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 SCEVHandle
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/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/Dominators.h"
70 #include "llvm/Analysis/LoopInfo.h"
71 #include "llvm/Assembly/Writer.h"
72 #include "llvm/Target/TargetData.h"
73 #include "llvm/Transforms/Scalar.h"
74 #include "llvm/Support/CFG.h"
75 #include "llvm/Support/CommandLine.h"
76 #include "llvm/Support/Compiler.h"
77 #include "llvm/Support/ConstantRange.h"
78 #include "llvm/Support/GetElementPtrTypeIterator.h"
79 #include "llvm/Support/InstIterator.h"
80 #include "llvm/Support/ManagedStatic.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"
90 STATISTIC(NumArrayLenItCounts,
91 "Number of trip counts computed with array length");
92 STATISTIC(NumTripCountsComputed,
93 "Number of loops with predictable loop counts");
94 STATISTIC(NumTripCountsNotComputed,
95 "Number of loops without predictable loop counts");
96 STATISTIC(NumBruteForceTripCountsComputed,
97 "Number of loops with trip counts computed by force");
99 static cl::opt<unsigned>
100 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
101 cl::desc("Maximum number of iterations SCEV will "
102 "symbolically execute a constant derived loop"),
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.
117 void SCEV::dump() const {
122 void SCEV::print(std::ostream &o) const {
123 raw_os_ostream OS(o);
127 bool SCEV::isZero() const {
128 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
129 return SC->getValue()->isZero();
134 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
135 SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
137 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
138 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
142 const Type *SCEVCouldNotCompute::getType() const {
143 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
147 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
148 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
152 SCEVHandle SCEVCouldNotCompute::
153 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
154 const SCEVHandle &Conc,
155 ScalarEvolution &SE) const {
159 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
160 OS << "***COULDNOTCOMPUTE***";
163 bool SCEVCouldNotCompute::classof(const SCEV *S) {
164 return S->getSCEVType() == scCouldNotCompute;
168 // SCEVConstants - Only allow the creation of one SCEVConstant for any
169 // particular value. Don't use a SCEVHandle here, or else the object will
171 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
174 SCEVConstant::~SCEVConstant() {
175 SCEVConstants->erase(V);
178 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
179 SCEVConstant *&R = (*SCEVConstants)[V];
180 if (R == 0) R = new SCEVConstant(V);
184 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
185 return getConstant(ConstantInt::get(Val));
188 const Type *SCEVConstant::getType() const { return V->getType(); }
190 void SCEVConstant::print(raw_ostream &OS) const {
191 WriteAsOperand(OS, V, false);
194 SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
195 const SCEVHandle &op, const Type *ty)
196 : SCEV(SCEVTy), Op(op), Ty(ty) {}
198 SCEVCastExpr::~SCEVCastExpr() {}
200 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
201 return Op->dominates(BB, DT);
204 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
205 // particular input. Don't use a SCEVHandle here, or else the object will
207 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
208 SCEVTruncateExpr*> > SCEVTruncates;
210 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
211 : SCEVCastExpr(scTruncate, op, ty) {
212 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
213 (Ty->isInteger() || isa<PointerType>(Ty)) &&
214 "Cannot truncate non-integer value!");
217 SCEVTruncateExpr::~SCEVTruncateExpr() {
218 SCEVTruncates->erase(std::make_pair(Op, Ty));
221 void SCEVTruncateExpr::print(raw_ostream &OS) const {
222 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
225 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
226 // particular input. Don't use a SCEVHandle here, or else the object will never
228 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
229 SCEVZeroExtendExpr*> > SCEVZeroExtends;
231 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
232 : SCEVCastExpr(scZeroExtend, op, ty) {
233 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
234 (Ty->isInteger() || isa<PointerType>(Ty)) &&
235 "Cannot zero extend non-integer value!");
238 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
239 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
242 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
243 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
246 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
247 // particular input. Don't use a SCEVHandle here, or else the object will never
249 static ManagedStatic<std::map<std::pair<SCEV*, const Type*>,
250 SCEVSignExtendExpr*> > SCEVSignExtends;
252 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
253 : SCEVCastExpr(scSignExtend, op, ty) {
254 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
255 (Ty->isInteger() || isa<PointerType>(Ty)) &&
256 "Cannot sign extend non-integer value!");
259 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
260 SCEVSignExtends->erase(std::make_pair(Op, Ty));
263 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
264 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
267 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
268 // particular input. Don't use a SCEVHandle here, or else the object will never
270 static ManagedStatic<std::map<std::pair<unsigned, std::vector<SCEV*> >,
271 SCEVCommutativeExpr*> > SCEVCommExprs;
273 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
274 SCEVCommExprs->erase(std::make_pair(getSCEVType(),
275 std::vector<SCEV*>(Operands.begin(),
279 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
280 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
281 const char *OpStr = getOperationStr();
282 OS << "(" << *Operands[0];
283 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
284 OS << OpStr << *Operands[i];
288 SCEVHandle SCEVCommutativeExpr::
289 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
290 const SCEVHandle &Conc,
291 ScalarEvolution &SE) const {
292 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
294 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
295 if (H != getOperand(i)) {
296 std::vector<SCEVHandle> NewOps;
297 NewOps.reserve(getNumOperands());
298 for (unsigned j = 0; j != i; ++j)
299 NewOps.push_back(getOperand(j));
301 for (++i; i != e; ++i)
302 NewOps.push_back(getOperand(i)->
303 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
305 if (isa<SCEVAddExpr>(this))
306 return SE.getAddExpr(NewOps);
307 else if (isa<SCEVMulExpr>(this))
308 return SE.getMulExpr(NewOps);
309 else if (isa<SCEVSMaxExpr>(this))
310 return SE.getSMaxExpr(NewOps);
311 else if (isa<SCEVUMaxExpr>(this))
312 return SE.getUMaxExpr(NewOps);
314 assert(0 && "Unknown commutative expr!");
320 bool SCEVCommutativeExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
321 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
322 if (!getOperand(i)->dominates(BB, DT))
329 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
330 // input. Don't use a SCEVHandle here, or else the object will never be
332 static ManagedStatic<std::map<std::pair<SCEV*, SCEV*>,
333 SCEVUDivExpr*> > SCEVUDivs;
335 SCEVUDivExpr::~SCEVUDivExpr() {
336 SCEVUDivs->erase(std::make_pair(LHS, RHS));
339 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
340 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
343 void SCEVUDivExpr::print(raw_ostream &OS) const {
344 OS << "(" << *LHS << " /u " << *RHS << ")";
347 const Type *SCEVUDivExpr::getType() const {
348 return LHS->getType();
351 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
352 // particular input. Don't use a SCEVHandle here, or else the object will never
354 static ManagedStatic<std::map<std::pair<const Loop *, std::vector<SCEV*> >,
355 SCEVAddRecExpr*> > SCEVAddRecExprs;
357 SCEVAddRecExpr::~SCEVAddRecExpr() {
358 SCEVAddRecExprs->erase(std::make_pair(L,
359 std::vector<SCEV*>(Operands.begin(),
363 bool SCEVAddRecExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
364 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
365 if (!getOperand(i)->dominates(BB, DT))
372 SCEVHandle SCEVAddRecExpr::
373 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
374 const SCEVHandle &Conc,
375 ScalarEvolution &SE) const {
376 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
378 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
379 if (H != getOperand(i)) {
380 std::vector<SCEVHandle> NewOps;
381 NewOps.reserve(getNumOperands());
382 for (unsigned j = 0; j != i; ++j)
383 NewOps.push_back(getOperand(j));
385 for (++i; i != e; ++i)
386 NewOps.push_back(getOperand(i)->
387 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
389 return SE.getAddRecExpr(NewOps, L);
396 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
397 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
398 // contain L and if the start is invariant.
399 return !QueryLoop->contains(L->getHeader()) &&
400 getOperand(0)->isLoopInvariant(QueryLoop);
404 void SCEVAddRecExpr::print(raw_ostream &OS) const {
405 OS << "{" << *Operands[0];
406 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
407 OS << ",+," << *Operands[i];
408 OS << "}<" << L->getHeader()->getName() + ">";
411 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
412 // value. Don't use a SCEVHandle here, or else the object will never be
414 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
416 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
418 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
419 // All non-instruction values are loop invariant. All instructions are loop
420 // invariant if they are not contained in the specified loop.
421 if (Instruction *I = dyn_cast<Instruction>(V))
422 return !L->contains(I->getParent());
426 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
427 if (Instruction *I = dyn_cast<Instruction>(getValue()))
428 return DT->dominates(I->getParent(), BB);
432 const Type *SCEVUnknown::getType() const {
436 void SCEVUnknown::print(raw_ostream &OS) const {
437 if (isa<PointerType>(V->getType()))
438 OS << "(ptrtoint " << *V->getType() << " ";
439 WriteAsOperand(OS, V, false);
440 if (isa<PointerType>(V->getType()))
444 //===----------------------------------------------------------------------===//
446 //===----------------------------------------------------------------------===//
449 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
450 /// than the complexity of the RHS. This comparator is used to canonicalize
452 struct VISIBILITY_HIDDEN SCEVComplexityCompare {
453 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
454 return LHS->getSCEVType() < RHS->getSCEVType();
459 /// GroupByComplexity - Given a list of SCEV objects, order them by their
460 /// complexity, and group objects of the same complexity together by value.
461 /// When this routine is finished, we know that any duplicates in the vector are
462 /// consecutive and that complexity is monotonically increasing.
464 /// Note that we go take special precautions to ensure that we get determinstic
465 /// results from this routine. In other words, we don't want the results of
466 /// this to depend on where the addresses of various SCEV objects happened to
469 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
470 if (Ops.size() < 2) return; // Noop
471 if (Ops.size() == 2) {
472 // This is the common case, which also happens to be trivially simple.
474 if (SCEVComplexityCompare()(Ops[1], Ops[0]))
475 std::swap(Ops[0], Ops[1]);
479 // Do the rough sort by complexity.
480 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
482 // Now that we are sorted by complexity, group elements of the same
483 // complexity. Note that this is, at worst, N^2, but the vector is likely to
484 // be extremely short in practice. Note that we take this approach because we
485 // do not want to depend on the addresses of the objects we are grouping.
486 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
488 unsigned Complexity = S->getSCEVType();
490 // If there are any objects of the same complexity and same value as this
492 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
493 if (Ops[j] == S) { // Found a duplicate.
494 // Move it to immediately after i'th element.
495 std::swap(Ops[i+1], Ops[j]);
496 ++i; // no need to rescan it.
497 if (i == e-2) return; // Done!
505 //===----------------------------------------------------------------------===//
506 // Simple SCEV method implementations
507 //===----------------------------------------------------------------------===//
509 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
511 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
513 const Type* ResultTy) {
514 // Handle the simplest case efficiently.
516 return SE.getTruncateOrZeroExtend(It, ResultTy);
518 // We are using the following formula for BC(It, K):
520 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
522 // Suppose, W is the bitwidth of the return value. We must be prepared for
523 // overflow. Hence, we must assure that the result of our computation is
524 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
525 // safe in modular arithmetic.
527 // However, this code doesn't use exactly that formula; the formula it uses
528 // is something like the following, where T is the number of factors of 2 in
529 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
532 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
534 // This formula is trivially equivalent to the previous formula. However,
535 // this formula can be implemented much more efficiently. The trick is that
536 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
537 // arithmetic. To do exact division in modular arithmetic, all we have
538 // to do is multiply by the inverse. Therefore, this step can be done at
541 // The next issue is how to safely do the division by 2^T. The way this
542 // is done is by doing the multiplication step at a width of at least W + T
543 // bits. This way, the bottom W+T bits of the product are accurate. Then,
544 // when we perform the division by 2^T (which is equivalent to a right shift
545 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
546 // truncated out after the division by 2^T.
548 // In comparison to just directly using the first formula, this technique
549 // is much more efficient; using the first formula requires W * K bits,
550 // but this formula less than W + K bits. Also, the first formula requires
551 // a division step, whereas this formula only requires multiplies and shifts.
553 // It doesn't matter whether the subtraction step is done in the calculation
554 // width or the input iteration count's width; if the subtraction overflows,
555 // the result must be zero anyway. We prefer here to do it in the width of
556 // the induction variable because it helps a lot for certain cases; CodeGen
557 // isn't smart enough to ignore the overflow, which leads to much less
558 // efficient code if the width of the subtraction is wider than the native
561 // (It's possible to not widen at all by pulling out factors of 2 before
562 // the multiplication; for example, K=2 can be calculated as
563 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
564 // extra arithmetic, so it's not an obvious win, and it gets
565 // much more complicated for K > 3.)
567 // Protection from insane SCEVs; this bound is conservative,
568 // but it probably doesn't matter.
570 return SE.getCouldNotCompute();
572 unsigned W = SE.getTypeSizeInBits(ResultTy);
574 // Calculate K! / 2^T and T; we divide out the factors of two before
575 // multiplying for calculating K! / 2^T to avoid overflow.
576 // Other overflow doesn't matter because we only care about the bottom
577 // W bits of the result.
578 APInt OddFactorial(W, 1);
580 for (unsigned i = 3; i <= K; ++i) {
582 unsigned TwoFactors = Mult.countTrailingZeros();
584 Mult = Mult.lshr(TwoFactors);
585 OddFactorial *= Mult;
588 // We need at least W + T bits for the multiplication step
589 unsigned CalculationBits = W + T;
591 // Calcuate 2^T, at width T+W.
592 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
594 // Calculate the multiplicative inverse of K! / 2^T;
595 // this multiplication factor will perform the exact division by
597 APInt Mod = APInt::getSignedMinValue(W+1);
598 APInt MultiplyFactor = OddFactorial.zext(W+1);
599 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
600 MultiplyFactor = MultiplyFactor.trunc(W);
602 // Calculate the product, at width T+W
603 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
604 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
605 for (unsigned i = 1; i != K; ++i) {
606 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
607 Dividend = SE.getMulExpr(Dividend,
608 SE.getTruncateOrZeroExtend(S, CalculationTy));
612 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
614 // Truncate the result, and divide by K! / 2^T.
616 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
617 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
620 /// evaluateAtIteration - Return the value of this chain of recurrences at
621 /// the specified iteration number. We can evaluate this recurrence by
622 /// multiplying each element in the chain by the binomial coefficient
623 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
625 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
627 /// where BC(It, k) stands for binomial coefficient.
629 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
630 ScalarEvolution &SE) const {
631 SCEVHandle Result = getStart();
632 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
633 // The computation is correct in the face of overflow provided that the
634 // multiplication is performed _after_ the evaluation of the binomial
636 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
637 if (isa<SCEVCouldNotCompute>(Coeff))
640 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
645 //===----------------------------------------------------------------------===//
646 // SCEV Expression folder implementations
647 //===----------------------------------------------------------------------===//
649 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op, const Type *Ty) {
650 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
651 "This is not a truncating conversion!");
653 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
655 ConstantExpr::getTrunc(SC->getValue(), Ty));
657 // trunc(trunc(x)) --> trunc(x)
658 if (SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
659 return getTruncateExpr(ST->getOperand(), Ty);
661 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
662 if (SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
663 return getTruncateOrSignExtend(SS->getOperand(), Ty);
665 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
666 if (SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
667 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
669 // If the input value is a chrec scev made out of constants, truncate
670 // all of the constants.
671 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
672 std::vector<SCEVHandle> Operands;
673 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
674 // FIXME: This should allow truncation of other expression types!
675 if (isa<SCEVConstant>(AddRec->getOperand(i)))
676 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
679 if (Operands.size() == AddRec->getNumOperands())
680 return getAddRecExpr(Operands, AddRec->getLoop());
683 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
684 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
688 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
690 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
691 "This is not an extending conversion!");
693 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
694 const Type *IntTy = getEffectiveSCEVType(Ty);
695 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
696 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
697 return getUnknown(C);
700 // zext(zext(x)) --> zext(x)
701 if (SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
702 return getZeroExtendExpr(SZ->getOperand(), Ty);
704 // If the input value is a chrec scev, and we can prove that the value
705 // did not overflow the old, smaller, value, we can zero extend all of the
706 // operands (often constants). This allows analysis of something like
707 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
708 if (SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
709 if (AR->isAffine()) {
710 // Check whether the backedge-taken count is SCEVCouldNotCompute.
711 // Note that this serves two purposes: It filters out loops that are
712 // simply not analyzable, and it covers the case where this code is
713 // being called from within backedge-taken count analysis, such that
714 // attempting to ask for the backedge-taken count would likely result
715 // in infinite recursion. In the later case, the analysis code will
716 // cope with a conservative value, and it will take care to purge
717 // that value once it has finished.
718 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
719 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
720 // Manually compute the final value for AR, checking for
722 SCEVHandle Start = AR->getStart();
723 SCEVHandle Step = AR->getStepRecurrence(*this);
725 // Check whether the backedge-taken count can be losslessly casted to
726 // the addrec's type. The count is always unsigned.
727 SCEVHandle CastedMaxBECount =
728 getTruncateOrZeroExtend(MaxBECount, Start->getType());
730 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) {
732 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
733 // Check whether Start+Step*MaxBECount has no unsigned overflow.
735 getMulExpr(CastedMaxBECount,
736 getTruncateOrZeroExtend(Step, Start->getType()));
737 SCEVHandle Add = getAddExpr(Start, ZMul);
738 if (getZeroExtendExpr(Add, WideTy) ==
739 getAddExpr(getZeroExtendExpr(Start, WideTy),
740 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
741 getZeroExtendExpr(Step, WideTy))))
742 // Return the expression with the addrec on the outside.
743 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
744 getZeroExtendExpr(Step, Ty),
747 // Similar to above, only this time treat the step value as signed.
748 // This covers loops that count down.
750 getMulExpr(CastedMaxBECount,
751 getTruncateOrSignExtend(Step, Start->getType()));
752 Add = getAddExpr(Start, SMul);
753 if (getZeroExtendExpr(Add, WideTy) ==
754 getAddExpr(getZeroExtendExpr(Start, WideTy),
755 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
756 getSignExtendExpr(Step, WideTy))))
757 // Return the expression with the addrec on the outside.
758 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
759 getSignExtendExpr(Step, Ty),
765 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
766 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
770 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
772 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
773 "This is not an extending conversion!");
775 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
776 const Type *IntTy = getEffectiveSCEVType(Ty);
777 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
778 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
779 return getUnknown(C);
782 // sext(sext(x)) --> sext(x)
783 if (SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
784 return getSignExtendExpr(SS->getOperand(), Ty);
786 // If the input value is a chrec scev, and we can prove that the value
787 // did not overflow the old, smaller, value, we can sign extend all of the
788 // operands (often constants). This allows analysis of something like
789 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
790 if (SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
791 if (AR->isAffine()) {
792 // Check whether the backedge-taken count is SCEVCouldNotCompute.
793 // Note that this serves two purposes: It filters out loops that are
794 // simply not analyzable, and it covers the case where this code is
795 // being called from within backedge-taken count analysis, such that
796 // attempting to ask for the backedge-taken count would likely result
797 // in infinite recursion. In the later case, the analysis code will
798 // cope with a conservative value, and it will take care to purge
799 // that value once it has finished.
800 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
801 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
802 // Manually compute the final value for AR, checking for
804 SCEVHandle Start = AR->getStart();
805 SCEVHandle Step = AR->getStepRecurrence(*this);
807 // Check whether the backedge-taken count can be losslessly casted to
808 // the addrec's type. The count is always unsigned.
809 SCEVHandle CastedMaxBECount =
810 getTruncateOrZeroExtend(MaxBECount, Start->getType());
812 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) {
814 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
815 // Check whether Start+Step*MaxBECount has no signed overflow.
817 getMulExpr(CastedMaxBECount,
818 getTruncateOrSignExtend(Step, Start->getType()));
819 SCEVHandle Add = getAddExpr(Start, SMul);
820 if (getSignExtendExpr(Add, WideTy) ==
821 getAddExpr(getSignExtendExpr(Start, WideTy),
822 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
823 getSignExtendExpr(Step, WideTy))))
824 // Return the expression with the addrec on the outside.
825 return getAddRecExpr(getSignExtendExpr(Start, Ty),
826 getSignExtendExpr(Step, Ty),
832 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
833 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
837 // get - Get a canonical add expression, or something simpler if possible.
838 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
839 assert(!Ops.empty() && "Cannot get empty add!");
840 if (Ops.size() == 1) return Ops[0];
842 // Sort by complexity, this groups all similar expression types together.
843 GroupByComplexity(Ops);
845 // If there are any constants, fold them together.
847 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
849 assert(Idx < Ops.size());
850 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
851 // We found two constants, fold them together!
852 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
853 RHSC->getValue()->getValue());
854 Ops[0] = getConstant(Fold);
855 Ops.erase(Ops.begin()+1); // Erase the folded element
856 if (Ops.size() == 1) return Ops[0];
857 LHSC = cast<SCEVConstant>(Ops[0]);
860 // If we are left with a constant zero being added, strip it off.
861 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
862 Ops.erase(Ops.begin());
867 if (Ops.size() == 1) return Ops[0];
869 // Okay, check to see if the same value occurs in the operand list twice. If
870 // so, merge them together into an multiply expression. Since we sorted the
871 // list, these values are required to be adjacent.
872 const Type *Ty = Ops[0]->getType();
873 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
874 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
875 // Found a match, merge the two values into a multiply, and add any
876 // remaining values to the result.
877 SCEVHandle Two = getIntegerSCEV(2, Ty);
878 SCEVHandle Mul = getMulExpr(Ops[i], Two);
881 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
883 return getAddExpr(Ops);
886 // Now we know the first non-constant operand. Skip past any cast SCEVs.
887 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
890 // If there are add operands they would be next.
891 if (Idx < Ops.size()) {
892 bool DeletedAdd = false;
893 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
894 // If we have an add, expand the add operands onto the end of the operands
896 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
897 Ops.erase(Ops.begin()+Idx);
901 // If we deleted at least one add, we added operands to the end of the list,
902 // and they are not necessarily sorted. Recurse to resort and resimplify
903 // any operands we just aquired.
905 return getAddExpr(Ops);
908 // Skip over the add expression until we get to a multiply.
909 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
912 // If we are adding something to a multiply expression, make sure the
913 // something is not already an operand of the multiply. If so, merge it into
915 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
916 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
917 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
918 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
919 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
920 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
921 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
922 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
923 if (Mul->getNumOperands() != 2) {
924 // If the multiply has more than two operands, we must get the
926 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
927 MulOps.erase(MulOps.begin()+MulOp);
928 InnerMul = getMulExpr(MulOps);
930 SCEVHandle One = getIntegerSCEV(1, Ty);
931 SCEVHandle AddOne = getAddExpr(InnerMul, One);
932 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
933 if (Ops.size() == 2) return OuterMul;
935 Ops.erase(Ops.begin()+AddOp);
936 Ops.erase(Ops.begin()+Idx-1);
938 Ops.erase(Ops.begin()+Idx);
939 Ops.erase(Ops.begin()+AddOp-1);
941 Ops.push_back(OuterMul);
942 return getAddExpr(Ops);
945 // Check this multiply against other multiplies being added together.
946 for (unsigned OtherMulIdx = Idx+1;
947 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
949 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
950 // If MulOp occurs in OtherMul, we can fold the two multiplies
952 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
953 OMulOp != e; ++OMulOp)
954 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
955 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
956 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
957 if (Mul->getNumOperands() != 2) {
958 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
959 MulOps.erase(MulOps.begin()+MulOp);
960 InnerMul1 = getMulExpr(MulOps);
962 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
963 if (OtherMul->getNumOperands() != 2) {
964 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
966 MulOps.erase(MulOps.begin()+OMulOp);
967 InnerMul2 = getMulExpr(MulOps);
969 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
970 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
971 if (Ops.size() == 2) return OuterMul;
972 Ops.erase(Ops.begin()+Idx);
973 Ops.erase(Ops.begin()+OtherMulIdx-1);
974 Ops.push_back(OuterMul);
975 return getAddExpr(Ops);
981 // If there are any add recurrences in the operands list, see if any other
982 // added values are loop invariant. If so, we can fold them into the
984 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
987 // Scan over all recurrences, trying to fold loop invariants into them.
988 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
989 // Scan all of the other operands to this add and add them to the vector if
990 // they are loop invariant w.r.t. the recurrence.
991 std::vector<SCEVHandle> LIOps;
992 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
993 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
994 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
995 LIOps.push_back(Ops[i]);
996 Ops.erase(Ops.begin()+i);
1000 // If we found some loop invariants, fold them into the recurrence.
1001 if (!LIOps.empty()) {
1002 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1003 LIOps.push_back(AddRec->getStart());
1005 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
1006 AddRecOps[0] = getAddExpr(LIOps);
1008 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1009 // If all of the other operands were loop invariant, we are done.
1010 if (Ops.size() == 1) return NewRec;
1012 // Otherwise, add the folded AddRec by the non-liv parts.
1013 for (unsigned i = 0;; ++i)
1014 if (Ops[i] == AddRec) {
1018 return getAddExpr(Ops);
1021 // Okay, if there weren't any loop invariants to be folded, check to see if
1022 // there are multiple AddRec's with the same loop induction variable being
1023 // added together. If so, we can fold them.
1024 for (unsigned OtherIdx = Idx+1;
1025 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1026 if (OtherIdx != Idx) {
1027 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1028 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1029 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1030 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
1031 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1032 if (i >= NewOps.size()) {
1033 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1034 OtherAddRec->op_end());
1037 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1039 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1041 if (Ops.size() == 2) return NewAddRec;
1043 Ops.erase(Ops.begin()+Idx);
1044 Ops.erase(Ops.begin()+OtherIdx-1);
1045 Ops.push_back(NewAddRec);
1046 return getAddExpr(Ops);
1050 // Otherwise couldn't fold anything into this recurrence. Move onto the
1054 // Okay, it looks like we really DO need an add expr. Check to see if we
1055 // already have one, otherwise create a new one.
1056 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1057 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
1059 if (Result == 0) Result = new SCEVAddExpr(Ops);
1064 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
1065 assert(!Ops.empty() && "Cannot get empty mul!");
1067 // Sort by complexity, this groups all similar expression types together.
1068 GroupByComplexity(Ops);
1070 // If there are any constants, fold them together.
1072 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1074 // C1*(C2+V) -> C1*C2 + C1*V
1075 if (Ops.size() == 2)
1076 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1077 if (Add->getNumOperands() == 2 &&
1078 isa<SCEVConstant>(Add->getOperand(0)))
1079 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1080 getMulExpr(LHSC, Add->getOperand(1)));
1084 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1085 // We found two constants, fold them together!
1086 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1087 RHSC->getValue()->getValue());
1088 Ops[0] = getConstant(Fold);
1089 Ops.erase(Ops.begin()+1); // Erase the folded element
1090 if (Ops.size() == 1) return Ops[0];
1091 LHSC = cast<SCEVConstant>(Ops[0]);
1094 // If we are left with a constant one being multiplied, strip it off.
1095 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1096 Ops.erase(Ops.begin());
1098 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1099 // If we have a multiply of zero, it will always be zero.
1104 // Skip over the add expression until we get to a multiply.
1105 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1108 if (Ops.size() == 1)
1111 // If there are mul operands inline them all into this expression.
1112 if (Idx < Ops.size()) {
1113 bool DeletedMul = false;
1114 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1115 // If we have an mul, expand the mul operands onto the end of the operands
1117 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1118 Ops.erase(Ops.begin()+Idx);
1122 // If we deleted at least one mul, we added operands to the end of the list,
1123 // and they are not necessarily sorted. Recurse to resort and resimplify
1124 // any operands we just aquired.
1126 return getMulExpr(Ops);
1129 // If there are any add recurrences in the operands list, see if any other
1130 // added values are loop invariant. If so, we can fold them into the
1132 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1135 // Scan over all recurrences, trying to fold loop invariants into them.
1136 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1137 // Scan all of the other operands to this mul and add them to the vector if
1138 // they are loop invariant w.r.t. the recurrence.
1139 std::vector<SCEVHandle> LIOps;
1140 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1141 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1142 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1143 LIOps.push_back(Ops[i]);
1144 Ops.erase(Ops.begin()+i);
1148 // If we found some loop invariants, fold them into the recurrence.
1149 if (!LIOps.empty()) {
1150 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1151 std::vector<SCEVHandle> NewOps;
1152 NewOps.reserve(AddRec->getNumOperands());
1153 if (LIOps.size() == 1) {
1154 SCEV *Scale = LIOps[0];
1155 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1156 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1158 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1159 std::vector<SCEVHandle> MulOps(LIOps);
1160 MulOps.push_back(AddRec->getOperand(i));
1161 NewOps.push_back(getMulExpr(MulOps));
1165 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1167 // If all of the other operands were loop invariant, we are done.
1168 if (Ops.size() == 1) return NewRec;
1170 // Otherwise, multiply the folded AddRec by the non-liv parts.
1171 for (unsigned i = 0;; ++i)
1172 if (Ops[i] == AddRec) {
1176 return getMulExpr(Ops);
1179 // Okay, if there weren't any loop invariants to be folded, check to see if
1180 // there are multiple AddRec's with the same loop induction variable being
1181 // multiplied together. If so, we can fold them.
1182 for (unsigned OtherIdx = Idx+1;
1183 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1184 if (OtherIdx != Idx) {
1185 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1186 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1187 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1188 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1189 SCEVHandle NewStart = getMulExpr(F->getStart(),
1191 SCEVHandle B = F->getStepRecurrence(*this);
1192 SCEVHandle D = G->getStepRecurrence(*this);
1193 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1196 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1198 if (Ops.size() == 2) return NewAddRec;
1200 Ops.erase(Ops.begin()+Idx);
1201 Ops.erase(Ops.begin()+OtherIdx-1);
1202 Ops.push_back(NewAddRec);
1203 return getMulExpr(Ops);
1207 // Otherwise couldn't fold anything into this recurrence. Move onto the
1211 // Okay, it looks like we really DO need an mul expr. Check to see if we
1212 // already have one, otherwise create a new one.
1213 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1214 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1217 Result = new SCEVMulExpr(Ops);
1221 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS, const SCEVHandle &RHS) {
1222 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1223 if (RHSC->getValue()->equalsInt(1))
1224 return LHS; // X udiv 1 --> x
1226 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1227 Constant *LHSCV = LHSC->getValue();
1228 Constant *RHSCV = RHSC->getValue();
1229 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1233 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
1235 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1236 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1241 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1242 /// specified loop. Simplify the expression as much as possible.
1243 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1244 const SCEVHandle &Step, const Loop *L) {
1245 std::vector<SCEVHandle> Operands;
1246 Operands.push_back(Start);
1247 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1248 if (StepChrec->getLoop() == L) {
1249 Operands.insert(Operands.end(), StepChrec->op_begin(),
1250 StepChrec->op_end());
1251 return getAddRecExpr(Operands, L);
1254 Operands.push_back(Step);
1255 return getAddRecExpr(Operands, L);
1258 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1259 /// specified loop. Simplify the expression as much as possible.
1260 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1262 if (Operands.size() == 1) return Operands[0];
1264 if (Operands.back()->isZero()) {
1265 Operands.pop_back();
1266 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1269 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1270 if (SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1271 const Loop* NestedLoop = NestedAR->getLoop();
1272 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1273 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1274 NestedAR->op_end());
1275 SCEVHandle NestedARHandle(NestedAR);
1276 Operands[0] = NestedAR->getStart();
1277 NestedOperands[0] = getAddRecExpr(Operands, L);
1278 return getAddRecExpr(NestedOperands, NestedLoop);
1282 SCEVAddRecExpr *&Result =
1283 (*SCEVAddRecExprs)[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
1285 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1289 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1290 const SCEVHandle &RHS) {
1291 std::vector<SCEVHandle> Ops;
1294 return getSMaxExpr(Ops);
1297 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1298 assert(!Ops.empty() && "Cannot get empty smax!");
1299 if (Ops.size() == 1) return Ops[0];
1301 // Sort by complexity, this groups all similar expression types together.
1302 GroupByComplexity(Ops);
1304 // If there are any constants, fold them together.
1306 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1308 assert(Idx < Ops.size());
1309 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1310 // We found two constants, fold them together!
1311 ConstantInt *Fold = ConstantInt::get(
1312 APIntOps::smax(LHSC->getValue()->getValue(),
1313 RHSC->getValue()->getValue()));
1314 Ops[0] = getConstant(Fold);
1315 Ops.erase(Ops.begin()+1); // Erase the folded element
1316 if (Ops.size() == 1) return Ops[0];
1317 LHSC = cast<SCEVConstant>(Ops[0]);
1320 // If we are left with a constant -inf, strip it off.
1321 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1322 Ops.erase(Ops.begin());
1327 if (Ops.size() == 1) return Ops[0];
1329 // Find the first SMax
1330 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1333 // Check to see if one of the operands is an SMax. If so, expand its operands
1334 // onto our operand list, and recurse to simplify.
1335 if (Idx < Ops.size()) {
1336 bool DeletedSMax = false;
1337 while (SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1338 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1339 Ops.erase(Ops.begin()+Idx);
1344 return getSMaxExpr(Ops);
1347 // Okay, check to see if the same value occurs in the operand list twice. If
1348 // so, delete one. Since we sorted the list, these values are required to
1350 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1351 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1352 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1356 if (Ops.size() == 1) return Ops[0];
1358 assert(!Ops.empty() && "Reduced smax down to nothing!");
1360 // Okay, it looks like we really DO need an smax expr. Check to see if we
1361 // already have one, otherwise create a new one.
1362 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1363 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1365 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1369 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1370 const SCEVHandle &RHS) {
1371 std::vector<SCEVHandle> Ops;
1374 return getUMaxExpr(Ops);
1377 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1378 assert(!Ops.empty() && "Cannot get empty umax!");
1379 if (Ops.size() == 1) return Ops[0];
1381 // Sort by complexity, this groups all similar expression types together.
1382 GroupByComplexity(Ops);
1384 // If there are any constants, fold them together.
1386 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1388 assert(Idx < Ops.size());
1389 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1390 // We found two constants, fold them together!
1391 ConstantInt *Fold = ConstantInt::get(
1392 APIntOps::umax(LHSC->getValue()->getValue(),
1393 RHSC->getValue()->getValue()));
1394 Ops[0] = getConstant(Fold);
1395 Ops.erase(Ops.begin()+1); // Erase the folded element
1396 if (Ops.size() == 1) return Ops[0];
1397 LHSC = cast<SCEVConstant>(Ops[0]);
1400 // If we are left with a constant zero, strip it off.
1401 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1402 Ops.erase(Ops.begin());
1407 if (Ops.size() == 1) return Ops[0];
1409 // Find the first UMax
1410 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1413 // Check to see if one of the operands is a UMax. If so, expand its operands
1414 // onto our operand list, and recurse to simplify.
1415 if (Idx < Ops.size()) {
1416 bool DeletedUMax = false;
1417 while (SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1418 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1419 Ops.erase(Ops.begin()+Idx);
1424 return getUMaxExpr(Ops);
1427 // Okay, check to see if the same value occurs in the operand list twice. If
1428 // so, delete one. Since we sorted the list, these values are required to
1430 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1431 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1432 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1436 if (Ops.size() == 1) return Ops[0];
1438 assert(!Ops.empty() && "Reduced umax down to nothing!");
1440 // Okay, it looks like we really DO need a umax expr. Check to see if we
1441 // already have one, otherwise create a new one.
1442 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
1443 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1445 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1449 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1450 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1451 return getConstant(CI);
1452 if (isa<ConstantPointerNull>(V))
1453 return getIntegerSCEV(0, V->getType());
1454 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1455 if (Result == 0) Result = new SCEVUnknown(V);
1459 //===----------------------------------------------------------------------===//
1460 // Basic SCEV Analysis and PHI Idiom Recognition Code
1463 /// deleteValueFromRecords - This method should be called by the
1464 /// client before it removes an instruction from the program, to make sure
1465 /// that no dangling references are left around.
1466 void ScalarEvolution::deleteValueFromRecords(Value *V) {
1467 SmallVector<Value *, 16> Worklist;
1469 if (Scalars.erase(V)) {
1470 if (PHINode *PN = dyn_cast<PHINode>(V))
1471 ConstantEvolutionLoopExitValue.erase(PN);
1472 Worklist.push_back(V);
1475 while (!Worklist.empty()) {
1476 Value *VV = Worklist.back();
1477 Worklist.pop_back();
1479 for (Instruction::use_iterator UI = VV->use_begin(), UE = VV->use_end();
1481 Instruction *Inst = cast<Instruction>(*UI);
1482 if (Scalars.erase(Inst)) {
1483 if (PHINode *PN = dyn_cast<PHINode>(VV))
1484 ConstantEvolutionLoopExitValue.erase(PN);
1485 Worklist.push_back(Inst);
1491 /// isSCEVable - Test if values of the given type are analyzable within
1492 /// the SCEV framework. This primarily includes integer types, and it
1493 /// can optionally include pointer types if the ScalarEvolution class
1494 /// has access to target-specific information.
1495 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1496 // Integers are always SCEVable.
1497 if (Ty->isInteger())
1500 // Pointers are SCEVable if TargetData information is available
1501 // to provide pointer size information.
1502 if (isa<PointerType>(Ty))
1505 // Otherwise it's not SCEVable.
1509 /// getTypeSizeInBits - Return the size in bits of the specified type,
1510 /// for which isSCEVable must return true.
1511 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1512 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1514 // If we have a TargetData, use it!
1516 return TD->getTypeSizeInBits(Ty);
1518 // Otherwise, we support only integer types.
1519 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1520 return Ty->getPrimitiveSizeInBits();
1523 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1524 /// the given type and which represents how SCEV will treat the given
1525 /// type, for which isSCEVable must return true. For pointer types,
1526 /// this is the pointer-sized integer type.
1527 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1528 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1530 if (Ty->isInteger())
1533 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1534 return TD->getIntPtrType();
1537 SCEVHandle ScalarEvolution::getCouldNotCompute() {
1538 return UnknownValue;
1541 // hasSCEV - Return true if the SCEV for this value has already been
1543 bool ScalarEvolution::hasSCEV(Value *V) const {
1544 return Scalars.count(V);
1547 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1548 /// expression and create a new one.
1549 SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1550 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1552 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1553 if (I != Scalars.end()) return I->second;
1554 SCEVHandle S = createSCEV(V);
1555 Scalars.insert(std::make_pair(V, S));
1559 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1560 /// specified signed integer value and return a SCEV for the constant.
1561 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1562 Ty = getEffectiveSCEVType(Ty);
1565 C = Constant::getNullValue(Ty);
1566 else if (Ty->isFloatingPoint())
1567 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1568 APFloat::IEEEdouble, Val));
1570 C = ConstantInt::get(Ty, Val);
1571 return getUnknown(C);
1574 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1576 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1577 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1578 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1580 const Type *Ty = V->getType();
1581 Ty = getEffectiveSCEVType(Ty);
1582 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1585 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1586 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1587 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1588 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1590 const Type *Ty = V->getType();
1591 Ty = getEffectiveSCEVType(Ty);
1592 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1593 return getMinusSCEV(AllOnes, V);
1596 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1598 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1599 const SCEVHandle &RHS) {
1601 return getAddExpr(LHS, getNegativeSCEV(RHS));
1604 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1605 /// input value to the specified type. If the type must be extended, it is zero
1608 ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1610 const Type *SrcTy = V->getType();
1611 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1612 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1613 "Cannot truncate or zero extend with non-integer arguments!");
1614 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1615 return V; // No conversion
1616 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1617 return getTruncateExpr(V, Ty);
1618 return getZeroExtendExpr(V, Ty);
1621 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1622 /// input value to the specified type. If the type must be extended, it is sign
1625 ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1627 const Type *SrcTy = V->getType();
1628 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1629 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1630 "Cannot truncate or zero extend with non-integer arguments!");
1631 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1632 return V; // No conversion
1633 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1634 return getTruncateExpr(V, Ty);
1635 return getSignExtendExpr(V, Ty);
1638 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1639 /// the specified instruction and replaces any references to the symbolic value
1640 /// SymName with the specified value. This is used during PHI resolution.
1641 void ScalarEvolution::
1642 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1643 const SCEVHandle &NewVal) {
1644 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1645 if (SI == Scalars.end()) return;
1648 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
1649 if (NV == SI->second) return; // No change.
1651 SI->second = NV; // Update the scalars map!
1653 // Any instruction values that use this instruction might also need to be
1655 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1657 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1660 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1661 /// a loop header, making it a potential recurrence, or it doesn't.
1663 SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
1664 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1665 if (const Loop *L = LI->getLoopFor(PN->getParent()))
1666 if (L->getHeader() == PN->getParent()) {
1667 // If it lives in the loop header, it has two incoming values, one
1668 // from outside the loop, and one from inside.
1669 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1670 unsigned BackEdge = IncomingEdge^1;
1672 // While we are analyzing this PHI node, handle its value symbolically.
1673 SCEVHandle SymbolicName = getUnknown(PN);
1674 assert(Scalars.find(PN) == Scalars.end() &&
1675 "PHI node already processed?");
1676 Scalars.insert(std::make_pair(PN, SymbolicName));
1678 // Using this symbolic name for the PHI, analyze the value coming around
1680 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1682 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1683 // has a special value for the first iteration of the loop.
1685 // If the value coming around the backedge is an add with the symbolic
1686 // value we just inserted, then we found a simple induction variable!
1687 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1688 // If there is a single occurrence of the symbolic value, replace it
1689 // with a recurrence.
1690 unsigned FoundIndex = Add->getNumOperands();
1691 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1692 if (Add->getOperand(i) == SymbolicName)
1693 if (FoundIndex == e) {
1698 if (FoundIndex != Add->getNumOperands()) {
1699 // Create an add with everything but the specified operand.
1700 std::vector<SCEVHandle> Ops;
1701 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1702 if (i != FoundIndex)
1703 Ops.push_back(Add->getOperand(i));
1704 SCEVHandle Accum = getAddExpr(Ops);
1706 // This is not a valid addrec if the step amount is varying each
1707 // loop iteration, but is not itself an addrec in this loop.
1708 if (Accum->isLoopInvariant(L) ||
1709 (isa<SCEVAddRecExpr>(Accum) &&
1710 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1711 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1712 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
1714 // Okay, for the entire analysis of this edge we assumed the PHI
1715 // to be symbolic. We now need to go back and update all of the
1716 // entries for the scalars that use the PHI (except for the PHI
1717 // itself) to use the new analyzed value instead of the "symbolic"
1719 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1723 } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
1724 // Otherwise, this could be a loop like this:
1725 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1726 // In this case, j = {1,+,1} and BEValue is j.
1727 // Because the other in-value of i (0) fits the evolution of BEValue
1728 // i really is an addrec evolution.
1729 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1730 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1732 // If StartVal = j.start - j.stride, we can use StartVal as the
1733 // initial step of the addrec evolution.
1734 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
1735 AddRec->getOperand(1))) {
1736 SCEVHandle PHISCEV =
1737 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
1739 // Okay, for the entire analysis of this edge we assumed the PHI
1740 // to be symbolic. We now need to go back and update all of the
1741 // entries for the scalars that use the PHI (except for the PHI
1742 // itself) to use the new analyzed value instead of the "symbolic"
1744 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1750 return SymbolicName;
1753 // If it's not a loop phi, we can't handle it yet.
1754 return getUnknown(PN);
1757 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
1758 /// guaranteed to end in (at every loop iteration). It is, at the same time,
1759 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
1760 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
1761 static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
1762 if (SCEVConstant *C = dyn_cast<SCEVConstant>(S))
1763 return C->getValue()->getValue().countTrailingZeros();
1765 if (SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1766 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
1767 (uint32_t)SE.getTypeSizeInBits(T->getType()));
1769 if (SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
1770 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1771 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1772 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
1775 if (SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
1776 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1777 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1778 SE.getTypeSizeInBits(E->getOperand()->getType()) : OpRes;
1781 if (SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1782 // The result is the min of all operands results.
1783 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
1784 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1785 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
1789 if (SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
1790 // The result is the sum of all operands results.
1791 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1792 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
1793 for (unsigned i = 1, e = M->getNumOperands();
1794 SumOpRes != BitWidth && i != e; ++i)
1795 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
1800 if (SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
1801 // The result is the min of all operands results.
1802 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
1803 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
1804 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
1808 if (SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
1809 // The result is the min of all operands results.
1810 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1811 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1812 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
1816 if (SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
1817 // The result is the min of all operands results.
1818 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
1819 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
1820 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
1824 // SCEVUDivExpr, SCEVUnknown
1828 /// createSCEV - We know that there is no SCEV for the specified value.
1829 /// Analyze the expression.
1831 SCEVHandle ScalarEvolution::createSCEV(Value *V) {
1832 if (!isSCEVable(V->getType()))
1833 return getUnknown(V);
1835 unsigned Opcode = Instruction::UserOp1;
1836 if (Instruction *I = dyn_cast<Instruction>(V))
1837 Opcode = I->getOpcode();
1838 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
1839 Opcode = CE->getOpcode();
1841 return getUnknown(V);
1843 User *U = cast<User>(V);
1845 case Instruction::Add:
1846 return getAddExpr(getSCEV(U->getOperand(0)),
1847 getSCEV(U->getOperand(1)));
1848 case Instruction::Mul:
1849 return getMulExpr(getSCEV(U->getOperand(0)),
1850 getSCEV(U->getOperand(1)));
1851 case Instruction::UDiv:
1852 return getUDivExpr(getSCEV(U->getOperand(0)),
1853 getSCEV(U->getOperand(1)));
1854 case Instruction::Sub:
1855 return getMinusSCEV(getSCEV(U->getOperand(0)),
1856 getSCEV(U->getOperand(1)));
1857 case Instruction::And:
1858 // For an expression like x&255 that merely masks off the high bits,
1859 // use zext(trunc(x)) as the SCEV expression.
1860 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1861 if (CI->isNullValue())
1862 return getSCEV(U->getOperand(1));
1863 if (CI->isAllOnesValue())
1864 return getSCEV(U->getOperand(0));
1865 const APInt &A = CI->getValue();
1866 unsigned Ones = A.countTrailingOnes();
1867 if (APIntOps::isMask(Ones, A))
1869 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
1870 IntegerType::get(Ones)),
1874 case Instruction::Or:
1875 // If the RHS of the Or is a constant, we may have something like:
1876 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
1877 // optimizations will transparently handle this case.
1879 // In order for this transformation to be safe, the LHS must be of the
1880 // form X*(2^n) and the Or constant must be less than 2^n.
1881 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1882 SCEVHandle LHS = getSCEV(U->getOperand(0));
1883 const APInt &CIVal = CI->getValue();
1884 if (GetMinTrailingZeros(LHS, *this) >=
1885 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
1886 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
1889 case Instruction::Xor:
1890 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
1891 // If the RHS of the xor is a signbit, then this is just an add.
1892 // Instcombine turns add of signbit into xor as a strength reduction step.
1893 if (CI->getValue().isSignBit())
1894 return getAddExpr(getSCEV(U->getOperand(0)),
1895 getSCEV(U->getOperand(1)));
1897 // If the RHS of xor is -1, then this is a not operation.
1898 else if (CI->isAllOnesValue())
1899 return getNotSCEV(getSCEV(U->getOperand(0)));
1903 case Instruction::Shl:
1904 // Turn shift left of a constant amount into a multiply.
1905 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1906 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1907 Constant *X = ConstantInt::get(
1908 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1909 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1913 case Instruction::LShr:
1914 // Turn logical shift right of a constant into a unsigned divide.
1915 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
1916 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
1917 Constant *X = ConstantInt::get(
1918 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
1919 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
1923 case Instruction::AShr:
1924 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
1925 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
1926 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
1927 if (L->getOpcode() == Instruction::Shl &&
1928 L->getOperand(1) == U->getOperand(1)) {
1929 unsigned BitWidth = getTypeSizeInBits(U->getType());
1930 uint64_t Amt = BitWidth - CI->getZExtValue();
1931 if (Amt == BitWidth)
1932 return getSCEV(L->getOperand(0)); // shift by zero --> noop
1934 return getIntegerSCEV(0, U->getType()); // value is undefined
1936 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
1937 IntegerType::get(Amt)),
1942 case Instruction::Trunc:
1943 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
1945 case Instruction::ZExt:
1946 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1948 case Instruction::SExt:
1949 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
1951 case Instruction::BitCast:
1952 // BitCasts are no-op casts so we just eliminate the cast.
1953 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
1954 return getSCEV(U->getOperand(0));
1957 case Instruction::IntToPtr:
1958 if (!TD) break; // Without TD we can't analyze pointers.
1959 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
1960 TD->getIntPtrType());
1962 case Instruction::PtrToInt:
1963 if (!TD) break; // Without TD we can't analyze pointers.
1964 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
1967 case Instruction::GetElementPtr: {
1968 if (!TD) break; // Without TD we can't analyze pointers.
1969 const Type *IntPtrTy = TD->getIntPtrType();
1970 Value *Base = U->getOperand(0);
1971 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
1972 gep_type_iterator GTI = gep_type_begin(U);
1973 for (GetElementPtrInst::op_iterator I = next(U->op_begin()),
1977 // Compute the (potentially symbolic) offset in bytes for this index.
1978 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
1979 // For a struct, add the member offset.
1980 const StructLayout &SL = *TD->getStructLayout(STy);
1981 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
1982 uint64_t Offset = SL.getElementOffset(FieldNo);
1983 TotalOffset = getAddExpr(TotalOffset,
1984 getIntegerSCEV(Offset, IntPtrTy));
1986 // For an array, add the element offset, explicitly scaled.
1987 SCEVHandle LocalOffset = getSCEV(Index);
1988 if (!isa<PointerType>(LocalOffset->getType()))
1989 // Getelementptr indicies are signed.
1990 LocalOffset = getTruncateOrSignExtend(LocalOffset,
1993 getMulExpr(LocalOffset,
1994 getIntegerSCEV(TD->getTypePaddedSize(*GTI),
1996 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
1999 return getAddExpr(getSCEV(Base), TotalOffset);
2002 case Instruction::PHI:
2003 return createNodeForPHI(cast<PHINode>(U));
2005 case Instruction::Select:
2006 // This could be a smax or umax that was lowered earlier.
2007 // Try to recover it.
2008 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2009 Value *LHS = ICI->getOperand(0);
2010 Value *RHS = ICI->getOperand(1);
2011 switch (ICI->getPredicate()) {
2012 case ICmpInst::ICMP_SLT:
2013 case ICmpInst::ICMP_SLE:
2014 std::swap(LHS, RHS);
2016 case ICmpInst::ICMP_SGT:
2017 case ICmpInst::ICMP_SGE:
2018 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2019 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2020 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2021 // ~smax(~x, ~y) == smin(x, y).
2022 return getNotSCEV(getSMaxExpr(
2023 getNotSCEV(getSCEV(LHS)),
2024 getNotSCEV(getSCEV(RHS))));
2026 case ICmpInst::ICMP_ULT:
2027 case ICmpInst::ICMP_ULE:
2028 std::swap(LHS, RHS);
2030 case ICmpInst::ICMP_UGT:
2031 case ICmpInst::ICMP_UGE:
2032 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2033 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2034 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2035 // ~umax(~x, ~y) == umin(x, y)
2036 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2037 getNotSCEV(getSCEV(RHS))));
2044 default: // We cannot analyze this expression.
2048 return getUnknown(V);
2053 //===----------------------------------------------------------------------===//
2054 // Iteration Count Computation Code
2057 /// getBackedgeTakenCount - If the specified loop has a predictable
2058 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2059 /// object. The backedge-taken count is the number of times the loop header
2060 /// will be branched to from within the loop. This is one less than the
2061 /// trip count of the loop, since it doesn't count the first iteration,
2062 /// when the header is branched to from outside the loop.
2064 /// Note that it is not valid to call this method on a loop without a
2065 /// loop-invariant backedge-taken count (see
2066 /// hasLoopInvariantBackedgeTakenCount).
2068 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2069 return getBackedgeTakenInfo(L).Exact;
2072 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2073 /// return the least SCEV value that is known never to be less than the
2074 /// actual backedge taken count.
2075 SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2076 return getBackedgeTakenInfo(L).Max;
2079 const ScalarEvolution::BackedgeTakenInfo &
2080 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2081 // Initially insert a CouldNotCompute for this loop. If the insertion
2082 // succeeds, procede to actually compute a backedge-taken count and
2083 // update the value. The temporary CouldNotCompute value tells SCEV
2084 // code elsewhere that it shouldn't attempt to request a new
2085 // backedge-taken count, which could result in infinite recursion.
2086 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2087 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2089 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2090 if (ItCount.Exact != UnknownValue) {
2091 assert(ItCount.Exact->isLoopInvariant(L) &&
2092 ItCount.Max->isLoopInvariant(L) &&
2093 "Computed trip count isn't loop invariant for loop!");
2094 ++NumTripCountsComputed;
2096 // Update the value in the map.
2097 Pair.first->second = ItCount;
2098 } else if (isa<PHINode>(L->getHeader()->begin())) {
2099 // Only count loops that have phi nodes as not being computable.
2100 ++NumTripCountsNotComputed;
2103 // Now that we know more about the trip count for this loop, forget any
2104 // existing SCEV values for PHI nodes in this loop since they are only
2105 // conservative estimates made without the benefit
2106 // of trip count information.
2107 if (ItCount.hasAnyInfo())
2108 for (BasicBlock::iterator I = L->getHeader()->begin();
2109 PHINode *PN = dyn_cast<PHINode>(I); ++I)
2110 deleteValueFromRecords(PN);
2112 return Pair.first->second;
2115 /// forgetLoopBackedgeTakenCount - This method should be called by the
2116 /// client when it has changed a loop in a way that may effect
2117 /// ScalarEvolution's ability to compute a trip count, or if the loop
2119 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2120 BackedgeTakenCounts.erase(L);
2123 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2124 /// of the specified loop will execute.
2125 ScalarEvolution::BackedgeTakenInfo
2126 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2127 // If the loop has a non-one exit block count, we can't analyze it.
2128 SmallVector<BasicBlock*, 8> ExitBlocks;
2129 L->getExitBlocks(ExitBlocks);
2130 if (ExitBlocks.size() != 1) return UnknownValue;
2132 // Okay, there is one exit block. Try to find the condition that causes the
2133 // loop to be exited.
2134 BasicBlock *ExitBlock = ExitBlocks[0];
2136 BasicBlock *ExitingBlock = 0;
2137 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
2139 if (L->contains(*PI)) {
2140 if (ExitingBlock == 0)
2143 return UnknownValue; // More than one block exiting!
2145 assert(ExitingBlock && "No exits from loop, something is broken!");
2147 // Okay, we've computed the exiting block. See what condition causes us to
2150 // FIXME: we should be able to handle switch instructions (with a single exit)
2151 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2152 if (ExitBr == 0) return UnknownValue;
2153 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2155 // At this point, we know we have a conditional branch that determines whether
2156 // the loop is exited. However, we don't know if the branch is executed each
2157 // time through the loop. If not, then the execution count of the branch will
2158 // not be equal to the trip count of the loop.
2160 // Currently we check for this by checking to see if the Exit branch goes to
2161 // the loop header. If so, we know it will always execute the same number of
2162 // times as the loop. We also handle the case where the exit block *is* the
2163 // loop header. This is common for un-rotated loops. More extensive analysis
2164 // could be done to handle more cases here.
2165 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2166 ExitBr->getSuccessor(1) != L->getHeader() &&
2167 ExitBr->getParent() != L->getHeader())
2168 return UnknownValue;
2170 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2172 // If it's not an integer comparison then compute it the hard way.
2173 // Note that ICmpInst deals with pointer comparisons too so we must check
2174 // the type of the operand.
2175 if (ExitCond == 0 || isa<PointerType>(ExitCond->getOperand(0)->getType()))
2176 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2177 ExitBr->getSuccessor(0) == ExitBlock);
2179 // If the condition was exit on true, convert the condition to exit on false
2180 ICmpInst::Predicate Cond;
2181 if (ExitBr->getSuccessor(1) == ExitBlock)
2182 Cond = ExitCond->getPredicate();
2184 Cond = ExitCond->getInversePredicate();
2186 // Handle common loops like: for (X = "string"; *X; ++X)
2187 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2188 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2190 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2191 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2194 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2195 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2197 // Try to evaluate any dependencies out of the loop.
2198 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
2199 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
2200 Tmp = getSCEVAtScope(RHS, L);
2201 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
2203 // At this point, we would like to compute how many iterations of the
2204 // loop the predicate will return true for these inputs.
2205 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2206 // If there is a loop-invariant, force it into the RHS.
2207 std::swap(LHS, RHS);
2208 Cond = ICmpInst::getSwappedPredicate(Cond);
2211 // If we have a comparison of a chrec against a constant, try to use value
2212 // ranges to answer this query.
2213 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2214 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2215 if (AddRec->getLoop() == L) {
2216 // Form the comparison range using the constant of the correct type so
2217 // that the ConstantRange class knows to do a signed or unsigned
2219 ConstantInt *CompVal = RHSC->getValue();
2220 const Type *RealTy = ExitCond->getOperand(0)->getType();
2221 CompVal = dyn_cast<ConstantInt>(
2222 ConstantExpr::getBitCast(CompVal, RealTy));
2224 // Form the constant range.
2225 ConstantRange CompRange(
2226 ICmpInst::makeConstantRange(Cond, CompVal->getValue()));
2228 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2229 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2234 case ICmpInst::ICMP_NE: { // while (X != Y)
2235 // Convert to: while (X-Y != 0)
2236 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2237 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2240 case ICmpInst::ICMP_EQ: {
2241 // Convert to: while (X-Y == 0) // while (X == Y)
2242 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2243 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2246 case ICmpInst::ICMP_SLT: {
2247 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2248 if (BTI.hasAnyInfo()) return BTI;
2251 case ICmpInst::ICMP_SGT: {
2252 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2253 getNotSCEV(RHS), L, true);
2254 if (BTI.hasAnyInfo()) return BTI;
2257 case ICmpInst::ICMP_ULT: {
2258 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2259 if (BTI.hasAnyInfo()) return BTI;
2262 case ICmpInst::ICMP_UGT: {
2263 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2264 getNotSCEV(RHS), L, false);
2265 if (BTI.hasAnyInfo()) return BTI;
2270 errs() << "ComputeBackedgeTakenCount ";
2271 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2272 errs() << "[unsigned] ";
2273 errs() << *LHS << " "
2274 << Instruction::getOpcodeName(Instruction::ICmp)
2275 << " " << *RHS << "\n";
2280 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2281 ExitBr->getSuccessor(0) == ExitBlock);
2284 static ConstantInt *
2285 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2286 ScalarEvolution &SE) {
2287 SCEVHandle InVal = SE.getConstant(C);
2288 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2289 assert(isa<SCEVConstant>(Val) &&
2290 "Evaluation of SCEV at constant didn't fold correctly?");
2291 return cast<SCEVConstant>(Val)->getValue();
2294 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2295 /// and a GEP expression (missing the pointer index) indexing into it, return
2296 /// the addressed element of the initializer or null if the index expression is
2299 GetAddressedElementFromGlobal(GlobalVariable *GV,
2300 const std::vector<ConstantInt*> &Indices) {
2301 Constant *Init = GV->getInitializer();
2302 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2303 uint64_t Idx = Indices[i]->getZExtValue();
2304 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2305 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2306 Init = cast<Constant>(CS->getOperand(Idx));
2307 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2308 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2309 Init = cast<Constant>(CA->getOperand(Idx));
2310 } else if (isa<ConstantAggregateZero>(Init)) {
2311 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2312 assert(Idx < STy->getNumElements() && "Bad struct index!");
2313 Init = Constant::getNullValue(STy->getElementType(Idx));
2314 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2315 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2316 Init = Constant::getNullValue(ATy->getElementType());
2318 assert(0 && "Unknown constant aggregate type!");
2322 return 0; // Unknown initializer type
2328 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2329 /// 'icmp op load X, cst', try to see if we can compute the backedge
2330 /// execution count.
2331 SCEVHandle ScalarEvolution::
2332 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2334 ICmpInst::Predicate predicate) {
2335 if (LI->isVolatile()) return UnknownValue;
2337 // Check to see if the loaded pointer is a getelementptr of a global.
2338 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2339 if (!GEP) return UnknownValue;
2341 // Make sure that it is really a constant global we are gepping, with an
2342 // initializer, and make sure the first IDX is really 0.
2343 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2344 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2345 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2346 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2347 return UnknownValue;
2349 // Okay, we allow one non-constant index into the GEP instruction.
2351 std::vector<ConstantInt*> Indexes;
2352 unsigned VarIdxNum = 0;
2353 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2354 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2355 Indexes.push_back(CI);
2356 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2357 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2358 VarIdx = GEP->getOperand(i);
2360 Indexes.push_back(0);
2363 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2364 // Check to see if X is a loop variant variable value now.
2365 SCEVHandle Idx = getSCEV(VarIdx);
2366 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2367 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2369 // We can only recognize very limited forms of loop index expressions, in
2370 // particular, only affine AddRec's like {C1,+,C2}.
2371 SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2372 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2373 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2374 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2375 return UnknownValue;
2377 unsigned MaxSteps = MaxBruteForceIterations;
2378 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2379 ConstantInt *ItCst =
2380 ConstantInt::get(IdxExpr->getType(), IterationNum);
2381 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2383 // Form the GEP offset.
2384 Indexes[VarIdxNum] = Val;
2386 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2387 if (Result == 0) break; // Cannot compute!
2389 // Evaluate the condition for this iteration.
2390 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2391 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2392 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2394 errs() << "\n***\n*** Computed loop count " << *ItCst
2395 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2398 ++NumArrayLenItCounts;
2399 return getConstant(ItCst); // Found terminating iteration!
2402 return UnknownValue;
2406 /// CanConstantFold - Return true if we can constant fold an instruction of the
2407 /// specified type, assuming that all operands were constants.
2408 static bool CanConstantFold(const Instruction *I) {
2409 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2410 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2413 if (const CallInst *CI = dyn_cast<CallInst>(I))
2414 if (const Function *F = CI->getCalledFunction())
2415 return canConstantFoldCallTo(F);
2419 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2420 /// in the loop that V is derived from. We allow arbitrary operations along the
2421 /// way, but the operands of an operation must either be constants or a value
2422 /// derived from a constant PHI. If this expression does not fit with these
2423 /// constraints, return null.
2424 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2425 // If this is not an instruction, or if this is an instruction outside of the
2426 // loop, it can't be derived from a loop PHI.
2427 Instruction *I = dyn_cast<Instruction>(V);
2428 if (I == 0 || !L->contains(I->getParent())) return 0;
2430 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2431 if (L->getHeader() == I->getParent())
2434 // We don't currently keep track of the control flow needed to evaluate
2435 // PHIs, so we cannot handle PHIs inside of loops.
2439 // If we won't be able to constant fold this expression even if the operands
2440 // are constants, return early.
2441 if (!CanConstantFold(I)) return 0;
2443 // Otherwise, we can evaluate this instruction if all of its operands are
2444 // constant or derived from a PHI node themselves.
2446 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2447 if (!(isa<Constant>(I->getOperand(Op)) ||
2448 isa<GlobalValue>(I->getOperand(Op)))) {
2449 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2450 if (P == 0) return 0; // Not evolving from PHI
2454 return 0; // Evolving from multiple different PHIs.
2457 // This is a expression evolving from a constant PHI!
2461 /// EvaluateExpression - Given an expression that passes the
2462 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2463 /// in the loop has the value PHIVal. If we can't fold this expression for some
2464 /// reason, return null.
2465 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2466 if (isa<PHINode>(V)) return PHIVal;
2467 if (Constant *C = dyn_cast<Constant>(V)) return C;
2468 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2469 Instruction *I = cast<Instruction>(V);
2471 std::vector<Constant*> Operands;
2472 Operands.resize(I->getNumOperands());
2474 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2475 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2476 if (Operands[i] == 0) return 0;
2479 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2480 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2481 &Operands[0], Operands.size());
2483 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2484 &Operands[0], Operands.size());
2487 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2488 /// in the header of its containing loop, we know the loop executes a
2489 /// constant number of times, and the PHI node is just a recurrence
2490 /// involving constants, fold it.
2491 Constant *ScalarEvolution::
2492 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2493 std::map<PHINode*, Constant*>::iterator I =
2494 ConstantEvolutionLoopExitValue.find(PN);
2495 if (I != ConstantEvolutionLoopExitValue.end())
2498 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2499 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2501 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2503 // Since the loop is canonicalized, the PHI node must have two entries. One
2504 // entry must be a constant (coming in from outside of the loop), and the
2505 // second must be derived from the same PHI.
2506 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2507 Constant *StartCST =
2508 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2510 return RetVal = 0; // Must be a constant.
2512 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2513 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2515 return RetVal = 0; // Not derived from same PHI.
2517 // Execute the loop symbolically to determine the exit value.
2518 if (BEs.getActiveBits() >= 32)
2519 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2521 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2522 unsigned IterationNum = 0;
2523 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2524 if (IterationNum == NumIterations)
2525 return RetVal = PHIVal; // Got exit value!
2527 // Compute the value of the PHI node for the next iteration.
2528 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2529 if (NextPHI == PHIVal)
2530 return RetVal = NextPHI; // Stopped evolving!
2532 return 0; // Couldn't evaluate!
2537 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2538 /// constant number of times (the condition evolves only from constants),
2539 /// try to evaluate a few iterations of the loop until we get the exit
2540 /// condition gets a value of ExitWhen (true or false). If we cannot
2541 /// evaluate the trip count of the loop, return UnknownValue.
2542 SCEVHandle ScalarEvolution::
2543 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2544 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2545 if (PN == 0) return UnknownValue;
2547 // Since the loop is canonicalized, the PHI node must have two entries. One
2548 // entry must be a constant (coming in from outside of the loop), and the
2549 // second must be derived from the same PHI.
2550 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2551 Constant *StartCST =
2552 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2553 if (StartCST == 0) return UnknownValue; // Must be a constant.
2555 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2556 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2557 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2559 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2560 // the loop symbolically to determine when the condition gets a value of
2562 unsigned IterationNum = 0;
2563 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2564 for (Constant *PHIVal = StartCST;
2565 IterationNum != MaxIterations; ++IterationNum) {
2566 ConstantInt *CondVal =
2567 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2569 // Couldn't symbolically evaluate.
2570 if (!CondVal) return UnknownValue;
2572 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2573 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2574 ++NumBruteForceTripCountsComputed;
2575 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2578 // Compute the value of the PHI node for the next iteration.
2579 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2580 if (NextPHI == 0 || NextPHI == PHIVal)
2581 return UnknownValue; // Couldn't evaluate or not making progress...
2585 // Too many iterations were needed to evaluate.
2586 return UnknownValue;
2589 /// getSCEVAtScope - Compute the value of the specified expression within the
2590 /// indicated loop (which may be null to indicate in no loop). If the
2591 /// expression cannot be evaluated, return UnknownValue.
2592 SCEVHandle ScalarEvolution::getSCEVAtScope(SCEV *V, const Loop *L) {
2593 // FIXME: this should be turned into a virtual method on SCEV!
2595 if (isa<SCEVConstant>(V)) return V;
2597 // If this instruction is evolved from a constant-evolving PHI, compute the
2598 // exit value from the loop without using SCEVs.
2599 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2600 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2601 const Loop *LI = (*this->LI)[I->getParent()];
2602 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2603 if (PHINode *PN = dyn_cast<PHINode>(I))
2604 if (PN->getParent() == LI->getHeader()) {
2605 // Okay, there is no closed form solution for the PHI node. Check
2606 // to see if the loop that contains it has a known backedge-taken
2607 // count. If so, we may be able to force computation of the exit
2609 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2610 if (SCEVConstant *BTCC =
2611 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2612 // Okay, we know how many times the containing loop executes. If
2613 // this is a constant evolving PHI node, get the final value at
2614 // the specified iteration number.
2615 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2616 BTCC->getValue()->getValue(),
2618 if (RV) return getUnknown(RV);
2622 // Okay, this is an expression that we cannot symbolically evaluate
2623 // into a SCEV. Check to see if it's possible to symbolically evaluate
2624 // the arguments into constants, and if so, try to constant propagate the
2625 // result. This is particularly useful for computing loop exit values.
2626 if (CanConstantFold(I)) {
2627 std::vector<Constant*> Operands;
2628 Operands.reserve(I->getNumOperands());
2629 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2630 Value *Op = I->getOperand(i);
2631 if (Constant *C = dyn_cast<Constant>(Op)) {
2632 Operands.push_back(C);
2634 // If any of the operands is non-constant and if they are
2635 // non-integer and non-pointer, don't even try to analyze them
2636 // with scev techniques.
2637 if (!isSCEVable(Op->getType()))
2640 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2641 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
2642 Constant *C = SC->getValue();
2643 if (C->getType() != Op->getType())
2644 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2648 Operands.push_back(C);
2649 } else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2650 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
2651 if (C->getType() != Op->getType())
2653 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2657 Operands.push_back(C);
2667 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2668 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2669 &Operands[0], Operands.size());
2671 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2672 &Operands[0], Operands.size());
2673 return getUnknown(C);
2677 // This is some other type of SCEVUnknown, just return it.
2681 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2682 // Avoid performing the look-up in the common case where the specified
2683 // expression has no loop-variant portions.
2684 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2685 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2686 if (OpAtScope != Comm->getOperand(i)) {
2687 if (OpAtScope == UnknownValue) return UnknownValue;
2688 // Okay, at least one of these operands is loop variant but might be
2689 // foldable. Build a new instance of the folded commutative expression.
2690 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2691 NewOps.push_back(OpAtScope);
2693 for (++i; i != e; ++i) {
2694 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2695 if (OpAtScope == UnknownValue) return UnknownValue;
2696 NewOps.push_back(OpAtScope);
2698 if (isa<SCEVAddExpr>(Comm))
2699 return getAddExpr(NewOps);
2700 if (isa<SCEVMulExpr>(Comm))
2701 return getMulExpr(NewOps);
2702 if (isa<SCEVSMaxExpr>(Comm))
2703 return getSMaxExpr(NewOps);
2704 if (isa<SCEVUMaxExpr>(Comm))
2705 return getUMaxExpr(NewOps);
2706 assert(0 && "Unknown commutative SCEV type!");
2709 // If we got here, all operands are loop invariant.
2713 if (SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
2714 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2715 if (LHS == UnknownValue) return LHS;
2716 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2717 if (RHS == UnknownValue) return RHS;
2718 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2719 return Div; // must be loop invariant
2720 return getUDivExpr(LHS, RHS);
2723 // If this is a loop recurrence for a loop that does not contain L, then we
2724 // are dealing with the final value computed by the loop.
2725 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2726 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2727 // To evaluate this recurrence, we need to know how many times the AddRec
2728 // loop iterates. Compute this now.
2729 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
2730 if (BackedgeTakenCount == UnknownValue) return UnknownValue;
2732 // Then, evaluate the AddRec.
2733 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
2735 return UnknownValue;
2738 if (SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
2739 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2740 if (Op == UnknownValue) return Op;
2741 if (Op == Cast->getOperand())
2742 return Cast; // must be loop invariant
2743 return getZeroExtendExpr(Op, Cast->getType());
2746 if (SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
2747 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2748 if (Op == UnknownValue) return Op;
2749 if (Op == Cast->getOperand())
2750 return Cast; // must be loop invariant
2751 return getSignExtendExpr(Op, Cast->getType());
2754 if (SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
2755 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2756 if (Op == UnknownValue) return Op;
2757 if (Op == Cast->getOperand())
2758 return Cast; // must be loop invariant
2759 return getTruncateExpr(Op, Cast->getType());
2762 assert(0 && "Unknown SCEV type!");
2765 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
2766 /// at the specified scope in the program. The L value specifies a loop
2767 /// nest to evaluate the expression at, where null is the top-level or a
2768 /// specified loop is immediately inside of the loop.
2770 /// This method can be used to compute the exit value for a variable defined
2771 /// in a loop by querying what the value will hold in the parent loop.
2773 /// If this value is not computable at this scope, a SCEVCouldNotCompute
2774 /// object is returned.
2775 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
2776 return getSCEVAtScope(getSCEV(V), L);
2779 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
2780 /// following equation:
2782 /// A * X = B (mod N)
2784 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
2785 /// A and B isn't important.
2787 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
2788 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
2789 ScalarEvolution &SE) {
2790 uint32_t BW = A.getBitWidth();
2791 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
2792 assert(A != 0 && "A must be non-zero.");
2796 // The gcd of A and N may have only one prime factor: 2. The number of
2797 // trailing zeros in A is its multiplicity
2798 uint32_t Mult2 = A.countTrailingZeros();
2801 // 2. Check if B is divisible by D.
2803 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
2804 // is not less than multiplicity of this prime factor for D.
2805 if (B.countTrailingZeros() < Mult2)
2806 return SE.getCouldNotCompute();
2808 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
2811 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
2812 // bit width during computations.
2813 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
2814 APInt Mod(BW + 1, 0);
2815 Mod.set(BW - Mult2); // Mod = N / D
2816 APInt I = AD.multiplicativeInverse(Mod);
2818 // 4. Compute the minimum unsigned root of the equation:
2819 // I * (B / D) mod (N / D)
2820 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
2822 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
2824 return SE.getConstant(Result.trunc(BW));
2827 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
2828 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
2829 /// might be the same) or two SCEVCouldNotCompute objects.
2831 static std::pair<SCEVHandle,SCEVHandle>
2832 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
2833 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
2834 SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
2835 SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
2836 SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
2838 // We currently can only solve this if the coefficients are constants.
2839 if (!LC || !MC || !NC) {
2840 SCEV *CNC = SE.getCouldNotCompute();
2841 return std::make_pair(CNC, CNC);
2844 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
2845 const APInt &L = LC->getValue()->getValue();
2846 const APInt &M = MC->getValue()->getValue();
2847 const APInt &N = NC->getValue()->getValue();
2848 APInt Two(BitWidth, 2);
2849 APInt Four(BitWidth, 4);
2852 using namespace APIntOps;
2854 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
2855 // The B coefficient is M-N/2
2859 // The A coefficient is N/2
2860 APInt A(N.sdiv(Two));
2862 // Compute the B^2-4ac term.
2865 SqrtTerm -= Four * (A * C);
2867 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
2868 // integer value or else APInt::sqrt() will assert.
2869 APInt SqrtVal(SqrtTerm.sqrt());
2871 // Compute the two solutions for the quadratic formula.
2872 // The divisions must be performed as signed divisions.
2874 APInt TwoA( A << 1 );
2875 if (TwoA.isMinValue()) {
2876 SCEV *CNC = SE.getCouldNotCompute();
2877 return std::make_pair(CNC, CNC);
2880 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
2881 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
2883 return std::make_pair(SE.getConstant(Solution1),
2884 SE.getConstant(Solution2));
2885 } // end APIntOps namespace
2888 /// HowFarToZero - Return the number of times a backedge comparing the specified
2889 /// value to zero will execute. If not computable, return UnknownValue
2890 SCEVHandle ScalarEvolution::HowFarToZero(SCEV *V, const Loop *L) {
2891 // If the value is a constant
2892 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2893 // If the value is already zero, the branch will execute zero times.
2894 if (C->getValue()->isZero()) return C;
2895 return UnknownValue; // Otherwise it will loop infinitely.
2898 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
2899 if (!AddRec || AddRec->getLoop() != L)
2900 return UnknownValue;
2902 if (AddRec->isAffine()) {
2903 // If this is an affine expression, the execution count of this branch is
2904 // the minimum unsigned root of the following equation:
2906 // Start + Step*N = 0 (mod 2^BW)
2910 // Step*N = -Start (mod 2^BW)
2912 // where BW is the common bit width of Start and Step.
2914 // Get the initial value for the loop.
2915 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
2916 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
2918 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
2920 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2921 // For now we handle only constant steps.
2923 // First, handle unitary steps.
2924 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
2925 return getNegativeSCEV(Start); // N = -Start (as unsigned)
2926 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
2927 return Start; // N = Start (as unsigned)
2929 // Then, try to solve the above equation provided that Start is constant.
2930 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
2931 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
2932 -StartC->getValue()->getValue(),
2935 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2936 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2937 // the quadratic equation to solve it.
2938 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
2940 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2941 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2944 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
2945 << " sol#2: " << *R2 << "\n";
2947 // Pick the smallest positive root value.
2948 if (ConstantInt *CB =
2949 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
2950 R1->getValue(), R2->getValue()))) {
2951 if (CB->getZExtValue() == false)
2952 std::swap(R1, R2); // R1 is the minimum root now.
2954 // We can only use this value if the chrec ends up with an exact zero
2955 // value at this index. When solving for "X*X != 5", for example, we
2956 // should not accept a root of 2.
2957 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
2959 return R1; // We found a quadratic root!
2964 return UnknownValue;
2967 /// HowFarToNonZero - Return the number of times a backedge checking the
2968 /// specified value for nonzero will execute. If not computable, return
2970 SCEVHandle ScalarEvolution::HowFarToNonZero(SCEV *V, const Loop *L) {
2971 // Loops that look like: while (X == 0) are very strange indeed. We don't
2972 // handle them yet except for the trivial case. This could be expanded in the
2973 // future as needed.
2975 // If the value is a constant, check to see if it is known to be non-zero
2976 // already. If so, the backedge will execute zero times.
2977 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2978 if (!C->getValue()->isNullValue())
2979 return getIntegerSCEV(0, C->getType());
2980 return UnknownValue; // Otherwise it will loop infinitely.
2983 // We could implement others, but I really doubt anyone writes loops like
2984 // this, and if they did, they would already be constant folded.
2985 return UnknownValue;
2988 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
2989 /// (which may not be an immediate predecessor) which has exactly one
2990 /// successor from which BB is reachable, or null if no such block is
2994 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
2995 // If the block has a unique predecessor, then there is no path from the
2996 // predecessor to the block that does not go through the direct edge
2997 // from the predecessor to the block.
2998 if (BasicBlock *Pred = BB->getSinglePredecessor())
3001 // A loop's header is defined to be a block that dominates the loop.
3002 // If the loop has a preheader, it must be a block that has exactly
3003 // one successor that can reach BB. This is slightly more strict
3004 // than necessary, but works if critical edges are split.
3005 if (Loop *L = LI->getLoopFor(BB))
3006 return L->getLoopPreheader();
3011 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
3012 /// a conditional between LHS and RHS. This is used to help avoid max
3013 /// expressions in loop trip counts.
3014 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3015 ICmpInst::Predicate Pred,
3016 SCEV *LHS, SCEV *RHS) {
3017 BasicBlock *Preheader = L->getLoopPreheader();
3018 BasicBlock *PreheaderDest = L->getHeader();
3020 // Starting at the preheader, climb up the predecessor chain, as long as
3021 // there are predecessors that can be found that have unique successors
3022 // leading to the original header.
3024 PreheaderDest = Preheader,
3025 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) {
3027 BranchInst *LoopEntryPredicate =
3028 dyn_cast<BranchInst>(Preheader->getTerminator());
3029 if (!LoopEntryPredicate ||
3030 LoopEntryPredicate->isUnconditional())
3033 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3036 // Now that we found a conditional branch that dominates the loop, check to
3037 // see if it is the comparison we are looking for.
3038 Value *PreCondLHS = ICI->getOperand(0);
3039 Value *PreCondRHS = ICI->getOperand(1);
3040 ICmpInst::Predicate Cond;
3041 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
3042 Cond = ICI->getPredicate();
3044 Cond = ICI->getInversePredicate();
3047 ; // An exact match.
3048 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3049 ; // The actual condition is beyond sufficient.
3051 // Check a few special cases.
3053 case ICmpInst::ICMP_UGT:
3054 if (Pred == ICmpInst::ICMP_ULT) {
3055 std::swap(PreCondLHS, PreCondRHS);
3056 Cond = ICmpInst::ICMP_ULT;
3060 case ICmpInst::ICMP_SGT:
3061 if (Pred == ICmpInst::ICMP_SLT) {
3062 std::swap(PreCondLHS, PreCondRHS);
3063 Cond = ICmpInst::ICMP_SLT;
3067 case ICmpInst::ICMP_NE:
3068 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3069 // so check for this case by checking if the NE is comparing against
3070 // a minimum or maximum constant.
3071 if (!ICmpInst::isTrueWhenEqual(Pred))
3072 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3073 const APInt &A = CI->getValue();
3075 case ICmpInst::ICMP_SLT:
3076 if (A.isMaxSignedValue()) break;
3078 case ICmpInst::ICMP_SGT:
3079 if (A.isMinSignedValue()) break;
3081 case ICmpInst::ICMP_ULT:
3082 if (A.isMaxValue()) break;
3084 case ICmpInst::ICMP_UGT:
3085 if (A.isMinValue()) break;
3090 Cond = ICmpInst::ICMP_NE;
3091 // NE is symmetric but the original comparison may not be. Swap
3092 // the operands if necessary so that they match below.
3093 if (isa<SCEVConstant>(LHS))
3094 std::swap(PreCondLHS, PreCondRHS);
3099 // We weren't able to reconcile the condition.
3103 if (!PreCondLHS->getType()->isInteger()) continue;
3105 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3106 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3107 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3108 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3109 RHS == getNotSCEV(PreCondLHSSCEV)))
3116 /// HowManyLessThans - Return the number of times a backedge containing the
3117 /// specified less-than comparison will execute. If not computable, return
3119 ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3120 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L, bool isSigned) {
3121 // Only handle: "ADDREC < LoopInvariant".
3122 if (!RHS->isLoopInvariant(L)) return UnknownValue;
3124 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3125 if (!AddRec || AddRec->getLoop() != L)
3126 return UnknownValue;
3128 if (AddRec->isAffine()) {
3129 // FORNOW: We only support unit strides.
3130 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3131 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3132 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3134 // TODO: handle non-constant strides.
3135 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3136 if (!CStep || CStep->isZero())
3137 return UnknownValue;
3138 if (CStep->getValue()->getValue() == 1) {
3139 // With unit stride, the iteration never steps past the limit value.
3140 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3141 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3142 // Test whether a positive iteration iteration can step past the limit
3143 // value and past the maximum value for its type in a single step.
3145 APInt Max = APInt::getSignedMaxValue(BitWidth);
3146 if ((Max - CStep->getValue()->getValue())
3147 .slt(CLimit->getValue()->getValue()))
3148 return UnknownValue;
3150 APInt Max = APInt::getMaxValue(BitWidth);
3151 if ((Max - CStep->getValue()->getValue())
3152 .ult(CLimit->getValue()->getValue()))
3153 return UnknownValue;
3156 // TODO: handle non-constant limit values below.
3157 return UnknownValue;
3159 // TODO: handle negative strides below.
3160 return UnknownValue;
3162 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3163 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3164 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3165 // treat m-n as signed nor unsigned due to overflow possibility.
3167 // First, we get the value of the LHS in the first iteration: n
3168 SCEVHandle Start = AddRec->getOperand(0);
3170 // Determine the minimum constant start value.
3171 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3172 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3173 APInt::getMinValue(BitWidth));
3175 // If we know that the condition is true in order to enter the loop,
3176 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3177 // only know if will execute (max(m,n)-n)/s times. In both cases, the
3178 // division must round up.
3179 SCEVHandle End = RHS;
3180 if (!isLoopGuardedByCond(L,
3181 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3182 getMinusSCEV(Start, Step), RHS))
3183 End = isSigned ? getSMaxExpr(RHS, Start)
3184 : getUMaxExpr(RHS, Start);
3186 // Determine the maximum constant end value.
3187 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3188 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3189 APInt::getMaxValue(BitWidth));
3191 // Finally, we subtract these two values and divide, rounding up, to get
3192 // the number of times the backedge is executed.
3193 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3194 getAddExpr(Step, NegOne)),
3197 // The maximum backedge count is similar, except using the minimum start
3198 // value and the maximum end value.
3199 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3201 getAddExpr(Step, NegOne)),
3204 return BackedgeTakenInfo(BECount, MaxBECount);
3207 return UnknownValue;
3210 /// getNumIterationsInRange - Return the number of iterations of this loop that
3211 /// produce values in the specified constant range. Another way of looking at
3212 /// this is that it returns the first iteration number where the value is not in
3213 /// the condition, thus computing the exit count. If the iteration count can't
3214 /// be computed, an instance of SCEVCouldNotCompute is returned.
3215 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3216 ScalarEvolution &SE) const {
3217 if (Range.isFullSet()) // Infinite loop.
3218 return SE.getCouldNotCompute();
3220 // If the start is a non-zero constant, shift the range to simplify things.
3221 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3222 if (!SC->getValue()->isZero()) {
3223 std::vector<SCEVHandle> Operands(op_begin(), op_end());
3224 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3225 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3226 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
3227 return ShiftedAddRec->getNumIterationsInRange(
3228 Range.subtract(SC->getValue()->getValue()), SE);
3229 // This is strange and shouldn't happen.
3230 return SE.getCouldNotCompute();
3233 // The only time we can solve this is when we have all constant indices.
3234 // Otherwise, we cannot determine the overflow conditions.
3235 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3236 if (!isa<SCEVConstant>(getOperand(i)))
3237 return SE.getCouldNotCompute();
3240 // Okay at this point we know that all elements of the chrec are constants and
3241 // that the start element is zero.
3243 // First check to see if the range contains zero. If not, the first
3245 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3246 if (!Range.contains(APInt(BitWidth, 0)))
3247 return SE.getConstant(ConstantInt::get(getType(),0));
3250 // If this is an affine expression then we have this situation:
3251 // Solve {0,+,A} in Range === Ax in Range
3253 // We know that zero is in the range. If A is positive then we know that
3254 // the upper value of the range must be the first possible exit value.
3255 // If A is negative then the lower of the range is the last possible loop
3256 // value. Also note that we already checked for a full range.
3257 APInt One(BitWidth,1);
3258 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3259 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3261 // The exit value should be (End+A)/A.
3262 APInt ExitVal = (End + A).udiv(A);
3263 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3265 // Evaluate at the exit value. If we really did fall out of the valid
3266 // range, then we computed our trip count, otherwise wrap around or other
3267 // things must have happened.
3268 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3269 if (Range.contains(Val->getValue()))
3270 return SE.getCouldNotCompute(); // Something strange happened
3272 // Ensure that the previous value is in the range. This is a sanity check.
3273 assert(Range.contains(
3274 EvaluateConstantChrecAtConstant(this,
3275 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3276 "Linear scev computation is off in a bad way!");
3277 return SE.getConstant(ExitValue);
3278 } else if (isQuadratic()) {
3279 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3280 // quadratic equation to solve it. To do this, we must frame our problem in
3281 // terms of figuring out when zero is crossed, instead of when
3282 // Range.getUpper() is crossed.
3283 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3284 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3285 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3287 // Next, solve the constructed addrec
3288 std::pair<SCEVHandle,SCEVHandle> Roots =
3289 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3290 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3291 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3293 // Pick the smallest positive root value.
3294 if (ConstantInt *CB =
3295 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3296 R1->getValue(), R2->getValue()))) {
3297 if (CB->getZExtValue() == false)
3298 std::swap(R1, R2); // R1 is the minimum root now.
3300 // Make sure the root is not off by one. The returned iteration should
3301 // not be in the range, but the previous one should be. When solving
3302 // for "X*X < 5", for example, we should not return a root of 2.
3303 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3306 if (Range.contains(R1Val->getValue())) {
3307 // The next iteration must be out of the range...
3308 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3310 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3311 if (!Range.contains(R1Val->getValue()))
3312 return SE.getConstant(NextVal);
3313 return SE.getCouldNotCompute(); // Something strange happened
3316 // If R1 was not in the range, then it is a good return value. Make
3317 // sure that R1-1 WAS in the range though, just in case.
3318 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3319 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3320 if (Range.contains(R1Val->getValue()))
3322 return SE.getCouldNotCompute(); // Something strange happened
3327 return SE.getCouldNotCompute();
3332 //===----------------------------------------------------------------------===//
3333 // ScalarEvolution Class Implementation
3334 //===----------------------------------------------------------------------===//
3336 ScalarEvolution::ScalarEvolution()
3337 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) {
3340 bool ScalarEvolution::runOnFunction(Function &F) {
3342 LI = &getAnalysis<LoopInfo>();
3343 TD = getAnalysisIfAvailable<TargetData>();
3347 void ScalarEvolution::releaseMemory() {
3349 BackedgeTakenCounts.clear();
3350 ConstantEvolutionLoopExitValue.clear();
3353 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3354 AU.setPreservesAll();
3355 AU.addRequiredTransitive<LoopInfo>();
3358 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3359 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3362 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3364 // Print all inner loops first
3365 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3366 PrintLoopInfo(OS, SE, *I);
3368 OS << "Loop " << L->getHeader()->getName() << ": ";
3370 SmallVector<BasicBlock*, 8> ExitBlocks;
3371 L->getExitBlocks(ExitBlocks);
3372 if (ExitBlocks.size() != 1)
3373 OS << "<multiple exits> ";
3375 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3376 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3378 OS << "Unpredictable backedge-taken count. ";
3384 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3385 // ScalarEvolution's implementaiton of the print method is to print
3386 // out SCEV values of all instructions that are interesting. Doing
3387 // this potentially causes it to create new SCEV objects though,
3388 // which technically conflicts with the const qualifier. This isn't
3389 // observable from outside the class though (the hasSCEV function
3390 // notwithstanding), so casting away the const isn't dangerous.
3391 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3393 OS << "Classifying expressions for: " << F->getName() << "\n";
3394 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3395 if (isSCEVable(I->getType())) {
3398 SCEVHandle SV = SE.getSCEV(&*I);
3402 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3404 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3405 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3406 OS << "<<Unknown>>";
3416 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3417 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3418 PrintLoopInfo(OS, &SE, *I);
3421 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3422 raw_os_ostream OS(o);