1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the const SCEV *
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/LLVMContext.h"
69 #include "llvm/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!");
166 SCEVCouldNotCompute::replaceSymbolicValuesWithConcrete(
169 ScalarEvolution &SE) const {
173 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
174 OS << "***COULDNOTCOMPUTE***";
177 bool SCEVCouldNotCompute::classof(const SCEV *S) {
178 return S->getSCEVType() == scCouldNotCompute;
181 const SCEV *ScalarEvolution::getConstant(ConstantInt *V) {
183 ID.AddInteger(scConstant);
186 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
187 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>();
188 new (S) SCEVConstant(ID, V);
189 UniqueSCEVs.InsertNode(S, IP);
193 const SCEV *ScalarEvolution::getConstant(const APInt& Val) {
194 return getConstant(ConstantInt::get(Val));
198 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
199 return getConstant(ConstantInt::get(cast<IntegerType>(Ty), V, isSigned));
202 const Type *SCEVConstant::getType() const { return V->getType(); }
204 void SCEVConstant::print(raw_ostream &OS) const {
205 WriteAsOperand(OS, V, false);
208 SCEVCastExpr::SCEVCastExpr(const FoldingSetNodeID &ID,
209 unsigned SCEVTy, const SCEV *op, const Type *ty)
210 : SCEV(ID, SCEVTy), Op(op), Ty(ty) {}
212 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
213 return Op->dominates(BB, DT);
216 SCEVTruncateExpr::SCEVTruncateExpr(const FoldingSetNodeID &ID,
217 const SCEV *op, const Type *ty)
218 : SCEVCastExpr(ID, scTruncate, op, ty) {
219 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
220 (Ty->isInteger() || isa<PointerType>(Ty)) &&
221 "Cannot truncate non-integer value!");
224 void SCEVTruncateExpr::print(raw_ostream &OS) const {
225 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
228 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const FoldingSetNodeID &ID,
229 const SCEV *op, const Type *ty)
230 : SCEVCastExpr(ID, scZeroExtend, op, ty) {
231 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
232 (Ty->isInteger() || isa<PointerType>(Ty)) &&
233 "Cannot zero extend non-integer value!");
236 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
237 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
240 SCEVSignExtendExpr::SCEVSignExtendExpr(const FoldingSetNodeID &ID,
241 const SCEV *op, const Type *ty)
242 : SCEVCastExpr(ID, scSignExtend, op, ty) {
243 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
244 (Ty->isInteger() || isa<PointerType>(Ty)) &&
245 "Cannot sign extend non-integer value!");
248 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
249 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
252 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
253 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
254 const char *OpStr = getOperationStr();
255 OS << "(" << *Operands[0];
256 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
257 OS << OpStr << *Operands[i];
262 SCEVCommutativeExpr::replaceSymbolicValuesWithConcrete(
265 ScalarEvolution &SE) const {
266 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
268 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
269 if (H != getOperand(i)) {
270 SmallVector<const SCEV *, 8> NewOps;
271 NewOps.reserve(getNumOperands());
272 for (unsigned j = 0; j != i; ++j)
273 NewOps.push_back(getOperand(j));
275 for (++i; i != e; ++i)
276 NewOps.push_back(getOperand(i)->
277 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
279 if (isa<SCEVAddExpr>(this))
280 return SE.getAddExpr(NewOps);
281 else if (isa<SCEVMulExpr>(this))
282 return SE.getMulExpr(NewOps);
283 else if (isa<SCEVSMaxExpr>(this))
284 return SE.getSMaxExpr(NewOps);
285 else if (isa<SCEVUMaxExpr>(this))
286 return SE.getUMaxExpr(NewOps);
288 LLVM_UNREACHABLE("Unknown commutative expr!");
294 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
295 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
296 if (!getOperand(i)->dominates(BB, DT))
302 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
303 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
306 void SCEVUDivExpr::print(raw_ostream &OS) const {
307 OS << "(" << *LHS << " /u " << *RHS << ")";
310 const Type *SCEVUDivExpr::getType() const {
311 // In most cases the types of LHS and RHS will be the same, but in some
312 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
313 // depend on the type for correctness, but handling types carefully can
314 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
315 // a pointer type than the RHS, so use the RHS' type here.
316 return RHS->getType();
320 SCEVAddRecExpr::replaceSymbolicValuesWithConcrete(const SCEV *Sym,
322 ScalarEvolution &SE) const {
323 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
325 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
326 if (H != getOperand(i)) {
327 SmallVector<const SCEV *, 8> NewOps;
328 NewOps.reserve(getNumOperands());
329 for (unsigned j = 0; j != i; ++j)
330 NewOps.push_back(getOperand(j));
332 for (++i; i != e; ++i)
333 NewOps.push_back(getOperand(i)->
334 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
336 return SE.getAddRecExpr(NewOps, L);
343 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
344 // Add recurrences are never invariant in the function-body (null loop).
348 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
349 if (QueryLoop->contains(L->getHeader()))
352 // This recurrence is variant w.r.t. QueryLoop if any of its operands
354 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
355 if (!getOperand(i)->isLoopInvariant(QueryLoop))
358 // Otherwise it's loop-invariant.
362 void SCEVAddRecExpr::print(raw_ostream &OS) const {
363 OS << "{" << *Operands[0];
364 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
365 OS << ",+," << *Operands[i];
366 OS << "}<" << L->getHeader()->getName() + ">";
369 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
370 // All non-instruction values are loop invariant. All instructions are loop
371 // invariant if they are not contained in the specified loop.
372 // Instructions are never considered invariant in the function body
373 // (null loop) because they are defined within the "loop".
374 if (Instruction *I = dyn_cast<Instruction>(V))
375 return L && !L->contains(I->getParent());
379 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
380 if (Instruction *I = dyn_cast<Instruction>(getValue()))
381 return DT->dominates(I->getParent(), BB);
385 const Type *SCEVUnknown::getType() const {
389 void SCEVUnknown::print(raw_ostream &OS) const {
390 WriteAsOperand(OS, V, false);
393 //===----------------------------------------------------------------------===//
395 //===----------------------------------------------------------------------===//
398 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
399 /// than the complexity of the RHS. This comparator is used to canonicalize
401 class VISIBILITY_HIDDEN SCEVComplexityCompare {
404 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
406 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
407 // Primarily, sort the SCEVs by their getSCEVType().
408 if (LHS->getSCEVType() != RHS->getSCEVType())
409 return LHS->getSCEVType() < RHS->getSCEVType();
411 // Aside from the getSCEVType() ordering, the particular ordering
412 // isn't very important except that it's beneficial to be consistent,
413 // so that (a + b) and (b + a) don't end up as different expressions.
415 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
416 // not as complete as it could be.
417 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
418 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
420 // Order pointer values after integer values. This helps SCEVExpander
422 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
424 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
427 // Compare getValueID values.
428 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
429 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
431 // Sort arguments by their position.
432 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
433 const Argument *RA = cast<Argument>(RU->getValue());
434 return LA->getArgNo() < RA->getArgNo();
437 // For instructions, compare their loop depth, and their opcode.
438 // This is pretty loose.
439 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
440 Instruction *RV = cast<Instruction>(RU->getValue());
442 // Compare loop depths.
443 if (LI->getLoopDepth(LV->getParent()) !=
444 LI->getLoopDepth(RV->getParent()))
445 return LI->getLoopDepth(LV->getParent()) <
446 LI->getLoopDepth(RV->getParent());
449 if (LV->getOpcode() != RV->getOpcode())
450 return LV->getOpcode() < RV->getOpcode();
452 // Compare the number of operands.
453 if (LV->getNumOperands() != RV->getNumOperands())
454 return LV->getNumOperands() < RV->getNumOperands();
460 // Compare constant values.
461 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
462 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
463 if (LC->getValue()->getBitWidth() != RC->getValue()->getBitWidth())
464 return LC->getValue()->getBitWidth() < RC->getValue()->getBitWidth();
465 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
468 // Compare addrec loop depths.
469 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
470 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
471 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
472 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
475 // Lexicographically compare n-ary expressions.
476 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
477 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
478 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
479 if (i >= RC->getNumOperands())
481 if (operator()(LC->getOperand(i), RC->getOperand(i)))
483 if (operator()(RC->getOperand(i), LC->getOperand(i)))
486 return LC->getNumOperands() < RC->getNumOperands();
489 // Lexicographically compare udiv expressions.
490 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
491 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
492 if (operator()(LC->getLHS(), RC->getLHS()))
494 if (operator()(RC->getLHS(), LC->getLHS()))
496 if (operator()(LC->getRHS(), RC->getRHS()))
498 if (operator()(RC->getRHS(), LC->getRHS()))
503 // Compare cast expressions by operand.
504 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
505 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
506 return operator()(LC->getOperand(), RC->getOperand());
509 LLVM_UNREACHABLE("Unknown SCEV kind!");
515 /// GroupByComplexity - Given a list of SCEV objects, order them by their
516 /// complexity, and group objects of the same complexity together by value.
517 /// When this routine is finished, we know that any duplicates in the vector are
518 /// consecutive and that complexity is monotonically increasing.
520 /// Note that we go take special precautions to ensure that we get determinstic
521 /// results from this routine. In other words, we don't want the results of
522 /// this to depend on where the addresses of various SCEV objects happened to
525 static void GroupByComplexity(SmallVectorImpl<const SCEV *> &Ops,
527 if (Ops.size() < 2) return; // Noop
528 if (Ops.size() == 2) {
529 // This is the common case, which also happens to be trivially simple.
531 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
532 std::swap(Ops[0], Ops[1]);
536 // Do the rough sort by complexity.
537 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
539 // Now that we are sorted by complexity, group elements of the same
540 // complexity. Note that this is, at worst, N^2, but the vector is likely to
541 // be extremely short in practice. Note that we take this approach because we
542 // do not want to depend on the addresses of the objects we are grouping.
543 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
544 const SCEV *S = Ops[i];
545 unsigned Complexity = S->getSCEVType();
547 // If there are any objects of the same complexity and same value as this
549 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
550 if (Ops[j] == S) { // Found a duplicate.
551 // Move it to immediately after i'th element.
552 std::swap(Ops[i+1], Ops[j]);
553 ++i; // no need to rescan it.
554 if (i == e-2) return; // Done!
562 //===----------------------------------------------------------------------===//
563 // Simple SCEV method implementations
564 //===----------------------------------------------------------------------===//
566 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
568 static const SCEV *BinomialCoefficient(const SCEV *It, unsigned K,
570 const Type* ResultTy) {
571 // Handle the simplest case efficiently.
573 return SE.getTruncateOrZeroExtend(It, ResultTy);
575 // We are using the following formula for BC(It, K):
577 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
579 // Suppose, W is the bitwidth of the return value. We must be prepared for
580 // overflow. Hence, we must assure that the result of our computation is
581 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
582 // safe in modular arithmetic.
584 // However, this code doesn't use exactly that formula; the formula it uses
585 // is something like the following, where T is the number of factors of 2 in
586 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
589 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
591 // This formula is trivially equivalent to the previous formula. However,
592 // this formula can be implemented much more efficiently. The trick is that
593 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
594 // arithmetic. To do exact division in modular arithmetic, all we have
595 // to do is multiply by the inverse. Therefore, this step can be done at
598 // The next issue is how to safely do the division by 2^T. The way this
599 // is done is by doing the multiplication step at a width of at least W + T
600 // bits. This way, the bottom W+T bits of the product are accurate. Then,
601 // when we perform the division by 2^T (which is equivalent to a right shift
602 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
603 // truncated out after the division by 2^T.
605 // In comparison to just directly using the first formula, this technique
606 // is much more efficient; using the first formula requires W * K bits,
607 // but this formula less than W + K bits. Also, the first formula requires
608 // a division step, whereas this formula only requires multiplies and shifts.
610 // It doesn't matter whether the subtraction step is done in the calculation
611 // width or the input iteration count's width; if the subtraction overflows,
612 // the result must be zero anyway. We prefer here to do it in the width of
613 // the induction variable because it helps a lot for certain cases; CodeGen
614 // isn't smart enough to ignore the overflow, which leads to much less
615 // efficient code if the width of the subtraction is wider than the native
618 // (It's possible to not widen at all by pulling out factors of 2 before
619 // the multiplication; for example, K=2 can be calculated as
620 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
621 // extra arithmetic, so it's not an obvious win, and it gets
622 // much more complicated for K > 3.)
624 // Protection from insane SCEVs; this bound is conservative,
625 // but it probably doesn't matter.
627 return SE.getCouldNotCompute();
629 unsigned W = SE.getTypeSizeInBits(ResultTy);
631 // Calculate K! / 2^T and T; we divide out the factors of two before
632 // multiplying for calculating K! / 2^T to avoid overflow.
633 // Other overflow doesn't matter because we only care about the bottom
634 // W bits of the result.
635 APInt OddFactorial(W, 1);
637 for (unsigned i = 3; i <= K; ++i) {
639 unsigned TwoFactors = Mult.countTrailingZeros();
641 Mult = Mult.lshr(TwoFactors);
642 OddFactorial *= Mult;
645 // We need at least W + T bits for the multiplication step
646 unsigned CalculationBits = W + T;
648 // Calcuate 2^T, at width T+W.
649 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
651 // Calculate the multiplicative inverse of K! / 2^T;
652 // this multiplication factor will perform the exact division by
654 APInt Mod = APInt::getSignedMinValue(W+1);
655 APInt MultiplyFactor = OddFactorial.zext(W+1);
656 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
657 MultiplyFactor = MultiplyFactor.trunc(W);
659 // Calculate the product, at width T+W
660 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
661 const SCEV *Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
662 for (unsigned i = 1; i != K; ++i) {
663 const SCEV *S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
664 Dividend = SE.getMulExpr(Dividend,
665 SE.getTruncateOrZeroExtend(S, CalculationTy));
669 const SCEV *DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
671 // Truncate the result, and divide by K! / 2^T.
673 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
674 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
677 /// evaluateAtIteration - Return the value of this chain of recurrences at
678 /// the specified iteration number. We can evaluate this recurrence by
679 /// multiplying each element in the chain by the binomial coefficient
680 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
682 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
684 /// where BC(It, k) stands for binomial coefficient.
686 const SCEV *SCEVAddRecExpr::evaluateAtIteration(const SCEV *It,
687 ScalarEvolution &SE) const {
688 const SCEV *Result = getStart();
689 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
690 // The computation is correct in the face of overflow provided that the
691 // multiplication is performed _after_ the evaluation of the binomial
693 const SCEV *Coeff = BinomialCoefficient(It, i, SE, getType());
694 if (isa<SCEVCouldNotCompute>(Coeff))
697 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
702 //===----------------------------------------------------------------------===//
703 // SCEV Expression folder implementations
704 //===----------------------------------------------------------------------===//
706 const SCEV *ScalarEvolution::getTruncateExpr(const SCEV *Op,
708 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
709 "This is not a truncating conversion!");
710 assert(isSCEVable(Ty) &&
711 "This is not a conversion to a SCEVable type!");
712 Ty = getEffectiveSCEVType(Ty);
715 ID.AddInteger(scTruncate);
719 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
721 // Fold if the operand is constant.
722 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
724 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
726 // trunc(trunc(x)) --> trunc(x)
727 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
728 return getTruncateExpr(ST->getOperand(), Ty);
730 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
731 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
732 return getTruncateOrSignExtend(SS->getOperand(), Ty);
734 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
735 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
736 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
738 // If the input value is a chrec scev, truncate the chrec's operands.
739 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
740 SmallVector<const SCEV *, 4> Operands;
741 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
742 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
743 return getAddRecExpr(Operands, AddRec->getLoop());
746 // The cast wasn't folded; create an explicit cast node.
747 // Recompute the insert position, as it may have been invalidated.
748 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
749 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>();
750 new (S) SCEVTruncateExpr(ID, Op, Ty);
751 UniqueSCEVs.InsertNode(S, IP);
755 const SCEV *ScalarEvolution::getZeroExtendExpr(const SCEV *Op,
757 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
758 "This is not an extending conversion!");
759 assert(isSCEVable(Ty) &&
760 "This is not a conversion to a SCEVable type!");
761 Ty = getEffectiveSCEVType(Ty);
763 // Fold if the operand is constant.
764 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
765 const Type *IntTy = getEffectiveSCEVType(Ty);
766 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
767 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
768 return getConstant(cast<ConstantInt>(C));
771 // zext(zext(x)) --> zext(x)
772 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
773 return getZeroExtendExpr(SZ->getOperand(), Ty);
775 // If the input value is a chrec scev, and we can prove that the value
776 // did not overflow the old, smaller, value, we can zero extend all of the
777 // operands (often constants). This allows analysis of something like
778 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
779 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
780 if (AR->isAffine()) {
781 // Check whether the backedge-taken count is SCEVCouldNotCompute.
782 // Note that this serves two purposes: It filters out loops that are
783 // simply not analyzable, and it covers the case where this code is
784 // being called from within backedge-taken count analysis, such that
785 // attempting to ask for the backedge-taken count would likely result
786 // in infinite recursion. In the later case, the analysis code will
787 // cope with a conservative value, and it will take care to purge
788 // that value once it has finished.
789 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
790 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
791 // Manually compute the final value for AR, checking for
793 const SCEV *Start = AR->getStart();
794 const SCEV *Step = AR->getStepRecurrence(*this);
796 // Check whether the backedge-taken count can be losslessly casted to
797 // the addrec's type. The count is always unsigned.
798 const SCEV *CastedMaxBECount =
799 getTruncateOrZeroExtend(MaxBECount, Start->getType());
800 const SCEV *RecastedMaxBECount =
801 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
802 if (MaxBECount == RecastedMaxBECount) {
804 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
805 // Check whether Start+Step*MaxBECount has no unsigned overflow.
807 getMulExpr(CastedMaxBECount,
808 getTruncateOrZeroExtend(Step, Start->getType()));
809 const SCEV *Add = getAddExpr(Start, ZMul);
810 const SCEV *OperandExtendedAdd =
811 getAddExpr(getZeroExtendExpr(Start, WideTy),
812 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
813 getZeroExtendExpr(Step, WideTy)));
814 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
815 // Return the expression with the addrec on the outside.
816 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
817 getZeroExtendExpr(Step, Ty),
820 // Similar to above, only this time treat the step value as signed.
821 // This covers loops that count down.
823 getMulExpr(CastedMaxBECount,
824 getTruncateOrSignExtend(Step, Start->getType()));
825 Add = getAddExpr(Start, SMul);
827 getAddExpr(getZeroExtendExpr(Start, WideTy),
828 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
829 getSignExtendExpr(Step, WideTy)));
830 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
831 // Return the expression with the addrec on the outside.
832 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
833 getSignExtendExpr(Step, Ty),
840 ID.AddInteger(scZeroExtend);
844 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
845 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>();
846 new (S) SCEVZeroExtendExpr(ID, Op, Ty);
847 UniqueSCEVs.InsertNode(S, IP);
851 const SCEV *ScalarEvolution::getSignExtendExpr(const SCEV *Op,
853 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
854 "This is not an extending conversion!");
855 assert(isSCEVable(Ty) &&
856 "This is not a conversion to a SCEVable type!");
857 Ty = getEffectiveSCEVType(Ty);
859 // Fold if the operand is constant.
860 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
861 const Type *IntTy = getEffectiveSCEVType(Ty);
862 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
863 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
864 return getConstant(cast<ConstantInt>(C));
867 // sext(sext(x)) --> sext(x)
868 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
869 return getSignExtendExpr(SS->getOperand(), Ty);
871 // If the input value is a chrec scev, and we can prove that the value
872 // did not overflow the old, smaller, value, we can sign extend all of the
873 // operands (often constants). This allows analysis of something like
874 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
875 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
876 if (AR->isAffine()) {
877 // Check whether the backedge-taken count is SCEVCouldNotCompute.
878 // Note that this serves two purposes: It filters out loops that are
879 // simply not analyzable, and it covers the case where this code is
880 // being called from within backedge-taken count analysis, such that
881 // attempting to ask for the backedge-taken count would likely result
882 // in infinite recursion. In the later case, the analysis code will
883 // cope with a conservative value, and it will take care to purge
884 // that value once it has finished.
885 const SCEV *MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
886 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
887 // Manually compute the final value for AR, checking for
889 const SCEV *Start = AR->getStart();
890 const SCEV *Step = AR->getStepRecurrence(*this);
892 // Check whether the backedge-taken count can be losslessly casted to
893 // the addrec's type. The count is always unsigned.
894 const SCEV *CastedMaxBECount =
895 getTruncateOrZeroExtend(MaxBECount, Start->getType());
896 const SCEV *RecastedMaxBECount =
897 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
898 if (MaxBECount == RecastedMaxBECount) {
900 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
901 // Check whether Start+Step*MaxBECount has no signed overflow.
903 getMulExpr(CastedMaxBECount,
904 getTruncateOrSignExtend(Step, Start->getType()));
905 const SCEV *Add = getAddExpr(Start, SMul);
906 const SCEV *OperandExtendedAdd =
907 getAddExpr(getSignExtendExpr(Start, WideTy),
908 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
909 getSignExtendExpr(Step, WideTy)));
910 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
911 // Return the expression with the addrec on the outside.
912 return getAddRecExpr(getSignExtendExpr(Start, Ty),
913 getSignExtendExpr(Step, Ty),
920 ID.AddInteger(scSignExtend);
924 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
925 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>();
926 new (S) SCEVSignExtendExpr(ID, Op, Ty);
927 UniqueSCEVs.InsertNode(S, IP);
931 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
932 /// unspecified bits out to the given type.
934 const SCEV *ScalarEvolution::getAnyExtendExpr(const SCEV *Op,
936 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
937 "This is not an extending conversion!");
938 assert(isSCEVable(Ty) &&
939 "This is not a conversion to a SCEVable type!");
940 Ty = getEffectiveSCEVType(Ty);
942 // Sign-extend negative constants.
943 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
944 if (SC->getValue()->getValue().isNegative())
945 return getSignExtendExpr(Op, Ty);
947 // Peel off a truncate cast.
948 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
949 const SCEV *NewOp = T->getOperand();
950 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
951 return getAnyExtendExpr(NewOp, Ty);
952 return getTruncateOrNoop(NewOp, Ty);
955 // Next try a zext cast. If the cast is folded, use it.
956 const SCEV *ZExt = getZeroExtendExpr(Op, Ty);
957 if (!isa<SCEVZeroExtendExpr>(ZExt))
960 // Next try a sext cast. If the cast is folded, use it.
961 const SCEV *SExt = getSignExtendExpr(Op, Ty);
962 if (!isa<SCEVSignExtendExpr>(SExt))
965 // If the expression is obviously signed, use the sext cast value.
966 if (isa<SCEVSMaxExpr>(Op))
969 // Absent any other information, use the zext cast value.
973 /// CollectAddOperandsWithScales - Process the given Ops list, which is
974 /// a list of operands to be added under the given scale, update the given
975 /// map. This is a helper function for getAddRecExpr. As an example of
976 /// what it does, given a sequence of operands that would form an add
977 /// expression like this:
979 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
981 /// where A and B are constants, update the map with these values:
983 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
985 /// and add 13 + A*B*29 to AccumulatedConstant.
986 /// This will allow getAddRecExpr to produce this:
988 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
990 /// This form often exposes folding opportunities that are hidden in
991 /// the original operand list.
993 /// Return true iff it appears that any interesting folding opportunities
994 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
995 /// the common case where no interesting opportunities are present, and
996 /// is also used as a check to avoid infinite recursion.
999 CollectAddOperandsWithScales(DenseMap<const SCEV *, APInt> &M,
1000 SmallVector<const SCEV *, 8> &NewOps,
1001 APInt &AccumulatedConstant,
1002 const SmallVectorImpl<const SCEV *> &Ops,
1004 ScalarEvolution &SE) {
1005 bool Interesting = false;
1007 // Iterate over the add operands.
1008 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1009 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1010 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1012 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1013 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1014 // A multiplication of a constant with another add; recurse.
1016 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1017 cast<SCEVAddExpr>(Mul->getOperand(1))
1021 // A multiplication of a constant with some other value. Update
1023 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1024 const SCEV *Key = SE.getMulExpr(MulOps);
1025 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1026 M.insert(std::make_pair(Key, NewScale));
1028 NewOps.push_back(Pair.first->first);
1030 Pair.first->second += NewScale;
1031 // The map already had an entry for this value, which may indicate
1032 // a folding opportunity.
1036 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1037 // Pull a buried constant out to the outside.
1038 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
1040 AccumulatedConstant += Scale * C->getValue()->getValue();
1042 // An ordinary operand. Update the map.
1043 std::pair<DenseMap<const SCEV *, APInt>::iterator, bool> Pair =
1044 M.insert(std::make_pair(Ops[i], Scale));
1046 NewOps.push_back(Pair.first->first);
1048 Pair.first->second += Scale;
1049 // The map already had an entry for this value, which may indicate
1050 // a folding opportunity.
1060 struct APIntCompare {
1061 bool operator()(const APInt &LHS, const APInt &RHS) const {
1062 return LHS.ult(RHS);
1067 /// getAddExpr - Get a canonical add expression, or something simpler if
1069 const SCEV *ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV *> &Ops) {
1070 assert(!Ops.empty() && "Cannot get empty add!");
1071 if (Ops.size() == 1) return Ops[0];
1073 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1074 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1075 getEffectiveSCEVType(Ops[0]->getType()) &&
1076 "SCEVAddExpr operand types don't match!");
1079 // Sort by complexity, this groups all similar expression types together.
1080 GroupByComplexity(Ops, LI);
1082 // If there are any constants, fold them together.
1084 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1086 assert(Idx < Ops.size());
1087 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1088 // We found two constants, fold them together!
1089 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1090 RHSC->getValue()->getValue());
1091 if (Ops.size() == 2) return Ops[0];
1092 Ops.erase(Ops.begin()+1); // Erase the folded element
1093 LHSC = cast<SCEVConstant>(Ops[0]);
1096 // If we are left with a constant zero being added, strip it off.
1097 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1098 Ops.erase(Ops.begin());
1103 if (Ops.size() == 1) return Ops[0];
1105 // Okay, check to see if the same value occurs in the operand list twice. If
1106 // so, merge them together into an multiply expression. Since we sorted the
1107 // list, these values are required to be adjacent.
1108 const Type *Ty = Ops[0]->getType();
1109 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1110 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1111 // Found a match, merge the two values into a multiply, and add any
1112 // remaining values to the result.
1113 const SCEV *Two = getIntegerSCEV(2, Ty);
1114 const SCEV *Mul = getMulExpr(Ops[i], Two);
1115 if (Ops.size() == 2)
1117 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1119 return getAddExpr(Ops);
1122 // Check for truncates. If all the operands are truncated from the same
1123 // type, see if factoring out the truncate would permit the result to be
1124 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1125 // if the contents of the resulting outer trunc fold to something simple.
1126 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1127 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1128 const Type *DstType = Trunc->getType();
1129 const Type *SrcType = Trunc->getOperand()->getType();
1130 SmallVector<const SCEV *, 8> LargeOps;
1132 // Check all the operands to see if they can be represented in the
1133 // source type of the truncate.
1134 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1135 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1136 if (T->getOperand()->getType() != SrcType) {
1140 LargeOps.push_back(T->getOperand());
1141 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1142 // This could be either sign or zero extension, but sign extension
1143 // is much more likely to be foldable here.
1144 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1145 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1146 SmallVector<const SCEV *, 8> LargeMulOps;
1147 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1148 if (const SCEVTruncateExpr *T =
1149 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1150 if (T->getOperand()->getType() != SrcType) {
1154 LargeMulOps.push_back(T->getOperand());
1155 } else if (const SCEVConstant *C =
1156 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1157 // This could be either sign or zero extension, but sign extension
1158 // is much more likely to be foldable here.
1159 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1166 LargeOps.push_back(getMulExpr(LargeMulOps));
1173 // Evaluate the expression in the larger type.
1174 const SCEV *Fold = getAddExpr(LargeOps);
1175 // If it folds to something simple, use it. Otherwise, don't.
1176 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1177 return getTruncateExpr(Fold, DstType);
1181 // Skip past any other cast SCEVs.
1182 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1185 // If there are add operands they would be next.
1186 if (Idx < Ops.size()) {
1187 bool DeletedAdd = false;
1188 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1189 // If we have an add, expand the add operands onto the end of the operands
1191 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1192 Ops.erase(Ops.begin()+Idx);
1196 // If we deleted at least one add, we added operands to the end of the list,
1197 // and they are not necessarily sorted. Recurse to resort and resimplify
1198 // any operands we just aquired.
1200 return getAddExpr(Ops);
1203 // Skip over the add expression until we get to a multiply.
1204 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1207 // Check to see if there are any folding opportunities present with
1208 // operands multiplied by constant values.
1209 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1210 uint64_t BitWidth = getTypeSizeInBits(Ty);
1211 DenseMap<const SCEV *, APInt> M;
1212 SmallVector<const SCEV *, 8> NewOps;
1213 APInt AccumulatedConstant(BitWidth, 0);
1214 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1215 Ops, APInt(BitWidth, 1), *this)) {
1216 // Some interesting folding opportunity is present, so its worthwhile to
1217 // re-generate the operands list. Group the operands by constant scale,
1218 // to avoid multiplying by the same constant scale multiple times.
1219 std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare> MulOpLists;
1220 for (SmallVector<const SCEV *, 8>::iterator I = NewOps.begin(),
1221 E = NewOps.end(); I != E; ++I)
1222 MulOpLists[M.find(*I)->second].push_back(*I);
1223 // Re-generate the operands list.
1225 if (AccumulatedConstant != 0)
1226 Ops.push_back(getConstant(AccumulatedConstant));
1227 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1228 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1230 Ops.push_back(getMulExpr(getConstant(I->first),
1231 getAddExpr(I->second)));
1233 return getIntegerSCEV(0, Ty);
1234 if (Ops.size() == 1)
1236 return getAddExpr(Ops);
1240 // If we are adding something to a multiply expression, make sure the
1241 // something is not already an operand of the multiply. If so, merge it into
1243 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1244 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1245 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1246 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1247 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1248 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1249 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1250 const SCEV *InnerMul = Mul->getOperand(MulOp == 0);
1251 if (Mul->getNumOperands() != 2) {
1252 // If the multiply has more than two operands, we must get the
1254 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(), Mul->op_end());
1255 MulOps.erase(MulOps.begin()+MulOp);
1256 InnerMul = getMulExpr(MulOps);
1258 const SCEV *One = getIntegerSCEV(1, Ty);
1259 const SCEV *AddOne = getAddExpr(InnerMul, One);
1260 const SCEV *OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1261 if (Ops.size() == 2) return OuterMul;
1263 Ops.erase(Ops.begin()+AddOp);
1264 Ops.erase(Ops.begin()+Idx-1);
1266 Ops.erase(Ops.begin()+Idx);
1267 Ops.erase(Ops.begin()+AddOp-1);
1269 Ops.push_back(OuterMul);
1270 return getAddExpr(Ops);
1273 // Check this multiply against other multiplies being added together.
1274 for (unsigned OtherMulIdx = Idx+1;
1275 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1277 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1278 // If MulOp occurs in OtherMul, we can fold the two multiplies
1280 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1281 OMulOp != e; ++OMulOp)
1282 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1283 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1284 const SCEV *InnerMul1 = Mul->getOperand(MulOp == 0);
1285 if (Mul->getNumOperands() != 2) {
1286 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1288 MulOps.erase(MulOps.begin()+MulOp);
1289 InnerMul1 = getMulExpr(MulOps);
1291 const SCEV *InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1292 if (OtherMul->getNumOperands() != 2) {
1293 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1294 OtherMul->op_end());
1295 MulOps.erase(MulOps.begin()+OMulOp);
1296 InnerMul2 = getMulExpr(MulOps);
1298 const SCEV *InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1299 const SCEV *OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1300 if (Ops.size() == 2) return OuterMul;
1301 Ops.erase(Ops.begin()+Idx);
1302 Ops.erase(Ops.begin()+OtherMulIdx-1);
1303 Ops.push_back(OuterMul);
1304 return getAddExpr(Ops);
1310 // If there are any add recurrences in the operands list, see if any other
1311 // added values are loop invariant. If so, we can fold them into the
1313 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1316 // Scan over all recurrences, trying to fold loop invariants into them.
1317 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1318 // Scan all of the other operands to this add and add them to the vector if
1319 // they are loop invariant w.r.t. the recurrence.
1320 SmallVector<const SCEV *, 8> LIOps;
1321 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1322 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1323 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1324 LIOps.push_back(Ops[i]);
1325 Ops.erase(Ops.begin()+i);
1329 // If we found some loop invariants, fold them into the recurrence.
1330 if (!LIOps.empty()) {
1331 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1332 LIOps.push_back(AddRec->getStart());
1334 SmallVector<const SCEV *, 4> AddRecOps(AddRec->op_begin(),
1336 AddRecOps[0] = getAddExpr(LIOps);
1338 const SCEV *NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1339 // If all of the other operands were loop invariant, we are done.
1340 if (Ops.size() == 1) return NewRec;
1342 // Otherwise, add the folded AddRec by the non-liv parts.
1343 for (unsigned i = 0;; ++i)
1344 if (Ops[i] == AddRec) {
1348 return getAddExpr(Ops);
1351 // Okay, if there weren't any loop invariants to be folded, check to see if
1352 // there are multiple AddRec's with the same loop induction variable being
1353 // added together. If so, we can fold them.
1354 for (unsigned OtherIdx = Idx+1;
1355 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1356 if (OtherIdx != Idx) {
1357 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1358 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1359 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1360 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1362 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1363 if (i >= NewOps.size()) {
1364 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1365 OtherAddRec->op_end());
1368 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1370 const SCEV *NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1372 if (Ops.size() == 2) return NewAddRec;
1374 Ops.erase(Ops.begin()+Idx);
1375 Ops.erase(Ops.begin()+OtherIdx-1);
1376 Ops.push_back(NewAddRec);
1377 return getAddExpr(Ops);
1381 // Otherwise couldn't fold anything into this recurrence. Move onto the
1385 // Okay, it looks like we really DO need an add expr. Check to see if we
1386 // already have one, otherwise create a new one.
1387 FoldingSetNodeID ID;
1388 ID.AddInteger(scAddExpr);
1389 ID.AddInteger(Ops.size());
1390 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1391 ID.AddPointer(Ops[i]);
1393 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1394 SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>();
1395 new (S) SCEVAddExpr(ID, Ops);
1396 UniqueSCEVs.InsertNode(S, IP);
1401 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1403 const SCEV *ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV *> &Ops) {
1404 assert(!Ops.empty() && "Cannot get empty mul!");
1406 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1407 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1408 getEffectiveSCEVType(Ops[0]->getType()) &&
1409 "SCEVMulExpr operand types don't match!");
1412 // Sort by complexity, this groups all similar expression types together.
1413 GroupByComplexity(Ops, LI);
1415 // If there are any constants, fold them together.
1417 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1419 // C1*(C2+V) -> C1*C2 + C1*V
1420 if (Ops.size() == 2)
1421 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1422 if (Add->getNumOperands() == 2 &&
1423 isa<SCEVConstant>(Add->getOperand(0)))
1424 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1425 getMulExpr(LHSC, Add->getOperand(1)));
1429 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1430 // We found two constants, fold them together!
1431 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1432 RHSC->getValue()->getValue());
1433 Ops[0] = getConstant(Fold);
1434 Ops.erase(Ops.begin()+1); // Erase the folded element
1435 if (Ops.size() == 1) return Ops[0];
1436 LHSC = cast<SCEVConstant>(Ops[0]);
1439 // If we are left with a constant one being multiplied, strip it off.
1440 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1441 Ops.erase(Ops.begin());
1443 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1444 // If we have a multiply of zero, it will always be zero.
1449 // Skip over the add expression until we get to a multiply.
1450 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1453 if (Ops.size() == 1)
1456 // If there are mul operands inline them all into this expression.
1457 if (Idx < Ops.size()) {
1458 bool DeletedMul = false;
1459 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1460 // If we have an mul, expand the mul operands onto the end of the operands
1462 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1463 Ops.erase(Ops.begin()+Idx);
1467 // If we deleted at least one mul, we added operands to the end of the list,
1468 // and they are not necessarily sorted. Recurse to resort and resimplify
1469 // any operands we just aquired.
1471 return getMulExpr(Ops);
1474 // If there are any add recurrences in the operands list, see if any other
1475 // added values are loop invariant. If so, we can fold them into the
1477 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1480 // Scan over all recurrences, trying to fold loop invariants into them.
1481 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1482 // Scan all of the other operands to this mul and add them to the vector if
1483 // they are loop invariant w.r.t. the recurrence.
1484 SmallVector<const SCEV *, 8> LIOps;
1485 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1486 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1487 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1488 LIOps.push_back(Ops[i]);
1489 Ops.erase(Ops.begin()+i);
1493 // If we found some loop invariants, fold them into the recurrence.
1494 if (!LIOps.empty()) {
1495 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1496 SmallVector<const SCEV *, 4> NewOps;
1497 NewOps.reserve(AddRec->getNumOperands());
1498 if (LIOps.size() == 1) {
1499 const SCEV *Scale = LIOps[0];
1500 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1501 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1503 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1504 SmallVector<const SCEV *, 4> MulOps(LIOps.begin(), LIOps.end());
1505 MulOps.push_back(AddRec->getOperand(i));
1506 NewOps.push_back(getMulExpr(MulOps));
1510 const SCEV *NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1512 // If all of the other operands were loop invariant, we are done.
1513 if (Ops.size() == 1) return NewRec;
1515 // Otherwise, multiply the folded AddRec by the non-liv parts.
1516 for (unsigned i = 0;; ++i)
1517 if (Ops[i] == AddRec) {
1521 return getMulExpr(Ops);
1524 // Okay, if there weren't any loop invariants to be folded, check to see if
1525 // there are multiple AddRec's with the same loop induction variable being
1526 // multiplied together. If so, we can fold them.
1527 for (unsigned OtherIdx = Idx+1;
1528 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1529 if (OtherIdx != Idx) {
1530 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1531 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1532 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1533 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1534 const SCEV *NewStart = getMulExpr(F->getStart(),
1536 const SCEV *B = F->getStepRecurrence(*this);
1537 const SCEV *D = G->getStepRecurrence(*this);
1538 const SCEV *NewStep = getAddExpr(getMulExpr(F, D),
1541 const SCEV *NewAddRec = getAddRecExpr(NewStart, NewStep,
1543 if (Ops.size() == 2) return NewAddRec;
1545 Ops.erase(Ops.begin()+Idx);
1546 Ops.erase(Ops.begin()+OtherIdx-1);
1547 Ops.push_back(NewAddRec);
1548 return getMulExpr(Ops);
1552 // Otherwise couldn't fold anything into this recurrence. Move onto the
1556 // Okay, it looks like we really DO need an mul expr. Check to see if we
1557 // already have one, otherwise create a new one.
1558 FoldingSetNodeID ID;
1559 ID.AddInteger(scMulExpr);
1560 ID.AddInteger(Ops.size());
1561 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1562 ID.AddPointer(Ops[i]);
1564 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1565 SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>();
1566 new (S) SCEVMulExpr(ID, Ops);
1567 UniqueSCEVs.InsertNode(S, IP);
1571 /// getUDivExpr - Get a canonical multiply expression, or something simpler if
1573 const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1575 assert(getEffectiveSCEVType(LHS->getType()) ==
1576 getEffectiveSCEVType(RHS->getType()) &&
1577 "SCEVUDivExpr operand types don't match!");
1579 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1580 if (RHSC->getValue()->equalsInt(1))
1581 return LHS; // X udiv 1 --> x
1583 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1585 // Determine if the division can be folded into the operands of
1587 // TODO: Generalize this to non-constants by using known-bits information.
1588 const Type *Ty = LHS->getType();
1589 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1590 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1591 // For non-power-of-two values, effectively round the value up to the
1592 // nearest power of two.
1593 if (!RHSC->getValue()->getValue().isPowerOf2())
1595 const IntegerType *ExtTy =
1596 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1597 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1598 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1599 if (const SCEVConstant *Step =
1600 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1601 if (!Step->getValue()->getValue()
1602 .urem(RHSC->getValue()->getValue()) &&
1603 getZeroExtendExpr(AR, ExtTy) ==
1604 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1605 getZeroExtendExpr(Step, ExtTy),
1607 SmallVector<const SCEV *, 4> Operands;
1608 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1609 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1610 return getAddRecExpr(Operands, AR->getLoop());
1612 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1613 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1614 SmallVector<const SCEV *, 4> Operands;
1615 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1616 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1617 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1618 // Find an operand that's safely divisible.
1619 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1620 const SCEV *Op = M->getOperand(i);
1621 const SCEV *Div = getUDivExpr(Op, RHSC);
1622 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1623 const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands();
1624 Operands = SmallVector<const SCEV *, 4>(MOperands.begin(),
1627 return getMulExpr(Operands);
1631 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1632 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1633 SmallVector<const SCEV *, 4> Operands;
1634 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1635 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1636 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1638 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1639 const SCEV *Op = getUDivExpr(A->getOperand(i), RHS);
1640 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1642 Operands.push_back(Op);
1644 if (Operands.size() == A->getNumOperands())
1645 return getAddExpr(Operands);
1649 // Fold if both operands are constant.
1650 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1651 Constant *LHSCV = LHSC->getValue();
1652 Constant *RHSCV = RHSC->getValue();
1653 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1658 FoldingSetNodeID ID;
1659 ID.AddInteger(scUDivExpr);
1663 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1664 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>();
1665 new (S) SCEVUDivExpr(ID, LHS, RHS);
1666 UniqueSCEVs.InsertNode(S, IP);
1671 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1672 /// Simplify the expression as much as possible.
1673 const SCEV *ScalarEvolution::getAddRecExpr(const SCEV *Start,
1674 const SCEV *Step, const Loop *L) {
1675 SmallVector<const SCEV *, 4> Operands;
1676 Operands.push_back(Start);
1677 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1678 if (StepChrec->getLoop() == L) {
1679 Operands.insert(Operands.end(), StepChrec->op_begin(),
1680 StepChrec->op_end());
1681 return getAddRecExpr(Operands, L);
1684 Operands.push_back(Step);
1685 return getAddRecExpr(Operands, L);
1688 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1689 /// Simplify the expression as much as possible.
1691 ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV *> &Operands,
1693 if (Operands.size() == 1) return Operands[0];
1695 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1696 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1697 getEffectiveSCEVType(Operands[0]->getType()) &&
1698 "SCEVAddRecExpr operand types don't match!");
1701 if (Operands.back()->isZero()) {
1702 Operands.pop_back();
1703 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1706 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1707 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1708 const Loop* NestedLoop = NestedAR->getLoop();
1709 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1710 SmallVector<const SCEV *, 4> NestedOperands(NestedAR->op_begin(),
1711 NestedAR->op_end());
1712 Operands[0] = NestedAR->getStart();
1713 // AddRecs require their operands be loop-invariant with respect to their
1714 // loops. Don't perform this transformation if it would break this
1716 bool AllInvariant = true;
1717 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1718 if (!Operands[i]->isLoopInvariant(L)) {
1719 AllInvariant = false;
1723 NestedOperands[0] = getAddRecExpr(Operands, L);
1724 AllInvariant = true;
1725 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
1726 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
1727 AllInvariant = false;
1731 // Ok, both add recurrences are valid after the transformation.
1732 return getAddRecExpr(NestedOperands, NestedLoop);
1734 // Reset Operands to its original state.
1735 Operands[0] = NestedAR;
1739 FoldingSetNodeID ID;
1740 ID.AddInteger(scAddRecExpr);
1741 ID.AddInteger(Operands.size());
1742 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1743 ID.AddPointer(Operands[i]);
1746 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1747 SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>();
1748 new (S) SCEVAddRecExpr(ID, Operands, L);
1749 UniqueSCEVs.InsertNode(S, IP);
1753 const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
1755 SmallVector<const SCEV *, 2> Ops;
1758 return getSMaxExpr(Ops);
1762 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1763 assert(!Ops.empty() && "Cannot get empty smax!");
1764 if (Ops.size() == 1) return Ops[0];
1766 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1767 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1768 getEffectiveSCEVType(Ops[0]->getType()) &&
1769 "SCEVSMaxExpr operand types don't match!");
1772 // Sort by complexity, this groups all similar expression types together.
1773 GroupByComplexity(Ops, LI);
1775 // If there are any constants, fold them together.
1777 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1779 assert(Idx < Ops.size());
1780 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1781 // We found two constants, fold them together!
1782 ConstantInt *Fold = ConstantInt::get(
1783 APIntOps::smax(LHSC->getValue()->getValue(),
1784 RHSC->getValue()->getValue()));
1785 Ops[0] = getConstant(Fold);
1786 Ops.erase(Ops.begin()+1); // Erase the folded element
1787 if (Ops.size() == 1) return Ops[0];
1788 LHSC = cast<SCEVConstant>(Ops[0]);
1791 // If we are left with a constant minimum-int, strip it off.
1792 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1793 Ops.erase(Ops.begin());
1795 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
1796 // If we have an smax with a constant maximum-int, it will always be
1802 if (Ops.size() == 1) return Ops[0];
1804 // Find the first SMax
1805 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1808 // Check to see if one of the operands is an SMax. If so, expand its operands
1809 // onto our operand list, and recurse to simplify.
1810 if (Idx < Ops.size()) {
1811 bool DeletedSMax = false;
1812 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1813 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1814 Ops.erase(Ops.begin()+Idx);
1819 return getSMaxExpr(Ops);
1822 // Okay, check to see if the same value occurs in the operand list twice. If
1823 // so, delete one. Since we sorted the list, these values are required to
1825 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1826 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1827 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1831 if (Ops.size() == 1) return Ops[0];
1833 assert(!Ops.empty() && "Reduced smax down to nothing!");
1835 // Okay, it looks like we really DO need an smax expr. Check to see if we
1836 // already have one, otherwise create a new one.
1837 FoldingSetNodeID ID;
1838 ID.AddInteger(scSMaxExpr);
1839 ID.AddInteger(Ops.size());
1840 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1841 ID.AddPointer(Ops[i]);
1843 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1844 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>();
1845 new (S) SCEVSMaxExpr(ID, Ops);
1846 UniqueSCEVs.InsertNode(S, IP);
1850 const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
1852 SmallVector<const SCEV *, 2> Ops;
1855 return getUMaxExpr(Ops);
1859 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV *> &Ops) {
1860 assert(!Ops.empty() && "Cannot get empty umax!");
1861 if (Ops.size() == 1) return Ops[0];
1863 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1864 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1865 getEffectiveSCEVType(Ops[0]->getType()) &&
1866 "SCEVUMaxExpr operand types don't match!");
1869 // Sort by complexity, this groups all similar expression types together.
1870 GroupByComplexity(Ops, LI);
1872 // If there are any constants, fold them together.
1874 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1876 assert(Idx < Ops.size());
1877 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1878 // We found two constants, fold them together!
1879 ConstantInt *Fold = ConstantInt::get(
1880 APIntOps::umax(LHSC->getValue()->getValue(),
1881 RHSC->getValue()->getValue()));
1882 Ops[0] = getConstant(Fold);
1883 Ops.erase(Ops.begin()+1); // Erase the folded element
1884 if (Ops.size() == 1) return Ops[0];
1885 LHSC = cast<SCEVConstant>(Ops[0]);
1888 // If we are left with a constant minimum-int, strip it off.
1889 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1890 Ops.erase(Ops.begin());
1892 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
1893 // If we have an umax with a constant maximum-int, it will always be
1899 if (Ops.size() == 1) return Ops[0];
1901 // Find the first UMax
1902 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1905 // Check to see if one of the operands is a UMax. If so, expand its operands
1906 // onto our operand list, and recurse to simplify.
1907 if (Idx < Ops.size()) {
1908 bool DeletedUMax = false;
1909 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1910 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1911 Ops.erase(Ops.begin()+Idx);
1916 return getUMaxExpr(Ops);
1919 // Okay, check to see if the same value occurs in the operand list twice. If
1920 // so, delete one. Since we sorted the list, these values are required to
1922 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1923 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1924 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1928 if (Ops.size() == 1) return Ops[0];
1930 assert(!Ops.empty() && "Reduced umax down to nothing!");
1932 // Okay, it looks like we really DO need a umax expr. Check to see if we
1933 // already have one, otherwise create a new one.
1934 FoldingSetNodeID ID;
1935 ID.AddInteger(scUMaxExpr);
1936 ID.AddInteger(Ops.size());
1937 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1938 ID.AddPointer(Ops[i]);
1940 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1941 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>();
1942 new (S) SCEVUMaxExpr(ID, Ops);
1943 UniqueSCEVs.InsertNode(S, IP);
1947 const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
1949 // ~smax(~x, ~y) == smin(x, y).
1950 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
1953 const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
1955 // ~umax(~x, ~y) == umin(x, y)
1956 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
1959 const SCEV *ScalarEvolution::getUnknown(Value *V) {
1960 // Don't attempt to do anything other than create a SCEVUnknown object
1961 // here. createSCEV only calls getUnknown after checking for all other
1962 // interesting possibilities, and any other code that calls getUnknown
1963 // is doing so in order to hide a value from SCEV canonicalization.
1965 FoldingSetNodeID ID;
1966 ID.AddInteger(scUnknown);
1969 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1970 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>();
1971 new (S) SCEVUnknown(ID, V);
1972 UniqueSCEVs.InsertNode(S, IP);
1976 //===----------------------------------------------------------------------===//
1977 // Basic SCEV Analysis and PHI Idiom Recognition Code
1980 /// isSCEVable - Test if values of the given type are analyzable within
1981 /// the SCEV framework. This primarily includes integer types, and it
1982 /// can optionally include pointer types if the ScalarEvolution class
1983 /// has access to target-specific information.
1984 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1985 // Integers are always SCEVable.
1986 if (Ty->isInteger())
1989 // Pointers are SCEVable if TargetData information is available
1990 // to provide pointer size information.
1991 if (isa<PointerType>(Ty))
1994 // Otherwise it's not SCEVable.
1998 /// getTypeSizeInBits - Return the size in bits of the specified type,
1999 /// for which isSCEVable must return true.
2000 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2001 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2003 // If we have a TargetData, use it!
2005 return TD->getTypeSizeInBits(Ty);
2007 // Otherwise, we support only integer types.
2008 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
2009 return Ty->getPrimitiveSizeInBits();
2012 /// getEffectiveSCEVType - Return a type with the same bitwidth as
2013 /// the given type and which represents how SCEV will treat the given
2014 /// type, for which isSCEVable must return true. For pointer types,
2015 /// this is the pointer-sized integer type.
2016 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2017 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2019 if (Ty->isInteger())
2022 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
2023 return TD->getIntPtrType();
2026 const SCEV *ScalarEvolution::getCouldNotCompute() {
2027 return &CouldNotCompute;
2030 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2031 /// expression and create a new one.
2032 const SCEV *ScalarEvolution::getSCEV(Value *V) {
2033 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2035 std::map<SCEVCallbackVH, const SCEV *>::iterator I = Scalars.find(V);
2036 if (I != Scalars.end()) return I->second;
2037 const SCEV *S = createSCEV(V);
2038 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2042 /// getIntegerSCEV - Given a SCEVable type, create a constant for the
2043 /// specified signed integer value and return a SCEV for the constant.
2044 const SCEV *ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
2045 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2046 return getConstant(ConstantInt::get(ITy, Val));
2049 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2051 const SCEV *ScalarEvolution::getNegativeSCEV(const SCEV *V) {
2052 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2054 cast<ConstantInt>(Context->getConstantExprNeg(VC->getValue())));
2056 const Type *Ty = V->getType();
2057 Ty = getEffectiveSCEVType(Ty);
2058 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
2061 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2062 const SCEV *ScalarEvolution::getNotSCEV(const SCEV *V) {
2063 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2064 return getConstant(cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2066 const Type *Ty = V->getType();
2067 Ty = getEffectiveSCEVType(Ty);
2068 const SCEV *AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
2069 return getMinusSCEV(AllOnes, V);
2072 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2074 const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2077 return getAddExpr(LHS, getNegativeSCEV(RHS));
2080 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2081 /// input value to the specified type. If the type must be extended, it is zero
2084 ScalarEvolution::getTruncateOrZeroExtend(const SCEV *V,
2086 const Type *SrcTy = V->getType();
2087 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2088 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2089 "Cannot truncate or zero extend with non-integer arguments!");
2090 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2091 return V; // No conversion
2092 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2093 return getTruncateExpr(V, Ty);
2094 return getZeroExtendExpr(V, Ty);
2097 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2098 /// input value to the specified type. If the type must be extended, it is sign
2101 ScalarEvolution::getTruncateOrSignExtend(const SCEV *V,
2103 const Type *SrcTy = V->getType();
2104 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2105 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2106 "Cannot truncate or zero extend with non-integer arguments!");
2107 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2108 return V; // No conversion
2109 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2110 return getTruncateExpr(V, Ty);
2111 return getSignExtendExpr(V, Ty);
2114 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2115 /// input value to the specified type. If the type must be extended, it is zero
2116 /// extended. The conversion must not be narrowing.
2118 ScalarEvolution::getNoopOrZeroExtend(const SCEV *V, const Type *Ty) {
2119 const Type *SrcTy = V->getType();
2120 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2121 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2122 "Cannot noop or zero extend with non-integer arguments!");
2123 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2124 "getNoopOrZeroExtend cannot truncate!");
2125 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2126 return V; // No conversion
2127 return getZeroExtendExpr(V, Ty);
2130 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2131 /// input value to the specified type. If the type must be extended, it is sign
2132 /// extended. The conversion must not be narrowing.
2134 ScalarEvolution::getNoopOrSignExtend(const SCEV *V, const Type *Ty) {
2135 const Type *SrcTy = V->getType();
2136 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2137 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2138 "Cannot noop or sign extend with non-integer arguments!");
2139 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2140 "getNoopOrSignExtend cannot truncate!");
2141 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2142 return V; // No conversion
2143 return getSignExtendExpr(V, Ty);
2146 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2147 /// the input value to the specified type. If the type must be extended,
2148 /// it is extended with unspecified bits. The conversion must not be
2151 ScalarEvolution::getNoopOrAnyExtend(const SCEV *V, const Type *Ty) {
2152 const Type *SrcTy = V->getType();
2153 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2154 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2155 "Cannot noop or any extend with non-integer arguments!");
2156 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2157 "getNoopOrAnyExtend cannot truncate!");
2158 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2159 return V; // No conversion
2160 return getAnyExtendExpr(V, Ty);
2163 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2164 /// input value to the specified type. The conversion must not be widening.
2166 ScalarEvolution::getTruncateOrNoop(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 truncate or noop with non-integer arguments!");
2171 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2172 "getTruncateOrNoop cannot extend!");
2173 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2174 return V; // No conversion
2175 return getTruncateExpr(V, Ty);
2178 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2179 /// the types using zero-extension, and then perform a umax operation
2181 const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2183 const SCEV *PromotedLHS = LHS;
2184 const SCEV *PromotedRHS = RHS;
2186 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2187 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2189 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2191 return getUMaxExpr(PromotedLHS, PromotedRHS);
2194 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2195 /// the types using zero-extension, and then perform a umin operation
2197 const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2199 const SCEV *PromotedLHS = LHS;
2200 const SCEV *PromotedRHS = RHS;
2202 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2203 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2205 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2207 return getUMinExpr(PromotedLHS, PromotedRHS);
2210 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
2211 /// the specified instruction and replaces any references to the symbolic value
2212 /// SymName with the specified value. This is used during PHI resolution.
2214 ScalarEvolution::ReplaceSymbolicValueWithConcrete(Instruction *I,
2215 const SCEV *SymName,
2216 const SCEV *NewVal) {
2217 std::map<SCEVCallbackVH, const SCEV *>::iterator SI =
2218 Scalars.find(SCEVCallbackVH(I, this));
2219 if (SI == Scalars.end()) return;
2222 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
2223 if (NV == SI->second) return; // No change.
2225 SI->second = NV; // Update the scalars map!
2227 // Any instruction values that use this instruction might also need to be
2229 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
2231 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
2234 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2235 /// a loop header, making it a potential recurrence, or it doesn't.
2237 const SCEV *ScalarEvolution::createNodeForPHI(PHINode *PN) {
2238 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2239 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2240 if (L->getHeader() == PN->getParent()) {
2241 // If it lives in the loop header, it has two incoming values, one
2242 // from outside the loop, and one from inside.
2243 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2244 unsigned BackEdge = IncomingEdge^1;
2246 // While we are analyzing this PHI node, handle its value symbolically.
2247 const SCEV *SymbolicName = getUnknown(PN);
2248 assert(Scalars.find(PN) == Scalars.end() &&
2249 "PHI node already processed?");
2250 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2252 // Using this symbolic name for the PHI, analyze the value coming around
2254 const SCEV *BEValue = getSCEV(PN->getIncomingValue(BackEdge));
2256 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2257 // has a special value for the first iteration of the loop.
2259 // If the value coming around the backedge is an add with the symbolic
2260 // value we just inserted, then we found a simple induction variable!
2261 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2262 // If there is a single occurrence of the symbolic value, replace it
2263 // with a recurrence.
2264 unsigned FoundIndex = Add->getNumOperands();
2265 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2266 if (Add->getOperand(i) == SymbolicName)
2267 if (FoundIndex == e) {
2272 if (FoundIndex != Add->getNumOperands()) {
2273 // Create an add with everything but the specified operand.
2274 SmallVector<const SCEV *, 8> Ops;
2275 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2276 if (i != FoundIndex)
2277 Ops.push_back(Add->getOperand(i));
2278 const SCEV *Accum = getAddExpr(Ops);
2280 // This is not a valid addrec if the step amount is varying each
2281 // loop iteration, but is not itself an addrec in this loop.
2282 if (Accum->isLoopInvariant(L) ||
2283 (isa<SCEVAddRecExpr>(Accum) &&
2284 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2285 const SCEV *StartVal =
2286 getSCEV(PN->getIncomingValue(IncomingEdge));
2287 const SCEV *PHISCEV =
2288 getAddRecExpr(StartVal, Accum, L);
2290 // Okay, for the entire analysis of this edge we assumed the PHI
2291 // to be symbolic. We now need to go back and update all of the
2292 // entries for the scalars that use the PHI (except for the PHI
2293 // itself) to use the new analyzed value instead of the "symbolic"
2295 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2299 } else if (const SCEVAddRecExpr *AddRec =
2300 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2301 // Otherwise, this could be a loop like this:
2302 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2303 // In this case, j = {1,+,1} and BEValue is j.
2304 // Because the other in-value of i (0) fits the evolution of BEValue
2305 // i really is an addrec evolution.
2306 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2307 const SCEV *StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2309 // If StartVal = j.start - j.stride, we can use StartVal as the
2310 // initial step of the addrec evolution.
2311 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2312 AddRec->getOperand(1))) {
2313 const SCEV *PHISCEV =
2314 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2316 // Okay, for the entire analysis of this edge we assumed the PHI
2317 // to be symbolic. We now need to go back and update all of the
2318 // entries for the scalars that use the PHI (except for the PHI
2319 // itself) to use the new analyzed value instead of the "symbolic"
2321 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2327 return SymbolicName;
2330 // If it's not a loop phi, we can't handle it yet.
2331 return getUnknown(PN);
2334 /// createNodeForGEP - Expand GEP instructions into add and multiply
2335 /// operations. This allows them to be analyzed by regular SCEV code.
2337 const SCEV *ScalarEvolution::createNodeForGEP(User *GEP) {
2339 const Type *IntPtrTy = TD->getIntPtrType();
2340 Value *Base = GEP->getOperand(0);
2341 // Don't attempt to analyze GEPs over unsized objects.
2342 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2343 return getUnknown(GEP);
2344 const SCEV *TotalOffset = getIntegerSCEV(0, IntPtrTy);
2345 gep_type_iterator GTI = gep_type_begin(GEP);
2346 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2350 // Compute the (potentially symbolic) offset in bytes for this index.
2351 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2352 // For a struct, add the member offset.
2353 const StructLayout &SL = *TD->getStructLayout(STy);
2354 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2355 uint64_t Offset = SL.getElementOffset(FieldNo);
2356 TotalOffset = getAddExpr(TotalOffset,
2357 getIntegerSCEV(Offset, IntPtrTy));
2359 // For an array, add the element offset, explicitly scaled.
2360 const SCEV *LocalOffset = getSCEV(Index);
2361 if (!isa<PointerType>(LocalOffset->getType()))
2362 // Getelementptr indicies are signed.
2363 LocalOffset = getTruncateOrSignExtend(LocalOffset,
2366 getMulExpr(LocalOffset,
2367 getIntegerSCEV(TD->getTypeAllocSize(*GTI),
2369 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2372 return getAddExpr(getSCEV(Base), TotalOffset);
2375 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2376 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2377 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2378 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2380 ScalarEvolution::GetMinTrailingZeros(const SCEV *S) {
2381 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2382 return C->getValue()->getValue().countTrailingZeros();
2384 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2385 return std::min(GetMinTrailingZeros(T->getOperand()),
2386 (uint32_t)getTypeSizeInBits(T->getType()));
2388 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2389 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2390 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2391 getTypeSizeInBits(E->getType()) : OpRes;
2394 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2395 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2396 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2397 getTypeSizeInBits(E->getType()) : OpRes;
2400 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2401 // The result is the min of all operands results.
2402 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2403 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2404 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2408 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2409 // The result is the sum of all operands results.
2410 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2411 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2412 for (unsigned i = 1, e = M->getNumOperands();
2413 SumOpRes != BitWidth && i != e; ++i)
2414 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2419 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2420 // The result is the min of all operands results.
2421 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2422 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2423 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2427 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2428 // The result is the min of all operands results.
2429 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2430 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2431 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2435 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2436 // The result is the min of all operands results.
2437 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2438 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2439 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2443 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2444 // For a SCEVUnknown, ask ValueTracking.
2445 unsigned BitWidth = getTypeSizeInBits(U->getType());
2446 APInt Mask = APInt::getAllOnesValue(BitWidth);
2447 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2448 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2449 return Zeros.countTrailingOnes();
2457 ScalarEvolution::GetMinLeadingZeros(const SCEV *S) {
2458 // TODO: Handle other SCEV expression types here.
2460 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2461 return C->getValue()->getValue().countLeadingZeros();
2463 if (const SCEVZeroExtendExpr *C = dyn_cast<SCEVZeroExtendExpr>(S)) {
2464 // A zero-extension cast adds zero bits.
2465 return GetMinLeadingZeros(C->getOperand()) +
2466 (getTypeSizeInBits(C->getType()) -
2467 getTypeSizeInBits(C->getOperand()->getType()));
2470 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2471 // For a SCEVUnknown, ask ValueTracking.
2472 unsigned BitWidth = getTypeSizeInBits(U->getType());
2473 APInt Mask = APInt::getAllOnesValue(BitWidth);
2474 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2475 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
2476 return Zeros.countLeadingOnes();
2483 ScalarEvolution::GetMinSignBits(const SCEV *S) {
2484 // TODO: Handle other SCEV expression types here.
2486 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
2487 const APInt &A = C->getValue()->getValue();
2488 return A.isNegative() ? A.countLeadingOnes() :
2489 A.countLeadingZeros();
2492 if (const SCEVSignExtendExpr *C = dyn_cast<SCEVSignExtendExpr>(S)) {
2493 // A sign-extension cast adds sign bits.
2494 return GetMinSignBits(C->getOperand()) +
2495 (getTypeSizeInBits(C->getType()) -
2496 getTypeSizeInBits(C->getOperand()->getType()));
2499 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2500 unsigned BitWidth = getTypeSizeInBits(A->getType());
2502 // Special case decrementing a value (ADD X, -1):
2503 if (const SCEVConstant *CRHS = dyn_cast<SCEVConstant>(A->getOperand(0)))
2504 if (CRHS->isAllOnesValue()) {
2505 SmallVector<const SCEV *, 4> OtherOps(A->op_begin() + 1, A->op_end());
2506 const SCEV *OtherOpsAdd = getAddExpr(OtherOps);
2507 unsigned LZ = GetMinLeadingZeros(OtherOpsAdd);
2509 // If the input is known to be 0 or 1, the output is 0/-1, which is all
2511 if (LZ == BitWidth - 1)
2514 // If we are subtracting one from a positive number, there is no carry
2515 // out of the result.
2517 return GetMinSignBits(OtherOpsAdd);
2520 // Add can have at most one carry bit. Thus we know that the output
2521 // is, at worst, one more bit than the inputs.
2522 unsigned Min = BitWidth;
2523 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2524 unsigned N = GetMinSignBits(A->getOperand(i));
2525 Min = std::min(Min, N) - 1;
2526 if (Min == 0) return 1;
2531 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2532 // For a SCEVUnknown, ask ValueTracking.
2533 return ComputeNumSignBits(U->getValue(), TD);
2539 /// createSCEV - We know that there is no SCEV for the specified value.
2540 /// Analyze the expression.
2542 const SCEV *ScalarEvolution::createSCEV(Value *V) {
2543 if (!isSCEVable(V->getType()))
2544 return getUnknown(V);
2546 unsigned Opcode = Instruction::UserOp1;
2547 if (Instruction *I = dyn_cast<Instruction>(V))
2548 Opcode = I->getOpcode();
2549 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2550 Opcode = CE->getOpcode();
2551 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
2552 return getConstant(CI);
2553 else if (isa<ConstantPointerNull>(V))
2554 return getIntegerSCEV(0, V->getType());
2555 else if (isa<UndefValue>(V))
2556 return getIntegerSCEV(0, V->getType());
2558 return getUnknown(V);
2560 User *U = cast<User>(V);
2562 case Instruction::Add:
2563 return getAddExpr(getSCEV(U->getOperand(0)),
2564 getSCEV(U->getOperand(1)));
2565 case Instruction::Mul:
2566 return getMulExpr(getSCEV(U->getOperand(0)),
2567 getSCEV(U->getOperand(1)));
2568 case Instruction::UDiv:
2569 return getUDivExpr(getSCEV(U->getOperand(0)),
2570 getSCEV(U->getOperand(1)));
2571 case Instruction::Sub:
2572 return getMinusSCEV(getSCEV(U->getOperand(0)),
2573 getSCEV(U->getOperand(1)));
2574 case Instruction::And:
2575 // For an expression like x&255 that merely masks off the high bits,
2576 // use zext(trunc(x)) as the SCEV expression.
2577 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2578 if (CI->isNullValue())
2579 return getSCEV(U->getOperand(1));
2580 if (CI->isAllOnesValue())
2581 return getSCEV(U->getOperand(0));
2582 const APInt &A = CI->getValue();
2584 // Instcombine's ShrinkDemandedConstant may strip bits out of
2585 // constants, obscuring what would otherwise be a low-bits mask.
2586 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
2587 // knew about to reconstruct a low-bits mask value.
2588 unsigned LZ = A.countLeadingZeros();
2589 unsigned BitWidth = A.getBitWidth();
2590 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
2591 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
2592 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
2594 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
2596 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
2598 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2599 IntegerType::get(BitWidth - LZ)),
2604 case Instruction::Or:
2605 // If the RHS of the Or is a constant, we may have something like:
2606 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2607 // optimizations will transparently handle this case.
2609 // In order for this transformation to be safe, the LHS must be of the
2610 // form X*(2^n) and the Or constant must be less than 2^n.
2611 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2612 const SCEV *LHS = getSCEV(U->getOperand(0));
2613 const APInt &CIVal = CI->getValue();
2614 if (GetMinTrailingZeros(LHS) >=
2615 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2616 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2619 case Instruction::Xor:
2620 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2621 // If the RHS of the xor is a signbit, then this is just an add.
2622 // Instcombine turns add of signbit into xor as a strength reduction step.
2623 if (CI->getValue().isSignBit())
2624 return getAddExpr(getSCEV(U->getOperand(0)),
2625 getSCEV(U->getOperand(1)));
2627 // If the RHS of xor is -1, then this is a not operation.
2628 if (CI->isAllOnesValue())
2629 return getNotSCEV(getSCEV(U->getOperand(0)));
2631 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2632 // This is a variant of the check for xor with -1, and it handles
2633 // the case where instcombine has trimmed non-demanded bits out
2634 // of an xor with -1.
2635 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2636 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2637 if (BO->getOpcode() == Instruction::And &&
2638 LCI->getValue() == CI->getValue())
2639 if (const SCEVZeroExtendExpr *Z =
2640 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
2641 const Type *UTy = U->getType();
2642 const SCEV *Z0 = Z->getOperand();
2643 const Type *Z0Ty = Z0->getType();
2644 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
2646 // If C is a low-bits mask, the zero extend is zerving to
2647 // mask off the high bits. Complement the operand and
2648 // re-apply the zext.
2649 if (APIntOps::isMask(Z0TySize, CI->getValue()))
2650 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
2652 // If C is a single bit, it may be in the sign-bit position
2653 // before the zero-extend. In this case, represent the xor
2654 // using an add, which is equivalent, and re-apply the zext.
2655 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
2656 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
2658 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
2664 case Instruction::Shl:
2665 // Turn shift left of a constant amount into a multiply.
2666 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2667 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2668 Constant *X = ConstantInt::get(
2669 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2670 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2674 case Instruction::LShr:
2675 // Turn logical shift right of a constant into a unsigned divide.
2676 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2677 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2678 Constant *X = ConstantInt::get(
2679 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2680 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2684 case Instruction::AShr:
2685 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2686 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2687 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2688 if (L->getOpcode() == Instruction::Shl &&
2689 L->getOperand(1) == U->getOperand(1)) {
2690 unsigned BitWidth = getTypeSizeInBits(U->getType());
2691 uint64_t Amt = BitWidth - CI->getZExtValue();
2692 if (Amt == BitWidth)
2693 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2695 return getIntegerSCEV(0, U->getType()); // value is undefined
2697 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2698 IntegerType::get(Amt)),
2703 case Instruction::Trunc:
2704 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2706 case Instruction::ZExt:
2707 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2709 case Instruction::SExt:
2710 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2712 case Instruction::BitCast:
2713 // BitCasts are no-op casts so we just eliminate the cast.
2714 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2715 return getSCEV(U->getOperand(0));
2718 case Instruction::IntToPtr:
2719 if (!TD) break; // Without TD we can't analyze pointers.
2720 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2721 TD->getIntPtrType());
2723 case Instruction::PtrToInt:
2724 if (!TD) break; // Without TD we can't analyze pointers.
2725 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2728 case Instruction::GetElementPtr:
2729 if (!TD) break; // Without TD we can't analyze pointers.
2730 return createNodeForGEP(U);
2732 case Instruction::PHI:
2733 return createNodeForPHI(cast<PHINode>(U));
2735 case Instruction::Select:
2736 // This could be a smax or umax that was lowered earlier.
2737 // Try to recover it.
2738 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2739 Value *LHS = ICI->getOperand(0);
2740 Value *RHS = ICI->getOperand(1);
2741 switch (ICI->getPredicate()) {
2742 case ICmpInst::ICMP_SLT:
2743 case ICmpInst::ICMP_SLE:
2744 std::swap(LHS, RHS);
2746 case ICmpInst::ICMP_SGT:
2747 case ICmpInst::ICMP_SGE:
2748 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2749 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2750 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2751 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
2753 case ICmpInst::ICMP_ULT:
2754 case ICmpInst::ICMP_ULE:
2755 std::swap(LHS, RHS);
2757 case ICmpInst::ICMP_UGT:
2758 case ICmpInst::ICMP_UGE:
2759 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2760 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2761 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2762 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
2764 case ICmpInst::ICMP_NE:
2765 // n != 0 ? n : 1 -> umax(n, 1)
2766 if (LHS == U->getOperand(1) &&
2767 isa<ConstantInt>(U->getOperand(2)) &&
2768 cast<ConstantInt>(U->getOperand(2))->isOne() &&
2769 isa<ConstantInt>(RHS) &&
2770 cast<ConstantInt>(RHS)->isZero())
2771 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
2773 case ICmpInst::ICMP_EQ:
2774 // n == 0 ? 1 : n -> umax(n, 1)
2775 if (LHS == U->getOperand(2) &&
2776 isa<ConstantInt>(U->getOperand(1)) &&
2777 cast<ConstantInt>(U->getOperand(1))->isOne() &&
2778 isa<ConstantInt>(RHS) &&
2779 cast<ConstantInt>(RHS)->isZero())
2780 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
2787 default: // We cannot analyze this expression.
2791 return getUnknown(V);
2796 //===----------------------------------------------------------------------===//
2797 // Iteration Count Computation Code
2800 /// getBackedgeTakenCount - If the specified loop has a predictable
2801 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2802 /// object. The backedge-taken count is the number of times the loop header
2803 /// will be branched to from within the loop. This is one less than the
2804 /// trip count of the loop, since it doesn't count the first iteration,
2805 /// when the header is branched to from outside the loop.
2807 /// Note that it is not valid to call this method on a loop without a
2808 /// loop-invariant backedge-taken count (see
2809 /// hasLoopInvariantBackedgeTakenCount).
2811 const SCEV *ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2812 return getBackedgeTakenInfo(L).Exact;
2815 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2816 /// return the least SCEV value that is known never to be less than the
2817 /// actual backedge taken count.
2818 const SCEV *ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2819 return getBackedgeTakenInfo(L).Max;
2822 /// PushLoopPHIs - Push PHI nodes in the header of the given loop
2823 /// onto the given Worklist.
2825 PushLoopPHIs(const Loop *L, SmallVectorImpl<Instruction *> &Worklist) {
2826 BasicBlock *Header = L->getHeader();
2828 // Push all Loop-header PHIs onto the Worklist stack.
2829 for (BasicBlock::iterator I = Header->begin();
2830 PHINode *PN = dyn_cast<PHINode>(I); ++I)
2831 Worklist.push_back(PN);
2834 /// PushDefUseChildren - Push users of the given Instruction
2835 /// onto the given Worklist.
2837 PushDefUseChildren(Instruction *I,
2838 SmallVectorImpl<Instruction *> &Worklist) {
2839 // Push the def-use children onto the Worklist stack.
2840 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2842 Worklist.push_back(cast<Instruction>(UI));
2845 const ScalarEvolution::BackedgeTakenInfo &
2846 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2847 // Initially insert a CouldNotCompute for this loop. If the insertion
2848 // succeeds, procede to actually compute a backedge-taken count and
2849 // update the value. The temporary CouldNotCompute value tells SCEV
2850 // code elsewhere that it shouldn't attempt to request a new
2851 // backedge-taken count, which could result in infinite recursion.
2852 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2853 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2855 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2856 if (ItCount.Exact != getCouldNotCompute()) {
2857 assert(ItCount.Exact->isLoopInvariant(L) &&
2858 ItCount.Max->isLoopInvariant(L) &&
2859 "Computed trip count isn't loop invariant for loop!");
2860 ++NumTripCountsComputed;
2862 // Update the value in the map.
2863 Pair.first->second = ItCount;
2865 if (ItCount.Max != getCouldNotCompute())
2866 // Update the value in the map.
2867 Pair.first->second = ItCount;
2868 if (isa<PHINode>(L->getHeader()->begin()))
2869 // Only count loops that have phi nodes as not being computable.
2870 ++NumTripCountsNotComputed;
2873 // Now that we know more about the trip count for this loop, forget any
2874 // existing SCEV values for PHI nodes in this loop since they are only
2875 // conservative estimates made without the benefit of trip count
2876 // information. This is similar to the code in
2877 // forgetLoopBackedgeTakenCount, except that it handles SCEVUnknown PHI
2879 if (ItCount.hasAnyInfo()) {
2880 SmallVector<Instruction *, 16> Worklist;
2881 PushLoopPHIs(L, Worklist);
2883 SmallPtrSet<Instruction *, 8> Visited;
2884 while (!Worklist.empty()) {
2885 Instruction *I = Worklist.pop_back_val();
2886 if (!Visited.insert(I)) continue;
2888 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
2889 Scalars.find(static_cast<Value *>(I));
2890 if (It != Scalars.end()) {
2891 // SCEVUnknown for a PHI either means that it has an unrecognized
2892 // structure, or it's a PHI that's in the progress of being computed
2893 // by createNodeForPHI. In the former case, additional loop trip count
2894 // information isn't going to change anything. In the later case,
2895 // createNodeForPHI will perform the necessary updates on its own when
2896 // it gets to that point.
2897 if (!isa<PHINode>(I) || !isa<SCEVUnknown>(It->second))
2899 ValuesAtScopes.erase(I);
2900 if (PHINode *PN = dyn_cast<PHINode>(I))
2901 ConstantEvolutionLoopExitValue.erase(PN);
2904 PushDefUseChildren(I, Worklist);
2908 return Pair.first->second;
2911 /// forgetLoopBackedgeTakenCount - This method should be called by the
2912 /// client when it has changed a loop in a way that may effect
2913 /// ScalarEvolution's ability to compute a trip count, or if the loop
2915 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2916 BackedgeTakenCounts.erase(L);
2918 SmallVector<Instruction *, 16> Worklist;
2919 PushLoopPHIs(L, Worklist);
2921 SmallPtrSet<Instruction *, 8> Visited;
2922 while (!Worklist.empty()) {
2923 Instruction *I = Worklist.pop_back_val();
2924 if (!Visited.insert(I)) continue;
2926 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
2927 Scalars.find(static_cast<Value *>(I));
2928 if (It != Scalars.end()) {
2930 ValuesAtScopes.erase(I);
2931 if (PHINode *PN = dyn_cast<PHINode>(I))
2932 ConstantEvolutionLoopExitValue.erase(PN);
2935 PushDefUseChildren(I, Worklist);
2939 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2940 /// of the specified loop will execute.
2941 ScalarEvolution::BackedgeTakenInfo
2942 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2943 SmallVector<BasicBlock*, 8> ExitingBlocks;
2944 L->getExitingBlocks(ExitingBlocks);
2946 // Examine all exits and pick the most conservative values.
2947 const SCEV *BECount = getCouldNotCompute();
2948 const SCEV *MaxBECount = getCouldNotCompute();
2949 bool CouldNotComputeBECount = false;
2950 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
2951 BackedgeTakenInfo NewBTI =
2952 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
2954 if (NewBTI.Exact == getCouldNotCompute()) {
2955 // We couldn't compute an exact value for this exit, so
2956 // we won't be able to compute an exact value for the loop.
2957 CouldNotComputeBECount = true;
2958 BECount = getCouldNotCompute();
2959 } else if (!CouldNotComputeBECount) {
2960 if (BECount == getCouldNotCompute())
2961 BECount = NewBTI.Exact;
2963 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
2965 if (MaxBECount == getCouldNotCompute())
2966 MaxBECount = NewBTI.Max;
2967 else if (NewBTI.Max != getCouldNotCompute())
2968 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
2971 return BackedgeTakenInfo(BECount, MaxBECount);
2974 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
2975 /// of the specified loop will execute if it exits via the specified block.
2976 ScalarEvolution::BackedgeTakenInfo
2977 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
2978 BasicBlock *ExitingBlock) {
2980 // Okay, we've chosen an exiting block. See what condition causes us to
2981 // exit at this block.
2983 // FIXME: we should be able to handle switch instructions (with a single exit)
2984 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2985 if (ExitBr == 0) return getCouldNotCompute();
2986 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2988 // At this point, we know we have a conditional branch that determines whether
2989 // the loop is exited. However, we don't know if the branch is executed each
2990 // time through the loop. If not, then the execution count of the branch will
2991 // not be equal to the trip count of the loop.
2993 // Currently we check for this by checking to see if the Exit branch goes to
2994 // the loop header. If so, we know it will always execute the same number of
2995 // times as the loop. We also handle the case where the exit block *is* the
2996 // loop header. This is common for un-rotated loops.
2998 // If both of those tests fail, walk up the unique predecessor chain to the
2999 // header, stopping if there is an edge that doesn't exit the loop. If the
3000 // header is reached, the execution count of the branch will be equal to the
3001 // trip count of the loop.
3003 // More extensive analysis could be done to handle more cases here.
3005 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3006 ExitBr->getSuccessor(1) != L->getHeader() &&
3007 ExitBr->getParent() != L->getHeader()) {
3008 // The simple checks failed, try climbing the unique predecessor chain
3009 // up to the header.
3011 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3012 BasicBlock *Pred = BB->getUniquePredecessor();
3014 return getCouldNotCompute();
3015 TerminatorInst *PredTerm = Pred->getTerminator();
3016 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3017 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3020 // If the predecessor has a successor that isn't BB and isn't
3021 // outside the loop, assume the worst.
3022 if (L->contains(PredSucc))
3023 return getCouldNotCompute();
3025 if (Pred == L->getHeader()) {
3032 return getCouldNotCompute();
3035 // Procede to the next level to examine the exit condition expression.
3036 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3037 ExitBr->getSuccessor(0),
3038 ExitBr->getSuccessor(1));
3041 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3042 /// backedge of the specified loop will execute if its exit condition
3043 /// were a conditional branch of ExitCond, TBB, and FBB.
3044 ScalarEvolution::BackedgeTakenInfo
3045 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3049 // Check if the controlling expression for this loop is an And or Or.
3050 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3051 if (BO->getOpcode() == Instruction::And) {
3052 // Recurse on the operands of the and.
3053 BackedgeTakenInfo BTI0 =
3054 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3055 BackedgeTakenInfo BTI1 =
3056 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3057 const SCEV *BECount = getCouldNotCompute();
3058 const SCEV *MaxBECount = getCouldNotCompute();
3059 if (L->contains(TBB)) {
3060 // Both conditions must be true for the loop to continue executing.
3061 // Choose the less conservative count.
3062 if (BTI0.Exact == getCouldNotCompute() ||
3063 BTI1.Exact == getCouldNotCompute())
3064 BECount = getCouldNotCompute();
3066 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3067 if (BTI0.Max == getCouldNotCompute())
3068 MaxBECount = BTI1.Max;
3069 else if (BTI1.Max == getCouldNotCompute())
3070 MaxBECount = BTI0.Max;
3072 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3074 // Both conditions must be true for the loop to exit.
3075 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3076 if (BTI0.Exact != getCouldNotCompute() &&
3077 BTI1.Exact != getCouldNotCompute())
3078 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3079 if (BTI0.Max != getCouldNotCompute() &&
3080 BTI1.Max != getCouldNotCompute())
3081 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3084 return BackedgeTakenInfo(BECount, MaxBECount);
3086 if (BO->getOpcode() == Instruction::Or) {
3087 // Recurse on the operands of the or.
3088 BackedgeTakenInfo BTI0 =
3089 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3090 BackedgeTakenInfo BTI1 =
3091 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3092 const SCEV *BECount = getCouldNotCompute();
3093 const SCEV *MaxBECount = getCouldNotCompute();
3094 if (L->contains(FBB)) {
3095 // Both conditions must be false for the loop to continue executing.
3096 // Choose the less conservative count.
3097 if (BTI0.Exact == getCouldNotCompute() ||
3098 BTI1.Exact == getCouldNotCompute())
3099 BECount = getCouldNotCompute();
3101 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3102 if (BTI0.Max == getCouldNotCompute())
3103 MaxBECount = BTI1.Max;
3104 else if (BTI1.Max == getCouldNotCompute())
3105 MaxBECount = BTI0.Max;
3107 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3109 // Both conditions must be false for the loop to exit.
3110 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3111 if (BTI0.Exact != getCouldNotCompute() &&
3112 BTI1.Exact != getCouldNotCompute())
3113 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3114 if (BTI0.Max != getCouldNotCompute() &&
3115 BTI1.Max != getCouldNotCompute())
3116 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3119 return BackedgeTakenInfo(BECount, MaxBECount);
3123 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3124 // Procede to the next level to examine the icmp.
3125 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3126 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3128 // If it's not an integer or pointer comparison then compute it the hard way.
3129 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3132 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3133 /// backedge of the specified loop will execute if its exit condition
3134 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3135 ScalarEvolution::BackedgeTakenInfo
3136 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3141 // If the condition was exit on true, convert the condition to exit on false
3142 ICmpInst::Predicate Cond;
3143 if (!L->contains(FBB))
3144 Cond = ExitCond->getPredicate();
3146 Cond = ExitCond->getInversePredicate();
3148 // Handle common loops like: for (X = "string"; *X; ++X)
3149 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3150 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3152 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3153 if (!isa<SCEVCouldNotCompute>(ItCnt)) {
3154 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType());
3155 return BackedgeTakenInfo(ItCnt,
3156 isa<SCEVConstant>(ItCnt) ? ItCnt :
3157 getConstant(APInt::getMaxValue(BitWidth)-1));
3161 const SCEV *LHS = getSCEV(ExitCond->getOperand(0));
3162 const SCEV *RHS = getSCEV(ExitCond->getOperand(1));
3164 // Try to evaluate any dependencies out of the loop.
3165 LHS = getSCEVAtScope(LHS, L);
3166 RHS = getSCEVAtScope(RHS, L);
3168 // At this point, we would like to compute how many iterations of the
3169 // loop the predicate will return true for these inputs.
3170 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3171 // If there is a loop-invariant, force it into the RHS.
3172 std::swap(LHS, RHS);
3173 Cond = ICmpInst::getSwappedPredicate(Cond);
3176 // If we have a comparison of a chrec against a constant, try to use value
3177 // ranges to answer this query.
3178 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3179 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3180 if (AddRec->getLoop() == L) {
3181 // Form the constant range.
3182 ConstantRange CompRange(
3183 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3185 const SCEV *Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3186 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3190 case ICmpInst::ICMP_NE: { // while (X != Y)
3191 // Convert to: while (X-Y != 0)
3192 const SCEV *TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3193 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3196 case ICmpInst::ICMP_EQ: {
3197 // Convert to: while (X-Y == 0) // while (X == Y)
3198 const SCEV *TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3199 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3202 case ICmpInst::ICMP_SLT: {
3203 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3204 if (BTI.hasAnyInfo()) return BTI;
3207 case ICmpInst::ICMP_SGT: {
3208 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3209 getNotSCEV(RHS), L, true);
3210 if (BTI.hasAnyInfo()) return BTI;
3213 case ICmpInst::ICMP_ULT: {
3214 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3215 if (BTI.hasAnyInfo()) return BTI;
3218 case ICmpInst::ICMP_UGT: {
3219 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3220 getNotSCEV(RHS), L, false);
3221 if (BTI.hasAnyInfo()) return BTI;
3226 errs() << "ComputeBackedgeTakenCount ";
3227 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3228 errs() << "[unsigned] ";
3229 errs() << *LHS << " "
3230 << Instruction::getOpcodeName(Instruction::ICmp)
3231 << " " << *RHS << "\n";
3236 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3239 static ConstantInt *
3240 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3241 ScalarEvolution &SE) {
3242 const SCEV *InVal = SE.getConstant(C);
3243 const SCEV *Val = AddRec->evaluateAtIteration(InVal, SE);
3244 assert(isa<SCEVConstant>(Val) &&
3245 "Evaluation of SCEV at constant didn't fold correctly?");
3246 return cast<SCEVConstant>(Val)->getValue();
3249 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3250 /// and a GEP expression (missing the pointer index) indexing into it, return
3251 /// the addressed element of the initializer or null if the index expression is
3254 GetAddressedElementFromGlobal(LLVMContext *Context, GlobalVariable *GV,
3255 const std::vector<ConstantInt*> &Indices) {
3256 Constant *Init = GV->getInitializer();
3257 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3258 uint64_t Idx = Indices[i]->getZExtValue();
3259 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3260 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3261 Init = cast<Constant>(CS->getOperand(Idx));
3262 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3263 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3264 Init = cast<Constant>(CA->getOperand(Idx));
3265 } else if (isa<ConstantAggregateZero>(Init)) {
3266 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3267 assert(Idx < STy->getNumElements() && "Bad struct index!");
3268 Init = Context->getNullValue(STy->getElementType(Idx));
3269 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3270 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3271 Init = Context->getNullValue(ATy->getElementType());
3273 LLVM_UNREACHABLE("Unknown constant aggregate type!");
3277 return 0; // Unknown initializer type
3283 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3284 /// 'icmp op load X, cst', try to see if we can compute the backedge
3285 /// execution count.
3287 ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3291 ICmpInst::Predicate predicate) {
3292 if (LI->isVolatile()) return getCouldNotCompute();
3294 // Check to see if the loaded pointer is a getelementptr of a global.
3295 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3296 if (!GEP) return getCouldNotCompute();
3298 // Make sure that it is really a constant global we are gepping, with an
3299 // initializer, and make sure the first IDX is really 0.
3300 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3301 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
3302 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3303 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3304 return getCouldNotCompute();
3306 // Okay, we allow one non-constant index into the GEP instruction.
3308 std::vector<ConstantInt*> Indexes;
3309 unsigned VarIdxNum = 0;
3310 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3311 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3312 Indexes.push_back(CI);
3313 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3314 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3315 VarIdx = GEP->getOperand(i);
3317 Indexes.push_back(0);
3320 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3321 // Check to see if X is a loop variant variable value now.
3322 const SCEV *Idx = getSCEV(VarIdx);
3323 Idx = getSCEVAtScope(Idx, L);
3325 // We can only recognize very limited forms of loop index expressions, in
3326 // particular, only affine AddRec's like {C1,+,C2}.
3327 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3328 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3329 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3330 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
3331 return getCouldNotCompute();
3333 unsigned MaxSteps = MaxBruteForceIterations;
3334 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3335 ConstantInt *ItCst =
3336 ConstantInt::get(cast<IntegerType>(IdxExpr->getType()), IterationNum);
3337 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
3339 // Form the GEP offset.
3340 Indexes[VarIdxNum] = Val;
3342 Constant *Result = GetAddressedElementFromGlobal(Context, GV, Indexes);
3343 if (Result == 0) break; // Cannot compute!
3345 // Evaluate the condition for this iteration.
3346 Result = ConstantExpr::getICmp(predicate, Result, RHS);
3347 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
3348 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
3350 errs() << "\n***\n*** Computed loop count " << *ItCst
3351 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
3354 ++NumArrayLenItCounts;
3355 return getConstant(ItCst); // Found terminating iteration!
3358 return getCouldNotCompute();
3362 /// CanConstantFold - Return true if we can constant fold an instruction of the
3363 /// specified type, assuming that all operands were constants.
3364 static bool CanConstantFold(const Instruction *I) {
3365 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
3366 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
3369 if (const CallInst *CI = dyn_cast<CallInst>(I))
3370 if (const Function *F = CI->getCalledFunction())
3371 return canConstantFoldCallTo(F);
3375 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
3376 /// in the loop that V is derived from. We allow arbitrary operations along the
3377 /// way, but the operands of an operation must either be constants or a value
3378 /// derived from a constant PHI. If this expression does not fit with these
3379 /// constraints, return null.
3380 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
3381 // If this is not an instruction, or if this is an instruction outside of the
3382 // loop, it can't be derived from a loop PHI.
3383 Instruction *I = dyn_cast<Instruction>(V);
3384 if (I == 0 || !L->contains(I->getParent())) return 0;
3386 if (PHINode *PN = dyn_cast<PHINode>(I)) {
3387 if (L->getHeader() == I->getParent())
3390 // We don't currently keep track of the control flow needed to evaluate
3391 // PHIs, so we cannot handle PHIs inside of loops.
3395 // If we won't be able to constant fold this expression even if the operands
3396 // are constants, return early.
3397 if (!CanConstantFold(I)) return 0;
3399 // Otherwise, we can evaluate this instruction if all of its operands are
3400 // constant or derived from a PHI node themselves.
3402 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
3403 if (!(isa<Constant>(I->getOperand(Op)) ||
3404 isa<GlobalValue>(I->getOperand(Op)))) {
3405 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
3406 if (P == 0) return 0; // Not evolving from PHI
3410 return 0; // Evolving from multiple different PHIs.
3413 // This is a expression evolving from a constant PHI!
3417 /// EvaluateExpression - Given an expression that passes the
3418 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
3419 /// in the loop has the value PHIVal. If we can't fold this expression for some
3420 /// reason, return null.
3421 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
3422 if (isa<PHINode>(V)) return PHIVal;
3423 if (Constant *C = dyn_cast<Constant>(V)) return C;
3424 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
3425 Instruction *I = cast<Instruction>(V);
3426 LLVMContext *Context = I->getParent()->getContext();
3428 std::vector<Constant*> Operands;
3429 Operands.resize(I->getNumOperands());
3431 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3432 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
3433 if (Operands[i] == 0) return 0;
3436 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3437 return ConstantFoldCompareInstOperands(CI->getPredicate(),
3438 &Operands[0], Operands.size(),
3441 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3442 &Operands[0], Operands.size(),
3446 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
3447 /// in the header of its containing loop, we know the loop executes a
3448 /// constant number of times, and the PHI node is just a recurrence
3449 /// involving constants, fold it.
3451 ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
3454 std::map<PHINode*, Constant*>::iterator I =
3455 ConstantEvolutionLoopExitValue.find(PN);
3456 if (I != ConstantEvolutionLoopExitValue.end())
3459 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
3460 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
3462 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
3464 // Since the loop is canonicalized, the PHI node must have two entries. One
3465 // entry must be a constant (coming in from outside of the loop), and the
3466 // second must be derived from the same PHI.
3467 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3468 Constant *StartCST =
3469 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3471 return RetVal = 0; // Must be a constant.
3473 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3474 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3476 return RetVal = 0; // Not derived from same PHI.
3478 // Execute the loop symbolically to determine the exit value.
3479 if (BEs.getActiveBits() >= 32)
3480 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
3482 unsigned NumIterations = BEs.getZExtValue(); // must be in range
3483 unsigned IterationNum = 0;
3484 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
3485 if (IterationNum == NumIterations)
3486 return RetVal = PHIVal; // Got exit value!
3488 // Compute the value of the PHI node for the next iteration.
3489 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3490 if (NextPHI == PHIVal)
3491 return RetVal = NextPHI; // Stopped evolving!
3493 return 0; // Couldn't evaluate!
3498 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
3499 /// constant number of times (the condition evolves only from constants),
3500 /// try to evaluate a few iterations of the loop until we get the exit
3501 /// condition gets a value of ExitWhen (true or false). If we cannot
3502 /// evaluate the trip count of the loop, return getCouldNotCompute().
3504 ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
3507 PHINode *PN = getConstantEvolvingPHI(Cond, L);
3508 if (PN == 0) return getCouldNotCompute();
3510 // Since the loop is canonicalized, the PHI node must have two entries. One
3511 // entry must be a constant (coming in from outside of the loop), and the
3512 // second must be derived from the same PHI.
3513 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3514 Constant *StartCST =
3515 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3516 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
3518 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3519 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3520 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
3522 // Okay, we find a PHI node that defines the trip count of this loop. Execute
3523 // the loop symbolically to determine when the condition gets a value of
3525 unsigned IterationNum = 0;
3526 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
3527 for (Constant *PHIVal = StartCST;
3528 IterationNum != MaxIterations; ++IterationNum) {
3529 ConstantInt *CondVal =
3530 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
3532 // Couldn't symbolically evaluate.
3533 if (!CondVal) return getCouldNotCompute();
3535 if (CondVal->getValue() == uint64_t(ExitWhen)) {
3536 ++NumBruteForceTripCountsComputed;
3537 return getConstant(Type::Int32Ty, IterationNum);
3540 // Compute the value of the PHI node for the next iteration.
3541 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3542 if (NextPHI == 0 || NextPHI == PHIVal)
3543 return getCouldNotCompute();// Couldn't evaluate or not making progress...
3547 // Too many iterations were needed to evaluate.
3548 return getCouldNotCompute();
3551 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
3552 /// at the specified scope in the program. The L value specifies a loop
3553 /// nest to evaluate the expression at, where null is the top-level or a
3554 /// specified loop is immediately inside of the loop.
3556 /// This method can be used to compute the exit value for a variable defined
3557 /// in a loop by querying what the value will hold in the parent loop.
3559 /// In the case that a relevant loop exit value cannot be computed, the
3560 /// original value V is returned.
3561 const SCEV *ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
3562 // FIXME: this should be turned into a virtual method on SCEV!
3564 if (isa<SCEVConstant>(V)) return V;
3566 // If this instruction is evolved from a constant-evolving PHI, compute the
3567 // exit value from the loop without using SCEVs.
3568 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
3569 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
3570 const Loop *LI = (*this->LI)[I->getParent()];
3571 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
3572 if (PHINode *PN = dyn_cast<PHINode>(I))
3573 if (PN->getParent() == LI->getHeader()) {
3574 // Okay, there is no closed form solution for the PHI node. Check
3575 // to see if the loop that contains it has a known backedge-taken
3576 // count. If so, we may be able to force computation of the exit
3578 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(LI);
3579 if (const SCEVConstant *BTCC =
3580 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
3581 // Okay, we know how many times the containing loop executes. If
3582 // this is a constant evolving PHI node, get the final value at
3583 // the specified iteration number.
3584 Constant *RV = getConstantEvolutionLoopExitValue(PN,
3585 BTCC->getValue()->getValue(),
3587 if (RV) return getSCEV(RV);
3591 // Okay, this is an expression that we cannot symbolically evaluate
3592 // into a SCEV. Check to see if it's possible to symbolically evaluate
3593 // the arguments into constants, and if so, try to constant propagate the
3594 // result. This is particularly useful for computing loop exit values.
3595 if (CanConstantFold(I)) {
3596 // Check to see if we've folded this instruction at this loop before.
3597 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
3598 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
3599 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
3601 return Pair.first->second ? &*getSCEV(Pair.first->second) : V;
3603 std::vector<Constant*> Operands;
3604 Operands.reserve(I->getNumOperands());
3605 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3606 Value *Op = I->getOperand(i);
3607 if (Constant *C = dyn_cast<Constant>(Op)) {
3608 Operands.push_back(C);
3610 // If any of the operands is non-constant and if they are
3611 // non-integer and non-pointer, don't even try to analyze them
3612 // with scev techniques.
3613 if (!isSCEVable(Op->getType()))
3616 const SCEV *OpV = getSCEVAtScope(getSCEV(Op), L);
3617 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
3618 Constant *C = SC->getValue();
3619 if (C->getType() != Op->getType())
3620 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3624 Operands.push_back(C);
3625 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
3626 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
3627 if (C->getType() != Op->getType())
3629 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3633 Operands.push_back(C);
3643 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3644 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
3645 &Operands[0], Operands.size(),
3648 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3649 &Operands[0], Operands.size(), Context);
3650 Pair.first->second = C;
3655 // This is some other type of SCEVUnknown, just return it.
3659 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3660 // Avoid performing the look-up in the common case where the specified
3661 // expression has no loop-variant portions.
3662 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3663 const SCEV *OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3664 if (OpAtScope != Comm->getOperand(i)) {
3665 // Okay, at least one of these operands is loop variant but might be
3666 // foldable. Build a new instance of the folded commutative expression.
3667 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
3668 Comm->op_begin()+i);
3669 NewOps.push_back(OpAtScope);
3671 for (++i; i != e; ++i) {
3672 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3673 NewOps.push_back(OpAtScope);
3675 if (isa<SCEVAddExpr>(Comm))
3676 return getAddExpr(NewOps);
3677 if (isa<SCEVMulExpr>(Comm))
3678 return getMulExpr(NewOps);
3679 if (isa<SCEVSMaxExpr>(Comm))
3680 return getSMaxExpr(NewOps);
3681 if (isa<SCEVUMaxExpr>(Comm))
3682 return getUMaxExpr(NewOps);
3683 LLVM_UNREACHABLE("Unknown commutative SCEV type!");
3686 // If we got here, all operands are loop invariant.
3690 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3691 const SCEV *LHS = getSCEVAtScope(Div->getLHS(), L);
3692 const SCEV *RHS = getSCEVAtScope(Div->getRHS(), L);
3693 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3694 return Div; // must be loop invariant
3695 return getUDivExpr(LHS, RHS);
3698 // If this is a loop recurrence for a loop that does not contain L, then we
3699 // are dealing with the final value computed by the loop.
3700 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3701 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3702 // To evaluate this recurrence, we need to know how many times the AddRec
3703 // loop iterates. Compute this now.
3704 const SCEV *BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3705 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
3707 // Then, evaluate the AddRec.
3708 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3713 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3714 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3715 if (Op == Cast->getOperand())
3716 return Cast; // must be loop invariant
3717 return getZeroExtendExpr(Op, Cast->getType());
3720 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3721 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3722 if (Op == Cast->getOperand())
3723 return Cast; // must be loop invariant
3724 return getSignExtendExpr(Op, Cast->getType());
3727 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3728 const SCEV *Op = getSCEVAtScope(Cast->getOperand(), L);
3729 if (Op == Cast->getOperand())
3730 return Cast; // must be loop invariant
3731 return getTruncateExpr(Op, Cast->getType());
3734 LLVM_UNREACHABLE("Unknown SCEV type!");
3738 /// getSCEVAtScope - This is a convenience function which does
3739 /// getSCEVAtScope(getSCEV(V), L).
3740 const SCEV *ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3741 return getSCEVAtScope(getSCEV(V), L);
3744 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3745 /// following equation:
3747 /// A * X = B (mod N)
3749 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3750 /// A and B isn't important.
3752 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3753 static const SCEV *SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3754 ScalarEvolution &SE) {
3755 uint32_t BW = A.getBitWidth();
3756 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3757 assert(A != 0 && "A must be non-zero.");
3761 // The gcd of A and N may have only one prime factor: 2. The number of
3762 // trailing zeros in A is its multiplicity
3763 uint32_t Mult2 = A.countTrailingZeros();
3766 // 2. Check if B is divisible by D.
3768 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3769 // is not less than multiplicity of this prime factor for D.
3770 if (B.countTrailingZeros() < Mult2)
3771 return SE.getCouldNotCompute();
3773 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3776 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3777 // bit width during computations.
3778 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3779 APInt Mod(BW + 1, 0);
3780 Mod.set(BW - Mult2); // Mod = N / D
3781 APInt I = AD.multiplicativeInverse(Mod);
3783 // 4. Compute the minimum unsigned root of the equation:
3784 // I * (B / D) mod (N / D)
3785 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3787 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3789 return SE.getConstant(Result.trunc(BW));
3792 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3793 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
3794 /// might be the same) or two SCEVCouldNotCompute objects.
3796 static std::pair<const SCEV *,const SCEV *>
3797 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
3798 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
3799 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
3800 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
3801 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
3803 // We currently can only solve this if the coefficients are constants.
3804 if (!LC || !MC || !NC) {
3805 const SCEV *CNC = SE.getCouldNotCompute();
3806 return std::make_pair(CNC, CNC);
3809 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
3810 const APInt &L = LC->getValue()->getValue();
3811 const APInt &M = MC->getValue()->getValue();
3812 const APInt &N = NC->getValue()->getValue();
3813 APInt Two(BitWidth, 2);
3814 APInt Four(BitWidth, 4);
3817 using namespace APIntOps;
3819 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
3820 // The B coefficient is M-N/2
3824 // The A coefficient is N/2
3825 APInt A(N.sdiv(Two));
3827 // Compute the B^2-4ac term.
3830 SqrtTerm -= Four * (A * C);
3832 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
3833 // integer value or else APInt::sqrt() will assert.
3834 APInt SqrtVal(SqrtTerm.sqrt());
3836 // Compute the two solutions for the quadratic formula.
3837 // The divisions must be performed as signed divisions.
3839 APInt TwoA( A << 1 );
3840 if (TwoA.isMinValue()) {
3841 const SCEV *CNC = SE.getCouldNotCompute();
3842 return std::make_pair(CNC, CNC);
3845 LLVMContext *Context = SE.getContext();
3847 ConstantInt *Solution1 =
3848 Context->getConstantInt((NegB + SqrtVal).sdiv(TwoA));
3849 ConstantInt *Solution2 =
3850 Context->getConstantInt((NegB - SqrtVal).sdiv(TwoA));
3852 return std::make_pair(SE.getConstant(Solution1),
3853 SE.getConstant(Solution2));
3854 } // end APIntOps namespace
3857 /// HowFarToZero - Return the number of times a backedge comparing the specified
3858 /// value to zero will execute. If not computable, return CouldNotCompute.
3859 const SCEV *ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
3860 // If the value is a constant
3861 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3862 // If the value is already zero, the branch will execute zero times.
3863 if (C->getValue()->isZero()) return C;
3864 return getCouldNotCompute(); // Otherwise it will loop infinitely.
3867 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
3868 if (!AddRec || AddRec->getLoop() != L)
3869 return getCouldNotCompute();
3871 if (AddRec->isAffine()) {
3872 // If this is an affine expression, the execution count of this branch is
3873 // the minimum unsigned root of the following equation:
3875 // Start + Step*N = 0 (mod 2^BW)
3879 // Step*N = -Start (mod 2^BW)
3881 // where BW is the common bit width of Start and Step.
3883 // Get the initial value for the loop.
3884 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
3885 L->getParentLoop());
3886 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
3887 L->getParentLoop());
3889 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
3890 // For now we handle only constant steps.
3892 // First, handle unitary steps.
3893 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
3894 return getNegativeSCEV(Start); // N = -Start (as unsigned)
3895 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
3896 return Start; // N = Start (as unsigned)
3898 // Then, try to solve the above equation provided that Start is constant.
3899 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
3900 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
3901 -StartC->getValue()->getValue(),
3904 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
3905 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
3906 // the quadratic equation to solve it.
3907 std::pair<const SCEV *,const SCEV *> Roots = SolveQuadraticEquation(AddRec,
3909 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3910 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3913 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
3914 << " sol#2: " << *R2 << "\n";
3916 // Pick the smallest positive root value.
3917 if (ConstantInt *CB =
3918 dyn_cast<ConstantInt>(Context->getConstantExprICmp(ICmpInst::ICMP_ULT,
3919 R1->getValue(), R2->getValue()))) {
3920 if (CB->getZExtValue() == false)
3921 std::swap(R1, R2); // R1 is the minimum root now.
3923 // We can only use this value if the chrec ends up with an exact zero
3924 // value at this index. When solving for "X*X != 5", for example, we
3925 // should not accept a root of 2.
3926 const SCEV *Val = AddRec->evaluateAtIteration(R1, *this);
3928 return R1; // We found a quadratic root!
3933 return getCouldNotCompute();
3936 /// HowFarToNonZero - Return the number of times a backedge checking the
3937 /// specified value for nonzero will execute. If not computable, return
3939 const SCEV *ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
3940 // Loops that look like: while (X == 0) are very strange indeed. We don't
3941 // handle them yet except for the trivial case. This could be expanded in the
3942 // future as needed.
3944 // If the value is a constant, check to see if it is known to be non-zero
3945 // already. If so, the backedge will execute zero times.
3946 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3947 if (!C->getValue()->isNullValue())
3948 return getIntegerSCEV(0, C->getType());
3949 return getCouldNotCompute(); // Otherwise it will loop infinitely.
3952 // We could implement others, but I really doubt anyone writes loops like
3953 // this, and if they did, they would already be constant folded.
3954 return getCouldNotCompute();
3957 /// getLoopPredecessor - If the given loop's header has exactly one unique
3958 /// predecessor outside the loop, return it. Otherwise return null.
3960 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
3961 BasicBlock *Header = L->getHeader();
3962 BasicBlock *Pred = 0;
3963 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
3965 if (!L->contains(*PI)) {
3966 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
3972 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3973 /// (which may not be an immediate predecessor) which has exactly one
3974 /// successor from which BB is reachable, or null if no such block is
3978 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3979 // If the block has a unique predecessor, then there is no path from the
3980 // predecessor to the block that does not go through the direct edge
3981 // from the predecessor to the block.
3982 if (BasicBlock *Pred = BB->getSinglePredecessor())
3985 // A loop's header is defined to be a block that dominates the loop.
3986 // If the header has a unique predecessor outside the loop, it must be
3987 // a block that has exactly one successor that can reach the loop.
3988 if (Loop *L = LI->getLoopFor(BB))
3989 return getLoopPredecessor(L);
3994 /// HasSameValue - SCEV structural equivalence is usually sufficient for
3995 /// testing whether two expressions are equal, however for the purposes of
3996 /// looking for a condition guarding a loop, it can be useful to be a little
3997 /// more general, since a front-end may have replicated the controlling
4000 static bool HasSameValue(const SCEV *A, const SCEV *B) {
4001 // Quick check to see if they are the same SCEV.
4002 if (A == B) return true;
4004 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
4005 // two different instructions with the same value. Check for this case.
4006 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
4007 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
4008 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
4009 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
4010 if (AI->isIdenticalTo(BI))
4013 // Otherwise assume they may have a different value.
4017 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
4018 /// a conditional between LHS and RHS. This is used to help avoid max
4019 /// expressions in loop trip counts.
4020 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
4021 ICmpInst::Predicate Pred,
4022 const SCEV *LHS, const SCEV *RHS) {
4023 // Interpret a null as meaning no loop, where there is obviously no guard
4024 // (interprocedural conditions notwithstanding).
4025 if (!L) return false;
4027 BasicBlock *Predecessor = getLoopPredecessor(L);
4028 BasicBlock *PredecessorDest = L->getHeader();
4030 // Starting at the loop predecessor, climb up the predecessor chain, as long
4031 // as there are predecessors that can be found that have unique successors
4032 // leading to the original header.
4034 PredecessorDest = Predecessor,
4035 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4037 BranchInst *LoopEntryPredicate =
4038 dyn_cast<BranchInst>(Predecessor->getTerminator());
4039 if (!LoopEntryPredicate ||
4040 LoopEntryPredicate->isUnconditional())
4043 if (isNecessaryCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4044 LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4051 /// isNecessaryCond - Test whether the given CondValue value is a condition
4052 /// which is at least as strict as the one described by Pred, LHS, and RHS.
4053 bool ScalarEvolution::isNecessaryCond(Value *CondValue,
4054 ICmpInst::Predicate Pred,
4055 const SCEV *LHS, const SCEV *RHS,
4057 // Recursivly handle And and Or conditions.
4058 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4059 if (BO->getOpcode() == Instruction::And) {
4061 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4062 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4063 } else if (BO->getOpcode() == Instruction::Or) {
4065 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4066 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4070 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4071 if (!ICI) return false;
4073 // Now that we found a conditional branch that dominates the loop, check to
4074 // see if it is the comparison we are looking for.
4075 Value *PreCondLHS = ICI->getOperand(0);
4076 Value *PreCondRHS = ICI->getOperand(1);
4077 ICmpInst::Predicate Cond;
4079 Cond = ICI->getInversePredicate();
4081 Cond = ICI->getPredicate();
4084 ; // An exact match.
4085 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
4086 ; // The actual condition is beyond sufficient.
4088 // Check a few special cases.
4090 case ICmpInst::ICMP_UGT:
4091 if (Pred == ICmpInst::ICMP_ULT) {
4092 std::swap(PreCondLHS, PreCondRHS);
4093 Cond = ICmpInst::ICMP_ULT;
4097 case ICmpInst::ICMP_SGT:
4098 if (Pred == ICmpInst::ICMP_SLT) {
4099 std::swap(PreCondLHS, PreCondRHS);
4100 Cond = ICmpInst::ICMP_SLT;
4104 case ICmpInst::ICMP_NE:
4105 // Expressions like (x >u 0) are often canonicalized to (x != 0),
4106 // so check for this case by checking if the NE is comparing against
4107 // a minimum or maximum constant.
4108 if (!ICmpInst::isTrueWhenEqual(Pred))
4109 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
4110 const APInt &A = CI->getValue();
4112 case ICmpInst::ICMP_SLT:
4113 if (A.isMaxSignedValue()) break;
4115 case ICmpInst::ICMP_SGT:
4116 if (A.isMinSignedValue()) break;
4118 case ICmpInst::ICMP_ULT:
4119 if (A.isMaxValue()) break;
4121 case ICmpInst::ICMP_UGT:
4122 if (A.isMinValue()) break;
4127 Cond = ICmpInst::ICMP_NE;
4128 // NE is symmetric but the original comparison may not be. Swap
4129 // the operands if necessary so that they match below.
4130 if (isa<SCEVConstant>(LHS))
4131 std::swap(PreCondLHS, PreCondRHS);
4136 // We weren't able to reconcile the condition.
4140 if (!PreCondLHS->getType()->isInteger()) return false;
4142 const SCEV *PreCondLHSSCEV = getSCEV(PreCondLHS);
4143 const SCEV *PreCondRHSSCEV = getSCEV(PreCondRHS);
4144 return (HasSameValue(LHS, PreCondLHSSCEV) &&
4145 HasSameValue(RHS, PreCondRHSSCEV)) ||
4146 (HasSameValue(LHS, getNotSCEV(PreCondRHSSCEV)) &&
4147 HasSameValue(RHS, getNotSCEV(PreCondLHSSCEV)));
4150 /// getBECount - Subtract the end and start values and divide by the step,
4151 /// rounding up, to get the number of times the backedge is executed. Return
4152 /// CouldNotCompute if an intermediate computation overflows.
4153 const SCEV *ScalarEvolution::getBECount(const SCEV *Start,
4156 const Type *Ty = Start->getType();
4157 const SCEV *NegOne = getIntegerSCEV(-1, Ty);
4158 const SCEV *Diff = getMinusSCEV(End, Start);
4159 const SCEV *RoundUp = getAddExpr(Step, NegOne);
4161 // Add an adjustment to the difference between End and Start so that
4162 // the division will effectively round up.
4163 const SCEV *Add = getAddExpr(Diff, RoundUp);
4165 // Check Add for unsigned overflow.
4166 // TODO: More sophisticated things could be done here.
4167 const Type *WideTy = Context->getIntegerType(getTypeSizeInBits(Ty) + 1);
4168 const SCEV *OperandExtendedAdd =
4169 getAddExpr(getZeroExtendExpr(Diff, WideTy),
4170 getZeroExtendExpr(RoundUp, WideTy));
4171 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
4172 return getCouldNotCompute();
4174 return getUDivExpr(Add, Step);
4177 /// HowManyLessThans - Return the number of times a backedge containing the
4178 /// specified less-than comparison will execute. If not computable, return
4179 /// CouldNotCompute.
4180 ScalarEvolution::BackedgeTakenInfo
4181 ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
4182 const Loop *L, bool isSigned) {
4183 // Only handle: "ADDREC < LoopInvariant".
4184 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
4186 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
4187 if (!AddRec || AddRec->getLoop() != L)
4188 return getCouldNotCompute();
4190 if (AddRec->isAffine()) {
4191 // FORNOW: We only support unit strides.
4192 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
4193 const SCEV *Step = AddRec->getStepRecurrence(*this);
4195 // TODO: handle non-constant strides.
4196 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
4197 if (!CStep || CStep->isZero())
4198 return getCouldNotCompute();
4199 if (CStep->isOne()) {
4200 // With unit stride, the iteration never steps past the limit value.
4201 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
4202 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
4203 // Test whether a positive iteration iteration can step past the limit
4204 // value and past the maximum value for its type in a single step.
4206 APInt Max = APInt::getSignedMaxValue(BitWidth);
4207 if ((Max - CStep->getValue()->getValue())
4208 .slt(CLimit->getValue()->getValue()))
4209 return getCouldNotCompute();
4211 APInt Max = APInt::getMaxValue(BitWidth);
4212 if ((Max - CStep->getValue()->getValue())
4213 .ult(CLimit->getValue()->getValue()))
4214 return getCouldNotCompute();
4217 // TODO: handle non-constant limit values below.
4218 return getCouldNotCompute();
4220 // TODO: handle negative strides below.
4221 return getCouldNotCompute();
4223 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
4224 // m. So, we count the number of iterations in which {n,+,s} < m is true.
4225 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
4226 // treat m-n as signed nor unsigned due to overflow possibility.
4228 // First, we get the value of the LHS in the first iteration: n
4229 const SCEV *Start = AddRec->getOperand(0);
4231 // Determine the minimum constant start value.
4232 const SCEV *MinStart = isa<SCEVConstant>(Start) ? Start :
4233 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
4234 APInt::getMinValue(BitWidth));
4236 // If we know that the condition is true in order to enter the loop,
4237 // then we know that it will run exactly (m-n)/s times. Otherwise, we
4238 // only know that it will execute (max(m,n)-n)/s times. In both cases,
4239 // the division must round up.
4240 const SCEV *End = RHS;
4241 if (!isLoopGuardedByCond(L,
4242 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
4243 getMinusSCEV(Start, Step), RHS))
4244 End = isSigned ? getSMaxExpr(RHS, Start)
4245 : getUMaxExpr(RHS, Start);
4247 // Determine the maximum constant end value.
4248 const SCEV *MaxEnd =
4249 isa<SCEVConstant>(End) ? End :
4250 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth)
4251 .ashr(GetMinSignBits(End) - 1) :
4252 APInt::getMaxValue(BitWidth)
4253 .lshr(GetMinLeadingZeros(End)));
4255 // Finally, we subtract these two values and divide, rounding up, to get
4256 // the number of times the backedge is executed.
4257 const SCEV *BECount = getBECount(Start, End, Step);
4259 // The maximum backedge count is similar, except using the minimum start
4260 // value and the maximum end value.
4261 const SCEV *MaxBECount = getBECount(MinStart, MaxEnd, Step);
4263 return BackedgeTakenInfo(BECount, MaxBECount);
4266 return getCouldNotCompute();
4269 /// getNumIterationsInRange - Return the number of iterations of this loop that
4270 /// produce values in the specified constant range. Another way of looking at
4271 /// this is that it returns the first iteration number where the value is not in
4272 /// the condition, thus computing the exit count. If the iteration count can't
4273 /// be computed, an instance of SCEVCouldNotCompute is returned.
4274 const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
4275 ScalarEvolution &SE) const {
4276 if (Range.isFullSet()) // Infinite loop.
4277 return SE.getCouldNotCompute();
4279 // If the start is a non-zero constant, shift the range to simplify things.
4280 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
4281 if (!SC->getValue()->isZero()) {
4282 SmallVector<const SCEV *, 4> Operands(op_begin(), op_end());
4283 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
4284 const SCEV *Shifted = SE.getAddRecExpr(Operands, getLoop());
4285 if (const SCEVAddRecExpr *ShiftedAddRec =
4286 dyn_cast<SCEVAddRecExpr>(Shifted))
4287 return ShiftedAddRec->getNumIterationsInRange(
4288 Range.subtract(SC->getValue()->getValue()), SE);
4289 // This is strange and shouldn't happen.
4290 return SE.getCouldNotCompute();
4293 // The only time we can solve this is when we have all constant indices.
4294 // Otherwise, we cannot determine the overflow conditions.
4295 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
4296 if (!isa<SCEVConstant>(getOperand(i)))
4297 return SE.getCouldNotCompute();
4300 // Okay at this point we know that all elements of the chrec are constants and
4301 // that the start element is zero.
4303 // First check to see if the range contains zero. If not, the first
4305 unsigned BitWidth = SE.getTypeSizeInBits(getType());
4306 if (!Range.contains(APInt(BitWidth, 0)))
4307 return SE.getIntegerSCEV(0, getType());
4310 // If this is an affine expression then we have this situation:
4311 // Solve {0,+,A} in Range === Ax in Range
4313 // We know that zero is in the range. If A is positive then we know that
4314 // the upper value of the range must be the first possible exit value.
4315 // If A is negative then the lower of the range is the last possible loop
4316 // value. Also note that we already checked for a full range.
4317 APInt One(BitWidth,1);
4318 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
4319 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
4321 // The exit value should be (End+A)/A.
4322 APInt ExitVal = (End + A).udiv(A);
4323 ConstantInt *ExitValue = SE.getContext()->getConstantInt(ExitVal);
4325 // Evaluate at the exit value. If we really did fall out of the valid
4326 // range, then we computed our trip count, otherwise wrap around or other
4327 // things must have happened.
4328 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
4329 if (Range.contains(Val->getValue()))
4330 return SE.getCouldNotCompute(); // Something strange happened
4332 // Ensure that the previous value is in the range. This is a sanity check.
4333 assert(Range.contains(
4334 EvaluateConstantChrecAtConstant(this,
4335 SE.getContext()->getConstantInt(ExitVal - One), SE)->getValue()) &&
4336 "Linear scev computation is off in a bad way!");
4337 return SE.getConstant(ExitValue);
4338 } else if (isQuadratic()) {
4339 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
4340 // quadratic equation to solve it. To do this, we must frame our problem in
4341 // terms of figuring out when zero is crossed, instead of when
4342 // Range.getUpper() is crossed.
4343 SmallVector<const SCEV *, 4> NewOps(op_begin(), op_end());
4344 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
4345 const SCEV *NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
4347 // Next, solve the constructed addrec
4348 std::pair<const SCEV *,const SCEV *> Roots =
4349 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
4350 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4351 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4353 // Pick the smallest positive root value.
4354 if (ConstantInt *CB =
4355 dyn_cast<ConstantInt>(
4356 SE.getContext()->getConstantExprICmp(ICmpInst::ICMP_ULT,
4357 R1->getValue(), R2->getValue()))) {
4358 if (CB->getZExtValue() == false)
4359 std::swap(R1, R2); // R1 is the minimum root now.
4361 // Make sure the root is not off by one. The returned iteration should
4362 // not be in the range, but the previous one should be. When solving
4363 // for "X*X < 5", for example, we should not return a root of 2.
4364 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
4367 if (Range.contains(R1Val->getValue())) {
4368 // The next iteration must be out of the range...
4369 ConstantInt *NextVal =
4370 SE.getContext()->getConstantInt(R1->getValue()->getValue()+1);
4372 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4373 if (!Range.contains(R1Val->getValue()))
4374 return SE.getConstant(NextVal);
4375 return SE.getCouldNotCompute(); // Something strange happened
4378 // If R1 was not in the range, then it is a good return value. Make
4379 // sure that R1-1 WAS in the range though, just in case.
4380 ConstantInt *NextVal =
4381 SE.getContext()->getConstantInt(R1->getValue()->getValue()-1);
4382 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4383 if (Range.contains(R1Val->getValue()))
4385 return SE.getCouldNotCompute(); // Something strange happened
4390 return SE.getCouldNotCompute();
4395 //===----------------------------------------------------------------------===//
4396 // SCEVCallbackVH Class Implementation
4397 //===----------------------------------------------------------------------===//
4399 void ScalarEvolution::SCEVCallbackVH::deleted() {
4400 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
4401 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
4402 SE->ConstantEvolutionLoopExitValue.erase(PN);
4403 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
4404 SE->ValuesAtScopes.erase(I);
4405 SE->Scalars.erase(getValPtr());
4406 // this now dangles!
4409 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
4410 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
4412 // Forget all the expressions associated with users of the old value,
4413 // so that future queries will recompute the expressions using the new
4415 SmallVector<User *, 16> Worklist;
4416 Value *Old = getValPtr();
4417 bool DeleteOld = false;
4418 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
4420 Worklist.push_back(*UI);
4421 while (!Worklist.empty()) {
4422 User *U = Worklist.pop_back_val();
4423 // Deleting the Old value will cause this to dangle. Postpone
4424 // that until everything else is done.
4429 if (PHINode *PN = dyn_cast<PHINode>(U))
4430 SE->ConstantEvolutionLoopExitValue.erase(PN);
4431 if (Instruction *I = dyn_cast<Instruction>(U))
4432 SE->ValuesAtScopes.erase(I);
4433 if (SE->Scalars.erase(U))
4434 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
4436 Worklist.push_back(*UI);
4439 if (PHINode *PN = dyn_cast<PHINode>(Old))
4440 SE->ConstantEvolutionLoopExitValue.erase(PN);
4441 if (Instruction *I = dyn_cast<Instruction>(Old))
4442 SE->ValuesAtScopes.erase(I);
4443 SE->Scalars.erase(Old);
4444 // this now dangles!
4449 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
4450 : CallbackVH(V), SE(se) {}
4452 //===----------------------------------------------------------------------===//
4453 // ScalarEvolution Class Implementation
4454 //===----------------------------------------------------------------------===//
4456 ScalarEvolution::ScalarEvolution()
4457 : FunctionPass(&ID) {
4460 bool ScalarEvolution::runOnFunction(Function &F) {
4462 LI = &getAnalysis<LoopInfo>();
4463 TD = getAnalysisIfAvailable<TargetData>();
4467 void ScalarEvolution::releaseMemory() {
4469 BackedgeTakenCounts.clear();
4470 ConstantEvolutionLoopExitValue.clear();
4471 ValuesAtScopes.clear();
4472 UniqueSCEVs.clear();
4473 SCEVAllocator.Reset();
4476 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
4477 AU.setPreservesAll();
4478 AU.addRequiredTransitive<LoopInfo>();
4481 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
4482 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
4485 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
4487 // Print all inner loops first
4488 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4489 PrintLoopInfo(OS, SE, *I);
4491 OS << "Loop " << L->getHeader()->getName() << ": ";
4493 SmallVector<BasicBlock*, 8> ExitBlocks;
4494 L->getExitBlocks(ExitBlocks);
4495 if (ExitBlocks.size() != 1)
4496 OS << "<multiple exits> ";
4498 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
4499 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
4501 OS << "Unpredictable backedge-taken count. ";
4505 OS << "Loop " << L->getHeader()->getName() << ": ";
4507 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
4508 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
4510 OS << "Unpredictable max backedge-taken count. ";
4516 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
4517 // ScalarEvolution's implementaiton of the print method is to print
4518 // out SCEV values of all instructions that are interesting. Doing
4519 // this potentially causes it to create new SCEV objects though,
4520 // which technically conflicts with the const qualifier. This isn't
4521 // observable from outside the class though, so casting away the
4522 // const isn't dangerous.
4523 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
4525 OS << "Classifying expressions for: " << F->getName() << "\n";
4526 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
4527 if (isSCEVable(I->getType())) {
4530 const SCEV *SV = SE.getSCEV(&*I);
4533 const Loop *L = LI->getLoopFor((*I).getParent());
4535 const SCEV *AtUse = SE.getSCEVAtScope(SV, L);
4542 OS << "\t\t" "Exits: ";
4543 const SCEV *ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
4544 if (!ExitValue->isLoopInvariant(L)) {
4545 OS << "<<Unknown>>";
4554 OS << "Determining loop execution counts for: " << F->getName() << "\n";
4555 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
4556 PrintLoopInfo(OS, &SE, *I);
4559 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
4560 raw_os_ostream OS(o);