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3917 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3918 // To evaluate this recurrence, we need to know how many times the AddRec
3919 // loop iterates. Compute this now.
3920 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3921 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
3923 // Then, evaluate the AddRec.
3924 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3929 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3930 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3931 if (Op == Cast->getOperand())
3932 return Cast; // must be loop invariant
3933 return getZeroExtendExpr(Op, Cast->getType());
3936 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3937 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3938 if (Op == Cast->getOperand())
3939 return Cast; // must be loop invariant
3940 return getSignExtendExpr(Op, Cast->getType());
3943 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3944 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3945 if (Op == Cast->getOperand())
3946 return Cast; // must be loop invariant
3947 return getTruncateExpr(Op, Cast->getType());
3950 llvm_unreachable("Unknown SCEV type!");
3954 /// getSCEVAtScope - This is a convenience function which does
3955 /// getSCEVAtScope(getSCEV(V), L).
3956 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3957 return getSCEVAtScope(getSCEV(V), L);
3960 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3961 /// following equation:
3963 /// A * X = B (mod N)
3965 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3966 /// A and B isn't important.
3968 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3969 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3970 ScalarEvolution &SE) {
3971 uint32_t BW = A.getBitWidth();
3972 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3973 assert(A != 0 && "A must be non-zero.");
3977 // The gcd of A and N may have only one prime factor: 2. The number of
3978 // trailing zeros in A is its multiplicity
3979 uint32_t Mult2 = A.countTrailingZeros();
3982 // 2. Check if B is divisible by D.
3984 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3985 // is not less than multiplicity of this prime factor for D.
3986 if (B.countTrailingZeros() < Mult2)
3987 return SE.getCouldNotCompute();
3989 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3992 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3993 // bit width during computations.
3994 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3995 APInt Mod(BW + 1, 0);
3996 Mod.set(BW - Mult2); // Mod = N / D
3997 APInt I = AD.multiplicativeInverse(Mod);
3999 // 4. Compute the minimum unsigned root of the equation:
4000 // I * (B / D) mod (N / D)
4001 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
4003 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
4005 return SE.getConstant(Result.trunc(BW));
4008 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
4009 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
4010 /// might be the same) or two SCEVCouldNotCompute objects.
4012 static std::pair<const SCEV *,const SCEV *>
4013 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
4014 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
4015 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
4016 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
4017 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
4019 // We currently can only solve this if the coefficients are constants.
4020 if (!LC || !MC || !NC) {
4021 const SCEV *CNC = SE.getCouldNotCompute();
4022 return std::make_pair(CNC, CNC);
4025 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
4026 const APInt &L = LC->getValue()->getValue();
4027 const APInt &M = MC->getValue()->getValue();
4028 const APInt &N = NC->getValue()->getValue();
4029 APInt Two(BitWidth, 2);
4030 APInt Four(BitWidth, 4);
4033 using namespace APIntOps;
4035 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
4036 // The B coefficient is M-N/2
4040 // The A coefficient is N/2
4041 APInt A(N.sdiv(Two));
4043 // Compute the B^2-4ac term.
4046 SqrtTerm -= Four * (A * C);
4048 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
4049 // integer value or else APInt::sqrt() will assert.
4050 APInt SqrtVal(SqrtTerm.sqrt());
4052 // Compute the two solutions for the quadratic formula.
4053 // The divisions must be performed as signed divisions.
4055 APInt TwoA( A << 1 );
4056 if (TwoA.isMinValue()) {
4057 const SCEV *CNC = SE.getCouldNotCompute();
4058 return std::make_pair(CNC, CNC);
4061 LLVMContext &Context = SE.getContext();
4063 ConstantInt *Solution1 =
4064 ConstantInt::get(Context, (NegB + SqrtVal).sdiv(TwoA));
4065 ConstantInt *Solution2 =
4066 ConstantInt::get(Context, (NegB - SqrtVal).sdiv(TwoA));
4068 return std::make_pair(SE.getConstant(Solution1),
4069 SE.getConstant(Solution2));
4070 } // end APIntOps namespace
4073 /// HowFarToZero - Return the number of times a backedge comparing the specified
4074 /// value to zero will execute. If not computable, return CouldNotCompute.
4075 const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
4076 // If the value is a constant
4077 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4078 // If the value is already zero, the branch will execute zero times.
4079 if (C->getValue()->isZero()) return C;
4080 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4083 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
4084 if (!AddRec || AddRec->getLoop() != L)
4085 return getCouldNotCompute();
4087 if (AddRec->isAffine()) {
4088 // If this is an affine expression, the execution count of this branch is
4089 // the minimum unsigned root of the following equation:
4091 // Start + Step*N = 0 (mod 2^BW)
4095 // Step*N = -Start (mod 2^BW)
4097 // where BW is the common bit width of Start and Step.
4099 // Get the initial value for the loop.
4100 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
4101 L->getParentLoop());
4102 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
4103 L->getParentLoop());
4105 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
4106 // For now we handle only constant steps.
4108 // First, handle unitary steps.
4109 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
4110 return getNegativeSCEV(Start); // N = -Start (as unsigned)
4111 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
4112 return Start; // N = Start (as unsigned)
4114 // Then, try to solve the above equation provided that Start is constant.
4115 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
4116 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
4117 -StartC->getValue()->getValue(),
4120 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
4121 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
4122 // the quadratic equation to solve it.
4123 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
4125 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4126 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4129 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
4130 << " sol#2: " << *R2 << "\n";
4132 // Pick the smallest positive root value.
4133 if (ConstantInt *CB =
4134 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4135 R1->getValue(), R2->getValue()))) {
4136 if (CB->getZExtValue() == false)
4137 std::swap(R1, R2); // R1 is the minimum root now.
4139 // We can only use this value if the chrec ends up with an exact zero
4140 // value at this index. When solving for "X*X != 5", for example, we
4141 // should not accept a root of 2.
4142 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
4144 return R1; // We found a quadratic root!
4149 return getCouldNotCompute();
4152 /// HowFarToNonZero - Return the number of times a backedge checking the
4153 /// specified value for nonzero will execute. If not computable, return
4155 const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
4156 // Loops that look like: while (X == 0) are very strange indeed. We don't
4157 // handle them yet except for the trivial case. This could be expanded in the
4158 // future as needed.
4160 // If the value is a constant, check to see if it is known to be non-zero
4161 // already. If so, the backedge will execute zero times.
4162 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
4163 if (!C->getValue()->isNullValue())
4164 return getIntegerSCEV(0, C->getType());
4165 return getCouldNotCompute(); // Otherwise it will loop infinitely.
4168 // We could implement others, but I really doubt anyone writes loops like
4169 // this, and if they did, they would already be constant folded.
4170 return getCouldNotCompute();
4173 /// getLoopPredecessor - If the given loop's header has exactly one unique
4174 /// predecessor outside the loop, return it. Otherwise return null.
4176 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
4177 BasicBlock *Header = L->getHeader();
4178 BasicBlock *Pred = 0;
4179 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
4181 if (!L->contains(*PI)) {
4182 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
4188 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
4189 /// (which may not be an immediate predecessor) which has exactly one
4190 /// successor from which BB is reachable, or null if no such block is
4194 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
4195 // If the block has a unique predecessor, then there is no path from the
4196 // predecessor to the block that does not go through the direct edge
4197 // from the predecessor to the block.
4198 if (BasicBlock *Pred = BB->getSinglePredecessor())
4201 // A loop's header is defined to be a block that dominates the loop.
4202 // If the header has a unique predecessor outside the loop, it must be
4203 // a block that has exactly one successor that can reach the loop.
4204 if (Loop *L = LI->getLoopFor(BB))
4205 return getLoopPredecessor(L);
4210 /// HasSameValue - SCEV structural equivalence is usually sufficient for
4211 /// testing whether two expressions are equal, however for the purposes of
4212 /// looking for a condition guarding a loop, it can be useful to be a little
4213 /// more general, since a front-end may have replicated the controlling
4216 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4217 // Quick check to see if they are the same SCEV.
4218 if (A == B) return true;
4220 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4221 // two different instructions with the same value. Check for this case.
4222 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4223 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4224 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4225 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4226 if (AI->isIdenticalTo(BI))
4229 // Otherwise assume they may have a different value.
4233 bool ScalarEvolution::isKnownNegative(const SCEV *S) {
4234 return getSignedRange(S).getSignedMax().isNegative();
4237 bool ScalarEvolution::isKnownPositive(const SCEV *S) {
4238 return getSignedRange(S).getSignedMin().isStrictlyPositive();
4241 bool ScalarEvolution::isKnownNonNegative(const SCEV *S) {
4242 return !getSignedRange(S).getSignedMin().isNegative();
4245 bool ScalarEvolution::isKnownNonPositive(const SCEV *S) {
4246 return !getSignedRange(S).getSignedMax().isStrictlyPositive();
4249 bool ScalarEvolution::isKnownNonZero(const SCEV *S) {
4250 return isKnownNegative(S) || isKnownPositive(S);
4253 bool ScalarEvolution::isKnownPredicate(ICmpInst::Predicate Pred,
4254 const SCEV *LHS, const SCEV *RHS) {
4256 if (HasSameValue(LHS, RHS))
4257 return ICmpInst::isTrueWhenEqual(Pred);
4261 llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4263 case ICmpInst::ICMP_SGT:
4264 Pred = ICmpInst::ICMP_SLT;
4265 std::swap(LHS, RHS);
4266 case ICmpInst::ICMP_SLT: {
4267 ConstantRange LHSRange = getSignedRange(LHS);
4268 ConstantRange RHSRange = getSignedRange(RHS);
4269 if (LHSRange.getSignedMax().slt(RHSRange.getSignedMin()))
4271 if (LHSRange.getSignedMin().sge(RHSRange.getSignedMax()))
4275 case ICmpInst::ICMP_SGE:
4276 Pred = ICmpInst::ICMP_SLE;
4277 std::swap(LHS, RHS);
4278 case ICmpInst::ICMP_SLE: {
4279 ConstantRange LHSRange = getSignedRange(LHS);
4280 ConstantRange RHSRange = getSignedRange(RHS);
4281 if (LHSRange.getSignedMax().sle(RHSRange.getSignedMin()))
4283 if (LHSRange.getSignedMin().sgt(RHSRange.getSignedMax()))
4287 case ICmpInst::ICMP_UGT:
4288 Pred = ICmpInst::ICMP_ULT;
4289 std::swap(LHS, RHS);
4290 case ICmpInst::ICMP_ULT: {
4291 ConstantRange LHSRange = getUnsignedRange(LHS);
4292 ConstantRange RHSRange = getUnsignedRange(RHS);
4293 if (LHSRange.getUnsignedMax().ult(RHSRange.getUnsignedMin()))
4295 if (LHSRange.getUnsignedMin().uge(RHSRange.getUnsignedMax()))
4299 case ICmpInst::ICMP_UGE:
4300 Pred = ICmpInst::ICMP_ULE;
4301 std::swap(LHS, RHS);
4302 case ICmpInst::ICMP_ULE: {
4303 ConstantRange LHSRange = getUnsignedRange(LHS);
4304 ConstantRange RHSRange = getUnsignedRange(RHS);
4305 if (LHSRange.getUnsignedMax().ule(RHSRange.getUnsignedMin()))
4307 if (LHSRange.getUnsignedMin().ugt(RHSRange.getUnsignedMax()))
4311 case ICmpInst::ICMP_NE: {
4312 if (getUnsignedRange(LHS).intersectWith(getUnsignedRange(RHS)).isEmptySet())
4314 if (getSignedRange(LHS).intersectWith(getSignedRange(RHS)).isEmptySet())
4317 const SCEV *Diff = getMinusSCEV(LHS, RHS);
4318 if (isKnownNonZero(Diff))
4322 case ICmpInst::ICMP_EQ:
4323 // The check at the top of the function catches the case where
4324 // the values are known to be equal.
4330 /// isLoopBackedgeGuardedByCond - Test whether the backedge of the loop is
4331 /// protected by a conditional between LHS and RHS. This is used to
4332 /// to eliminate casts.
4334 ScalarEvolution::isLoopBackedgeGuardedByCond(const Loop *L,
4335 ICmpInst::Predicate Pred,
4336 const SCEV *LHS, const SCEV *RHS) {
4337 // Interpret a null as meaning no loop, where there is obviously no guard
4338 // (interprocedural conditions notwithstanding).
4339 if (!L) return true;
4341 BasicBlock *Latch = L->getLoopLatch();
4345 BranchInst *LoopContinuePredicate =
4346 dyn_cast<BranchInst>(Latch->getTerminator());
4347 if (!LoopContinuePredicate ||
4348 LoopContinuePredicate->isUnconditional())
4351 return isImpliedCond(LoopContinuePredicate->getCondition(), Pred, LHS, RHS,
4352 LoopContinuePredicate->getSuccessor(0) != L->getHeader());
4355 /// isLoopGuardedByCond - Test whether entry to the loop is protected
4356 /// by a conditional between LHS and RHS. This is used to help avoid max
4357 /// expressions in loop trip counts, and to eliminate casts.
4359 ScalarEvolution::isLoopGuardedByCond(const Loop *L,
4360 ICmpInst::Predicate Pred,
4361 const SCEV *LHS, const SCEV *RHS) {
4362 // Interpret a null as meaning no loop, where there is obviously no guard
4363 // (interprocedural conditions notwithstanding).
4364 if (!L) return false;
4366 BasicBlock *Predecessor = getLoopPredecessor(L);
4367 BasicBlock *PredecessorDest = L->getHeader();
4369 // Starting at the loop predecessor, climb up the predecessor chain, as long
4370 // as there are predecessors that can be found that have unique successors
4371 // leading to the original header.
4373 PredecessorDest = Predecessor,
4374 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4376 BranchInst *LoopEntryPredicate =
4377 dyn_cast<BranchInst>(Predecessor->getTerminator());
4378 if (!LoopEntryPredicate ||
4379 LoopEntryPredicate->isUnconditional())
4382 if (isImpliedCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4383 LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4390 /// isImpliedCond - Test whether the condition described by Pred, LHS,
4391 /// and RHS is true whenever the given Cond value evaluates to true.
4392 bool ScalarEvolution::isImpliedCond(Value *CondValue,
4393 ICmpInst::Predicate Pred,
4394 const SCEV *LHS, const SCEV *RHS,
4396 // Recursivly handle And and Or conditions.
4397 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4398 if (BO->getOpcode() == Instruction::And) {
4400 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4401 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4402 } else if (BO->getOpcode() == Instruction::Or) {
4404 return isImpliedCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4405 isImpliedCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4409 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4410 if (!ICI) return false;
4412 // Bail if the ICmp's operands' types are wider than the needed type
4413 // before attempting to call getSCEV on them. This avoids infinite
4414 // recursion, since the analysis of widening casts can require loop
4415 // exit condition information for overflow checking, which would
4417 if (getTypeSizeInBits(LHS->getType()) <
4418 getTypeSizeInBits(ICI->getOperand(0)->getType()))
4421 // Now that we found a conditional branch that dominates the loop, check to
4422 // see if it is the comparison we are looking for.
4423 ICmpInst::Predicate FoundPred;
4425 FoundPred = ICI->getInversePredicate();
4427 FoundPred = ICI->getPredicate();
4429 const SCEV *FoundLHS = getSCEV(ICI->getOperand(0));
4430 const SCEV *FoundRHS = getSCEV(ICI->getOperand(1));
4432 // Balance the types. The case where FoundLHS' type is wider than
4433 // LHS' type is checked for above.
4434 if (getTypeSizeInBits(LHS->getType()) >
4435 getTypeSizeInBits(FoundLHS->getType())) {
4436 if (CmpInst::isSigned(Pred)) {
4437 FoundLHS = getSignExtendExpr(FoundLHS, LHS->getType());
4438 FoundRHS = getSignExtendExpr(FoundRHS, LHS->getType());
4440 FoundLHS = getZeroExtendExpr(FoundLHS, LHS->getType());
4441 FoundRHS = getZeroExtendExpr(FoundRHS, LHS->getType());
4445 // Canonicalize the query to match the way instcombine will have
4446 // canonicalized the comparison.
4447 // First, put a constant operand on the right.
4448 if (isa<SCEVConstant>(LHS)) {
4449 std::swap(LHS, RHS);
4450 Pred = ICmpInst::getSwappedPredicate(Pred);
4452 // Then, canonicalize comparisons with boundary cases.
4453 if (const SCEVConstant *RC = dyn_cast<SCEVConstant>(RHS)) {
4454 const APInt &RA = RC->getValue()->getValue();
4456 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4457 case ICmpInst::ICMP_EQ:
4458 case ICmpInst::ICMP_NE:
4460 case ICmpInst::ICMP_UGE:
4461 if ((RA - 1).isMinValue()) {
4462 Pred = ICmpInst::ICMP_NE;
4463 RHS = getConstant(RA - 1);
4466 if (RA.isMaxValue()) {
4467 Pred = ICmpInst::ICMP_EQ;
4470 if (RA.isMinValue()) return true;
4472 case ICmpInst::ICMP_ULE:
4473 if ((RA + 1).isMaxValue()) {
4474 Pred = ICmpInst::ICMP_NE;
4475 RHS = getConstant(RA + 1);
4478 if (RA.isMinValue()) {
4479 Pred = ICmpInst::ICMP_EQ;
4482 if (RA.isMaxValue()) return true;
4484 case ICmpInst::ICMP_SGE:
4485 if ((RA - 1).isMinSignedValue()) {
4486 Pred = ICmpInst::ICMP_NE;
4487 RHS = getConstant(RA - 1);
4490 if (RA.isMaxSignedValue()) {
4491 Pred = ICmpInst::ICMP_EQ;
4494 if (RA.isMinSignedValue()) return true;
4496 case ICmpInst::ICMP_SLE:
4497 if ((RA + 1).isMaxSignedValue()) {
4498 Pred = ICmpInst::ICMP_NE;
4499 RHS = getConstant(RA + 1);
4502 if (RA.isMinSignedValue()) {
4503 Pred = ICmpInst::ICMP_EQ;
4506 if (RA.isMaxSignedValue()) return true;
4508 case ICmpInst::ICMP_UGT:
4509 if (RA.isMinValue()) {
4510 Pred = ICmpInst::ICMP_NE;
4513 if ((RA + 1).isMaxValue()) {
4514 Pred = ICmpInst::ICMP_EQ;
4515 RHS = getConstant(RA + 1);
4518 if (RA.isMaxValue()) return false;
4520 case ICmpInst::ICMP_ULT:
4521 if (RA.isMaxValue()) {
4522 Pred = ICmpInst::ICMP_NE;
4525 if ((RA - 1).isMinValue()) {
4526 Pred = ICmpInst::ICMP_EQ;
4527 RHS = getConstant(RA - 1);
4530 if (RA.isMinValue()) return false;
4532 case ICmpInst::ICMP_SGT:
4533 if (RA.isMinSignedValue()) {
4534 Pred = ICmpInst::ICMP_NE;
4537 if ((RA + 1).isMaxSignedValue()) {
4538 Pred = ICmpInst::ICMP_EQ;
4539 RHS = getConstant(RA + 1);
4542 if (RA.isMaxSignedValue()) return false;
4544 case ICmpInst::ICMP_SLT:
4545 if (RA.isMaxSignedValue()) {
4546 Pred = ICmpInst::ICMP_NE;
4549 if ((RA - 1).isMinSignedValue()) {
4550 Pred = ICmpInst::ICMP_EQ;
4551 RHS = getConstant(RA - 1);
4554 if (RA.isMinSignedValue()) return false;
4559 // Check to see if we can make the LHS or RHS match.
4560 if (LHS == FoundRHS || RHS == FoundLHS) {
4561 if (isa<SCEVConstant>(RHS)) {
4562 std::swap(FoundLHS, FoundRHS);
4563 FoundPred = ICmpInst::getSwappedPredicate(FoundPred);
4565 std::swap(LHS, RHS);
4566 Pred = ICmpInst::getSwappedPredicate(Pred);
4570 // Check whether the found predicate is the same as the desired predicate.
4571 if (FoundPred == Pred)
4572 return isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS);
4574 // Check whether swapping the found predicate makes it the same as the
4575 // desired predicate.
4576 if (ICmpInst::getSwappedPredicate(FoundPred) == Pred) {
4577 if (isa<SCEVConstant>(RHS))
4578 return isImpliedCondOperands(Pred, LHS, RHS, FoundRHS, FoundLHS);
4580 return isImpliedCondOperands(ICmpInst::getSwappedPredicate(Pred),
4581 RHS, LHS, FoundLHS, FoundRHS);
4584 // Check whether the actual condition is beyond sufficient.
4585 if (FoundPred == ICmpInst::ICMP_EQ)
4586 if (ICmpInst::isTrueWhenEqual(Pred))
4587 if (isImpliedCondOperands(Pred, LHS, RHS, FoundLHS, FoundRHS))
4589 if (Pred == ICmpInst::ICMP_NE)
4590 if (!ICmpInst::isTrueWhenEqual(FoundPred))
4591 if (isImpliedCondOperands(FoundPred, LHS, RHS, FoundLHS, FoundRHS))
4594 // Otherwise assume the worst.
4598 /// isImpliedCondOperands - Test whether the condition described by Pred,
4599 /// LHS, and RHS is true whenever the condition desribed by Pred, FoundLHS,
4600 /// and FoundRHS is true.
4601 bool ScalarEvolution::isImpliedCondOperands(ICmpInst::Predicate Pred,
4602 const SCEV *LHS, const SCEV *RHS,
4603 const SCEV *FoundLHS,
4604 const SCEV *FoundRHS) {
4605 return isImpliedCondOperandsHelper(Pred, LHS, RHS,
4606 FoundLHS, FoundRHS) ||
4607 // ~x < ~y --> x > y
4608 isImpliedCondOperandsHelper(Pred, LHS, RHS,
4609 getNotSCEV(FoundRHS),
4610 getNotSCEV(FoundLHS));
4613 /// isImpliedCondOperandsHelper - Test whether the condition described by
4614 /// Pred, LHS, and RHS is true whenever the condition desribed by Pred,
4615 /// FoundLHS, and FoundRHS is true.
4617 ScalarEvolution::isImpliedCondOperandsHelper(ICmpInst::Predicate Pred,
4618 const SCEV *LHS, const SCEV *RHS,
4619 const SCEV *FoundLHS,
4620 const SCEV *FoundRHS) {
4622 default: llvm_unreachable("Unexpected ICmpInst::Predicate value!");
4623 case ICmpInst::ICMP_EQ:
4624 case ICmpInst::ICMP_NE:
4625 if (HasSameValue(LHS, FoundLHS) && HasSameValue(RHS, FoundRHS))
4628 case ICmpInst::ICMP_SLT:
4629 case ICmpInst::ICMP_SLE:
4630 if (isKnownPredicate(ICmpInst::ICMP_SLE, LHS, FoundLHS) &&
4631 isKnownPredicate(ICmpInst::ICMP_SGE, RHS, FoundRHS))
4634 case ICmpInst::ICMP_SGT:
4635 case ICmpInst::ICMP_SGE:
4636 if (isKnownPredicate(ICmpInst::ICMP_SGE, LHS, FoundLHS) &&
4637 isKnownPredicate(ICmpInst::ICMP_SLE, RHS, FoundRHS))
4640 case ICmpInst::ICMP_ULT:
4641 case ICmpInst::ICMP_ULE:
4642 if (isKnownPredicate(ICmpInst::ICMP_ULE, LHS, FoundLHS) &&
4643 isKnownPredicate(ICmpInst::ICMP_UGE, RHS, FoundRHS))
4646 case ICmpInst::ICMP_UGT:
4647 case ICmpInst::ICMP_UGE:
4648 if (isKnownPredicate(ICmpInst::ICMP_UGE, LHS, FoundLHS) &&
4649 isKnownPredicate(ICmpInst::ICMP_ULE, RHS, FoundRHS))
4657 /// getBECount - Subtract the end and start values and divide by the step,
4658 /// rounding up, to get the number of times the backedge is executed. Return
4659 /// CouldNotCompute if an intermediate computation overflows.
4660 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
4663 const Type *Ty = Start->getType();
4664 const SCEV *NegOne = getIntegerSCEV(-1, Ty);
4665 const SCEV *Diff = getMinusSCEV(End, Start);
4666 const SCEV *RoundUp = getAddExpr(Step, NegOne);
4668 // Add an adjustment to the difference between End and Start so that
4669 // the division will effectively round up.
4670 const SCEV *Add = getAddExpr(Diff, RoundUp);
4672 // Check Add for unsigned overflow.
4673 // TODO: More sophisticated things could be done here.
4674 const Type *WideTy = IntegerType::get(getContext(),
4675 getTypeSizeInBits(Ty) + 1);
4676 const SCEV *EDiff = getZeroExtendExpr(Diff, WideTy);
4677 const SCEV *ERoundUp = getZeroExtendExpr(RoundUp, WideTy);
4678 const SCEV *OperandExtendedAdd = getAddExpr(EDiff, ERoundUp);
4679 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
4680 return getCouldNotCompute();
4682 return getUDivExpr(Add, Step);
4685 /// HowManyLessThans - Return the number of times a backedge containing the
4686 /// specified less-than comparison will execute. If not computable, return
4687 /// CouldNotCompute.
4688 ScalarEvolution::BackedgeTakenInfo
4689 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
4690 const Loop *L, bool isSigned) {
4691 // Only handle: "ADDREC < LoopInvariant".
4692 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
4694 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
4695 if (!AddRec || AddRec->getLoop() != L)
4696 return getCouldNotCompute();
4698 if (AddRec->isAffine()) {
4699 // FORNOW: We only support unit strides.
4700 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
4701 const SCEV *Step = AddRec->getStepRecurrence(*this);
4703 // TODO: handle non-constant strides.
4704 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
4705 if (!CStep || CStep->isZero())
4706 return getCouldNotCompute();
4707 if (CStep->isOne()) {
4708 // With unit stride, the iteration never steps past the limit value.
4709 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
4710 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
4711 // Test whether a positive iteration iteration can step past the limit
4712 // value and past the maximum value for its type in a single step.
4714 APInt Max = APInt::getSignedMaxValue(BitWidth);
4715 if ((Max - CStep->getValue()->getValue())
4716 .slt(CLimit->getValue()->getValue()))
4717 return getCouldNotCompute();
4719 APInt Max = APInt::getMaxValue(BitWidth);
4720 if ((Max - CStep->getValue()->getValue())
4721 .ult(CLimit->getValue()->getValue()))
4722 return getCouldNotCompute();
4725 // TODO: handle non-constant limit values below.
4726 return getCouldNotCompute();
4728 // TODO: handle negative strides below.
4729 return getCouldNotCompute();
4731 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
4732 // m. So, we count the number of iterations in which {n,+,s} < m is true.
4733 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
4734 // treat m-n as signed nor unsigned due to overflow possibility.
4736 // First, we get the value of the LHS in the first iteration: n
4737 const SCEV *Start = AddRec->getOperand(0);
4739 // Determine the minimum constant start value.
4740 const SCEV *MinStart = getConstant(isSigned ?
4741 getSignedRange(Start).getSignedMin() :
4742 getUnsignedRange(Start).getUnsignedMin());
4744 // If we know that the condition is true in order to enter the loop,
4745 // then we know that it will run exactly (m-n)/s times. Otherwise, we
4746 // only know that it will execute (max(m,n)-n)/s times. In both cases,
4747 // the division must round up.
4748 const SCEV *End = RHS;
4749 if (!isLoopGuardedByCond(L,
4750 isSigned ? ICmpInst::ICMP_SLT :
4752 getMinusSCEV(Start, Step), RHS))
4753 End = isSigned ? getSMaxExpr(RHS, Start)
4754 : getUMaxExpr(RHS, Start);
4756 // Determine the maximum constant end value.
4757 const SCEV *MaxEnd = getConstant(isSigned ?
4758 getSignedRange(End).getSignedMax() :
4759 getUnsignedRange(End).getUnsignedMax());
4761 // Finally, we subtract these two values and divide, rounding up, to get
4762 // the number of times the backedge is executed.
4763 const SCEV *BECount = getBECount(Start, End, Step);
4765 // The maximum backedge count is similar, except using the minimum start
4766 // value and the maximum end value.
4767 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step);
4769 return BackedgeTakenInfo(BECount, MaxBECount);
4772 return getCouldNotCompute();
4775 /// getNumIterationsInRange - Return the number of iterations of this loop that
4776 /// produce values in the specified constant range. Another way of looking at
4777 /// this is that it returns the first iteration number where the value is not in
4778 /// the condition, thus computing the exit count. If the iteration count can't
4779 /// be computed, an instance of SCEVCouldNotCompute is returned.
4780 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
4781 ScalarEvolution &SE) const {
4782 if (Range.isFullSet()) // Infinite loop.
4783 return SE.getCouldNotCompute();
4785 // If the start is a non-zero constant, shift the range to simplify things.
4786 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
4787 if (!SC->getValue()->isZero()) {
4788 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
4789 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
4790 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
4791 if (const SCEVAddRecExpr *ShiftedAddRec =
4792 dyn_cast<SCEVAddRecExpr>(Shifted))
4793 return ShiftedAddRec->getNumIterationsInRange(
4794 Range.subtract(SC->getValue()->getValue()), SE);
4795 // This is strange and shouldn't happen.
4796 return SE.getCouldNotCompute();
4799 // The only time we can solve this is when we have all constant indices.
4800 // Otherwise, we cannot determine the overflow conditions.
4801 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
4802 if (!isa<SCEVConstant>(getOperand(i)))
4803 return SE.getCouldNotCompute();
4806 // Okay at this point we know that all elements of the chrec are constants and
4807 // that the start element is zero.
4809 // First check to see if the range contains zero. If not, the first
4811 unsigned BitWidth = SE.getTypeSizeInBits(getType());
4812 if (!Range.contains(APInt(BitWidth, 0)))
4813 return SE.getIntegerSCEV(0, getType());
4816 // If this is an affine expression then we have this situation:
4817 // Solve {0,+,A} in Range === Ax in Range
4819 // We know that zero is in the range. If A is positive then we know that
4820 // the upper value of the range must be the first possible exit value.
4821 // If A is negative then the lower of the range is the last possible loop
4822 // value. Also note that we already checked for a full range.
4823 APInt One(BitWidth,1);
4824 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
4825 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
4827 // The exit value should be (End+A)/A.
4828 APInt ExitVal = (End + A).udiv(A);
4829 ConstantInt *ExitValue = ConstantInt::get(SE.getContext(), ExitVal);
4831 // Evaluate at the exit value. If we really did fall out of the valid
4832 // range, then we computed our trip count, otherwise wrap around or other
4833 // things must have happened.
4834 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
4835 if (Range.contains(Val->getValue()))
4836 return SE.getCouldNotCompute(); // Something strange happened
4838 // Ensure that the previous value is in the range. This is a sanity check.
4839 assert(Range.contains(
4840 EvaluateConstantChrecAtConstant(this,
4841 ConstantInt::get(SE.getContext(), ExitVal - One), SE)->getValue()) &&
4842 "Linear scev computation is off in a bad way!");
4843 return SE.getConstant(ExitValue);
4844 } else if (isQuadratic()) {
4845 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
4846 // quadratic equation to solve it. To do this, we must frame our problem in
4847 // terms of figuring out when zero is crossed, instead of when
4848 // Range.getUpper() is crossed.
4849 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
4850 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
4851 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
4853 // Next, solve the constructed addrec
4854 std::pair<const SCEV *,const SCEV *> Roots =
4855 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
4856 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4857 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4859 // Pick the smallest positive root value.
4860 if (ConstantInt *CB =
4861 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4862 R1->getValue(), R2->getValue()))) {
4863 if (CB->getZExtValue() == false)
4864 std::swap(R1, R2); // R1 is the minimum root now.
4866 // Make sure the root is not off by one. The returned iteration should
4867 // not be in the range, but the previous one should be. When solving
4868 // for "X*X < 5", for example, we should not return a root of 2.
4869 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
4872 if (Range.contains(R1Val->getValue())) {
4873 // The next iteration must be out of the range...
4874 ConstantInt *NextVal =
4875 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()+1);
4877 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4878 if (!Range.contains(R1Val->getValue()))
4879 return SE.getConstant(NextVal);
4880 return SE.getCouldNotCompute(); // Something strange happened
4883 // If R1 was not in the range, then it is a good return value. Make
4884 // sure that R1-1 WAS in the range though, just in case.
4885 ConstantInt *NextVal =
4886 ConstantInt::get(SE.getContext(), R1->getValue()->getValue()-1);
4887 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4888 if (Range.contains(R1Val->getValue()))
4890 return SE.getCouldNotCompute(); // Something strange happened
4895 return SE.getCouldNotCompute();
4900 //===----------------------------------------------------------------------===//
4901 // SCEVCallbackVH Class Implementation
4902 //===----------------------------------------------------------------------===//
4904 void ScalarEvolution::SCEVCallbackVH::deleted() {
4905 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
4906 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
4907 SE->ConstantEvolutionLoopExitValue.erase(PN);
4908 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
4909 SE->ValuesAtScopes.erase(I);
4910 SE->Scalars.erase(getValPtr());
4911 // this now dangles!
4914 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
4915 assert(SE && "SCEVCallbackVH called with a null ScalarEvolution!");
4917 // Forget all the expressions associated with users of the old value,
4918 // so that future queries will recompute the expressions using the new
4920 SmallVector<User *, 16> Worklist;
4921 SmallPtrSet<User *, 8> Visited;
4922 Value *Old = getValPtr();
4923 bool DeleteOld = false;
4924 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
4926 Worklist.push_back(*UI);
4927 while (!Worklist.empty()) {
4928 User *U = Worklist.pop_back_val();
4929 // Deleting the Old value will cause this to dangle. Postpone
4930 // that until everything else is done.
4935 if (!Visited.insert(U))
4937 if (PHINode *PN = dyn_cast<PHINode>(U))
4938 SE->ConstantEvolutionLoopExitValue.erase(PN);
4939 if (Instruction *I = dyn_cast<Instruction>(U))
4940 SE->ValuesAtScopes.erase(I);
4941 SE->Scalars.erase(U);
4942 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
4944 Worklist.push_back(*UI);
4946 // Delete the Old value if it (indirectly) references itself.
4948 if (PHINode *PN = dyn_cast<PHINode>(Old))
4949 SE->ConstantEvolutionLoopExitValue.erase(PN);
4950 if (Instruction *I = dyn_cast<Instruction>(Old))
4951 SE->ValuesAtScopes.erase(I);
4952 SE->Scalars.erase(Old);
4953 // this now dangles!
4958 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
4959 : CallbackVH(V), SE(se) {}
4961 //===----------------------------------------------------------------------===//
4962 // ScalarEvolution Class Implementation
4963 //===----------------------------------------------------------------------===//
4965 ScalarEvolution::ScalarEvolution()
4966 : FunctionPass(&ID) {
4969 bool ScalarEvolution::runOnFunction(Function &F) {
4971 LI = &getAnalysis<LoopInfo>();
4972 TD = getAnalysisIfAvailable<TargetData>();
4976 void ScalarEvolution::releaseMemory() {
4978 BackedgeTakenCounts.clear();
4979 ConstantEvolutionLoopExitValue.clear();
4980 ValuesAtScopes.clear();
4981 UniqueSCEVs.clear();
4982 SCEVAllocator.Reset();
4985 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
4986 AU.setPreservesAll();
4987 AU.addRequiredTransitive<LoopInfo>();
4990 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
4991 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
4994 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
4996 // Print all inner loops first
4997 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4998 PrintLoopInfo(OS, SE, *I);
5000 OS << "Loop " << L->getHeader()->getName() << ": ";
5002 SmallVector<BasicBlock*, 8> ExitBlocks;
5003 L->getExitBlocks(ExitBlocks);
5004 if (ExitBlocks.size() != 1)
5005 OS << "<multiple exits> ";
5007 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
5008 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
5010 OS << "Unpredictable backedge-taken count. ";
5014 OS << "Loop " << L->getHeader()->getName() << ": ";
5016 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
5017 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
5019 OS << "Unpredictable max backedge-taken count. ";
5025 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
5026 // ScalarEvolution's implementaiton of the print method is to print
5027 // out SCEV values of all instructions that are interesting. Doing
5028 // this potentially causes it to create new SCEV objects though,
5029 // which technically conflicts with the const qualifier. This isn't
5030 // observable from outside the class though, so casting away the
5031 // const isn't dangerous.
5032 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
5034 OS << "Classifying expressions for: " << F->getName() << "\n";
5035 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
5036 if (isSCEVable(I->getType())) {
5039 const SCEV *SV = SE.getSCEV(&*I);
5042 const Loop *L = LI->getLoopFor((*I).getParent());
5044 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
5051 OS << "\t\t" "Exits: ";
5052 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
5053 if (!ExitValue->isLoopInvariant(L)) {
5054 OS << "<<Unknown>>";
5063 OS << "Determining loop execution counts for: " << F->getName() << "\n";
5064 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
5065 PrintLoopInfo(OS, &SE, *I);
5068 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
5069 raw_os_ostream OS(o);