84#include <algorithm>
85using namespace llvm;
86
87STATISTIC(NumArrayLenItCounts,
88 "Number of trip counts computed with array length");
89STATISTIC(NumTripCountsComputed,
90 "Number of loops with predictable loop counts");
91STATISTIC(NumTripCountsNotComputed,
92 "Number of loops without predictable loop counts");
93STATISTIC(NumBruteForceTripCountsComputed,
94 "Number of loops with trip counts computed by force");
95
96static cl::opt<unsigned>
97MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
98 cl::desc("Maximum number of iterations SCEV will "
99 "symbolically execute a constant derived loop"),
100 cl::init(100));
101
102static RegisterPass<ScalarEvolution>
103R("scalar-evolution", "Scalar Evolution Analysis", false, true);
104char ScalarEvolution::ID = 0;
105
106//===----------------------------------------------------------------------===//
107// SCEV class definitions
108//===----------------------------------------------------------------------===//
109
110//===----------------------------------------------------------------------===//
111// Implementation of the SCEV class.
112//
113SCEV::~SCEV() {}
114void SCEV::dump() const {
115 print(errs());
116 errs() << '\n';
117}
118
119void SCEV::print(std::ostream &o) const {
120 raw_os_ostream OS(o);
121 print(OS);
122}
123
124bool SCEV::isZero() const {
125 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
126 return SC->getValue()->isZero();
127 return false;
128}
129
130bool SCEV::isOne() const {
131 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
132 return SC->getValue()->isOne();
133 return false;
134}
135
136SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
137SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
138
139bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
140 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
141 return false;
142}
143
144const Type *SCEVCouldNotCompute::getType() const {
145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
146 return 0;
147}
148
149bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
150 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
151 return false;
152}
153
154SCEVHandle SCEVCouldNotCompute::
155replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
156 const SCEVHandle &Conc,
157 ScalarEvolution &SE) const {
158 return this;
159}
160
161void SCEVCouldNotCompute::print(raw_ostream &OS) const {
162 OS << "***COULDNOTCOMPUTE***";
163}
164
165bool SCEVCouldNotCompute::classof(const SCEV *S) {
166 return S->getSCEVType() == scCouldNotCompute;
167}
168
169
170// SCEVConstants - Only allow the creation of one SCEVConstant for any
171// particular value. Don't use a SCEVHandle here, or else the object will
172// never be deleted!
173static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
174
175
176SCEVConstant::~SCEVConstant() {
177 SCEVConstants->erase(V);
178}
179
180SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
181 SCEVConstant *&R = (*SCEVConstants)[V];
182 if (R == 0) R = new SCEVConstant(V);
183 return R;
184}
185
186SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
187 return getConstant(ConstantInt::get(Val));
188}
189
190const Type *SCEVConstant::getType() const { return V->getType(); }
191
192void SCEVConstant::print(raw_ostream &OS) const {
193 WriteAsOperand(OS, V, false);
194}
195
196SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
197 const SCEVHandle &op, const Type *ty)
198 : SCEV(SCEVTy), Op(op), Ty(ty) {}
199
200SCEVCastExpr::~SCEVCastExpr() {}
201
202bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
203 return Op->dominates(BB, DT);
204}
205
206// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
207// particular input. Don't use a SCEVHandle here, or else the object will
208// never be deleted!
209static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
210 SCEVTruncateExpr*> > SCEVTruncates;
211
212SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
213 : SCEVCastExpr(scTruncate, op, ty) {
214 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
215 (Ty->isInteger() || isa<PointerType>(Ty)) &&
216 "Cannot truncate non-integer value!");
217}
218
219SCEVTruncateExpr::~SCEVTruncateExpr() {
220 SCEVTruncates->erase(std::make_pair(Op, Ty));
221}
222
223void SCEVTruncateExpr::print(raw_ostream &OS) const {
224 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
225}
226
227// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
228// particular input. Don't use a SCEVHandle here, or else the object will never
229// be deleted!
230static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
231 SCEVZeroExtendExpr*> > SCEVZeroExtends;
232
233SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
234 : SCEVCastExpr(scZeroExtend, op, ty) {
235 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
236 (Ty->isInteger() || isa<PointerType>(Ty)) &&
237 "Cannot zero extend non-integer value!");
238}
239
240SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
241 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
242}
243
244void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
245 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
246}
247
248// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
249// particular input. Don't use a SCEVHandle here, or else the object will never
250// be deleted!
251static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
252 SCEVSignExtendExpr*> > SCEVSignExtends;
253
254SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
255 : SCEVCastExpr(scSignExtend, op, ty) {
256 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
257 (Ty->isInteger() || isa<PointerType>(Ty)) &&
258 "Cannot sign extend non-integer value!");
259}
260
261SCEVSignExtendExpr::~SCEVSignExtendExpr() {
262 SCEVSignExtends->erase(std::make_pair(Op, Ty));
263}
264
265void SCEVSignExtendExpr::print(raw_ostream &OS) const {
266 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
267}
268
269// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
270// particular input. Don't use a SCEVHandle here, or else the object will never
271// be deleted!
272static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >,
273 SCEVCommutativeExpr*> > SCEVCommExprs;
274
275SCEVCommutativeExpr::~SCEVCommutativeExpr() {
276 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
277 SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps));
278}
279
280void SCEVCommutativeExpr::print(raw_ostream &OS) const {
281 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
282 const char *OpStr = getOperationStr();
283 OS << "(" << *Operands[0];
284 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
285 OS << OpStr << *Operands[i];
286 OS << ")";
287}
288
289SCEVHandle SCEVCommutativeExpr::
290replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
291 const SCEVHandle &Conc,
292 ScalarEvolution &SE) const {
293 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
294 SCEVHandle H =
295 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
296 if (H != getOperand(i)) {
297 std::vector<SCEVHandle> NewOps;
298 NewOps.reserve(getNumOperands());
299 for (unsigned j = 0; j != i; ++j)
300 NewOps.push_back(getOperand(j));
301 NewOps.push_back(H);
302 for (++i; i != e; ++i)
303 NewOps.push_back(getOperand(i)->
304 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
305
306 if (isa<SCEVAddExpr>(this))
307 return SE.getAddExpr(NewOps);
308 else if (isa<SCEVMulExpr>(this))
309 return SE.getMulExpr(NewOps);
310 else if (isa<SCEVSMaxExpr>(this))
311 return SE.getSMaxExpr(NewOps);
312 else if (isa<SCEVUMaxExpr>(this))
313 return SE.getUMaxExpr(NewOps);
314 else
315 assert(0 && "Unknown commutative expr!");
316 }
317 }
318 return this;
319}
320
321bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
322 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
323 if (!getOperand(i)->dominates(BB, DT))
324 return false;
325 }
326 return true;
327}
328
329
330// SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
331// input. Don't use a SCEVHandle here, or else the object will never be
332// deleted!
333static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>,
334 SCEVUDivExpr*> > SCEVUDivs;
335
336SCEVUDivExpr::~SCEVUDivExpr() {
337 SCEVUDivs->erase(std::make_pair(LHS, RHS));
338}
339
340bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
341 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
342}
343
344void SCEVUDivExpr::print(raw_ostream &OS) const {
345 OS << "(" << *LHS << " /u " << *RHS << ")";
346}
347
348const Type *SCEVUDivExpr::getType() const {
349 // In most cases the types of LHS and RHS will be the same, but in some
350 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
351 // depend on the type for correctness, but handling types carefully can
352 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
353 // a pointer type than the RHS, so use the RHS' type here.
354 return RHS->getType();
355}
356
357// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
358// particular input. Don't use a SCEVHandle here, or else the object will never
359// be deleted!
360static ManagedStatic<std::map<std::pair<const Loop *,
361 std::vector<const SCEV*> >,
362 SCEVAddRecExpr*> > SCEVAddRecExprs;
363
364SCEVAddRecExpr::~SCEVAddRecExpr() {
365 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
366 SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps));
367}
368
369SCEVHandle SCEVAddRecExpr::
370replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
371 const SCEVHandle &Conc,
372 ScalarEvolution &SE) const {
373 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
374 SCEVHandle H =
375 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
376 if (H != getOperand(i)) {
377 std::vector<SCEVHandle> NewOps;
378 NewOps.reserve(getNumOperands());
379 for (unsigned j = 0; j != i; ++j)
380 NewOps.push_back(getOperand(j));
381 NewOps.push_back(H);
382 for (++i; i != e; ++i)
383 NewOps.push_back(getOperand(i)->
384 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
385
386 return SE.getAddRecExpr(NewOps, L);
387 }
388 }
389 return this;
390}
391
392
393bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
394 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
395 // contain L and if the start is invariant.
396 // Add recurrences are never invariant in the function-body (null loop).
397 return QueryLoop &&
398 !QueryLoop->contains(L->getHeader()) &&
399 getOperand(0)->isLoopInvariant(QueryLoop);
400}
401
402
403void SCEVAddRecExpr::print(raw_ostream &OS) const {
404 OS << "{" << *Operands[0];
405 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
406 OS << ",+," << *Operands[i];
407 OS << "}<" << L->getHeader()->getName() + ">";
408}
409
410// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
411// value. Don't use a SCEVHandle here, or else the object will never be
412// deleted!
413static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
414
415SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
416
417bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
418 // All non-instruction values are loop invariant. All instructions are loop
419 // invariant if they are not contained in the specified loop.
420 // Instructions are never considered invariant in the function body
421 // (null loop) because they are defined within the "loop".
422 if (Instruction *I = dyn_cast<Instruction>(V))
423 return L && !L->contains(I->getParent());
424 return true;
425}
426
427bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
428 if (Instruction *I = dyn_cast<Instruction>(getValue()))
429 return DT->dominates(I->getParent(), BB);
430 return true;
431}
432
433const Type *SCEVUnknown::getType() const {
434 return V->getType();
435}
436
437void SCEVUnknown::print(raw_ostream &OS) const {
438 WriteAsOperand(OS, V, false);
439}
440
441//===----------------------------------------------------------------------===//
442// SCEV Utilities
443//===----------------------------------------------------------------------===//
444
445namespace {
446 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
447 /// than the complexity of the RHS. This comparator is used to canonicalize
448 /// expressions.
449 class VISIBILITY_HIDDEN SCEVComplexityCompare {
450 LoopInfo *LI;
451 public:
452 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
453
454 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
455 // Primarily, sort the SCEVs by their getSCEVType().
456 if (LHS->getSCEVType() != RHS->getSCEVType())
457 return LHS->getSCEVType() < RHS->getSCEVType();
458
459 // Aside from the getSCEVType() ordering, the particular ordering
460 // isn't very important except that it's beneficial to be consistent,
461 // so that (a + b) and (b + a) don't end up as different expressions.
462
463 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
464 // not as complete as it could be.
465 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
466 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
467
468 // Order pointer values after integer values. This helps SCEVExpander
469 // form GEPs.
470 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
471 return false;
472 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
473 return true;
474
475 // Compare getValueID values.
476 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
477 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
478
479 // Sort arguments by their position.
480 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
481 const Argument *RA = cast<Argument>(RU->getValue());
482 return LA->getArgNo() < RA->getArgNo();
483 }
484
485 // For instructions, compare their loop depth, and their opcode.
486 // This is pretty loose.
487 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
488 Instruction *RV = cast<Instruction>(RU->getValue());
489
490 // Compare loop depths.
491 if (LI->getLoopDepth(LV->getParent()) !=
492 LI->getLoopDepth(RV->getParent()))
493 return LI->getLoopDepth(LV->getParent()) <
494 LI->getLoopDepth(RV->getParent());
495
496 // Compare opcodes.
497 if (LV->getOpcode() != RV->getOpcode())
498 return LV->getOpcode() < RV->getOpcode();
499
500 // Compare the number of operands.
501 if (LV->getNumOperands() != RV->getNumOperands())
502 return LV->getNumOperands() < RV->getNumOperands();
503 }
504
505 return false;
506 }
507
508 // Constant sorting doesn't matter since they'll be folded.
509 if (isa<SCEVConstant>(LHS))
510 return false;
511
512 // Lexicographically compare n-ary expressions.
513 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
514 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
515 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
516 if (i >= RC->getNumOperands())
517 return false;
518 if (operator()(LC->getOperand(i), RC->getOperand(i)))
519 return true;
520 if (operator()(RC->getOperand(i), LC->getOperand(i)))
521 return false;
522 }
523 return LC->getNumOperands() < RC->getNumOperands();
524 }
525
526 // Lexicographically compare udiv expressions.
527 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
528 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
529 if (operator()(LC->getLHS(), RC->getLHS()))
530 return true;
531 if (operator()(RC->getLHS(), LC->getLHS()))
532 return false;
533 if (operator()(LC->getRHS(), RC->getRHS()))
534 return true;
535 if (operator()(RC->getRHS(), LC->getRHS()))
536 return false;
537 return false;
538 }
539
540 // Compare cast expressions by operand.
541 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
542 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
543 return operator()(LC->getOperand(), RC->getOperand());
544 }
545
546 assert(0 && "Unknown SCEV kind!");
547 return false;
548 }
549 };
550}
551
552/// GroupByComplexity - Given a list of SCEV objects, order them by their
553/// complexity, and group objects of the same complexity together by value.
554/// When this routine is finished, we know that any duplicates in the vector are
555/// consecutive and that complexity is monotonically increasing.
556///
557/// Note that we go take special precautions to ensure that we get determinstic
558/// results from this routine. In other words, we don't want the results of
559/// this to depend on where the addresses of various SCEV objects happened to
560/// land in memory.
561///
562static void GroupByComplexity(std::vector<SCEVHandle> &Ops,
563 LoopInfo *LI) {
564 if (Ops.size() < 2) return; // Noop
565 if (Ops.size() == 2) {
566 // This is the common case, which also happens to be trivially simple.
567 // Special case it.
568 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
569 std::swap(Ops[0], Ops[1]);
570 return;
571 }
572
573 // Do the rough sort by complexity.
574 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
575
576 // Now that we are sorted by complexity, group elements of the same
577 // complexity. Note that this is, at worst, N^2, but the vector is likely to
578 // be extremely short in practice. Note that we take this approach because we
579 // do not want to depend on the addresses of the objects we are grouping.
580 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
581 const SCEV *S = Ops[i];
582 unsigned Complexity = S->getSCEVType();
583
584 // If there are any objects of the same complexity and same value as this
585 // one, group them.
586 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
587 if (Ops[j] == S) { // Found a duplicate.
588 // Move it to immediately after i'th element.
589 std::swap(Ops[i+1], Ops[j]);
590 ++i; // no need to rescan it.
591 if (i == e-2) return; // Done!
592 }
593 }
594 }
595}
596
597
598
599//===----------------------------------------------------------------------===//
600// Simple SCEV method implementations
601//===----------------------------------------------------------------------===//
602
603/// BinomialCoefficient - Compute BC(It, K). The result has width W.
604/// Assume, K > 0.
605static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
606 ScalarEvolution &SE,
607 const Type* ResultTy) {
608 // Handle the simplest case efficiently.
609 if (K == 1)
610 return SE.getTruncateOrZeroExtend(It, ResultTy);
611
612 // We are using the following formula for BC(It, K):
613 //
614 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
615 //
616 // Suppose, W is the bitwidth of the return value. We must be prepared for
617 // overflow. Hence, we must assure that the result of our computation is
618 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
619 // safe in modular arithmetic.
620 //
621 // However, this code doesn't use exactly that formula; the formula it uses
622 // is something like the following, where T is the number of factors of 2 in
623 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
624 // exponentiation:
625 //
626 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
627 //
628 // This formula is trivially equivalent to the previous formula. However,
629 // this formula can be implemented much more efficiently. The trick is that
630 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
631 // arithmetic. To do exact division in modular arithmetic, all we have
632 // to do is multiply by the inverse. Therefore, this step can be done at
633 // width W.
634 //
635 // The next issue is how to safely do the division by 2^T. The way this
636 // is done is by doing the multiplication step at a width of at least W + T
637 // bits. This way, the bottom W+T bits of the product are accurate. Then,
638 // when we perform the division by 2^T (which is equivalent to a right shift
639 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
640 // truncated out after the division by 2^T.
641 //
642 // In comparison to just directly using the first formula, this technique
643 // is much more efficient; using the first formula requires W * K bits,
644 // but this formula less than W + K bits. Also, the first formula requires
645 // a division step, whereas this formula only requires multiplies and shifts.
646 //
647 // It doesn't matter whether the subtraction step is done in the calculation
648 // width or the input iteration count's width; if the subtraction overflows,
649 // the result must be zero anyway. We prefer here to do it in the width of
650 // the induction variable because it helps a lot for certain cases; CodeGen
651 // isn't smart enough to ignore the overflow, which leads to much less
652 // efficient code if the width of the subtraction is wider than the native
653 // register width.
654 //
655 // (It's possible to not widen at all by pulling out factors of 2 before
656 // the multiplication; for example, K=2 can be calculated as
657 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
658 // extra arithmetic, so it's not an obvious win, and it gets
659 // much more complicated for K > 3.)
660
661 // Protection from insane SCEVs; this bound is conservative,
662 // but it probably doesn't matter.
663 if (K > 1000)
664 return SE.getCouldNotCompute();
665
666 unsigned W = SE.getTypeSizeInBits(ResultTy);
667
668 // Calculate K! / 2^T and T; we divide out the factors of two before
669 // multiplying for calculating K! / 2^T to avoid overflow.
670 // Other overflow doesn't matter because we only care about the bottom
671 // W bits of the result.
672 APInt OddFactorial(W, 1);
673 unsigned T = 1;
674 for (unsigned i = 3; i <= K; ++i) {
675 APInt Mult(W, i);
676 unsigned TwoFactors = Mult.countTrailingZeros();
677 T += TwoFactors;
678 Mult = Mult.lshr(TwoFactors);
679 OddFactorial *= Mult;
680 }
681
682 // We need at least W + T bits for the multiplication step
683 unsigned CalculationBits = W + T;
684
685 // Calcuate 2^T, at width T+W.
686 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
687
688 // Calculate the multiplicative inverse of K! / 2^T;
689 // this multiplication factor will perform the exact division by
690 // K! / 2^T.
691 APInt Mod = APInt::getSignedMinValue(W+1);
692 APInt MultiplyFactor = OddFactorial.zext(W+1);
693 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
694 MultiplyFactor = MultiplyFactor.trunc(W);
695
696 // Calculate the product, at width T+W
697 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
698 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
699 for (unsigned i = 1; i != K; ++i) {
700 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
701 Dividend = SE.getMulExpr(Dividend,
702 SE.getTruncateOrZeroExtend(S, CalculationTy));
703 }
704
705 // Divide by 2^T
706 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
707
708 // Truncate the result, and divide by K! / 2^T.
709
710 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
711 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
712}
713
714/// evaluateAtIteration - Return the value of this chain of recurrences at
715/// the specified iteration number. We can evaluate this recurrence by
716/// multiplying each element in the chain by the binomial coefficient
717/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
718///
719/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
720///
721/// where BC(It, k) stands for binomial coefficient.
722///
723SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
724 ScalarEvolution &SE) const {
725 SCEVHandle Result = getStart();
726 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
727 // The computation is correct in the face of overflow provided that the
728 // multiplication is performed _after_ the evaluation of the binomial
729 // coefficient.
730 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
731 if (isa<SCEVCouldNotCompute>(Coeff))
732 return Coeff;
733
734 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
735 }
736 return Result;
737}
738
739//===----------------------------------------------------------------------===//
740// SCEV Expression folder implementations
741//===----------------------------------------------------------------------===//
742
743SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op,
744 const Type *Ty) {
745 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
746 "This is not a truncating conversion!");
747 assert(isSCEVable(Ty) &&
748 "This is not a conversion to a SCEVable type!");
749 Ty = getEffectiveSCEVType(Ty);
750
751 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
752 return getUnknown(
753 ConstantExpr::getTrunc(SC->getValue(), Ty));
754
755 // trunc(trunc(x)) --> trunc(x)
756 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
757 return getTruncateExpr(ST->getOperand(), Ty);
758
759 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
760 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
761 return getTruncateOrSignExtend(SS->getOperand(), Ty);
762
763 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
764 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
765 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
766
767 // If the input value is a chrec scev made out of constants, truncate
768 // all of the constants.
769 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
770 std::vector<SCEVHandle> Operands;
771 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
772 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
773 return getAddRecExpr(Operands, AddRec->getLoop());
774 }
775
776 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
777 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
778 return Result;
779}
780
781SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
782 const Type *Ty) {
783 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
784 "This is not an extending conversion!");
785 assert(isSCEVable(Ty) &&
786 "This is not a conversion to a SCEVable type!");
787 Ty = getEffectiveSCEVType(Ty);
788
789 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
790 const Type *IntTy = getEffectiveSCEVType(Ty);
791 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
792 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
793 return getUnknown(C);
794 }
795
796 // zext(zext(x)) --> zext(x)
797 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
798 return getZeroExtendExpr(SZ->getOperand(), Ty);
799
800 // If the input value is a chrec scev, and we can prove that the value
801 // did not overflow the old, smaller, value, we can zero extend all of the
802 // operands (often constants). This allows analysis of something like
803 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
804 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
805 if (AR->isAffine()) {
806 // Check whether the backedge-taken count is SCEVCouldNotCompute.
807 // Note that this serves two purposes: It filters out loops that are
808 // simply not analyzable, and it covers the case where this code is
809 // being called from within backedge-taken count analysis, such that
810 // attempting to ask for the backedge-taken count would likely result
811 // in infinite recursion. In the later case, the analysis code will
812 // cope with a conservative value, and it will take care to purge
813 // that value once it has finished.
814 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
815 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
816 // Manually compute the final value for AR, checking for
817 // overflow.
818 SCEVHandle Start = AR->getStart();
819 SCEVHandle Step = AR->getStepRecurrence(*this);
820
821 // Check whether the backedge-taken count can be losslessly casted to
822 // the addrec's type. The count is always unsigned.
823 SCEVHandle CastedMaxBECount =
824 getTruncateOrZeroExtend(MaxBECount, Start->getType());
825 SCEVHandle RecastedMaxBECount =
826 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
827 if (MaxBECount == RecastedMaxBECount) {
828 const Type *WideTy =
829 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
830 // Check whether Start+Step*MaxBECount has no unsigned overflow.
831 SCEVHandle ZMul =
832 getMulExpr(CastedMaxBECount,
833 getTruncateOrZeroExtend(Step, Start->getType()));
834 SCEVHandle Add = getAddExpr(Start, ZMul);
835 SCEVHandle OperandExtendedAdd =
836 getAddExpr(getZeroExtendExpr(Start, WideTy),
837 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
838 getZeroExtendExpr(Step, WideTy)));
839 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
840 // Return the expression with the addrec on the outside.
841 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
842 getZeroExtendExpr(Step, Ty),
843 AR->getLoop());
844
845 // Similar to above, only this time treat the step value as signed.
846 // This covers loops that count down.
847 SCEVHandle SMul =
848 getMulExpr(CastedMaxBECount,
849 getTruncateOrSignExtend(Step, Start->getType()));
850 Add = getAddExpr(Start, SMul);
851 OperandExtendedAdd =
852 getAddExpr(getZeroExtendExpr(Start, WideTy),
853 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
854 getSignExtendExpr(Step, WideTy)));
855 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
856 // Return the expression with the addrec on the outside.
857 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
858 getSignExtendExpr(Step, Ty),
859 AR->getLoop());
860 }
861 }
862 }
863
864 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
865 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
866 return Result;
867}
868
869SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
870 const Type *Ty) {
871 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
872 "This is not an extending conversion!");
873 assert(isSCEVable(Ty) &&
874 "This is not a conversion to a SCEVable type!");
875 Ty = getEffectiveSCEVType(Ty);
876
877 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
878 const Type *IntTy = getEffectiveSCEVType(Ty);
879 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
880 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
881 return getUnknown(C);
882 }
883
884 // sext(sext(x)) --> sext(x)
885 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
886 return getSignExtendExpr(SS->getOperand(), Ty);
887
888 // If the input value is a chrec scev, and we can prove that the value
889 // did not overflow the old, smaller, value, we can sign extend all of the
890 // operands (often constants). This allows analysis of something like
891 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
892 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
893 if (AR->isAffine()) {
894 // Check whether the backedge-taken count is SCEVCouldNotCompute.
895 // Note that this serves two purposes: It filters out loops that are
896 // simply not analyzable, and it covers the case where this code is
897 // being called from within backedge-taken count analysis, such that
898 // attempting to ask for the backedge-taken count would likely result
899 // in infinite recursion. In the later case, the analysis code will
900 // cope with a conservative value, and it will take care to purge
901 // that value once it has finished.
902 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
903 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
904 // Manually compute the final value for AR, checking for
905 // overflow.
906 SCEVHandle Start = AR->getStart();
907 SCEVHandle Step = AR->getStepRecurrence(*this);
908
909 // Check whether the backedge-taken count can be losslessly casted to
910 // the addrec's type. The count is always unsigned.
911 SCEVHandle CastedMaxBECount =
912 getTruncateOrZeroExtend(MaxBECount, Start->getType());
913 SCEVHandle RecastedMaxBECount =
914 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
915 if (MaxBECount == RecastedMaxBECount) {
916 const Type *WideTy =
917 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
918 // Check whether Start+Step*MaxBECount has no signed overflow.
919 SCEVHandle SMul =
920 getMulExpr(CastedMaxBECount,
921 getTruncateOrSignExtend(Step, Start->getType()));
922 SCEVHandle Add = getAddExpr(Start, SMul);
923 SCEVHandle OperandExtendedAdd =
924 getAddExpr(getSignExtendExpr(Start, WideTy),
925 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
926 getSignExtendExpr(Step, WideTy)));
927 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
928 // Return the expression with the addrec on the outside.
929 return getAddRecExpr(getSignExtendExpr(Start, Ty),
930 getSignExtendExpr(Step, Ty),
931 AR->getLoop());
932 }
933 }
934 }
935
936 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
937 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
938 return Result;
939}
940
941/// getAddExpr - Get a canonical add expression, or something simpler if
942/// possible.
943SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
944 assert(!Ops.empty() && "Cannot get empty add!");
945 if (Ops.size() == 1) return Ops[0];
946#ifndef NDEBUG
947 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
948 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
949 getEffectiveSCEVType(Ops[0]->getType()) &&
950 "SCEVAddExpr operand types don't match!");
951#endif
952
953 // Sort by complexity, this groups all similar expression types together.
954 GroupByComplexity(Ops, LI);
955
956 // If there are any constants, fold them together.
957 unsigned Idx = 0;
958 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
959 ++Idx;
960 assert(Idx < Ops.size());
961 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
962 // We found two constants, fold them together!
963 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
964 RHSC->getValue()->getValue());
965 Ops[0] = getConstant(Fold);
966 Ops.erase(Ops.begin()+1); // Erase the folded element
967 if (Ops.size() == 1) return Ops[0];
968 LHSC = cast<SCEVConstant>(Ops[0]);
969 }
970
971 // If we are left with a constant zero being added, strip it off.
972 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
973 Ops.erase(Ops.begin());
974 --Idx;
975 }
976 }
977
978 if (Ops.size() == 1) return Ops[0];
979
980 // Okay, check to see if the same value occurs in the operand list twice. If
981 // so, merge them together into an multiply expression. Since we sorted the
982 // list, these values are required to be adjacent.
983 const Type *Ty = Ops[0]->getType();
984 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
985 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
986 // Found a match, merge the two values into a multiply, and add any
987 // remaining values to the result.
988 SCEVHandle Two = getIntegerSCEV(2, Ty);
989 SCEVHandle Mul = getMulExpr(Ops[i], Two);
990 if (Ops.size() == 2)
991 return Mul;
992 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
993 Ops.push_back(Mul);
994 return getAddExpr(Ops);
995 }
996
997 // Check for truncates. If all the operands are truncated from the same
998 // type, see if factoring out the truncate would permit the result to be
999 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1000 // if the contents of the resulting outer trunc fold to something simple.
1001 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1002 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1003 const Type *DstType = Trunc->getType();
1004 const Type *SrcType = Trunc->getOperand()->getType();
1005 std::vector<SCEVHandle> LargeOps;
1006 bool Ok = true;
1007 // Check all the operands to see if they can be represented in the
1008 // source type of the truncate.
1009 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1010 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1011 if (T->getOperand()->getType() != SrcType) {
1012 Ok = false;
1013 break;
1014 }
1015 LargeOps.push_back(T->getOperand());
1016 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1017 // This could be either sign or zero extension, but sign extension
1018 // is much more likely to be foldable here.
1019 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1020 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1021 std::vector<SCEVHandle> LargeMulOps;
1022 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1023 if (const SCEVTruncateExpr *T =
1024 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1025 if (T->getOperand()->getType() != SrcType) {
1026 Ok = false;
1027 break;
1028 }
1029 LargeMulOps.push_back(T->getOperand());
1030 } else if (const SCEVConstant *C =
1031 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1032 // This could be either sign or zero extension, but sign extension
1033 // is much more likely to be foldable here.
1034 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1035 } else {
1036 Ok = false;
1037 break;
1038 }
1039 }
1040 if (Ok)
1041 LargeOps.push_back(getMulExpr(LargeMulOps));
1042 } else {
1043 Ok = false;
1044 break;
1045 }
1046 }
1047 if (Ok) {
1048 // Evaluate the expression in the larger type.
1049 SCEVHandle Fold = getAddExpr(LargeOps);
1050 // If it folds to something simple, use it. Otherwise, don't.
1051 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1052 return getTruncateExpr(Fold, DstType);
1053 }
1054 }
1055
1056 // Skip past any other cast SCEVs.
1057 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1058 ++Idx;
1059
1060 // If there are add operands they would be next.
1061 if (Idx < Ops.size()) {
1062 bool DeletedAdd = false;
1063 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1064 // If we have an add, expand the add operands onto the end of the operands
1065 // list.
1066 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1067 Ops.erase(Ops.begin()+Idx);
1068 DeletedAdd = true;
1069 }
1070
1071 // If we deleted at least one add, we added operands to the end of the list,
1072 // and they are not necessarily sorted. Recurse to resort and resimplify
1073 // any operands we just aquired.
1074 if (DeletedAdd)
1075 return getAddExpr(Ops);
1076 }
1077
1078 // Skip over the add expression until we get to a multiply.
1079 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1080 ++Idx;
1081
1082 // If we are adding something to a multiply expression, make sure the
1083 // something is not already an operand of the multiply. If so, merge it into
1084 // the multiply.
1085 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1086 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1087 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1088 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1089 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1090 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
1091 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1092 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
1093 if (Mul->getNumOperands() != 2) {
1094 // If the multiply has more than two operands, we must get the
1095 // Y*Z term.
1096 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1097 MulOps.erase(MulOps.begin()+MulOp);
1098 InnerMul = getMulExpr(MulOps);
1099 }
1100 SCEVHandle One = getIntegerSCEV(1, Ty);
1101 SCEVHandle AddOne = getAddExpr(InnerMul, One);
1102 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1103 if (Ops.size() == 2) return OuterMul;
1104 if (AddOp < Idx) {
1105 Ops.erase(Ops.begin()+AddOp);
1106 Ops.erase(Ops.begin()+Idx-1);
1107 } else {
1108 Ops.erase(Ops.begin()+Idx);
1109 Ops.erase(Ops.begin()+AddOp-1);
1110 }
1111 Ops.push_back(OuterMul);
1112 return getAddExpr(Ops);
1113 }
1114
1115 // Check this multiply against other multiplies being added together.
1116 for (unsigned OtherMulIdx = Idx+1;
1117 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1118 ++OtherMulIdx) {
1119 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1120 // If MulOp occurs in OtherMul, we can fold the two multiplies
1121 // together.
1122 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1123 OMulOp != e; ++OMulOp)
1124 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1125 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1126 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
1127 if (Mul->getNumOperands() != 2) {
1128 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1129 MulOps.erase(MulOps.begin()+MulOp);
1130 InnerMul1 = getMulExpr(MulOps);
1131 }
1132 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1133 if (OtherMul->getNumOperands() != 2) {
1134 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
1135 OtherMul->op_end());
1136 MulOps.erase(MulOps.begin()+OMulOp);
1137 InnerMul2 = getMulExpr(MulOps);
1138 }
1139 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1140 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1141 if (Ops.size() == 2) return OuterMul;
1142 Ops.erase(Ops.begin()+Idx);
1143 Ops.erase(Ops.begin()+OtherMulIdx-1);
1144 Ops.push_back(OuterMul);
1145 return getAddExpr(Ops);
1146 }
1147 }
1148 }
1149 }
1150
1151 // If there are any add recurrences in the operands list, see if any other
1152 // added values are loop invariant. If so, we can fold them into the
1153 // recurrence.
1154 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1155 ++Idx;
1156
1157 // Scan over all recurrences, trying to fold loop invariants into them.
1158 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1159 // Scan all of the other operands to this add and add them to the vector if
1160 // they are loop invariant w.r.t. the recurrence.
1161 std::vector<SCEVHandle> LIOps;
1162 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1163 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1164 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1165 LIOps.push_back(Ops[i]);
1166 Ops.erase(Ops.begin()+i);
1167 --i; --e;
1168 }
1169
1170 // If we found some loop invariants, fold them into the recurrence.
1171 if (!LIOps.empty()) {
1172 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1173 LIOps.push_back(AddRec->getStart());
1174
1175 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
1176 AddRecOps[0] = getAddExpr(LIOps);
1177
1178 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1179 // If all of the other operands were loop invariant, we are done.
1180 if (Ops.size() == 1) return NewRec;
1181
1182 // Otherwise, add the folded AddRec by the non-liv parts.
1183 for (unsigned i = 0;; ++i)
1184 if (Ops[i] == AddRec) {
1185 Ops[i] = NewRec;
1186 break;
1187 }
1188 return getAddExpr(Ops);
1189 }
1190
1191 // Okay, if there weren't any loop invariants to be folded, check to see if
1192 // there are multiple AddRec's with the same loop induction variable being
1193 // added together. If so, we can fold them.
1194 for (unsigned OtherIdx = Idx+1;
1195 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1196 if (OtherIdx != Idx) {
1197 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1198 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1199 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1200 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
1201 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1202 if (i >= NewOps.size()) {
1203 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1204 OtherAddRec->op_end());
1205 break;
1206 }
1207 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1208 }
1209 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1210
1211 if (Ops.size() == 2) return NewAddRec;
1212
1213 Ops.erase(Ops.begin()+Idx);
1214 Ops.erase(Ops.begin()+OtherIdx-1);
1215 Ops.push_back(NewAddRec);
1216 return getAddExpr(Ops);
1217 }
1218 }
1219
1220 // Otherwise couldn't fold anything into this recurrence. Move onto the
1221 // next one.
1222 }
1223
1224 // Okay, it looks like we really DO need an add expr. Check to see if we
1225 // already have one, otherwise create a new one.
1226 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1227 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
1228 SCEVOps)];
1229 if (Result == 0) Result = new SCEVAddExpr(Ops);
1230 return Result;
1231}
1232
1233
1234/// getMulExpr - Get a canonical multiply expression, or something simpler if
1235/// possible.
1236SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
1237 assert(!Ops.empty() && "Cannot get empty mul!");
1238#ifndef NDEBUG
1239 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1240 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1241 getEffectiveSCEVType(Ops[0]->getType()) &&
1242 "SCEVMulExpr operand types don't match!");
1243#endif
1244
1245 // Sort by complexity, this groups all similar expression types together.
1246 GroupByComplexity(Ops, LI);
1247
1248 // If there are any constants, fold them together.
1249 unsigned Idx = 0;
1250 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1251
1252 // C1*(C2+V) -> C1*C2 + C1*V
1253 if (Ops.size() == 2)
1254 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1255 if (Add->getNumOperands() == 2 &&
1256 isa<SCEVConstant>(Add->getOperand(0)))
1257 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1258 getMulExpr(LHSC, Add->getOperand(1)));
1259
1260
1261 ++Idx;
1262 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1263 // We found two constants, fold them together!
1264 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1265 RHSC->getValue()->getValue());
1266 Ops[0] = getConstant(Fold);
1267 Ops.erase(Ops.begin()+1); // Erase the folded element
1268 if (Ops.size() == 1) return Ops[0];
1269 LHSC = cast<SCEVConstant>(Ops[0]);
1270 }
1271
1272 // If we are left with a constant one being multiplied, strip it off.
1273 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1274 Ops.erase(Ops.begin());
1275 --Idx;
1276 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1277 // If we have a multiply of zero, it will always be zero.
1278 return Ops[0];
1279 }
1280 }
1281
1282 // Skip over the add expression until we get to a multiply.
1283 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1284 ++Idx;
1285
1286 if (Ops.size() == 1)
1287 return Ops[0];
1288
1289 // If there are mul operands inline them all into this expression.
1290 if (Idx < Ops.size()) {
1291 bool DeletedMul = false;
1292 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1293 // If we have an mul, expand the mul operands onto the end of the operands
1294 // list.
1295 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1296 Ops.erase(Ops.begin()+Idx);
1297 DeletedMul = true;
1298 }
1299
1300 // If we deleted at least one mul, we added operands to the end of the list,
1301 // and they are not necessarily sorted. Recurse to resort and resimplify
1302 // any operands we just aquired.
1303 if (DeletedMul)
1304 return getMulExpr(Ops);
1305 }
1306
1307 // If there are any add recurrences in the operands list, see if any other
1308 // added values are loop invariant. If so, we can fold them into the
1309 // recurrence.
1310 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1311 ++Idx;
1312
1313 // Scan over all recurrences, trying to fold loop invariants into them.
1314 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1315 // Scan all of the other operands to this mul and add them to the vector if
1316 // they are loop invariant w.r.t. the recurrence.
1317 std::vector<SCEVHandle> LIOps;
1318 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1319 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1320 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1321 LIOps.push_back(Ops[i]);
1322 Ops.erase(Ops.begin()+i);
1323 --i; --e;
1324 }
1325
1326 // If we found some loop invariants, fold them into the recurrence.
1327 if (!LIOps.empty()) {
1328 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1329 std::vector<SCEVHandle> NewOps;
1330 NewOps.reserve(AddRec->getNumOperands());
1331 if (LIOps.size() == 1) {
1332 const SCEV *Scale = LIOps[0];
1333 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1334 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1335 } else {
1336 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1337 std::vector<SCEVHandle> MulOps(LIOps);
1338 MulOps.push_back(AddRec->getOperand(i));
1339 NewOps.push_back(getMulExpr(MulOps));
1340 }
1341 }
1342
1343 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1344
1345 // If all of the other operands were loop invariant, we are done.
1346 if (Ops.size() == 1) return NewRec;
1347
1348 // Otherwise, multiply the folded AddRec by the non-liv parts.
1349 for (unsigned i = 0;; ++i)
1350 if (Ops[i] == AddRec) {
1351 Ops[i] = NewRec;
1352 break;
1353 }
1354 return getMulExpr(Ops);
1355 }
1356
1357 // Okay, if there weren't any loop invariants to be folded, check to see if
1358 // there are multiple AddRec's with the same loop induction variable being
1359 // multiplied together. If so, we can fold them.
1360 for (unsigned OtherIdx = Idx+1;
1361 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1362 if (OtherIdx != Idx) {
1363 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1364 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1365 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1366 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1367 SCEVHandle NewStart = getMulExpr(F->getStart(),
1368 G->getStart());
1369 SCEVHandle B = F->getStepRecurrence(*this);
1370 SCEVHandle D = G->getStepRecurrence(*this);
1371 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1372 getMulExpr(G, B),
1373 getMulExpr(B, D));
1374 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1375 F->getLoop());
1376 if (Ops.size() == 2) return NewAddRec;
1377
1378 Ops.erase(Ops.begin()+Idx);
1379 Ops.erase(Ops.begin()+OtherIdx-1);
1380 Ops.push_back(NewAddRec);
1381 return getMulExpr(Ops);
1382 }
1383 }
1384
1385 // Otherwise couldn't fold anything into this recurrence. Move onto the
1386 // next one.
1387 }
1388
1389 // Okay, it looks like we really DO need an mul expr. Check to see if we
1390 // already have one, otherwise create a new one.
1391 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1392 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1393 SCEVOps)];
1394 if (Result == 0)
1395 Result = new SCEVMulExpr(Ops);
1396 return Result;
1397}
1398
1399/// getUDivExpr - Get a canonical multiply expression, or something simpler if
1400/// possible.
1401SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS,
1402 const SCEVHandle &RHS) {
1403 assert(getEffectiveSCEVType(LHS->getType()) ==
1404 getEffectiveSCEVType(RHS->getType()) &&
1405 "SCEVUDivExpr operand types don't match!");
1406
1407 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1408 if (RHSC->getValue()->equalsInt(1))
1409 return LHS; // X udiv 1 --> x
1410 if (RHSC->isZero())
1411 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1412
1413 // Determine if the division can be folded into the operands of
1414 // its operands.
1415 // TODO: Generalize this to non-constants by using known-bits information.
1416 const Type *Ty = LHS->getType();
1417 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1418 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1419 // For non-power-of-two values, effectively round the value up to the
1420 // nearest power of two.
1421 if (!RHSC->getValue()->getValue().isPowerOf2())
1422 ++MaxShiftAmt;
1423 const IntegerType *ExtTy =
1424 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1425 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1426 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1427 if (const SCEVConstant *Step =
1428 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1429 if (!Step->getValue()->getValue()
1430 .urem(RHSC->getValue()->getValue()) &&
1431 getZeroExtendExpr(AR, ExtTy) ==
1432 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1433 getZeroExtendExpr(Step, ExtTy),
1434 AR->getLoop())) {
1435 std::vector<SCEVHandle> Operands;
1436 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1437 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1438 return getAddRecExpr(Operands, AR->getLoop());
1439 }
1440 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1441 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1442 std::vector<SCEVHandle> Operands;
1443 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1444 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1445 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1446 // Find an operand that's safely divisible.
1447 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1448 SCEVHandle Op = M->getOperand(i);
1449 SCEVHandle Div = getUDivExpr(Op, RHSC);
1450 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1451 Operands = M->getOperands();
1452 Operands[i] = Div;
1453 return getMulExpr(Operands);
1454 }
1455 }
1456 }
1457 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1458 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1459 std::vector<SCEVHandle> Operands;
1460 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1461 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1462 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1463 Operands.clear();
1464 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1465 SCEVHandle Op = getUDivExpr(A->getOperand(i), RHS);
1466 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1467 break;
1468 Operands.push_back(Op);
1469 }
1470 if (Operands.size() == A->getNumOperands())
1471 return getAddExpr(Operands);
1472 }
1473 }
1474
1475 // Fold if both operands are constant.
1476 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1477 Constant *LHSCV = LHSC->getValue();
1478 Constant *RHSCV = RHSC->getValue();
1479 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1480 }
1481 }
1482
1483 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1484 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1485 return Result;
1486}
1487
1488
1489/// getAddRecExpr - Get an add recurrence expression for the specified loop.
1490/// Simplify the expression as much as possible.
1491SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1492 const SCEVHandle &Step, const Loop *L) {
1493 std::vector<SCEVHandle> Operands;
1494 Operands.push_back(Start);
1495 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1496 if (StepChrec->getLoop() == L) {
1497 Operands.insert(Operands.end(), StepChrec->op_begin(),
1498 StepChrec->op_end());
1499 return getAddRecExpr(Operands, L);
1500 }
1501
1502 Operands.push_back(Step);
1503 return getAddRecExpr(Operands, L);
1504}
1505
1506/// getAddRecExpr - Get an add recurrence expression for the specified loop.
1507/// Simplify the expression as much as possible.
1508SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1509 const Loop *L) {
1510 if (Operands.size() == 1) return Operands[0];
1511#ifndef NDEBUG
1512 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1513 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1514 getEffectiveSCEVType(Operands[0]->getType()) &&
1515 "SCEVAddRecExpr operand types don't match!");
1516#endif
1517
1518 if (Operands.back()->isZero()) {
1519 Operands.pop_back();
1520 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1521 }
1522
1523 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1524 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1525 const Loop* NestedLoop = NestedAR->getLoop();
1526 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1527 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1528 NestedAR->op_end());
1529 SCEVHandle NestedARHandle(NestedAR);
1530 Operands[0] = NestedAR->getStart();
1531 NestedOperands[0] = getAddRecExpr(Operands, L);
1532 return getAddRecExpr(NestedOperands, NestedLoop);
1533 }
1534 }
1535
1536 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
1537 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)];
1538 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1539 return Result;
1540}
1541
1542SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1543 const SCEVHandle &RHS) {
1544 std::vector<SCEVHandle> Ops;
1545 Ops.push_back(LHS);
1546 Ops.push_back(RHS);
1547 return getSMaxExpr(Ops);
1548}
1549
1550SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1551 assert(!Ops.empty() && "Cannot get empty smax!");
1552 if (Ops.size() == 1) return Ops[0];
1553#ifndef NDEBUG
1554 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1555 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1556 getEffectiveSCEVType(Ops[0]->getType()) &&
1557 "SCEVSMaxExpr operand types don't match!");
1558#endif
1559
1560 // Sort by complexity, this groups all similar expression types together.
1561 GroupByComplexity(Ops, LI);
1562
1563 // If there are any constants, fold them together.
1564 unsigned Idx = 0;
1565 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1566 ++Idx;
1567 assert(Idx < Ops.size());
1568 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1569 // We found two constants, fold them together!
1570 ConstantInt *Fold = ConstantInt::get(
1571 APIntOps::smax(LHSC->getValue()->getValue(),
1572 RHSC->getValue()->getValue()));
1573 Ops[0] = getConstant(Fold);
1574 Ops.erase(Ops.begin()+1); // Erase the folded element
1575 if (Ops.size() == 1) return Ops[0];
1576 LHSC = cast<SCEVConstant>(Ops[0]);
1577 }
1578
1579 // If we are left with a constant -inf, strip it off.
1580 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1581 Ops.erase(Ops.begin());
1582 --Idx;
1583 }
1584 }
1585
1586 if (Ops.size() == 1) return Ops[0];
1587
1588 // Find the first SMax
1589 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1590 ++Idx;
1591
1592 // Check to see if one of the operands is an SMax. If so, expand its operands
1593 // onto our operand list, and recurse to simplify.
1594 if (Idx < Ops.size()) {
1595 bool DeletedSMax = false;
1596 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1597 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1598 Ops.erase(Ops.begin()+Idx);
1599 DeletedSMax = true;
1600 }
1601
1602 if (DeletedSMax)
1603 return getSMaxExpr(Ops);
1604 }
1605
1606 // Okay, check to see if the same value occurs in the operand list twice. If
1607 // so, delete one. Since we sorted the list, these values are required to
1608 // be adjacent.
1609 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1610 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1611 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1612 --i; --e;
1613 }
1614
1615 if (Ops.size() == 1) return Ops[0];
1616
1617 assert(!Ops.empty() && "Reduced smax down to nothing!");
1618
1619 // Okay, it looks like we really DO need an smax expr. Check to see if we
1620 // already have one, otherwise create a new one.
1621 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1622 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1623 SCEVOps)];
1624 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1625 return Result;
1626}
1627
1628SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1629 const SCEVHandle &RHS) {
1630 std::vector<SCEVHandle> Ops;
1631 Ops.push_back(LHS);
1632 Ops.push_back(RHS);
1633 return getUMaxExpr(Ops);
1634}
1635
1636SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1637 assert(!Ops.empty() && "Cannot get empty umax!");
1638 if (Ops.size() == 1) return Ops[0];
1639#ifndef NDEBUG
1640 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1641 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1642 getEffectiveSCEVType(Ops[0]->getType()) &&
1643 "SCEVUMaxExpr operand types don't match!");
1644#endif
1645
1646 // Sort by complexity, this groups all similar expression types together.
1647 GroupByComplexity(Ops, LI);
1648
1649 // If there are any constants, fold them together.
1650 unsigned Idx = 0;
1651 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1652 ++Idx;
1653 assert(Idx < Ops.size());
1654 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1655 // We found two constants, fold them together!
1656 ConstantInt *Fold = ConstantInt::get(
1657 APIntOps::umax(LHSC->getValue()->getValue(),
1658 RHSC->getValue()->getValue()));
1659 Ops[0] = getConstant(Fold);
1660 Ops.erase(Ops.begin()+1); // Erase the folded element
1661 if (Ops.size() == 1) return Ops[0];
1662 LHSC = cast<SCEVConstant>(Ops[0]);
1663 }
1664
1665 // If we are left with a constant zero, strip it off.
1666 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1667 Ops.erase(Ops.begin());
1668 --Idx;
1669 }
1670 }
1671
1672 if (Ops.size() == 1) return Ops[0];
1673
1674 // Find the first UMax
1675 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1676 ++Idx;
1677
1678 // Check to see if one of the operands is a UMax. If so, expand its operands
1679 // onto our operand list, and recurse to simplify.
1680 if (Idx < Ops.size()) {
1681 bool DeletedUMax = false;
1682 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1683 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1684 Ops.erase(Ops.begin()+Idx);
1685 DeletedUMax = true;
1686 }
1687
1688 if (DeletedUMax)
1689 return getUMaxExpr(Ops);
1690 }
1691
1692 // Okay, check to see if the same value occurs in the operand list twice. If
1693 // so, delete one. Since we sorted the list, these values are required to
1694 // be adjacent.
1695 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1696 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1697 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1698 --i; --e;
1699 }
1700
1701 if (Ops.size() == 1) return Ops[0];
1702
1703 assert(!Ops.empty() && "Reduced umax down to nothing!");
1704
1705 // Okay, it looks like we really DO need a umax expr. Check to see if we
1706 // already have one, otherwise create a new one.
1707 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1708 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1709 SCEVOps)];
1710 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1711 return Result;
1712}
1713
1714SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1715 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1716 return getConstant(CI);
1717 if (isa<ConstantPointerNull>(V))
1718 return getIntegerSCEV(0, V->getType());
1719 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1720 if (Result == 0) Result = new SCEVUnknown(V);
1721 return Result;
1722}
1723
1724//===----------------------------------------------------------------------===//
1725// Basic SCEV Analysis and PHI Idiom Recognition Code
1726//
1727
1728/// isSCEVable - Test if values of the given type are analyzable within
1729/// the SCEV framework. This primarily includes integer types, and it
1730/// can optionally include pointer types if the ScalarEvolution class
1731/// has access to target-specific information.
1732bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1733 // Integers are always SCEVable.
1734 if (Ty->isInteger())
1735 return true;
1736
1737 // Pointers are SCEVable if TargetData information is available
1738 // to provide pointer size information.
1739 if (isa<PointerType>(Ty))
1740 return TD != NULL;
1741
1742 // Otherwise it's not SCEVable.
1743 return false;
1744}
1745
1746/// getTypeSizeInBits - Return the size in bits of the specified type,
1747/// for which isSCEVable must return true.
1748uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1749 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1750
1751 // If we have a TargetData, use it!
1752 if (TD)
1753 return TD->getTypeSizeInBits(Ty);
1754
1755 // Otherwise, we support only integer types.
1756 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1757 return Ty->getPrimitiveSizeInBits();
1758}
1759
1760/// getEffectiveSCEVType - Return a type with the same bitwidth as
1761/// the given type and which represents how SCEV will treat the given
1762/// type, for which isSCEVable must return true. For pointer types,
1763/// this is the pointer-sized integer type.
1764const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1765 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1766
1767 if (Ty->isInteger())
1768 return Ty;
1769
1770 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1771 return TD->getIntPtrType();
1772}
1773
1774SCEVHandle ScalarEvolution::getCouldNotCompute() {
1775 return UnknownValue;
1776}
1777
1778/// hasSCEV - Return true if the SCEV for this value has already been
1779/// computed.
1780bool ScalarEvolution::hasSCEV(Value *V) const {
1781 return Scalars.count(V);
1782}
1783
1784/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1785/// expression and create a new one.
1786SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1787 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1788
1789 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
1790 if (I != Scalars.end()) return I->second;
1791 SCEVHandle S = createSCEV(V);
1792 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
1793 return S;
1794}
1795
1796/// getIntegerSCEV - Given an integer or FP type, create a constant for the
1797/// specified signed integer value and return a SCEV for the constant.
1798SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1799 Ty = getEffectiveSCEVType(Ty);
1800 Constant *C;
1801 if (Val == 0)
1802 C = Constant::getNullValue(Ty);
1803 else if (Ty->isFloatingPoint())
1804 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1805 APFloat::IEEEdouble, Val));
1806 else
1807 C = ConstantInt::get(Ty, Val);
1808 return getUnknown(C);
1809}
1810
1811/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1812///
1813SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1814 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1815 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1816
1817 const Type *Ty = V->getType();
1818 Ty = getEffectiveSCEVType(Ty);
1819 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1820}
1821
1822/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1823SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1824 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1825 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1826
1827 const Type *Ty = V->getType();
1828 Ty = getEffectiveSCEVType(Ty);
1829 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1830 return getMinusSCEV(AllOnes, V);
1831}
1832
1833/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1834///
1835SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1836 const SCEVHandle &RHS) {
1837 // X - Y --> X + -Y
1838 return getAddExpr(LHS, getNegativeSCEV(RHS));
1839}
1840
1841/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1842/// input value to the specified type. If the type must be extended, it is zero
1843/// extended.
1844SCEVHandle
1845ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1846 const Type *Ty) {
1847 const Type *SrcTy = V->getType();
1848 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1849 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1850 "Cannot truncate or zero extend with non-integer arguments!");
1851 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1852 return V; // No conversion
1853 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1854 return getTruncateExpr(V, Ty);
1855 return getZeroExtendExpr(V, Ty);
1856}
1857
1858/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1859/// input value to the specified type. If the type must be extended, it is sign
1860/// extended.
1861SCEVHandle
1862ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1863 const Type *Ty) {
1864 const Type *SrcTy = V->getType();
1865 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1866 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1867 "Cannot truncate or zero extend with non-integer arguments!");
1868 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1869 return V; // No conversion
1870 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1871 return getTruncateExpr(V, Ty);
1872 return getSignExtendExpr(V, Ty);
1873}
1874
1875/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
1876/// input value to the specified type. If the type must be extended, it is zero
1877/// extended. The conversion must not be narrowing.
1878SCEVHandle
1879ScalarEvolution::getNoopOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
1880 const Type *SrcTy = V->getType();
1881 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1882 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1883 "Cannot noop or zero extend with non-integer arguments!");
1884 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1885 "getNoopOrZeroExtend cannot truncate!");
1886 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1887 return V; // No conversion
1888 return getZeroExtendExpr(V, Ty);
1889}
1890
1891/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
1892/// input value to the specified type. If the type must be extended, it is sign
1893/// extended. The conversion must not be narrowing.
1894SCEVHandle
1895ScalarEvolution::getNoopOrSignExtend(const SCEVHandle &V, const Type *Ty) {
1896 const Type *SrcTy = V->getType();
1897 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1898 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1899 "Cannot noop or sign extend with non-integer arguments!");
1900 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1901 "getNoopOrSignExtend cannot truncate!");
1902 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1903 return V; // No conversion
1904 return getSignExtendExpr(V, Ty);
1905}
1906
1907/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
1908/// input value to the specified type. The conversion must not be widening.
1909SCEVHandle
1910ScalarEvolution::getTruncateOrNoop(const SCEVHandle &V, const Type *Ty) {
1911 const Type *SrcTy = V->getType();
1912 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1913 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1914 "Cannot truncate or noop with non-integer arguments!");
1915 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
1916 "getTruncateOrNoop cannot extend!");
1917 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1918 return V; // No conversion
1919 return getTruncateExpr(V, Ty);
1920}
1921
1922/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1923/// the specified instruction and replaces any references to the symbolic value
1924/// SymName with the specified value. This is used during PHI resolution.
1925void ScalarEvolution::
1926ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1927 const SCEVHandle &NewVal) {
1928 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
1929 Scalars.find(SCEVCallbackVH(I, this));
1930 if (SI == Scalars.end()) return;
1931
1932 SCEVHandle NV =
1933 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
1934 if (NV == SI->second) return; // No change.
1935
1936 SI->second = NV; // Update the scalars map!
1937
1938 // Any instruction values that use this instruction might also need to be
1939 // updated!
1940 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1941 UI != E; ++UI)
1942 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1943}
1944
1945/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1946/// a loop header, making it a potential recurrence, or it doesn't.
1947///
1948SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
1949 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1950 if (const Loop *L = LI->getLoopFor(PN->getParent()))
1951 if (L->getHeader() == PN->getParent()) {
1952 // If it lives in the loop header, it has two incoming values, one
1953 // from outside the loop, and one from inside.
1954 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1955 unsigned BackEdge = IncomingEdge^1;
1956
1957 // While we are analyzing this PHI node, handle its value symbolically.
1958 SCEVHandle SymbolicName = getUnknown(PN);
1959 assert(Scalars.find(PN) == Scalars.end() &&
1960 "PHI node already processed?");
1961 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
1962
1963 // Using this symbolic name for the PHI, analyze the value coming around
1964 // the back-edge.
1965 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1966
1967 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1968 // has a special value for the first iteration of the loop.
1969
1970 // If the value coming around the backedge is an add with the symbolic
1971 // value we just inserted, then we found a simple induction variable!
1972 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1973 // If there is a single occurrence of the symbolic value, replace it
1974 // with a recurrence.
1975 unsigned FoundIndex = Add->getNumOperands();
1976 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1977 if (Add->getOperand(i) == SymbolicName)
1978 if (FoundIndex == e) {
1979 FoundIndex = i;
1980 break;
1981 }
1982
1983 if (FoundIndex != Add->getNumOperands()) {
1984 // Create an add with everything but the specified operand.
1985 std::vector<SCEVHandle> Ops;
1986 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1987 if (i != FoundIndex)
1988 Ops.push_back(Add->getOperand(i));
1989 SCEVHandle Accum = getAddExpr(Ops);
1990
1991 // This is not a valid addrec if the step amount is varying each
1992 // loop iteration, but is not itself an addrec in this loop.
1993 if (Accum->isLoopInvariant(L) ||
1994 (isa<SCEVAddRecExpr>(Accum) &&
1995 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1996 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1997 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
1998
1999 // Okay, for the entire analysis of this edge we assumed the PHI
2000 // to be symbolic. We now need to go back and update all of the
2001 // entries for the scalars that use the PHI (except for the PHI
2002 // itself) to use the new analyzed value instead of the "symbolic"
2003 // value.
2004 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2005 return PHISCEV;
2006 }
2007 }
2008 } else if (const SCEVAddRecExpr *AddRec =
2009 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2010 // Otherwise, this could be a loop like this:
2011 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2012 // In this case, j = {1,+,1} and BEValue is j.
2013 // Because the other in-value of i (0) fits the evolution of BEValue
2014 // i really is an addrec evolution.
2015 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2016 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2017
2018 // If StartVal = j.start - j.stride, we can use StartVal as the
2019 // initial step of the addrec evolution.
2020 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2021 AddRec->getOperand(1))) {
2022 SCEVHandle PHISCEV =
2023 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2024
2025 // Okay, for the entire analysis of this edge we assumed the PHI
2026 // to be symbolic. We now need to go back and update all of the
2027 // entries for the scalars that use the PHI (except for the PHI
2028 // itself) to use the new analyzed value instead of the "symbolic"
2029 // value.
2030 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2031 return PHISCEV;
2032 }
2033 }
2034 }
2035
2036 return SymbolicName;
2037 }
2038
2039 // If it's not a loop phi, we can't handle it yet.
2040 return getUnknown(PN);
2041}
2042
2043/// createNodeForGEP - Expand GEP instructions into add and multiply
2044/// operations. This allows them to be analyzed by regular SCEV code.
2045///
2046SCEVHandle ScalarEvolution::createNodeForGEP(User *GEP) {
2047
2048 const Type *IntPtrTy = TD->getIntPtrType();
2049 Value *Base = GEP->getOperand(0);
2050 // Don't attempt to analyze GEPs over unsized objects.
2051 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2052 return getUnknown(GEP);
2053 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
2054 gep_type_iterator GTI = gep_type_begin(GEP);
2055 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2056 E = GEP->op_end();
2057 I != E; ++I) {
2058 Value *Index = *I;
2059 // Compute the (potentially symbolic) offset in bytes for this index.
2060 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2061 // For a struct, add the member offset.
2062 const StructLayout &SL = *TD->getStructLayout(STy);
2063 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2064 uint64_t Offset = SL.getElementOffset(FieldNo);
2065 TotalOffset = getAddExpr(TotalOffset,
2066 getIntegerSCEV(Offset, IntPtrTy));
2067 } else {
2068 // For an array, add the element offset, explicitly scaled.
2069 SCEVHandle LocalOffset = getSCEV(Index);
2070 if (!isa<PointerType>(LocalOffset->getType()))
2071 // Getelementptr indicies are signed.
2072 LocalOffset = getTruncateOrSignExtend(LocalOffset,
2073 IntPtrTy);
2074 LocalOffset =
2075 getMulExpr(LocalOffset,
2076 getIntegerSCEV(TD->getTypeAllocSize(*GTI),
2077 IntPtrTy));
2078 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2079 }
2080 }
2081 return getAddExpr(getSCEV(Base), TotalOffset);
2082}
2083
2084/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2085/// guaranteed to end in (at every loop iteration). It is, at the same time,
2086/// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2087/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2088static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
2089 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2090 return C->getValue()->getValue().countTrailingZeros();
2091
2092 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2093 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
2094 (uint32_t)SE.getTypeSizeInBits(T->getType()));
2095
2096 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2097 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2098 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2099 SE.getTypeSizeInBits(E->getType()) : OpRes;
2100 }
2101
2102 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2103 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2104 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2105 SE.getTypeSizeInBits(E->getType()) : OpRes;
2106 }
2107
2108 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2109 // The result is the min of all operands results.
2110 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2111 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2112 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2113 return MinOpRes;
2114 }
2115
2116 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2117 // The result is the sum of all operands results.
2118 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2119 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
2120 for (unsigned i = 1, e = M->getNumOperands();
2121 SumOpRes != BitWidth && i != e; ++i)
2122 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
2123 BitWidth);
2124 return SumOpRes;
2125 }
2126
2127 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2128 // The result is the min of all operands results.
2129 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2130 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2131 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2132 return MinOpRes;
2133 }
2134
2135 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2136 // The result is the min of all operands results.
2137 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2138 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2139 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2140 return MinOpRes;
2141 }
2142
2143 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2144 // The result is the min of all operands results.
2145 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2146 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2147 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2148 return MinOpRes;
2149 }
2150
2151 // SCEVUDivExpr, SCEVUnknown
2152 return 0;
2153}
2154
2155/// createSCEV - We know that there is no SCEV for the specified value.
2156/// Analyze the expression.
2157///
2158SCEVHandle ScalarEvolution::createSCEV(Value *V) {
2159 if (!isSCEVable(V->getType()))
2160 return getUnknown(V);
2161
2162 unsigned Opcode = Instruction::UserOp1;
2163 if (Instruction *I = dyn_cast<Instruction>(V))
2164 Opcode = I->getOpcode();
2165 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2166 Opcode = CE->getOpcode();
2167 else
2168 return getUnknown(V);
2169
2170 User *U = cast<User>(V);
2171 switch (Opcode) {
2172 case Instruction::Add:
2173 return getAddExpr(getSCEV(U->getOperand(0)),
2174 getSCEV(U->getOperand(1)));
2175 case Instruction::Mul:
2176 return getMulExpr(getSCEV(U->getOperand(0)),
2177 getSCEV(U->getOperand(1)));
2178 case Instruction::UDiv:
2179 return getUDivExpr(getSCEV(U->getOperand(0)),
2180 getSCEV(U->getOperand(1)));
2181 case Instruction::Sub:
2182 return getMinusSCEV(getSCEV(U->getOperand(0)),
2183 getSCEV(U->getOperand(1)));
2184 case Instruction::And:
2185 // For an expression like x&255 that merely masks off the high bits,
2186 // use zext(trunc(x)) as the SCEV expression.
2187 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2188 if (CI->isNullValue())
2189 return getSCEV(U->getOperand(1));
2190 if (CI->isAllOnesValue())
2191 return getSCEV(U->getOperand(0));
2192 const APInt &A = CI->getValue();
2193 unsigned Ones = A.countTrailingOnes();
2194 if (APIntOps::isMask(Ones, A))
2195 return
2196 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2197 IntegerType::get(Ones)),
2198 U->getType());
2199 }
2200 break;
2201 case Instruction::Or:
2202 // If the RHS of the Or is a constant, we may have something like:
2203 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2204 // optimizations will transparently handle this case.
2205 //
2206 // In order for this transformation to be safe, the LHS must be of the
2207 // form X*(2^n) and the Or constant must be less than 2^n.
2208 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2209 SCEVHandle LHS = getSCEV(U->getOperand(0));
2210 const APInt &CIVal = CI->getValue();
2211 if (GetMinTrailingZeros(LHS, *this) >=
2212 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2213 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2214 }
2215 break;
2216 case Instruction::Xor:
2217 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2218 // If the RHS of the xor is a signbit, then this is just an add.
2219 // Instcombine turns add of signbit into xor as a strength reduction step.
2220 if (CI->getValue().isSignBit())
2221 return getAddExpr(getSCEV(U->getOperand(0)),
2222 getSCEV(U->getOperand(1)));
2223
2224 // If the RHS of xor is -1, then this is a not operation.
2225 if (CI->isAllOnesValue())
2226 return getNotSCEV(getSCEV(U->getOperand(0)));
2227
2228 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2229 // This is a variant of the check for xor with -1, and it handles
2230 // the case where instcombine has trimmed non-demanded bits out
2231 // of an xor with -1.
2232 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2233 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2234 if (BO->getOpcode() == Instruction::And &&
2235 LCI->getValue() == CI->getValue())
2236 if (const SCEVZeroExtendExpr *Z =
2237 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0))))
2238 return getZeroExtendExpr(getNotSCEV(Z->getOperand()),
2239 U->getType());
2240 }
2241 break;
2242
2243 case Instruction::Shl:
2244 // Turn shift left of a constant amount into a multiply.
2245 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2246 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2247 Constant *X = ConstantInt::get(
2248 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2249 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2250 }
2251 break;
2252
2253 case Instruction::LShr:
2254 // Turn logical shift right of a constant into a unsigned divide.
2255 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2256 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2257 Constant *X = ConstantInt::get(
2258 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2259 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2260 }
2261 break;
2262
2263 case Instruction::AShr:
2264 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2265 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2266 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2267 if (L->getOpcode() == Instruction::Shl &&
2268 L->getOperand(1) == U->getOperand(1)) {
2269 unsigned BitWidth = getTypeSizeInBits(U->getType());
2270 uint64_t Amt = BitWidth - CI->getZExtValue();
2271 if (Amt == BitWidth)
2272 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2273 if (Amt > BitWidth)
2274 return getIntegerSCEV(0, U->getType()); // value is undefined
2275 return
2276 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2277 IntegerType::get(Amt)),
2278 U->getType());
2279 }
2280 break;
2281
2282 case Instruction::Trunc:
2283 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2284
2285 case Instruction::ZExt:
2286 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2287
2288 case Instruction::SExt:
2289 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2290
2291 case Instruction::BitCast:
2292 // BitCasts are no-op casts so we just eliminate the cast.
2293 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2294 return getSCEV(U->getOperand(0));
2295 break;
2296
2297 case Instruction::IntToPtr:
2298 if (!TD) break; // Without TD we can't analyze pointers.
2299 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2300 TD->getIntPtrType());
2301
2302 case Instruction::PtrToInt:
2303 if (!TD) break; // Without TD we can't analyze pointers.
2304 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2305 U->getType());
2306
2307 case Instruction::GetElementPtr:
2308 if (!TD) break; // Without TD we can't analyze pointers.
2309 return createNodeForGEP(U);
2310
2311 case Instruction::PHI:
2312 return createNodeForPHI(cast<PHINode>(U));
2313
2314 case Instruction::Select:
2315 // This could be a smax or umax that was lowered earlier.
2316 // Try to recover it.
2317 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2318 Value *LHS = ICI->getOperand(0);
2319 Value *RHS = ICI->getOperand(1);
2320 switch (ICI->getPredicate()) {
2321 case ICmpInst::ICMP_SLT:
2322 case ICmpInst::ICMP_SLE:
2323 std::swap(LHS, RHS);
2324 // fall through
2325 case ICmpInst::ICMP_SGT:
2326 case ICmpInst::ICMP_SGE:
2327 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2328 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2329 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2330 // ~smax(~x, ~y) == smin(x, y).
2331 return getNotSCEV(getSMaxExpr(
2332 getNotSCEV(getSCEV(LHS)),
2333 getNotSCEV(getSCEV(RHS))));
2334 break;
2335 case ICmpInst::ICMP_ULT:
2336 case ICmpInst::ICMP_ULE:
2337 std::swap(LHS, RHS);
2338 // fall through
2339 case ICmpInst::ICMP_UGT:
2340 case ICmpInst::ICMP_UGE:
2341 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2342 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2343 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2344 // ~umax(~x, ~y) == umin(x, y)
2345 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2346 getNotSCEV(getSCEV(RHS))));
2347 break;
2348 default:
2349 break;
2350 }
2351 }
2352
2353 default: // We cannot analyze this expression.
2354 break;
2355 }
2356
2357 return getUnknown(V);
2358}
2359
2360
2361
2362//===----------------------------------------------------------------------===//
2363// Iteration Count Computation Code
2364//
2365
2366/// getBackedgeTakenCount - If the specified loop has a predictable
2367/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2368/// object. The backedge-taken count is the number of times the loop header
2369/// will be branched to from within the loop. This is one less than the
2370/// trip count of the loop, since it doesn't count the first iteration,
2371/// when the header is branched to from outside the loop.
2372///
2373/// Note that it is not valid to call this method on a loop without a
2374/// loop-invariant backedge-taken count (see
2375/// hasLoopInvariantBackedgeTakenCount).
2376///
2377SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2378 return getBackedgeTakenInfo(L).Exact;
2379}
2380
2381/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2382/// return the least SCEV value that is known never to be less than the
2383/// actual backedge taken count.
2384SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2385 return getBackedgeTakenInfo(L).Max;
2386}
2387
2388const ScalarEvolution::BackedgeTakenInfo &
2389ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2390 // Initially insert a CouldNotCompute for this loop. If the insertion
2391 // succeeds, procede to actually compute a backedge-taken count and
2392 // update the value. The temporary CouldNotCompute value tells SCEV
2393 // code elsewhere that it shouldn't attempt to request a new
2394 // backedge-taken count, which could result in infinite recursion.
2395 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2396 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2397 if (Pair.second) {
2398 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2399 if (ItCount.Exact != UnknownValue) {
2400 assert(ItCount.Exact->isLoopInvariant(L) &&
2401 ItCount.Max->isLoopInvariant(L) &&
2402 "Computed trip count isn't loop invariant for loop!");
2403 ++NumTripCountsComputed;
2404
2405 // Update the value in the map.
2406 Pair.first->second = ItCount;
2407 } else if (isa<PHINode>(L->getHeader()->begin())) {
2408 // Only count loops that have phi nodes as not being computable.
2409 ++NumTripCountsNotComputed;
2410 }
2411
2412 // Now that we know more about the trip count for this loop, forget any
2413 // existing SCEV values for PHI nodes in this loop since they are only
2414 // conservative estimates made without the benefit
2415 // of trip count information.
2416 if (ItCount.hasAnyInfo())
2417 forgetLoopPHIs(L);
2418 }
2419 return Pair.first->second;
2420}
2421
2422/// forgetLoopBackedgeTakenCount - This method should be called by the
2423/// client when it has changed a loop in a way that may effect
2424/// ScalarEvolution's ability to compute a trip count, or if the loop
2425/// is deleted.
2426void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2427 BackedgeTakenCounts.erase(L);
2428 forgetLoopPHIs(L);
2429}
2430
2431/// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2432/// PHI nodes in the given loop. This is used when the trip count of
2433/// the loop may have changed.
2434void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2435 BasicBlock *Header = L->getHeader();
2436
2437 // Push all Loop-header PHIs onto the Worklist stack, except those
2438 // that are presently represented via a SCEVUnknown. SCEVUnknown for
2439 // a PHI either means that it has an unrecognized structure, or it's
2440 // a PHI that's in the progress of being computed by createNodeForPHI.
2441 // In the former case, additional loop trip count information isn't
2442 // going to change anything. In the later case, createNodeForPHI will
2443 // perform the necessary updates on its own when it gets to that point.
2444 SmallVector<Instruction *, 16> Worklist;
2445 for (BasicBlock::iterator I = Header->begin();
2446 PHINode *PN = dyn_cast<PHINode>(I); ++I) {
2447 std::map<SCEVCallbackVH, SCEVHandle>::iterator It = Scalars.find((Value*)I);
2448 if (It != Scalars.end() && !isa<SCEVUnknown>(It->second))
2449 Worklist.push_back(PN);
2450 }
2451
2452 while (!Worklist.empty()) {
2453 Instruction *I = Worklist.pop_back_val();
2454 if (Scalars.erase(I))
2455 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2456 UI != UE; ++UI)
2457 Worklist.push_back(cast<Instruction>(UI));
2458 }
2459}
2460
2461/// ComputeBackedgeTakenCount - Compute the number of times the backedge
2462/// of the specified loop will execute.
2463ScalarEvolution::BackedgeTakenInfo
2464ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2465 // If the loop has a non-one exit block count, we can't analyze it.
| 83#include <algorithm>
84using namespace llvm;
85
86STATISTIC(NumArrayLenItCounts,
87 "Number of trip counts computed with array length");
88STATISTIC(NumTripCountsComputed,
89 "Number of loops with predictable loop counts");
90STATISTIC(NumTripCountsNotComputed,
91 "Number of loops without predictable loop counts");
92STATISTIC(NumBruteForceTripCountsComputed,
93 "Number of loops with trip counts computed by force");
94
95static cl::opt<unsigned>
96MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
97 cl::desc("Maximum number of iterations SCEV will "
98 "symbolically execute a constant derived loop"),
99 cl::init(100));
100
101static RegisterPass<ScalarEvolution>
102R("scalar-evolution", "Scalar Evolution Analysis", false, true);
103char ScalarEvolution::ID = 0;
104
105//===----------------------------------------------------------------------===//
106// SCEV class definitions
107//===----------------------------------------------------------------------===//
108
109//===----------------------------------------------------------------------===//
110// Implementation of the SCEV class.
111//
112SCEV::~SCEV() {}
113void SCEV::dump() const {
114 print(errs());
115 errs() << '\n';
116}
117
118void SCEV::print(std::ostream &o) const {
119 raw_os_ostream OS(o);
120 print(OS);
121}
122
123bool SCEV::isZero() const {
124 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
125 return SC->getValue()->isZero();
126 return false;
127}
128
129bool SCEV::isOne() const {
130 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
131 return SC->getValue()->isOne();
132 return false;
133}
134
135SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
136SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
137
138bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
139 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
140 return false;
141}
142
143const Type *SCEVCouldNotCompute::getType() const {
144 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
145 return 0;
146}
147
148bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
149 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
150 return false;
151}
152
153SCEVHandle SCEVCouldNotCompute::
154replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
155 const SCEVHandle &Conc,
156 ScalarEvolution &SE) const {
157 return this;
158}
159
160void SCEVCouldNotCompute::print(raw_ostream &OS) const {
161 OS << "***COULDNOTCOMPUTE***";
162}
163
164bool SCEVCouldNotCompute::classof(const SCEV *S) {
165 return S->getSCEVType() == scCouldNotCompute;
166}
167
168
169// SCEVConstants - Only allow the creation of one SCEVConstant for any
170// particular value. Don't use a SCEVHandle here, or else the object will
171// never be deleted!
172static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
173
174
175SCEVConstant::~SCEVConstant() {
176 SCEVConstants->erase(V);
177}
178
179SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
180 SCEVConstant *&R = (*SCEVConstants)[V];
181 if (R == 0) R = new SCEVConstant(V);
182 return R;
183}
184
185SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
186 return getConstant(ConstantInt::get(Val));
187}
188
189const Type *SCEVConstant::getType() const { return V->getType(); }
190
191void SCEVConstant::print(raw_ostream &OS) const {
192 WriteAsOperand(OS, V, false);
193}
194
195SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
196 const SCEVHandle &op, const Type *ty)
197 : SCEV(SCEVTy), Op(op), Ty(ty) {}
198
199SCEVCastExpr::~SCEVCastExpr() {}
200
201bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
202 return Op->dominates(BB, DT);
203}
204
205// SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
206// particular input. Don't use a SCEVHandle here, or else the object will
207// never be deleted!
208static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
209 SCEVTruncateExpr*> > SCEVTruncates;
210
211SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
212 : SCEVCastExpr(scTruncate, op, ty) {
213 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
214 (Ty->isInteger() || isa<PointerType>(Ty)) &&
215 "Cannot truncate non-integer value!");
216}
217
218SCEVTruncateExpr::~SCEVTruncateExpr() {
219 SCEVTruncates->erase(std::make_pair(Op, Ty));
220}
221
222void SCEVTruncateExpr::print(raw_ostream &OS) const {
223 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
224}
225
226// SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
227// particular input. Don't use a SCEVHandle here, or else the object will never
228// be deleted!
229static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
230 SCEVZeroExtendExpr*> > SCEVZeroExtends;
231
232SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
233 : SCEVCastExpr(scZeroExtend, op, ty) {
234 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
235 (Ty->isInteger() || isa<PointerType>(Ty)) &&
236 "Cannot zero extend non-integer value!");
237}
238
239SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
240 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
241}
242
243void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
244 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
245}
246
247// SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
248// particular input. Don't use a SCEVHandle here, or else the object will never
249// be deleted!
250static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
251 SCEVSignExtendExpr*> > SCEVSignExtends;
252
253SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
254 : SCEVCastExpr(scSignExtend, op, ty) {
255 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
256 (Ty->isInteger() || isa<PointerType>(Ty)) &&
257 "Cannot sign extend non-integer value!");
258}
259
260SCEVSignExtendExpr::~SCEVSignExtendExpr() {
261 SCEVSignExtends->erase(std::make_pair(Op, Ty));
262}
263
264void SCEVSignExtendExpr::print(raw_ostream &OS) const {
265 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
266}
267
268// SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
269// particular input. Don't use a SCEVHandle here, or else the object will never
270// be deleted!
271static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >,
272 SCEVCommutativeExpr*> > SCEVCommExprs;
273
274SCEVCommutativeExpr::~SCEVCommutativeExpr() {
275 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
276 SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps));
277}
278
279void 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];
285 OS << ")";
286}
287
288SCEVHandle SCEVCommutativeExpr::
289replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
290 const SCEVHandle &Conc,
291 ScalarEvolution &SE) const {
292 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
293 SCEVHandle H =
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));
300 NewOps.push_back(H);
301 for (++i; i != e; ++i)
302 NewOps.push_back(getOperand(i)->
303 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
304
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);
313 else
314 assert(0 && "Unknown commutative expr!");
315 }
316 }
317 return this;
318}
319
320bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
321 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
322 if (!getOperand(i)->dominates(BB, DT))
323 return false;
324 }
325 return true;
326}
327
328
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
331// deleted!
332static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>,
333 SCEVUDivExpr*> > SCEVUDivs;
334
335SCEVUDivExpr::~SCEVUDivExpr() {
336 SCEVUDivs->erase(std::make_pair(LHS, RHS));
337}
338
339bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
340 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
341}
342
343void SCEVUDivExpr::print(raw_ostream &OS) const {
344 OS << "(" << *LHS << " /u " << *RHS << ")";
345}
346
347const Type *SCEVUDivExpr::getType() const {
348 // In most cases the types of LHS and RHS will be the same, but in some
349 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
350 // depend on the type for correctness, but handling types carefully can
351 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
352 // a pointer type than the RHS, so use the RHS' type here.
353 return RHS->getType();
354}
355
356// SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
357// particular input. Don't use a SCEVHandle here, or else the object will never
358// be deleted!
359static ManagedStatic<std::map<std::pair<const Loop *,
360 std::vector<const SCEV*> >,
361 SCEVAddRecExpr*> > SCEVAddRecExprs;
362
363SCEVAddRecExpr::~SCEVAddRecExpr() {
364 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
365 SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps));
366}
367
368SCEVHandle SCEVAddRecExpr::
369replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
370 const SCEVHandle &Conc,
371 ScalarEvolution &SE) const {
372 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
373 SCEVHandle H =
374 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
375 if (H != getOperand(i)) {
376 std::vector<SCEVHandle> NewOps;
377 NewOps.reserve(getNumOperands());
378 for (unsigned j = 0; j != i; ++j)
379 NewOps.push_back(getOperand(j));
380 NewOps.push_back(H);
381 for (++i; i != e; ++i)
382 NewOps.push_back(getOperand(i)->
383 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
384
385 return SE.getAddRecExpr(NewOps, L);
386 }
387 }
388 return this;
389}
390
391
392bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
393 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
394 // contain L and if the start is invariant.
395 // Add recurrences are never invariant in the function-body (null loop).
396 return QueryLoop &&
397 !QueryLoop->contains(L->getHeader()) &&
398 getOperand(0)->isLoopInvariant(QueryLoop);
399}
400
401
402void SCEVAddRecExpr::print(raw_ostream &OS) const {
403 OS << "{" << *Operands[0];
404 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
405 OS << ",+," << *Operands[i];
406 OS << "}<" << L->getHeader()->getName() + ">";
407}
408
409// SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
410// value. Don't use a SCEVHandle here, or else the object will never be
411// deleted!
412static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
413
414SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
415
416bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
417 // All non-instruction values are loop invariant. All instructions are loop
418 // invariant if they are not contained in the specified loop.
419 // Instructions are never considered invariant in the function body
420 // (null loop) because they are defined within the "loop".
421 if (Instruction *I = dyn_cast<Instruction>(V))
422 return L && !L->contains(I->getParent());
423 return true;
424}
425
426bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
427 if (Instruction *I = dyn_cast<Instruction>(getValue()))
428 return DT->dominates(I->getParent(), BB);
429 return true;
430}
431
432const Type *SCEVUnknown::getType() const {
433 return V->getType();
434}
435
436void SCEVUnknown::print(raw_ostream &OS) const {
437 WriteAsOperand(OS, V, false);
438}
439
440//===----------------------------------------------------------------------===//
441// SCEV Utilities
442//===----------------------------------------------------------------------===//
443
444namespace {
445 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
446 /// than the complexity of the RHS. This comparator is used to canonicalize
447 /// expressions.
448 class VISIBILITY_HIDDEN SCEVComplexityCompare {
449 LoopInfo *LI;
450 public:
451 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
452
453 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
454 // Primarily, sort the SCEVs by their getSCEVType().
455 if (LHS->getSCEVType() != RHS->getSCEVType())
456 return LHS->getSCEVType() < RHS->getSCEVType();
457
458 // Aside from the getSCEVType() ordering, the particular ordering
459 // isn't very important except that it's beneficial to be consistent,
460 // so that (a + b) and (b + a) don't end up as different expressions.
461
462 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
463 // not as complete as it could be.
464 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
465 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
466
467 // Order pointer values after integer values. This helps SCEVExpander
468 // form GEPs.
469 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
470 return false;
471 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
472 return true;
473
474 // Compare getValueID values.
475 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
476 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
477
478 // Sort arguments by their position.
479 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
480 const Argument *RA = cast<Argument>(RU->getValue());
481 return LA->getArgNo() < RA->getArgNo();
482 }
483
484 // For instructions, compare their loop depth, and their opcode.
485 // This is pretty loose.
486 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
487 Instruction *RV = cast<Instruction>(RU->getValue());
488
489 // Compare loop depths.
490 if (LI->getLoopDepth(LV->getParent()) !=
491 LI->getLoopDepth(RV->getParent()))
492 return LI->getLoopDepth(LV->getParent()) <
493 LI->getLoopDepth(RV->getParent());
494
495 // Compare opcodes.
496 if (LV->getOpcode() != RV->getOpcode())
497 return LV->getOpcode() < RV->getOpcode();
498
499 // Compare the number of operands.
500 if (LV->getNumOperands() != RV->getNumOperands())
501 return LV->getNumOperands() < RV->getNumOperands();
502 }
503
504 return false;
505 }
506
507 // Constant sorting doesn't matter since they'll be folded.
508 if (isa<SCEVConstant>(LHS))
509 return false;
510
511 // Lexicographically compare n-ary expressions.
512 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
513 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
514 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
515 if (i >= RC->getNumOperands())
516 return false;
517 if (operator()(LC->getOperand(i), RC->getOperand(i)))
518 return true;
519 if (operator()(RC->getOperand(i), LC->getOperand(i)))
520 return false;
521 }
522 return LC->getNumOperands() < RC->getNumOperands();
523 }
524
525 // Lexicographically compare udiv expressions.
526 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
527 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
528 if (operator()(LC->getLHS(), RC->getLHS()))
529 return true;
530 if (operator()(RC->getLHS(), LC->getLHS()))
531 return false;
532 if (operator()(LC->getRHS(), RC->getRHS()))
533 return true;
534 if (operator()(RC->getRHS(), LC->getRHS()))
535 return false;
536 return false;
537 }
538
539 // Compare cast expressions by operand.
540 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
541 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
542 return operator()(LC->getOperand(), RC->getOperand());
543 }
544
545 assert(0 && "Unknown SCEV kind!");
546 return false;
547 }
548 };
549}
550
551/// GroupByComplexity - Given a list of SCEV objects, order them by their
552/// complexity, and group objects of the same complexity together by value.
553/// When this routine is finished, we know that any duplicates in the vector are
554/// consecutive and that complexity is monotonically increasing.
555///
556/// Note that we go take special precautions to ensure that we get determinstic
557/// results from this routine. In other words, we don't want the results of
558/// this to depend on where the addresses of various SCEV objects happened to
559/// land in memory.
560///
561static void GroupByComplexity(std::vector<SCEVHandle> &Ops,
562 LoopInfo *LI) {
563 if (Ops.size() < 2) return; // Noop
564 if (Ops.size() == 2) {
565 // This is the common case, which also happens to be trivially simple.
566 // Special case it.
567 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
568 std::swap(Ops[0], Ops[1]);
569 return;
570 }
571
572 // Do the rough sort by complexity.
573 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
574
575 // Now that we are sorted by complexity, group elements of the same
576 // complexity. Note that this is, at worst, N^2, but the vector is likely to
577 // be extremely short in practice. Note that we take this approach because we
578 // do not want to depend on the addresses of the objects we are grouping.
579 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
580 const SCEV *S = Ops[i];
581 unsigned Complexity = S->getSCEVType();
582
583 // If there are any objects of the same complexity and same value as this
584 // one, group them.
585 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
586 if (Ops[j] == S) { // Found a duplicate.
587 // Move it to immediately after i'th element.
588 std::swap(Ops[i+1], Ops[j]);
589 ++i; // no need to rescan it.
590 if (i == e-2) return; // Done!
591 }
592 }
593 }
594}
595
596
597
598//===----------------------------------------------------------------------===//
599// Simple SCEV method implementations
600//===----------------------------------------------------------------------===//
601
602/// BinomialCoefficient - Compute BC(It, K). The result has width W.
603/// Assume, K > 0.
604static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
605 ScalarEvolution &SE,
606 const Type* ResultTy) {
607 // Handle the simplest case efficiently.
608 if (K == 1)
609 return SE.getTruncateOrZeroExtend(It, ResultTy);
610
611 // We are using the following formula for BC(It, K):
612 //
613 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
614 //
615 // Suppose, W is the bitwidth of the return value. We must be prepared for
616 // overflow. Hence, we must assure that the result of our computation is
617 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
618 // safe in modular arithmetic.
619 //
620 // However, this code doesn't use exactly that formula; the formula it uses
621 // is something like the following, where T is the number of factors of 2 in
622 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
623 // exponentiation:
624 //
625 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
626 //
627 // This formula is trivially equivalent to the previous formula. However,
628 // this formula can be implemented much more efficiently. The trick is that
629 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
630 // arithmetic. To do exact division in modular arithmetic, all we have
631 // to do is multiply by the inverse. Therefore, this step can be done at
632 // width W.
633 //
634 // The next issue is how to safely do the division by 2^T. The way this
635 // is done is by doing the multiplication step at a width of at least W + T
636 // bits. This way, the bottom W+T bits of the product are accurate. Then,
637 // when we perform the division by 2^T (which is equivalent to a right shift
638 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
639 // truncated out after the division by 2^T.
640 //
641 // In comparison to just directly using the first formula, this technique
642 // is much more efficient; using the first formula requires W * K bits,
643 // but this formula less than W + K bits. Also, the first formula requires
644 // a division step, whereas this formula only requires multiplies and shifts.
645 //
646 // It doesn't matter whether the subtraction step is done in the calculation
647 // width or the input iteration count's width; if the subtraction overflows,
648 // the result must be zero anyway. We prefer here to do it in the width of
649 // the induction variable because it helps a lot for certain cases; CodeGen
650 // isn't smart enough to ignore the overflow, which leads to much less
651 // efficient code if the width of the subtraction is wider than the native
652 // register width.
653 //
654 // (It's possible to not widen at all by pulling out factors of 2 before
655 // the multiplication; for example, K=2 can be calculated as
656 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
657 // extra arithmetic, so it's not an obvious win, and it gets
658 // much more complicated for K > 3.)
659
660 // Protection from insane SCEVs; this bound is conservative,
661 // but it probably doesn't matter.
662 if (K > 1000)
663 return SE.getCouldNotCompute();
664
665 unsigned W = SE.getTypeSizeInBits(ResultTy);
666
667 // Calculate K! / 2^T and T; we divide out the factors of two before
668 // multiplying for calculating K! / 2^T to avoid overflow.
669 // Other overflow doesn't matter because we only care about the bottom
670 // W bits of the result.
671 APInt OddFactorial(W, 1);
672 unsigned T = 1;
673 for (unsigned i = 3; i <= K; ++i) {
674 APInt Mult(W, i);
675 unsigned TwoFactors = Mult.countTrailingZeros();
676 T += TwoFactors;
677 Mult = Mult.lshr(TwoFactors);
678 OddFactorial *= Mult;
679 }
680
681 // We need at least W + T bits for the multiplication step
682 unsigned CalculationBits = W + T;
683
684 // Calcuate 2^T, at width T+W.
685 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
686
687 // Calculate the multiplicative inverse of K! / 2^T;
688 // this multiplication factor will perform the exact division by
689 // K! / 2^T.
690 APInt Mod = APInt::getSignedMinValue(W+1);
691 APInt MultiplyFactor = OddFactorial.zext(W+1);
692 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
693 MultiplyFactor = MultiplyFactor.trunc(W);
694
695 // Calculate the product, at width T+W
696 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
697 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
698 for (unsigned i = 1; i != K; ++i) {
699 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
700 Dividend = SE.getMulExpr(Dividend,
701 SE.getTruncateOrZeroExtend(S, CalculationTy));
702 }
703
704 // Divide by 2^T
705 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
706
707 // Truncate the result, and divide by K! / 2^T.
708
709 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
710 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
711}
712
713/// evaluateAtIteration - Return the value of this chain of recurrences at
714/// the specified iteration number. We can evaluate this recurrence by
715/// multiplying each element in the chain by the binomial coefficient
716/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
717///
718/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
719///
720/// where BC(It, k) stands for binomial coefficient.
721///
722SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
723 ScalarEvolution &SE) const {
724 SCEVHandle Result = getStart();
725 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
726 // The computation is correct in the face of overflow provided that the
727 // multiplication is performed _after_ the evaluation of the binomial
728 // coefficient.
729 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
730 if (isa<SCEVCouldNotCompute>(Coeff))
731 return Coeff;
732
733 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
734 }
735 return Result;
736}
737
738//===----------------------------------------------------------------------===//
739// SCEV Expression folder implementations
740//===----------------------------------------------------------------------===//
741
742SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op,
743 const Type *Ty) {
744 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
745 "This is not a truncating conversion!");
746 assert(isSCEVable(Ty) &&
747 "This is not a conversion to a SCEVable type!");
748 Ty = getEffectiveSCEVType(Ty);
749
750 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
751 return getUnknown(
752 ConstantExpr::getTrunc(SC->getValue(), Ty));
753
754 // trunc(trunc(x)) --> trunc(x)
755 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
756 return getTruncateExpr(ST->getOperand(), Ty);
757
758 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
759 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
760 return getTruncateOrSignExtend(SS->getOperand(), Ty);
761
762 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
763 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
764 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
765
766 // If the input value is a chrec scev made out of constants, truncate
767 // all of the constants.
768 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
769 std::vector<SCEVHandle> Operands;
770 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
771 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
772 return getAddRecExpr(Operands, AddRec->getLoop());
773 }
774
775 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
776 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
777 return Result;
778}
779
780SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
781 const Type *Ty) {
782 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
783 "This is not an extending conversion!");
784 assert(isSCEVable(Ty) &&
785 "This is not a conversion to a SCEVable type!");
786 Ty = getEffectiveSCEVType(Ty);
787
788 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
789 const Type *IntTy = getEffectiveSCEVType(Ty);
790 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
791 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
792 return getUnknown(C);
793 }
794
795 // zext(zext(x)) --> zext(x)
796 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
797 return getZeroExtendExpr(SZ->getOperand(), Ty);
798
799 // If the input value is a chrec scev, and we can prove that the value
800 // did not overflow the old, smaller, value, we can zero extend all of the
801 // operands (often constants). This allows analysis of something like
802 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
803 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
804 if (AR->isAffine()) {
805 // Check whether the backedge-taken count is SCEVCouldNotCompute.
806 // Note that this serves two purposes: It filters out loops that are
807 // simply not analyzable, and it covers the case where this code is
808 // being called from within backedge-taken count analysis, such that
809 // attempting to ask for the backedge-taken count would likely result
810 // in infinite recursion. In the later case, the analysis code will
811 // cope with a conservative value, and it will take care to purge
812 // that value once it has finished.
813 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
814 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
815 // Manually compute the final value for AR, checking for
816 // overflow.
817 SCEVHandle Start = AR->getStart();
818 SCEVHandle Step = AR->getStepRecurrence(*this);
819
820 // Check whether the backedge-taken count can be losslessly casted to
821 // the addrec's type. The count is always unsigned.
822 SCEVHandle CastedMaxBECount =
823 getTruncateOrZeroExtend(MaxBECount, Start->getType());
824 SCEVHandle RecastedMaxBECount =
825 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
826 if (MaxBECount == RecastedMaxBECount) {
827 const Type *WideTy =
828 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
829 // Check whether Start+Step*MaxBECount has no unsigned overflow.
830 SCEVHandle ZMul =
831 getMulExpr(CastedMaxBECount,
832 getTruncateOrZeroExtend(Step, Start->getType()));
833 SCEVHandle Add = getAddExpr(Start, ZMul);
834 SCEVHandle OperandExtendedAdd =
835 getAddExpr(getZeroExtendExpr(Start, WideTy),
836 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
837 getZeroExtendExpr(Step, WideTy)));
838 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
839 // Return the expression with the addrec on the outside.
840 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
841 getZeroExtendExpr(Step, Ty),
842 AR->getLoop());
843
844 // Similar to above, only this time treat the step value as signed.
845 // This covers loops that count down.
846 SCEVHandle SMul =
847 getMulExpr(CastedMaxBECount,
848 getTruncateOrSignExtend(Step, Start->getType()));
849 Add = getAddExpr(Start, SMul);
850 OperandExtendedAdd =
851 getAddExpr(getZeroExtendExpr(Start, WideTy),
852 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
853 getSignExtendExpr(Step, WideTy)));
854 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
855 // Return the expression with the addrec on the outside.
856 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
857 getSignExtendExpr(Step, Ty),
858 AR->getLoop());
859 }
860 }
861 }
862
863 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
864 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
865 return Result;
866}
867
868SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
869 const Type *Ty) {
870 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
871 "This is not an extending conversion!");
872 assert(isSCEVable(Ty) &&
873 "This is not a conversion to a SCEVable type!");
874 Ty = getEffectiveSCEVType(Ty);
875
876 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
877 const Type *IntTy = getEffectiveSCEVType(Ty);
878 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
879 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
880 return getUnknown(C);
881 }
882
883 // sext(sext(x)) --> sext(x)
884 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
885 return getSignExtendExpr(SS->getOperand(), Ty);
886
887 // If the input value is a chrec scev, and we can prove that the value
888 // did not overflow the old, smaller, value, we can sign extend all of the
889 // operands (often constants). This allows analysis of something like
890 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
891 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
892 if (AR->isAffine()) {
893 // Check whether the backedge-taken count is SCEVCouldNotCompute.
894 // Note that this serves two purposes: It filters out loops that are
895 // simply not analyzable, and it covers the case where this code is
896 // being called from within backedge-taken count analysis, such that
897 // attempting to ask for the backedge-taken count would likely result
898 // in infinite recursion. In the later case, the analysis code will
899 // cope with a conservative value, and it will take care to purge
900 // that value once it has finished.
901 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
902 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
903 // Manually compute the final value for AR, checking for
904 // overflow.
905 SCEVHandle Start = AR->getStart();
906 SCEVHandle Step = AR->getStepRecurrence(*this);
907
908 // Check whether the backedge-taken count can be losslessly casted to
909 // the addrec's type. The count is always unsigned.
910 SCEVHandle CastedMaxBECount =
911 getTruncateOrZeroExtend(MaxBECount, Start->getType());
912 SCEVHandle RecastedMaxBECount =
913 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
914 if (MaxBECount == RecastedMaxBECount) {
915 const Type *WideTy =
916 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
917 // Check whether Start+Step*MaxBECount has no signed overflow.
918 SCEVHandle SMul =
919 getMulExpr(CastedMaxBECount,
920 getTruncateOrSignExtend(Step, Start->getType()));
921 SCEVHandle Add = getAddExpr(Start, SMul);
922 SCEVHandle OperandExtendedAdd =
923 getAddExpr(getSignExtendExpr(Start, WideTy),
924 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
925 getSignExtendExpr(Step, WideTy)));
926 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
927 // Return the expression with the addrec on the outside.
928 return getAddRecExpr(getSignExtendExpr(Start, Ty),
929 getSignExtendExpr(Step, Ty),
930 AR->getLoop());
931 }
932 }
933 }
934
935 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
936 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
937 return Result;
938}
939
940/// getAddExpr - Get a canonical add expression, or something simpler if
941/// possible.
942SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
943 assert(!Ops.empty() && "Cannot get empty add!");
944 if (Ops.size() == 1) return Ops[0];
945#ifndef NDEBUG
946 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
947 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
948 getEffectiveSCEVType(Ops[0]->getType()) &&
949 "SCEVAddExpr operand types don't match!");
950#endif
951
952 // Sort by complexity, this groups all similar expression types together.
953 GroupByComplexity(Ops, LI);
954
955 // If there are any constants, fold them together.
956 unsigned Idx = 0;
957 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
958 ++Idx;
959 assert(Idx < Ops.size());
960 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
961 // We found two constants, fold them together!
962 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
963 RHSC->getValue()->getValue());
964 Ops[0] = getConstant(Fold);
965 Ops.erase(Ops.begin()+1); // Erase the folded element
966 if (Ops.size() == 1) return Ops[0];
967 LHSC = cast<SCEVConstant>(Ops[0]);
968 }
969
970 // If we are left with a constant zero being added, strip it off.
971 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
972 Ops.erase(Ops.begin());
973 --Idx;
974 }
975 }
976
977 if (Ops.size() == 1) return Ops[0];
978
979 // Okay, check to see if the same value occurs in the operand list twice. If
980 // so, merge them together into an multiply expression. Since we sorted the
981 // list, these values are required to be adjacent.
982 const Type *Ty = Ops[0]->getType();
983 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
984 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
985 // Found a match, merge the two values into a multiply, and add any
986 // remaining values to the result.
987 SCEVHandle Two = getIntegerSCEV(2, Ty);
988 SCEVHandle Mul = getMulExpr(Ops[i], Two);
989 if (Ops.size() == 2)
990 return Mul;
991 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
992 Ops.push_back(Mul);
993 return getAddExpr(Ops);
994 }
995
996 // Check for truncates. If all the operands are truncated from the same
997 // type, see if factoring out the truncate would permit the result to be
998 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
999 // if the contents of the resulting outer trunc fold to something simple.
1000 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1001 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1002 const Type *DstType = Trunc->getType();
1003 const Type *SrcType = Trunc->getOperand()->getType();
1004 std::vector<SCEVHandle> LargeOps;
1005 bool Ok = true;
1006 // Check all the operands to see if they can be represented in the
1007 // source type of the truncate.
1008 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1009 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1010 if (T->getOperand()->getType() != SrcType) {
1011 Ok = false;
1012 break;
1013 }
1014 LargeOps.push_back(T->getOperand());
1015 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1016 // This could be either sign or zero extension, but sign extension
1017 // is much more likely to be foldable here.
1018 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1019 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1020 std::vector<SCEVHandle> LargeMulOps;
1021 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1022 if (const SCEVTruncateExpr *T =
1023 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1024 if (T->getOperand()->getType() != SrcType) {
1025 Ok = false;
1026 break;
1027 }
1028 LargeMulOps.push_back(T->getOperand());
1029 } else if (const SCEVConstant *C =
1030 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1031 // This could be either sign or zero extension, but sign extension
1032 // is much more likely to be foldable here.
1033 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1034 } else {
1035 Ok = false;
1036 break;
1037 }
1038 }
1039 if (Ok)
1040 LargeOps.push_back(getMulExpr(LargeMulOps));
1041 } else {
1042 Ok = false;
1043 break;
1044 }
1045 }
1046 if (Ok) {
1047 // Evaluate the expression in the larger type.
1048 SCEVHandle Fold = getAddExpr(LargeOps);
1049 // If it folds to something simple, use it. Otherwise, don't.
1050 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1051 return getTruncateExpr(Fold, DstType);
1052 }
1053 }
1054
1055 // Skip past any other cast SCEVs.
1056 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1057 ++Idx;
1058
1059 // If there are add operands they would be next.
1060 if (Idx < Ops.size()) {
1061 bool DeletedAdd = false;
1062 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1063 // If we have an add, expand the add operands onto the end of the operands
1064 // list.
1065 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1066 Ops.erase(Ops.begin()+Idx);
1067 DeletedAdd = true;
1068 }
1069
1070 // If we deleted at least one add, we added operands to the end of the list,
1071 // and they are not necessarily sorted. Recurse to resort and resimplify
1072 // any operands we just aquired.
1073 if (DeletedAdd)
1074 return getAddExpr(Ops);
1075 }
1076
1077 // Skip over the add expression until we get to a multiply.
1078 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1079 ++Idx;
1080
1081 // If we are adding something to a multiply expression, make sure the
1082 // something is not already an operand of the multiply. If so, merge it into
1083 // the multiply.
1084 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1085 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1086 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1087 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1088 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1089 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
1090 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1091 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
1092 if (Mul->getNumOperands() != 2) {
1093 // If the multiply has more than two operands, we must get the
1094 // Y*Z term.
1095 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1096 MulOps.erase(MulOps.begin()+MulOp);
1097 InnerMul = getMulExpr(MulOps);
1098 }
1099 SCEVHandle One = getIntegerSCEV(1, Ty);
1100 SCEVHandle AddOne = getAddExpr(InnerMul, One);
1101 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1102 if (Ops.size() == 2) return OuterMul;
1103 if (AddOp < Idx) {
1104 Ops.erase(Ops.begin()+AddOp);
1105 Ops.erase(Ops.begin()+Idx-1);
1106 } else {
1107 Ops.erase(Ops.begin()+Idx);
1108 Ops.erase(Ops.begin()+AddOp-1);
1109 }
1110 Ops.push_back(OuterMul);
1111 return getAddExpr(Ops);
1112 }
1113
1114 // Check this multiply against other multiplies being added together.
1115 for (unsigned OtherMulIdx = Idx+1;
1116 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1117 ++OtherMulIdx) {
1118 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1119 // If MulOp occurs in OtherMul, we can fold the two multiplies
1120 // together.
1121 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1122 OMulOp != e; ++OMulOp)
1123 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1124 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1125 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
1126 if (Mul->getNumOperands() != 2) {
1127 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1128 MulOps.erase(MulOps.begin()+MulOp);
1129 InnerMul1 = getMulExpr(MulOps);
1130 }
1131 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1132 if (OtherMul->getNumOperands() != 2) {
1133 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
1134 OtherMul->op_end());
1135 MulOps.erase(MulOps.begin()+OMulOp);
1136 InnerMul2 = getMulExpr(MulOps);
1137 }
1138 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1139 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1140 if (Ops.size() == 2) return OuterMul;
1141 Ops.erase(Ops.begin()+Idx);
1142 Ops.erase(Ops.begin()+OtherMulIdx-1);
1143 Ops.push_back(OuterMul);
1144 return getAddExpr(Ops);
1145 }
1146 }
1147 }
1148 }
1149
1150 // If there are any add recurrences in the operands list, see if any other
1151 // added values are loop invariant. If so, we can fold them into the
1152 // recurrence.
1153 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1154 ++Idx;
1155
1156 // Scan over all recurrences, trying to fold loop invariants into them.
1157 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1158 // Scan all of the other operands to this add and add them to the vector if
1159 // they are loop invariant w.r.t. the recurrence.
1160 std::vector<SCEVHandle> LIOps;
1161 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1162 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1163 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1164 LIOps.push_back(Ops[i]);
1165 Ops.erase(Ops.begin()+i);
1166 --i; --e;
1167 }
1168
1169 // If we found some loop invariants, fold them into the recurrence.
1170 if (!LIOps.empty()) {
1171 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1172 LIOps.push_back(AddRec->getStart());
1173
1174 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
1175 AddRecOps[0] = getAddExpr(LIOps);
1176
1177 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1178 // If all of the other operands were loop invariant, we are done.
1179 if (Ops.size() == 1) return NewRec;
1180
1181 // Otherwise, add the folded AddRec by the non-liv parts.
1182 for (unsigned i = 0;; ++i)
1183 if (Ops[i] == AddRec) {
1184 Ops[i] = NewRec;
1185 break;
1186 }
1187 return getAddExpr(Ops);
1188 }
1189
1190 // Okay, if there weren't any loop invariants to be folded, check to see if
1191 // there are multiple AddRec's with the same loop induction variable being
1192 // added together. If so, we can fold them.
1193 for (unsigned OtherIdx = Idx+1;
1194 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1195 if (OtherIdx != Idx) {
1196 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1197 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1198 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1199 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
1200 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1201 if (i >= NewOps.size()) {
1202 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1203 OtherAddRec->op_end());
1204 break;
1205 }
1206 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1207 }
1208 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1209
1210 if (Ops.size() == 2) return NewAddRec;
1211
1212 Ops.erase(Ops.begin()+Idx);
1213 Ops.erase(Ops.begin()+OtherIdx-1);
1214 Ops.push_back(NewAddRec);
1215 return getAddExpr(Ops);
1216 }
1217 }
1218
1219 // Otherwise couldn't fold anything into this recurrence. Move onto the
1220 // next one.
1221 }
1222
1223 // Okay, it looks like we really DO need an add expr. Check to see if we
1224 // already have one, otherwise create a new one.
1225 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1226 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
1227 SCEVOps)];
1228 if (Result == 0) Result = new SCEVAddExpr(Ops);
1229 return Result;
1230}
1231
1232
1233/// getMulExpr - Get a canonical multiply expression, or something simpler if
1234/// possible.
1235SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
1236 assert(!Ops.empty() && "Cannot get empty mul!");
1237#ifndef NDEBUG
1238 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1239 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1240 getEffectiveSCEVType(Ops[0]->getType()) &&
1241 "SCEVMulExpr operand types don't match!");
1242#endif
1243
1244 // Sort by complexity, this groups all similar expression types together.
1245 GroupByComplexity(Ops, LI);
1246
1247 // If there are any constants, fold them together.
1248 unsigned Idx = 0;
1249 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1250
1251 // C1*(C2+V) -> C1*C2 + C1*V
1252 if (Ops.size() == 2)
1253 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1254 if (Add->getNumOperands() == 2 &&
1255 isa<SCEVConstant>(Add->getOperand(0)))
1256 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1257 getMulExpr(LHSC, Add->getOperand(1)));
1258
1259
1260 ++Idx;
1261 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1262 // We found two constants, fold them together!
1263 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1264 RHSC->getValue()->getValue());
1265 Ops[0] = getConstant(Fold);
1266 Ops.erase(Ops.begin()+1); // Erase the folded element
1267 if (Ops.size() == 1) return Ops[0];
1268 LHSC = cast<SCEVConstant>(Ops[0]);
1269 }
1270
1271 // If we are left with a constant one being multiplied, strip it off.
1272 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1273 Ops.erase(Ops.begin());
1274 --Idx;
1275 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1276 // If we have a multiply of zero, it will always be zero.
1277 return Ops[0];
1278 }
1279 }
1280
1281 // Skip over the add expression until we get to a multiply.
1282 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1283 ++Idx;
1284
1285 if (Ops.size() == 1)
1286 return Ops[0];
1287
1288 // If there are mul operands inline them all into this expression.
1289 if (Idx < Ops.size()) {
1290 bool DeletedMul = false;
1291 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1292 // If we have an mul, expand the mul operands onto the end of the operands
1293 // list.
1294 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1295 Ops.erase(Ops.begin()+Idx);
1296 DeletedMul = true;
1297 }
1298
1299 // If we deleted at least one mul, we added operands to the end of the list,
1300 // and they are not necessarily sorted. Recurse to resort and resimplify
1301 // any operands we just aquired.
1302 if (DeletedMul)
1303 return getMulExpr(Ops);
1304 }
1305
1306 // If there are any add recurrences in the operands list, see if any other
1307 // added values are loop invariant. If so, we can fold them into the
1308 // recurrence.
1309 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1310 ++Idx;
1311
1312 // Scan over all recurrences, trying to fold loop invariants into them.
1313 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1314 // Scan all of the other operands to this mul and add them to the vector if
1315 // they are loop invariant w.r.t. the recurrence.
1316 std::vector<SCEVHandle> LIOps;
1317 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1318 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1319 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1320 LIOps.push_back(Ops[i]);
1321 Ops.erase(Ops.begin()+i);
1322 --i; --e;
1323 }
1324
1325 // If we found some loop invariants, fold them into the recurrence.
1326 if (!LIOps.empty()) {
1327 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1328 std::vector<SCEVHandle> NewOps;
1329 NewOps.reserve(AddRec->getNumOperands());
1330 if (LIOps.size() == 1) {
1331 const SCEV *Scale = LIOps[0];
1332 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1333 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1334 } else {
1335 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1336 std::vector<SCEVHandle> MulOps(LIOps);
1337 MulOps.push_back(AddRec->getOperand(i));
1338 NewOps.push_back(getMulExpr(MulOps));
1339 }
1340 }
1341
1342 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1343
1344 // If all of the other operands were loop invariant, we are done.
1345 if (Ops.size() == 1) return NewRec;
1346
1347 // Otherwise, multiply the folded AddRec by the non-liv parts.
1348 for (unsigned i = 0;; ++i)
1349 if (Ops[i] == AddRec) {
1350 Ops[i] = NewRec;
1351 break;
1352 }
1353 return getMulExpr(Ops);
1354 }
1355
1356 // Okay, if there weren't any loop invariants to be folded, check to see if
1357 // there are multiple AddRec's with the same loop induction variable being
1358 // multiplied together. If so, we can fold them.
1359 for (unsigned OtherIdx = Idx+1;
1360 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1361 if (OtherIdx != Idx) {
1362 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1363 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1364 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1365 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1366 SCEVHandle NewStart = getMulExpr(F->getStart(),
1367 G->getStart());
1368 SCEVHandle B = F->getStepRecurrence(*this);
1369 SCEVHandle D = G->getStepRecurrence(*this);
1370 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1371 getMulExpr(G, B),
1372 getMulExpr(B, D));
1373 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1374 F->getLoop());
1375 if (Ops.size() == 2) return NewAddRec;
1376
1377 Ops.erase(Ops.begin()+Idx);
1378 Ops.erase(Ops.begin()+OtherIdx-1);
1379 Ops.push_back(NewAddRec);
1380 return getMulExpr(Ops);
1381 }
1382 }
1383
1384 // Otherwise couldn't fold anything into this recurrence. Move onto the
1385 // next one.
1386 }
1387
1388 // Okay, it looks like we really DO need an mul expr. Check to see if we
1389 // already have one, otherwise create a new one.
1390 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1391 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1392 SCEVOps)];
1393 if (Result == 0)
1394 Result = new SCEVMulExpr(Ops);
1395 return Result;
1396}
1397
1398/// getUDivExpr - Get a canonical multiply expression, or something simpler if
1399/// possible.
1400SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS,
1401 const SCEVHandle &RHS) {
1402 assert(getEffectiveSCEVType(LHS->getType()) ==
1403 getEffectiveSCEVType(RHS->getType()) &&
1404 "SCEVUDivExpr operand types don't match!");
1405
1406 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1407 if (RHSC->getValue()->equalsInt(1))
1408 return LHS; // X udiv 1 --> x
1409 if (RHSC->isZero())
1410 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1411
1412 // Determine if the division can be folded into the operands of
1413 // its operands.
1414 // TODO: Generalize this to non-constants by using known-bits information.
1415 const Type *Ty = LHS->getType();
1416 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1417 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1418 // For non-power-of-two values, effectively round the value up to the
1419 // nearest power of two.
1420 if (!RHSC->getValue()->getValue().isPowerOf2())
1421 ++MaxShiftAmt;
1422 const IntegerType *ExtTy =
1423 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1424 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1425 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1426 if (const SCEVConstant *Step =
1427 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1428 if (!Step->getValue()->getValue()
1429 .urem(RHSC->getValue()->getValue()) &&
1430 getZeroExtendExpr(AR, ExtTy) ==
1431 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1432 getZeroExtendExpr(Step, ExtTy),
1433 AR->getLoop())) {
1434 std::vector<SCEVHandle> Operands;
1435 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1436 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1437 return getAddRecExpr(Operands, AR->getLoop());
1438 }
1439 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1440 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1441 std::vector<SCEVHandle> Operands;
1442 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1443 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1444 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1445 // Find an operand that's safely divisible.
1446 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1447 SCEVHandle Op = M->getOperand(i);
1448 SCEVHandle Div = getUDivExpr(Op, RHSC);
1449 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1450 Operands = M->getOperands();
1451 Operands[i] = Div;
1452 return getMulExpr(Operands);
1453 }
1454 }
1455 }
1456 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1457 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1458 std::vector<SCEVHandle> Operands;
1459 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1460 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1461 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1462 Operands.clear();
1463 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1464 SCEVHandle Op = getUDivExpr(A->getOperand(i), RHS);
1465 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1466 break;
1467 Operands.push_back(Op);
1468 }
1469 if (Operands.size() == A->getNumOperands())
1470 return getAddExpr(Operands);
1471 }
1472 }
1473
1474 // Fold if both operands are constant.
1475 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1476 Constant *LHSCV = LHSC->getValue();
1477 Constant *RHSCV = RHSC->getValue();
1478 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1479 }
1480 }
1481
1482 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1483 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1484 return Result;
1485}
1486
1487
1488/// getAddRecExpr - Get an add recurrence expression for the specified loop.
1489/// Simplify the expression as much as possible.
1490SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1491 const SCEVHandle &Step, const Loop *L) {
1492 std::vector<SCEVHandle> Operands;
1493 Operands.push_back(Start);
1494 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1495 if (StepChrec->getLoop() == L) {
1496 Operands.insert(Operands.end(), StepChrec->op_begin(),
1497 StepChrec->op_end());
1498 return getAddRecExpr(Operands, L);
1499 }
1500
1501 Operands.push_back(Step);
1502 return getAddRecExpr(Operands, L);
1503}
1504
1505/// getAddRecExpr - Get an add recurrence expression for the specified loop.
1506/// Simplify the expression as much as possible.
1507SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1508 const Loop *L) {
1509 if (Operands.size() == 1) return Operands[0];
1510#ifndef NDEBUG
1511 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1512 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1513 getEffectiveSCEVType(Operands[0]->getType()) &&
1514 "SCEVAddRecExpr operand types don't match!");
1515#endif
1516
1517 if (Operands.back()->isZero()) {
1518 Operands.pop_back();
1519 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1520 }
1521
1522 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1523 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1524 const Loop* NestedLoop = NestedAR->getLoop();
1525 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1526 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1527 NestedAR->op_end());
1528 SCEVHandle NestedARHandle(NestedAR);
1529 Operands[0] = NestedAR->getStart();
1530 NestedOperands[0] = getAddRecExpr(Operands, L);
1531 return getAddRecExpr(NestedOperands, NestedLoop);
1532 }
1533 }
1534
1535 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
1536 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)];
1537 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1538 return Result;
1539}
1540
1541SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1542 const SCEVHandle &RHS) {
1543 std::vector<SCEVHandle> Ops;
1544 Ops.push_back(LHS);
1545 Ops.push_back(RHS);
1546 return getSMaxExpr(Ops);
1547}
1548
1549SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1550 assert(!Ops.empty() && "Cannot get empty smax!");
1551 if (Ops.size() == 1) return Ops[0];
1552#ifndef NDEBUG
1553 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1554 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1555 getEffectiveSCEVType(Ops[0]->getType()) &&
1556 "SCEVSMaxExpr operand types don't match!");
1557#endif
1558
1559 // Sort by complexity, this groups all similar expression types together.
1560 GroupByComplexity(Ops, LI);
1561
1562 // If there are any constants, fold them together.
1563 unsigned Idx = 0;
1564 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1565 ++Idx;
1566 assert(Idx < Ops.size());
1567 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1568 // We found two constants, fold them together!
1569 ConstantInt *Fold = ConstantInt::get(
1570 APIntOps::smax(LHSC->getValue()->getValue(),
1571 RHSC->getValue()->getValue()));
1572 Ops[0] = getConstant(Fold);
1573 Ops.erase(Ops.begin()+1); // Erase the folded element
1574 if (Ops.size() == 1) return Ops[0];
1575 LHSC = cast<SCEVConstant>(Ops[0]);
1576 }
1577
1578 // If we are left with a constant -inf, strip it off.
1579 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1580 Ops.erase(Ops.begin());
1581 --Idx;
1582 }
1583 }
1584
1585 if (Ops.size() == 1) return Ops[0];
1586
1587 // Find the first SMax
1588 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1589 ++Idx;
1590
1591 // Check to see if one of the operands is an SMax. If so, expand its operands
1592 // onto our operand list, and recurse to simplify.
1593 if (Idx < Ops.size()) {
1594 bool DeletedSMax = false;
1595 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1596 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1597 Ops.erase(Ops.begin()+Idx);
1598 DeletedSMax = true;
1599 }
1600
1601 if (DeletedSMax)
1602 return getSMaxExpr(Ops);
1603 }
1604
1605 // Okay, check to see if the same value occurs in the operand list twice. If
1606 // so, delete one. Since we sorted the list, these values are required to
1607 // be adjacent.
1608 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1609 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1610 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1611 --i; --e;
1612 }
1613
1614 if (Ops.size() == 1) return Ops[0];
1615
1616 assert(!Ops.empty() && "Reduced smax down to nothing!");
1617
1618 // Okay, it looks like we really DO need an smax expr. Check to see if we
1619 // already have one, otherwise create a new one.
1620 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1621 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1622 SCEVOps)];
1623 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1624 return Result;
1625}
1626
1627SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1628 const SCEVHandle &RHS) {
1629 std::vector<SCEVHandle> Ops;
1630 Ops.push_back(LHS);
1631 Ops.push_back(RHS);
1632 return getUMaxExpr(Ops);
1633}
1634
1635SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1636 assert(!Ops.empty() && "Cannot get empty umax!");
1637 if (Ops.size() == 1) return Ops[0];
1638#ifndef NDEBUG
1639 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1640 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1641 getEffectiveSCEVType(Ops[0]->getType()) &&
1642 "SCEVUMaxExpr operand types don't match!");
1643#endif
1644
1645 // Sort by complexity, this groups all similar expression types together.
1646 GroupByComplexity(Ops, LI);
1647
1648 // If there are any constants, fold them together.
1649 unsigned Idx = 0;
1650 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1651 ++Idx;
1652 assert(Idx < Ops.size());
1653 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1654 // We found two constants, fold them together!
1655 ConstantInt *Fold = ConstantInt::get(
1656 APIntOps::umax(LHSC->getValue()->getValue(),
1657 RHSC->getValue()->getValue()));
1658 Ops[0] = getConstant(Fold);
1659 Ops.erase(Ops.begin()+1); // Erase the folded element
1660 if (Ops.size() == 1) return Ops[0];
1661 LHSC = cast<SCEVConstant>(Ops[0]);
1662 }
1663
1664 // If we are left with a constant zero, strip it off.
1665 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1666 Ops.erase(Ops.begin());
1667 --Idx;
1668 }
1669 }
1670
1671 if (Ops.size() == 1) return Ops[0];
1672
1673 // Find the first UMax
1674 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1675 ++Idx;
1676
1677 // Check to see if one of the operands is a UMax. If so, expand its operands
1678 // onto our operand list, and recurse to simplify.
1679 if (Idx < Ops.size()) {
1680 bool DeletedUMax = false;
1681 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1682 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1683 Ops.erase(Ops.begin()+Idx);
1684 DeletedUMax = true;
1685 }
1686
1687 if (DeletedUMax)
1688 return getUMaxExpr(Ops);
1689 }
1690
1691 // Okay, check to see if the same value occurs in the operand list twice. If
1692 // so, delete one. Since we sorted the list, these values are required to
1693 // be adjacent.
1694 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1695 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1696 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1697 --i; --e;
1698 }
1699
1700 if (Ops.size() == 1) return Ops[0];
1701
1702 assert(!Ops.empty() && "Reduced umax down to nothing!");
1703
1704 // Okay, it looks like we really DO need a umax expr. Check to see if we
1705 // already have one, otherwise create a new one.
1706 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1707 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1708 SCEVOps)];
1709 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1710 return Result;
1711}
1712
1713SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1714 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1715 return getConstant(CI);
1716 if (isa<ConstantPointerNull>(V))
1717 return getIntegerSCEV(0, V->getType());
1718 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1719 if (Result == 0) Result = new SCEVUnknown(V);
1720 return Result;
1721}
1722
1723//===----------------------------------------------------------------------===//
1724// Basic SCEV Analysis and PHI Idiom Recognition Code
1725//
1726
1727/// isSCEVable - Test if values of the given type are analyzable within
1728/// the SCEV framework. This primarily includes integer types, and it
1729/// can optionally include pointer types if the ScalarEvolution class
1730/// has access to target-specific information.
1731bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1732 // Integers are always SCEVable.
1733 if (Ty->isInteger())
1734 return true;
1735
1736 // Pointers are SCEVable if TargetData information is available
1737 // to provide pointer size information.
1738 if (isa<PointerType>(Ty))
1739 return TD != NULL;
1740
1741 // Otherwise it's not SCEVable.
1742 return false;
1743}
1744
1745/// getTypeSizeInBits - Return the size in bits of the specified type,
1746/// for which isSCEVable must return true.
1747uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1748 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1749
1750 // If we have a TargetData, use it!
1751 if (TD)
1752 return TD->getTypeSizeInBits(Ty);
1753
1754 // Otherwise, we support only integer types.
1755 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1756 return Ty->getPrimitiveSizeInBits();
1757}
1758
1759/// getEffectiveSCEVType - Return a type with the same bitwidth as
1760/// the given type and which represents how SCEV will treat the given
1761/// type, for which isSCEVable must return true. For pointer types,
1762/// this is the pointer-sized integer type.
1763const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1764 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1765
1766 if (Ty->isInteger())
1767 return Ty;
1768
1769 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1770 return TD->getIntPtrType();
1771}
1772
1773SCEVHandle ScalarEvolution::getCouldNotCompute() {
1774 return UnknownValue;
1775}
1776
1777/// hasSCEV - Return true if the SCEV for this value has already been
1778/// computed.
1779bool ScalarEvolution::hasSCEV(Value *V) const {
1780 return Scalars.count(V);
1781}
1782
1783/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1784/// expression and create a new one.
1785SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1786 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1787
1788 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
1789 if (I != Scalars.end()) return I->second;
1790 SCEVHandle S = createSCEV(V);
1791 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
1792 return S;
1793}
1794
1795/// getIntegerSCEV - Given an integer or FP type, create a constant for the
1796/// specified signed integer value and return a SCEV for the constant.
1797SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1798 Ty = getEffectiveSCEVType(Ty);
1799 Constant *C;
1800 if (Val == 0)
1801 C = Constant::getNullValue(Ty);
1802 else if (Ty->isFloatingPoint())
1803 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1804 APFloat::IEEEdouble, Val));
1805 else
1806 C = ConstantInt::get(Ty, Val);
1807 return getUnknown(C);
1808}
1809
1810/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1811///
1812SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1813 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1814 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1815
1816 const Type *Ty = V->getType();
1817 Ty = getEffectiveSCEVType(Ty);
1818 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1819}
1820
1821/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1822SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1823 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1824 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1825
1826 const Type *Ty = V->getType();
1827 Ty = getEffectiveSCEVType(Ty);
1828 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1829 return getMinusSCEV(AllOnes, V);
1830}
1831
1832/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1833///
1834SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1835 const SCEVHandle &RHS) {
1836 // X - Y --> X + -Y
1837 return getAddExpr(LHS, getNegativeSCEV(RHS));
1838}
1839
1840/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1841/// input value to the specified type. If the type must be extended, it is zero
1842/// extended.
1843SCEVHandle
1844ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1845 const Type *Ty) {
1846 const Type *SrcTy = V->getType();
1847 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1848 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1849 "Cannot truncate or zero extend with non-integer arguments!");
1850 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1851 return V; // No conversion
1852 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1853 return getTruncateExpr(V, Ty);
1854 return getZeroExtendExpr(V, Ty);
1855}
1856
1857/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1858/// input value to the specified type. If the type must be extended, it is sign
1859/// extended.
1860SCEVHandle
1861ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1862 const Type *Ty) {
1863 const Type *SrcTy = V->getType();
1864 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1865 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1866 "Cannot truncate or zero extend with non-integer arguments!");
1867 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1868 return V; // No conversion
1869 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1870 return getTruncateExpr(V, Ty);
1871 return getSignExtendExpr(V, Ty);
1872}
1873
1874/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
1875/// input value to the specified type. If the type must be extended, it is zero
1876/// extended. The conversion must not be narrowing.
1877SCEVHandle
1878ScalarEvolution::getNoopOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
1879 const Type *SrcTy = V->getType();
1880 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1881 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1882 "Cannot noop or zero extend with non-integer arguments!");
1883 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1884 "getNoopOrZeroExtend cannot truncate!");
1885 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1886 return V; // No conversion
1887 return getZeroExtendExpr(V, Ty);
1888}
1889
1890/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
1891/// input value to the specified type. If the type must be extended, it is sign
1892/// extended. The conversion must not be narrowing.
1893SCEVHandle
1894ScalarEvolution::getNoopOrSignExtend(const SCEVHandle &V, const Type *Ty) {
1895 const Type *SrcTy = V->getType();
1896 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1897 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1898 "Cannot noop or sign extend with non-integer arguments!");
1899 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1900 "getNoopOrSignExtend cannot truncate!");
1901 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1902 return V; // No conversion
1903 return getSignExtendExpr(V, Ty);
1904}
1905
1906/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
1907/// input value to the specified type. The conversion must not be widening.
1908SCEVHandle
1909ScalarEvolution::getTruncateOrNoop(const SCEVHandle &V, const Type *Ty) {
1910 const Type *SrcTy = V->getType();
1911 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1912 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1913 "Cannot truncate or noop with non-integer arguments!");
1914 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
1915 "getTruncateOrNoop cannot extend!");
1916 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1917 return V; // No conversion
1918 return getTruncateExpr(V, Ty);
1919}
1920
1921/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1922/// the specified instruction and replaces any references to the symbolic value
1923/// SymName with the specified value. This is used during PHI resolution.
1924void ScalarEvolution::
1925ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1926 const SCEVHandle &NewVal) {
1927 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
1928 Scalars.find(SCEVCallbackVH(I, this));
1929 if (SI == Scalars.end()) return;
1930
1931 SCEVHandle NV =
1932 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
1933 if (NV == SI->second) return; // No change.
1934
1935 SI->second = NV; // Update the scalars map!
1936
1937 // Any instruction values that use this instruction might also need to be
1938 // updated!
1939 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1940 UI != E; ++UI)
1941 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1942}
1943
1944/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1945/// a loop header, making it a potential recurrence, or it doesn't.
1946///
1947SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
1948 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1949 if (const Loop *L = LI->getLoopFor(PN->getParent()))
1950 if (L->getHeader() == PN->getParent()) {
1951 // If it lives in the loop header, it has two incoming values, one
1952 // from outside the loop, and one from inside.
1953 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1954 unsigned BackEdge = IncomingEdge^1;
1955
1956 // While we are analyzing this PHI node, handle its value symbolically.
1957 SCEVHandle SymbolicName = getUnknown(PN);
1958 assert(Scalars.find(PN) == Scalars.end() &&
1959 "PHI node already processed?");
1960 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
1961
1962 // Using this symbolic name for the PHI, analyze the value coming around
1963 // the back-edge.
1964 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1965
1966 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1967 // has a special value for the first iteration of the loop.
1968
1969 // If the value coming around the backedge is an add with the symbolic
1970 // value we just inserted, then we found a simple induction variable!
1971 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1972 // If there is a single occurrence of the symbolic value, replace it
1973 // with a recurrence.
1974 unsigned FoundIndex = Add->getNumOperands();
1975 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1976 if (Add->getOperand(i) == SymbolicName)
1977 if (FoundIndex == e) {
1978 FoundIndex = i;
1979 break;
1980 }
1981
1982 if (FoundIndex != Add->getNumOperands()) {
1983 // Create an add with everything but the specified operand.
1984 std::vector<SCEVHandle> Ops;
1985 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1986 if (i != FoundIndex)
1987 Ops.push_back(Add->getOperand(i));
1988 SCEVHandle Accum = getAddExpr(Ops);
1989
1990 // This is not a valid addrec if the step amount is varying each
1991 // loop iteration, but is not itself an addrec in this loop.
1992 if (Accum->isLoopInvariant(L) ||
1993 (isa<SCEVAddRecExpr>(Accum) &&
1994 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1995 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1996 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
1997
1998 // Okay, for the entire analysis of this edge we assumed the PHI
1999 // to be symbolic. We now need to go back and update all of the
2000 // entries for the scalars that use the PHI (except for the PHI
2001 // itself) to use the new analyzed value instead of the "symbolic"
2002 // value.
2003 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2004 return PHISCEV;
2005 }
2006 }
2007 } else if (const SCEVAddRecExpr *AddRec =
2008 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2009 // Otherwise, this could be a loop like this:
2010 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2011 // In this case, j = {1,+,1} and BEValue is j.
2012 // Because the other in-value of i (0) fits the evolution of BEValue
2013 // i really is an addrec evolution.
2014 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2015 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2016
2017 // If StartVal = j.start - j.stride, we can use StartVal as the
2018 // initial step of the addrec evolution.
2019 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2020 AddRec->getOperand(1))) {
2021 SCEVHandle PHISCEV =
2022 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2023
2024 // Okay, for the entire analysis of this edge we assumed the PHI
2025 // to be symbolic. We now need to go back and update all of the
2026 // entries for the scalars that use the PHI (except for the PHI
2027 // itself) to use the new analyzed value instead of the "symbolic"
2028 // value.
2029 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2030 return PHISCEV;
2031 }
2032 }
2033 }
2034
2035 return SymbolicName;
2036 }
2037
2038 // If it's not a loop phi, we can't handle it yet.
2039 return getUnknown(PN);
2040}
2041
2042/// createNodeForGEP - Expand GEP instructions into add and multiply
2043/// operations. This allows them to be analyzed by regular SCEV code.
2044///
2045SCEVHandle ScalarEvolution::createNodeForGEP(User *GEP) {
2046
2047 const Type *IntPtrTy = TD->getIntPtrType();
2048 Value *Base = GEP->getOperand(0);
2049 // Don't attempt to analyze GEPs over unsized objects.
2050 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2051 return getUnknown(GEP);
2052 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
2053 gep_type_iterator GTI = gep_type_begin(GEP);
2054 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2055 E = GEP->op_end();
2056 I != E; ++I) {
2057 Value *Index = *I;
2058 // Compute the (potentially symbolic) offset in bytes for this index.
2059 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2060 // For a struct, add the member offset.
2061 const StructLayout &SL = *TD->getStructLayout(STy);
2062 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2063 uint64_t Offset = SL.getElementOffset(FieldNo);
2064 TotalOffset = getAddExpr(TotalOffset,
2065 getIntegerSCEV(Offset, IntPtrTy));
2066 } else {
2067 // For an array, add the element offset, explicitly scaled.
2068 SCEVHandle LocalOffset = getSCEV(Index);
2069 if (!isa<PointerType>(LocalOffset->getType()))
2070 // Getelementptr indicies are signed.
2071 LocalOffset = getTruncateOrSignExtend(LocalOffset,
2072 IntPtrTy);
2073 LocalOffset =
2074 getMulExpr(LocalOffset,
2075 getIntegerSCEV(TD->getTypeAllocSize(*GTI),
2076 IntPtrTy));
2077 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2078 }
2079 }
2080 return getAddExpr(getSCEV(Base), TotalOffset);
2081}
2082
2083/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2084/// guaranteed to end in (at every loop iteration). It is, at the same time,
2085/// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2086/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2087static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
2088 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2089 return C->getValue()->getValue().countTrailingZeros();
2090
2091 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2092 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
2093 (uint32_t)SE.getTypeSizeInBits(T->getType()));
2094
2095 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2096 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2097 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2098 SE.getTypeSizeInBits(E->getType()) : OpRes;
2099 }
2100
2101 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2102 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2103 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2104 SE.getTypeSizeInBits(E->getType()) : OpRes;
2105 }
2106
2107 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2108 // The result is the min of all operands results.
2109 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2110 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2111 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2112 return MinOpRes;
2113 }
2114
2115 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2116 // The result is the sum of all operands results.
2117 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2118 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
2119 for (unsigned i = 1, e = M->getNumOperands();
2120 SumOpRes != BitWidth && i != e; ++i)
2121 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
2122 BitWidth);
2123 return SumOpRes;
2124 }
2125
2126 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2127 // The result is the min of all operands results.
2128 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2129 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2130 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2131 return MinOpRes;
2132 }
2133
2134 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2135 // The result is the min of all operands results.
2136 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2137 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2138 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2139 return MinOpRes;
2140 }
2141
2142 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2143 // The result is the min of all operands results.
2144 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2145 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2146 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2147 return MinOpRes;
2148 }
2149
2150 // SCEVUDivExpr, SCEVUnknown
2151 return 0;
2152}
2153
2154/// createSCEV - We know that there is no SCEV for the specified value.
2155/// Analyze the expression.
2156///
2157SCEVHandle ScalarEvolution::createSCEV(Value *V) {
2158 if (!isSCEVable(V->getType()))
2159 return getUnknown(V);
2160
2161 unsigned Opcode = Instruction::UserOp1;
2162 if (Instruction *I = dyn_cast<Instruction>(V))
2163 Opcode = I->getOpcode();
2164 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2165 Opcode = CE->getOpcode();
2166 else
2167 return getUnknown(V);
2168
2169 User *U = cast<User>(V);
2170 switch (Opcode) {
2171 case Instruction::Add:
2172 return getAddExpr(getSCEV(U->getOperand(0)),
2173 getSCEV(U->getOperand(1)));
2174 case Instruction::Mul:
2175 return getMulExpr(getSCEV(U->getOperand(0)),
2176 getSCEV(U->getOperand(1)));
2177 case Instruction::UDiv:
2178 return getUDivExpr(getSCEV(U->getOperand(0)),
2179 getSCEV(U->getOperand(1)));
2180 case Instruction::Sub:
2181 return getMinusSCEV(getSCEV(U->getOperand(0)),
2182 getSCEV(U->getOperand(1)));
2183 case Instruction::And:
2184 // For an expression like x&255 that merely masks off the high bits,
2185 // use zext(trunc(x)) as the SCEV expression.
2186 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2187 if (CI->isNullValue())
2188 return getSCEV(U->getOperand(1));
2189 if (CI->isAllOnesValue())
2190 return getSCEV(U->getOperand(0));
2191 const APInt &A = CI->getValue();
2192 unsigned Ones = A.countTrailingOnes();
2193 if (APIntOps::isMask(Ones, A))
2194 return
2195 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2196 IntegerType::get(Ones)),
2197 U->getType());
2198 }
2199 break;
2200 case Instruction::Or:
2201 // If the RHS of the Or is a constant, we may have something like:
2202 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2203 // optimizations will transparently handle this case.
2204 //
2205 // In order for this transformation to be safe, the LHS must be of the
2206 // form X*(2^n) and the Or constant must be less than 2^n.
2207 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2208 SCEVHandle LHS = getSCEV(U->getOperand(0));
2209 const APInt &CIVal = CI->getValue();
2210 if (GetMinTrailingZeros(LHS, *this) >=
2211 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2212 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2213 }
2214 break;
2215 case Instruction::Xor:
2216 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2217 // If the RHS of the xor is a signbit, then this is just an add.
2218 // Instcombine turns add of signbit into xor as a strength reduction step.
2219 if (CI->getValue().isSignBit())
2220 return getAddExpr(getSCEV(U->getOperand(0)),
2221 getSCEV(U->getOperand(1)));
2222
2223 // If the RHS of xor is -1, then this is a not operation.
2224 if (CI->isAllOnesValue())
2225 return getNotSCEV(getSCEV(U->getOperand(0)));
2226
2227 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2228 // This is a variant of the check for xor with -1, and it handles
2229 // the case where instcombine has trimmed non-demanded bits out
2230 // of an xor with -1.
2231 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2232 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2233 if (BO->getOpcode() == Instruction::And &&
2234 LCI->getValue() == CI->getValue())
2235 if (const SCEVZeroExtendExpr *Z =
2236 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0))))
2237 return getZeroExtendExpr(getNotSCEV(Z->getOperand()),
2238 U->getType());
2239 }
2240 break;
2241
2242 case Instruction::Shl:
2243 // Turn shift left of a constant amount into a multiply.
2244 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2245 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2246 Constant *X = ConstantInt::get(
2247 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2248 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2249 }
2250 break;
2251
2252 case Instruction::LShr:
2253 // Turn logical shift right of a constant into a unsigned divide.
2254 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2255 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2256 Constant *X = ConstantInt::get(
2257 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2258 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2259 }
2260 break;
2261
2262 case Instruction::AShr:
2263 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2264 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2265 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2266 if (L->getOpcode() == Instruction::Shl &&
2267 L->getOperand(1) == U->getOperand(1)) {
2268 unsigned BitWidth = getTypeSizeInBits(U->getType());
2269 uint64_t Amt = BitWidth - CI->getZExtValue();
2270 if (Amt == BitWidth)
2271 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2272 if (Amt > BitWidth)
2273 return getIntegerSCEV(0, U->getType()); // value is undefined
2274 return
2275 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2276 IntegerType::get(Amt)),
2277 U->getType());
2278 }
2279 break;
2280
2281 case Instruction::Trunc:
2282 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2283
2284 case Instruction::ZExt:
2285 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2286
2287 case Instruction::SExt:
2288 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2289
2290 case Instruction::BitCast:
2291 // BitCasts are no-op casts so we just eliminate the cast.
2292 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2293 return getSCEV(U->getOperand(0));
2294 break;
2295
2296 case Instruction::IntToPtr:
2297 if (!TD) break; // Without TD we can't analyze pointers.
2298 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2299 TD->getIntPtrType());
2300
2301 case Instruction::PtrToInt:
2302 if (!TD) break; // Without TD we can't analyze pointers.
2303 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2304 U->getType());
2305
2306 case Instruction::GetElementPtr:
2307 if (!TD) break; // Without TD we can't analyze pointers.
2308 return createNodeForGEP(U);
2309
2310 case Instruction::PHI:
2311 return createNodeForPHI(cast<PHINode>(U));
2312
2313 case Instruction::Select:
2314 // This could be a smax or umax that was lowered earlier.
2315 // Try to recover it.
2316 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2317 Value *LHS = ICI->getOperand(0);
2318 Value *RHS = ICI->getOperand(1);
2319 switch (ICI->getPredicate()) {
2320 case ICmpInst::ICMP_SLT:
2321 case ICmpInst::ICMP_SLE:
2322 std::swap(LHS, RHS);
2323 // fall through
2324 case ICmpInst::ICMP_SGT:
2325 case ICmpInst::ICMP_SGE:
2326 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2327 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2328 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2329 // ~smax(~x, ~y) == smin(x, y).
2330 return getNotSCEV(getSMaxExpr(
2331 getNotSCEV(getSCEV(LHS)),
2332 getNotSCEV(getSCEV(RHS))));
2333 break;
2334 case ICmpInst::ICMP_ULT:
2335 case ICmpInst::ICMP_ULE:
2336 std::swap(LHS, RHS);
2337 // fall through
2338 case ICmpInst::ICMP_UGT:
2339 case ICmpInst::ICMP_UGE:
2340 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2341 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2342 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2343 // ~umax(~x, ~y) == umin(x, y)
2344 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2345 getNotSCEV(getSCEV(RHS))));
2346 break;
2347 default:
2348 break;
2349 }
2350 }
2351
2352 default: // We cannot analyze this expression.
2353 break;
2354 }
2355
2356 return getUnknown(V);
2357}
2358
2359
2360
2361//===----------------------------------------------------------------------===//
2362// Iteration Count Computation Code
2363//
2364
2365/// getBackedgeTakenCount - If the specified loop has a predictable
2366/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2367/// object. The backedge-taken count is the number of times the loop header
2368/// will be branched to from within the loop. This is one less than the
2369/// trip count of the loop, since it doesn't count the first iteration,
2370/// when the header is branched to from outside the loop.
2371///
2372/// Note that it is not valid to call this method on a loop without a
2373/// loop-invariant backedge-taken count (see
2374/// hasLoopInvariantBackedgeTakenCount).
2375///
2376SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2377 return getBackedgeTakenInfo(L).Exact;
2378}
2379
2380/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2381/// return the least SCEV value that is known never to be less than the
2382/// actual backedge taken count.
2383SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2384 return getBackedgeTakenInfo(L).Max;
2385}
2386
2387const ScalarEvolution::BackedgeTakenInfo &
2388ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2389 // Initially insert a CouldNotCompute for this loop. If the insertion
2390 // succeeds, procede to actually compute a backedge-taken count and
2391 // update the value. The temporary CouldNotCompute value tells SCEV
2392 // code elsewhere that it shouldn't attempt to request a new
2393 // backedge-taken count, which could result in infinite recursion.
2394 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2395 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2396 if (Pair.second) {
2397 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2398 if (ItCount.Exact != UnknownValue) {
2399 assert(ItCount.Exact->isLoopInvariant(L) &&
2400 ItCount.Max->isLoopInvariant(L) &&
2401 "Computed trip count isn't loop invariant for loop!");
2402 ++NumTripCountsComputed;
2403
2404 // Update the value in the map.
2405 Pair.first->second = ItCount;
2406 } else if (isa<PHINode>(L->getHeader()->begin())) {
2407 // Only count loops that have phi nodes as not being computable.
2408 ++NumTripCountsNotComputed;
2409 }
2410
2411 // Now that we know more about the trip count for this loop, forget any
2412 // existing SCEV values for PHI nodes in this loop since they are only
2413 // conservative estimates made without the benefit
2414 // of trip count information.
2415 if (ItCount.hasAnyInfo())
2416 forgetLoopPHIs(L);
2417 }
2418 return Pair.first->second;
2419}
2420
2421/// forgetLoopBackedgeTakenCount - This method should be called by the
2422/// client when it has changed a loop in a way that may effect
2423/// ScalarEvolution's ability to compute a trip count, or if the loop
2424/// is deleted.
2425void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2426 BackedgeTakenCounts.erase(L);
2427 forgetLoopPHIs(L);
2428}
2429
2430/// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2431/// PHI nodes in the given loop. This is used when the trip count of
2432/// the loop may have changed.
2433void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2434 BasicBlock *Header = L->getHeader();
2435
2436 // Push all Loop-header PHIs onto the Worklist stack, except those
2437 // that are presently represented via a SCEVUnknown. SCEVUnknown for
2438 // a PHI either means that it has an unrecognized structure, or it's
2439 // a PHI that's in the progress of being computed by createNodeForPHI.
2440 // In the former case, additional loop trip count information isn't
2441 // going to change anything. In the later case, createNodeForPHI will
2442 // perform the necessary updates on its own when it gets to that point.
2443 SmallVector<Instruction *, 16> Worklist;
2444 for (BasicBlock::iterator I = Header->begin();
2445 PHINode *PN = dyn_cast<PHINode>(I); ++I) {
2446 std::map<SCEVCallbackVH, SCEVHandle>::iterator It = Scalars.find((Value*)I);
2447 if (It != Scalars.end() && !isa<SCEVUnknown>(It->second))
2448 Worklist.push_back(PN);
2449 }
2450
2451 while (!Worklist.empty()) {
2452 Instruction *I = Worklist.pop_back_val();
2453 if (Scalars.erase(I))
2454 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2455 UI != UE; ++UI)
2456 Worklist.push_back(cast<Instruction>(UI));
2457 }
2458}
2459
2460/// ComputeBackedgeTakenCount - Compute the number of times the backedge
2461/// of the specified loop will execute.
2462ScalarEvolution::BackedgeTakenInfo
2463ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2464 // If the loop has a non-one exit block count, we can't analyze it.
|
2485 // Okay, we've computed the exiting block. See what condition causes us to
2486 // exit.
2487 //
2488 // FIXME: we should be able to handle switch instructions (with a single exit)
2489 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2490 if (ExitBr == 0) return UnknownValue;
2491 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2492
2493 // At this point, we know we have a conditional branch that determines whether
2494 // the loop is exited. However, we don't know if the branch is executed each
2495 // time through the loop. If not, then the execution count of the branch will
2496 // not be equal to the trip count of the loop.
2497 //
2498 // Currently we check for this by checking to see if the Exit branch goes to
2499 // the loop header. If so, we know it will always execute the same number of
2500 // times as the loop. We also handle the case where the exit block *is* the
2501 // loop header. This is common for un-rotated loops. More extensive analysis
2502 // could be done to handle more cases here.
2503 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2504 ExitBr->getSuccessor(1) != L->getHeader() &&
2505 ExitBr->getParent() != L->getHeader())
2506 return UnknownValue;
2507
2508 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2509
2510 // If it's not an integer or pointer comparison then compute it the hard way.
2511 if (ExitCond == 0)
2512 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2513 ExitBr->getSuccessor(0) == ExitBlock);
2514
2515 // If the condition was exit on true, convert the condition to exit on false
2516 ICmpInst::Predicate Cond;
2517 if (ExitBr->getSuccessor(1) == ExitBlock)
2518 Cond = ExitCond->getPredicate();
2519 else
2520 Cond = ExitCond->getInversePredicate();
2521
2522 // Handle common loops like: for (X = "string"; *X; ++X)
2523 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2524 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2525 SCEVHandle ItCnt =
2526 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2527 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2528 }
2529
2530 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2531 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2532
2533 // Try to evaluate any dependencies out of the loop.
2534 LHS = getSCEVAtScope(LHS, L);
2535 RHS = getSCEVAtScope(RHS, L);
2536
2537 // At this point, we would like to compute how many iterations of the
2538 // loop the predicate will return true for these inputs.
2539 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2540 // If there is a loop-invariant, force it into the RHS.
2541 std::swap(LHS, RHS);
2542 Cond = ICmpInst::getSwappedPredicate(Cond);
2543 }
2544
2545 // If we have a comparison of a chrec against a constant, try to use value
2546 // ranges to answer this query.
2547 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2548 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2549 if (AddRec->getLoop() == L) {
2550 // Form the constant range.
2551 ConstantRange CompRange(
2552 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
2553
2554 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2555 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2556 }
2557
2558 switch (Cond) {
2559 case ICmpInst::ICMP_NE: { // while (X != Y)
2560 // Convert to: while (X-Y != 0)
2561 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2562 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2563 break;
2564 }
2565 case ICmpInst::ICMP_EQ: {
2566 // Convert to: while (X-Y == 0) // while (X == Y)
2567 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2568 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2569 break;
2570 }
2571 case ICmpInst::ICMP_SLT: {
2572 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2573 if (BTI.hasAnyInfo()) return BTI;
2574 break;
2575 }
2576 case ICmpInst::ICMP_SGT: {
2577 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2578 getNotSCEV(RHS), L, true);
2579 if (BTI.hasAnyInfo()) return BTI;
2580 break;
2581 }
2582 case ICmpInst::ICMP_ULT: {
2583 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2584 if (BTI.hasAnyInfo()) return BTI;
2585 break;
2586 }
2587 case ICmpInst::ICMP_UGT: {
2588 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2589 getNotSCEV(RHS), L, false);
2590 if (BTI.hasAnyInfo()) return BTI;
2591 break;
2592 }
2593 default:
2594#if 0
2595 errs() << "ComputeBackedgeTakenCount ";
2596 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2597 errs() << "[unsigned] ";
2598 errs() << *LHS << " "
2599 << Instruction::getOpcodeName(Instruction::ICmp)
2600 << " " << *RHS << "\n";
2601#endif
2602 break;
2603 }
2604 return
2605 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2606 ExitBr->getSuccessor(0) == ExitBlock);
2607}
2608
2609static ConstantInt *
2610EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2611 ScalarEvolution &SE) {
2612 SCEVHandle InVal = SE.getConstant(C);
2613 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2614 assert(isa<SCEVConstant>(Val) &&
2615 "Evaluation of SCEV at constant didn't fold correctly?");
2616 return cast<SCEVConstant>(Val)->getValue();
2617}
2618
2619/// GetAddressedElementFromGlobal - Given a global variable with an initializer
2620/// and a GEP expression (missing the pointer index) indexing into it, return
2621/// the addressed element of the initializer or null if the index expression is
2622/// invalid.
2623static Constant *
2624GetAddressedElementFromGlobal(GlobalVariable *GV,
2625 const std::vector<ConstantInt*> &Indices) {
2626 Constant *Init = GV->getInitializer();
2627 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2628 uint64_t Idx = Indices[i]->getZExtValue();
2629 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2630 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2631 Init = cast<Constant>(CS->getOperand(Idx));
2632 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2633 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2634 Init = cast<Constant>(CA->getOperand(Idx));
2635 } else if (isa<ConstantAggregateZero>(Init)) {
2636 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2637 assert(Idx < STy->getNumElements() && "Bad struct index!");
2638 Init = Constant::getNullValue(STy->getElementType(Idx));
2639 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2640 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2641 Init = Constant::getNullValue(ATy->getElementType());
2642 } else {
2643 assert(0 && "Unknown constant aggregate type!");
2644 }
2645 return 0;
2646 } else {
2647 return 0; // Unknown initializer type
2648 }
2649 }
2650 return Init;
2651}
2652
2653/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2654/// 'icmp op load X, cst', try to see if we can compute the backedge
2655/// execution count.
2656SCEVHandle ScalarEvolution::
2657ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2658 const Loop *L,
2659 ICmpInst::Predicate predicate) {
2660 if (LI->isVolatile()) return UnknownValue;
2661
2662 // Check to see if the loaded pointer is a getelementptr of a global.
2663 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2664 if (!GEP) return UnknownValue;
2665
2666 // Make sure that it is really a constant global we are gepping, with an
2667 // initializer, and make sure the first IDX is really 0.
2668 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2669 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2670 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2671 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2672 return UnknownValue;
2673
2674 // Okay, we allow one non-constant index into the GEP instruction.
2675 Value *VarIdx = 0;
2676 std::vector<ConstantInt*> Indexes;
2677 unsigned VarIdxNum = 0;
2678 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2679 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2680 Indexes.push_back(CI);
2681 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2682 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2683 VarIdx = GEP->getOperand(i);
2684 VarIdxNum = i-2;
2685 Indexes.push_back(0);
2686 }
2687
2688 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2689 // Check to see if X is a loop variant variable value now.
2690 SCEVHandle Idx = getSCEV(VarIdx);
2691 Idx = getSCEVAtScope(Idx, L);
2692
2693 // We can only recognize very limited forms of loop index expressions, in
2694 // particular, only affine AddRec's like {C1,+,C2}.
2695 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2696 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2697 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2698 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2699 return UnknownValue;
2700
2701 unsigned MaxSteps = MaxBruteForceIterations;
2702 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2703 ConstantInt *ItCst =
2704 ConstantInt::get(IdxExpr->getType(), IterationNum);
2705 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2706
2707 // Form the GEP offset.
2708 Indexes[VarIdxNum] = Val;
2709
2710 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2711 if (Result == 0) break; // Cannot compute!
2712
2713 // Evaluate the condition for this iteration.
2714 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2715 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2716 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2717#if 0
2718 errs() << "\n***\n*** Computed loop count " << *ItCst
2719 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2720 << "***\n";
2721#endif
2722 ++NumArrayLenItCounts;
2723 return getConstant(ItCst); // Found terminating iteration!
2724 }
2725 }
2726 return UnknownValue;
2727}
2728
2729
2730/// CanConstantFold - Return true if we can constant fold an instruction of the
2731/// specified type, assuming that all operands were constants.
2732static bool CanConstantFold(const Instruction *I) {
2733 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2734 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2735 return true;
2736
2737 if (const CallInst *CI = dyn_cast<CallInst>(I))
2738 if (const Function *F = CI->getCalledFunction())
2739 return canConstantFoldCallTo(F);
2740 return false;
2741}
2742
2743/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2744/// in the loop that V is derived from. We allow arbitrary operations along the
2745/// way, but the operands of an operation must either be constants or a value
2746/// derived from a constant PHI. If this expression does not fit with these
2747/// constraints, return null.
2748static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2749 // If this is not an instruction, or if this is an instruction outside of the
2750 // loop, it can't be derived from a loop PHI.
2751 Instruction *I = dyn_cast<Instruction>(V);
2752 if (I == 0 || !L->contains(I->getParent())) return 0;
2753
2754 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2755 if (L->getHeader() == I->getParent())
2756 return PN;
2757 else
2758 // We don't currently keep track of the control flow needed to evaluate
2759 // PHIs, so we cannot handle PHIs inside of loops.
2760 return 0;
2761 }
2762
2763 // If we won't be able to constant fold this expression even if the operands
2764 // are constants, return early.
2765 if (!CanConstantFold(I)) return 0;
2766
2767 // Otherwise, we can evaluate this instruction if all of its operands are
2768 // constant or derived from a PHI node themselves.
2769 PHINode *PHI = 0;
2770 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2771 if (!(isa<Constant>(I->getOperand(Op)) ||
2772 isa<GlobalValue>(I->getOperand(Op)))) {
2773 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2774 if (P == 0) return 0; // Not evolving from PHI
2775 if (PHI == 0)
2776 PHI = P;
2777 else if (PHI != P)
2778 return 0; // Evolving from multiple different PHIs.
2779 }
2780
2781 // This is a expression evolving from a constant PHI!
2782 return PHI;
2783}
2784
2785/// EvaluateExpression - Given an expression that passes the
2786/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2787/// in the loop has the value PHIVal. If we can't fold this expression for some
2788/// reason, return null.
2789static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2790 if (isa<PHINode>(V)) return PHIVal;
2791 if (Constant *C = dyn_cast<Constant>(V)) return C;
2792 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2793 Instruction *I = cast<Instruction>(V);
2794
2795 std::vector<Constant*> Operands;
2796 Operands.resize(I->getNumOperands());
2797
2798 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2799 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2800 if (Operands[i] == 0) return 0;
2801 }
2802
2803 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2804 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2805 &Operands[0], Operands.size());
2806 else
2807 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2808 &Operands[0], Operands.size());
2809}
2810
2811/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2812/// in the header of its containing loop, we know the loop executes a
2813/// constant number of times, and the PHI node is just a recurrence
2814/// involving constants, fold it.
2815Constant *ScalarEvolution::
2816getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2817 std::map<PHINode*, Constant*>::iterator I =
2818 ConstantEvolutionLoopExitValue.find(PN);
2819 if (I != ConstantEvolutionLoopExitValue.end())
2820 return I->second;
2821
2822 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2823 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2824
2825 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2826
2827 // Since the loop is canonicalized, the PHI node must have two entries. One
2828 // entry must be a constant (coming in from outside of the loop), and the
2829 // second must be derived from the same PHI.
2830 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2831 Constant *StartCST =
2832 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2833 if (StartCST == 0)
2834 return RetVal = 0; // Must be a constant.
2835
2836 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2837 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2838 if (PN2 != PN)
2839 return RetVal = 0; // Not derived from same PHI.
2840
2841 // Execute the loop symbolically to determine the exit value.
2842 if (BEs.getActiveBits() >= 32)
2843 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2844
2845 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2846 unsigned IterationNum = 0;
2847 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2848 if (IterationNum == NumIterations)
2849 return RetVal = PHIVal; // Got exit value!
2850
2851 // Compute the value of the PHI node for the next iteration.
2852 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2853 if (NextPHI == PHIVal)
2854 return RetVal = NextPHI; // Stopped evolving!
2855 if (NextPHI == 0)
2856 return 0; // Couldn't evaluate!
2857 PHIVal = NextPHI;
2858 }
2859}
2860
2861/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2862/// constant number of times (the condition evolves only from constants),
2863/// try to evaluate a few iterations of the loop until we get the exit
2864/// condition gets a value of ExitWhen (true or false). If we cannot
2865/// evaluate the trip count of the loop, return UnknownValue.
2866SCEVHandle ScalarEvolution::
2867ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2868 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2869 if (PN == 0) return UnknownValue;
2870
2871 // Since the loop is canonicalized, the PHI node must have two entries. One
2872 // entry must be a constant (coming in from outside of the loop), and the
2873 // second must be derived from the same PHI.
2874 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2875 Constant *StartCST =
2876 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2877 if (StartCST == 0) return UnknownValue; // Must be a constant.
2878
2879 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2880 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2881 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2882
2883 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2884 // the loop symbolically to determine when the condition gets a value of
2885 // "ExitWhen".
2886 unsigned IterationNum = 0;
2887 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2888 for (Constant *PHIVal = StartCST;
2889 IterationNum != MaxIterations; ++IterationNum) {
2890 ConstantInt *CondVal =
2891 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2892
2893 // Couldn't symbolically evaluate.
2894 if (!CondVal) return UnknownValue;
2895
2896 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2897 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2898 ++NumBruteForceTripCountsComputed;
2899 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2900 }
2901
2902 // Compute the value of the PHI node for the next iteration.
2903 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2904 if (NextPHI == 0 || NextPHI == PHIVal)
2905 return UnknownValue; // Couldn't evaluate or not making progress...
2906 PHIVal = NextPHI;
2907 }
2908
2909 // Too many iterations were needed to evaluate.
2910 return UnknownValue;
2911}
2912
2913/// getSCEVAtScope - Return a SCEV expression handle for the specified value
2914/// at the specified scope in the program. The L value specifies a loop
2915/// nest to evaluate the expression at, where null is the top-level or a
2916/// specified loop is immediately inside of the loop.
2917///
2918/// This method can be used to compute the exit value for a variable defined
2919/// in a loop by querying what the value will hold in the parent loop.
2920///
2921/// In the case that a relevant loop exit value cannot be computed, the
2922/// original value V is returned.
2923SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
2924 // FIXME: this should be turned into a virtual method on SCEV!
2925
2926 if (isa<SCEVConstant>(V)) return V;
2927
2928 // If this instruction is evolved from a constant-evolving PHI, compute the
2929 // exit value from the loop without using SCEVs.
2930 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2931 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2932 const Loop *LI = (*this->LI)[I->getParent()];
2933 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2934 if (PHINode *PN = dyn_cast<PHINode>(I))
2935 if (PN->getParent() == LI->getHeader()) {
2936 // Okay, there is no closed form solution for the PHI node. Check
2937 // to see if the loop that contains it has a known backedge-taken
2938 // count. If so, we may be able to force computation of the exit
2939 // value.
2940 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2941 if (const SCEVConstant *BTCC =
2942 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2943 // Okay, we know how many times the containing loop executes. If
2944 // this is a constant evolving PHI node, get the final value at
2945 // the specified iteration number.
2946 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2947 BTCC->getValue()->getValue(),
2948 LI);
2949 if (RV) return getUnknown(RV);
2950 }
2951 }
2952
2953 // Okay, this is an expression that we cannot symbolically evaluate
2954 // into a SCEV. Check to see if it's possible to symbolically evaluate
2955 // the arguments into constants, and if so, try to constant propagate the
2956 // result. This is particularly useful for computing loop exit values.
2957 if (CanConstantFold(I)) {
2958 // Check to see if we've folded this instruction at this loop before.
2959 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
2960 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
2961 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
2962 if (!Pair.second)
2963 return Pair.first->second ? &*getUnknown(Pair.first->second) : V;
2964
2965 std::vector<Constant*> Operands;
2966 Operands.reserve(I->getNumOperands());
2967 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2968 Value *Op = I->getOperand(i);
2969 if (Constant *C = dyn_cast<Constant>(Op)) {
2970 Operands.push_back(C);
2971 } else {
2972 // If any of the operands is non-constant and if they are
2973 // non-integer and non-pointer, don't even try to analyze them
2974 // with scev techniques.
2975 if (!isSCEVable(Op->getType()))
2976 return V;
2977
2978 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2979 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
2980 Constant *C = SC->getValue();
2981 if (C->getType() != Op->getType())
2982 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2983 Op->getType(),
2984 false),
2985 C, Op->getType());
2986 Operands.push_back(C);
2987 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2988 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
2989 if (C->getType() != Op->getType())
2990 C =
2991 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2992 Op->getType(),
2993 false),
2994 C, Op->getType());
2995 Operands.push_back(C);
2996 } else
2997 return V;
2998 } else {
2999 return V;
3000 }
3001 }
3002 }
3003
3004 Constant *C;
3005 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3006 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
3007 &Operands[0], Operands.size());
3008 else
3009 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3010 &Operands[0], Operands.size());
3011 Pair.first->second = C;
3012 return getUnknown(C);
3013 }
3014 }
3015
3016 // This is some other type of SCEVUnknown, just return it.
3017 return V;
3018 }
3019
3020 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3021 // Avoid performing the look-up in the common case where the specified
3022 // expression has no loop-variant portions.
3023 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3024 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3025 if (OpAtScope != Comm->getOperand(i)) {
3026 // Okay, at least one of these operands is loop variant but might be
3027 // foldable. Build a new instance of the folded commutative expression.
3028 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
3029 NewOps.push_back(OpAtScope);
3030
3031 for (++i; i != e; ++i) {
3032 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3033 NewOps.push_back(OpAtScope);
3034 }
3035 if (isa<SCEVAddExpr>(Comm))
3036 return getAddExpr(NewOps);
3037 if (isa<SCEVMulExpr>(Comm))
3038 return getMulExpr(NewOps);
3039 if (isa<SCEVSMaxExpr>(Comm))
3040 return getSMaxExpr(NewOps);
3041 if (isa<SCEVUMaxExpr>(Comm))
3042 return getUMaxExpr(NewOps);
3043 assert(0 && "Unknown commutative SCEV type!");
3044 }
3045 }
3046 // If we got here, all operands are loop invariant.
3047 return Comm;
3048 }
3049
3050 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3051 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
3052 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
3053 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3054 return Div; // must be loop invariant
3055 return getUDivExpr(LHS, RHS);
3056 }
3057
3058 // If this is a loop recurrence for a loop that does not contain L, then we
3059 // are dealing with the final value computed by the loop.
3060 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3061 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3062 // To evaluate this recurrence, we need to know how many times the AddRec
3063 // loop iterates. Compute this now.
3064 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3065 if (BackedgeTakenCount == UnknownValue) return AddRec;
3066
3067 // Then, evaluate the AddRec.
3068 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3069 }
3070 return AddRec;
3071 }
3072
3073 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3074 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3075 if (Op == Cast->getOperand())
3076 return Cast; // must be loop invariant
3077 return getZeroExtendExpr(Op, Cast->getType());
3078 }
3079
3080 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3081 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3082 if (Op == Cast->getOperand())
3083 return Cast; // must be loop invariant
3084 return getSignExtendExpr(Op, Cast->getType());
3085 }
3086
3087 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3088 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3089 if (Op == Cast->getOperand())
3090 return Cast; // must be loop invariant
3091 return getTruncateExpr(Op, Cast->getType());
3092 }
3093
3094 assert(0 && "Unknown SCEV type!");
3095 return 0;
3096}
3097
3098/// getSCEVAtScope - This is a convenience function which does
3099/// getSCEVAtScope(getSCEV(V), L).
3100SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3101 return getSCEVAtScope(getSCEV(V), L);
3102}
3103
3104/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3105/// following equation:
3106///
3107/// A * X = B (mod N)
3108///
3109/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3110/// A and B isn't important.
3111///
3112/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3113static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3114 ScalarEvolution &SE) {
3115 uint32_t BW = A.getBitWidth();
3116 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3117 assert(A != 0 && "A must be non-zero.");
3118
3119 // 1. D = gcd(A, N)
3120 //
3121 // The gcd of A and N may have only one prime factor: 2. The number of
3122 // trailing zeros in A is its multiplicity
3123 uint32_t Mult2 = A.countTrailingZeros();
3124 // D = 2^Mult2
3125
3126 // 2. Check if B is divisible by D.
3127 //
3128 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3129 // is not less than multiplicity of this prime factor for D.
3130 if (B.countTrailingZeros() < Mult2)
3131 return SE.getCouldNotCompute();
3132
3133 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3134 // modulo (N / D).
3135 //
3136 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3137 // bit width during computations.
3138 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3139 APInt Mod(BW + 1, 0);
3140 Mod.set(BW - Mult2); // Mod = N / D
3141 APInt I = AD.multiplicativeInverse(Mod);
3142
3143 // 4. Compute the minimum unsigned root of the equation:
3144 // I * (B / D) mod (N / D)
3145 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3146
3147 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3148 // bits.
3149 return SE.getConstant(Result.trunc(BW));
3150}
3151
3152/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3153/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
3154/// might be the same) or two SCEVCouldNotCompute objects.
3155///
3156static std::pair<SCEVHandle,SCEVHandle>
3157SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
3158 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
3159 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
3160 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
3161 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
3162
3163 // We currently can only solve this if the coefficients are constants.
3164 if (!LC || !MC || !NC) {
3165 const SCEV *CNC = SE.getCouldNotCompute();
3166 return std::make_pair(CNC, CNC);
3167 }
3168
3169 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
3170 const APInt &L = LC->getValue()->getValue();
3171 const APInt &M = MC->getValue()->getValue();
3172 const APInt &N = NC->getValue()->getValue();
3173 APInt Two(BitWidth, 2);
3174 APInt Four(BitWidth, 4);
3175
3176 {
3177 using namespace APIntOps;
3178 const APInt& C = L;
3179 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
3180 // The B coefficient is M-N/2
3181 APInt B(M);
3182 B -= sdiv(N,Two);
3183
3184 // The A coefficient is N/2
3185 APInt A(N.sdiv(Two));
3186
3187 // Compute the B^2-4ac term.
3188 APInt SqrtTerm(B);
3189 SqrtTerm *= B;
3190 SqrtTerm -= Four * (A * C);
3191
3192 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
3193 // integer value or else APInt::sqrt() will assert.
3194 APInt SqrtVal(SqrtTerm.sqrt());
3195
3196 // Compute the two solutions for the quadratic formula.
3197 // The divisions must be performed as signed divisions.
3198 APInt NegB(-B);
3199 APInt TwoA( A << 1 );
3200 if (TwoA.isMinValue()) {
3201 const SCEV *CNC = SE.getCouldNotCompute();
3202 return std::make_pair(CNC, CNC);
3203 }
3204
3205 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
3206 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
3207
3208 return std::make_pair(SE.getConstant(Solution1),
3209 SE.getConstant(Solution2));
3210 } // end APIntOps namespace
3211}
3212
3213/// HowFarToZero - Return the number of times a backedge comparing the specified
3214/// value to zero will execute. If not computable, return UnknownValue.
3215SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
3216 // If the value is a constant
3217 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3218 // If the value is already zero, the branch will execute zero times.
3219 if (C->getValue()->isZero()) return C;
3220 return UnknownValue; // Otherwise it will loop infinitely.
3221 }
3222
3223 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
3224 if (!AddRec || AddRec->getLoop() != L)
3225 return UnknownValue;
3226
3227 if (AddRec->isAffine()) {
3228 // If this is an affine expression, the execution count of this branch is
3229 // the minimum unsigned root of the following equation:
3230 //
3231 // Start + Step*N = 0 (mod 2^BW)
3232 //
3233 // equivalent to:
3234 //
3235 // Step*N = -Start (mod 2^BW)
3236 //
3237 // where BW is the common bit width of Start and Step.
3238
3239 // Get the initial value for the loop.
3240 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
3241 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
3242
3243 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
3244 // For now we handle only constant steps.
3245
3246 // First, handle unitary steps.
3247 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
3248 return getNegativeSCEV(Start); // N = -Start (as unsigned)
3249 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
3250 return Start; // N = Start (as unsigned)
3251
3252 // Then, try to solve the above equation provided that Start is constant.
3253 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
3254 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
3255 -StartC->getValue()->getValue(),
3256 *this);
3257 }
3258 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
3259 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
3260 // the quadratic equation to solve it.
3261 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
3262 *this);
3263 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3264 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3265 if (R1) {
3266#if 0
3267 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
3268 << " sol#2: " << *R2 << "\n";
3269#endif
3270 // Pick the smallest positive root value.
3271 if (ConstantInt *CB =
3272 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3273 R1->getValue(), R2->getValue()))) {
3274 if (CB->getZExtValue() == false)
3275 std::swap(R1, R2); // R1 is the minimum root now.
3276
3277 // We can only use this value if the chrec ends up with an exact zero
3278 // value at this index. When solving for "X*X != 5", for example, we
3279 // should not accept a root of 2.
3280 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
3281 if (Val->isZero())
3282 return R1; // We found a quadratic root!
3283 }
3284 }
3285 }
3286
3287 return UnknownValue;
3288}
3289
3290/// HowFarToNonZero - Return the number of times a backedge checking the
3291/// specified value for nonzero will execute. If not computable, return
3292/// UnknownValue
3293SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
3294 // Loops that look like: while (X == 0) are very strange indeed. We don't
3295 // handle them yet except for the trivial case. This could be expanded in the
3296 // future as needed.
3297
3298 // If the value is a constant, check to see if it is known to be non-zero
3299 // already. If so, the backedge will execute zero times.
3300 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3301 if (!C->getValue()->isNullValue())
3302 return getIntegerSCEV(0, C->getType());
3303 return UnknownValue; // Otherwise it will loop infinitely.
3304 }
3305
3306 // We could implement others, but I really doubt anyone writes loops like
3307 // this, and if they did, they would already be constant folded.
3308 return UnknownValue;
3309}
3310
3311/// getLoopPredecessor - If the given loop's header has exactly one unique
3312/// predecessor outside the loop, return it. Otherwise return null.
3313///
3314BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
3315 BasicBlock *Header = L->getHeader();
3316 BasicBlock *Pred = 0;
3317 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
3318 PI != E; ++PI)
3319 if (!L->contains(*PI)) {
3320 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
3321 Pred = *PI;
3322 }
3323 return Pred;
3324}
3325
3326/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3327/// (which may not be an immediate predecessor) which has exactly one
3328/// successor from which BB is reachable, or null if no such block is
3329/// found.
3330///
3331BasicBlock *
3332ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3333 // If the block has a unique predecessor, then there is no path from the
3334 // predecessor to the block that does not go through the direct edge
3335 // from the predecessor to the block.
3336 if (BasicBlock *Pred = BB->getSinglePredecessor())
3337 return Pred;
3338
3339 // A loop's header is defined to be a block that dominates the loop.
3340 // If the header has a unique predecessor outside the loop, it must be
3341 // a block that has exactly one successor that can reach the loop.
3342 if (Loop *L = LI->getLoopFor(BB))
3343 return getLoopPredecessor(L);
3344
3345 return 0;
3346}
3347
3348/// isLoopGuardedByCond - Test whether entry to the loop is protected by
3349/// a conditional between LHS and RHS. This is used to help avoid max
3350/// expressions in loop trip counts.
3351bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3352 ICmpInst::Predicate Pred,
3353 const SCEV *LHS, const SCEV *RHS) {
3354 // Interpret a null as meaning no loop, where there is obviously no guard
3355 // (interprocedural conditions notwithstanding).
3356 if (!L) return false;
3357
3358 BasicBlock *Predecessor = getLoopPredecessor(L);
3359 BasicBlock *PredecessorDest = L->getHeader();
3360
3361 // Starting at the loop predecessor, climb up the predecessor chain, as long
3362 // as there are predecessors that can be found that have unique successors
3363 // leading to the original header.
3364 for (; Predecessor;
3365 PredecessorDest = Predecessor,
3366 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
3367
3368 BranchInst *LoopEntryPredicate =
3369 dyn_cast<BranchInst>(Predecessor->getTerminator());
3370 if (!LoopEntryPredicate ||
3371 LoopEntryPredicate->isUnconditional())
3372 continue;
3373
3374 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3375 if (!ICI) continue;
3376
3377 // Now that we found a conditional branch that dominates the loop, check to
3378 // see if it is the comparison we are looking for.
3379 Value *PreCondLHS = ICI->getOperand(0);
3380 Value *PreCondRHS = ICI->getOperand(1);
3381 ICmpInst::Predicate Cond;
3382 if (LoopEntryPredicate->getSuccessor(0) == PredecessorDest)
3383 Cond = ICI->getPredicate();
3384 else
3385 Cond = ICI->getInversePredicate();
3386
3387 if (Cond == Pred)
3388 ; // An exact match.
3389 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3390 ; // The actual condition is beyond sufficient.
3391 else
3392 // Check a few special cases.
3393 switch (Cond) {
3394 case ICmpInst::ICMP_UGT:
3395 if (Pred == ICmpInst::ICMP_ULT) {
3396 std::swap(PreCondLHS, PreCondRHS);
3397 Cond = ICmpInst::ICMP_ULT;
3398 break;
3399 }
3400 continue;
3401 case ICmpInst::ICMP_SGT:
3402 if (Pred == ICmpInst::ICMP_SLT) {
3403 std::swap(PreCondLHS, PreCondRHS);
3404 Cond = ICmpInst::ICMP_SLT;
3405 break;
3406 }
3407 continue;
3408 case ICmpInst::ICMP_NE:
3409 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3410 // so check for this case by checking if the NE is comparing against
3411 // a minimum or maximum constant.
3412 if (!ICmpInst::isTrueWhenEqual(Pred))
3413 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3414 const APInt &A = CI->getValue();
3415 switch (Pred) {
3416 case ICmpInst::ICMP_SLT:
3417 if (A.isMaxSignedValue()) break;
3418 continue;
3419 case ICmpInst::ICMP_SGT:
3420 if (A.isMinSignedValue()) break;
3421 continue;
3422 case ICmpInst::ICMP_ULT:
3423 if (A.isMaxValue()) break;
3424 continue;
3425 case ICmpInst::ICMP_UGT:
3426 if (A.isMinValue()) break;
3427 continue;
3428 default:
3429 continue;
3430 }
3431 Cond = ICmpInst::ICMP_NE;
3432 // NE is symmetric but the original comparison may not be. Swap
3433 // the operands if necessary so that they match below.
3434 if (isa<SCEVConstant>(LHS))
3435 std::swap(PreCondLHS, PreCondRHS);
3436 break;
3437 }
3438 continue;
3439 default:
3440 // We weren't able to reconcile the condition.
3441 continue;
3442 }
3443
3444 if (!PreCondLHS->getType()->isInteger()) continue;
3445
3446 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3447 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3448 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3449 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3450 RHS == getNotSCEV(PreCondLHSSCEV)))
3451 return true;
3452 }
3453
3454 return false;
3455}
3456
3457/// HowManyLessThans - Return the number of times a backedge containing the
3458/// specified less-than comparison will execute. If not computable, return
3459/// UnknownValue.
3460ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3461HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
3462 const Loop *L, bool isSigned) {
3463 // Only handle: "ADDREC < LoopInvariant".
3464 if (!RHS->isLoopInvariant(L)) return UnknownValue;
3465
3466 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3467 if (!AddRec || AddRec->getLoop() != L)
3468 return UnknownValue;
3469
3470 if (AddRec->isAffine()) {
3471 // FORNOW: We only support unit strides.
3472 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3473 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3474 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3475
3476 // TODO: handle non-constant strides.
3477 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3478 if (!CStep || CStep->isZero())
3479 return UnknownValue;
3480 if (CStep->isOne()) {
3481 // With unit stride, the iteration never steps past the limit value.
3482 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3483 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3484 // Test whether a positive iteration iteration can step past the limit
3485 // value and past the maximum value for its type in a single step.
3486 if (isSigned) {
3487 APInt Max = APInt::getSignedMaxValue(BitWidth);
3488 if ((Max - CStep->getValue()->getValue())
3489 .slt(CLimit->getValue()->getValue()))
3490 return UnknownValue;
3491 } else {
3492 APInt Max = APInt::getMaxValue(BitWidth);
3493 if ((Max - CStep->getValue()->getValue())
3494 .ult(CLimit->getValue()->getValue()))
3495 return UnknownValue;
3496 }
3497 } else
3498 // TODO: handle non-constant limit values below.
3499 return UnknownValue;
3500 } else
3501 // TODO: handle negative strides below.
3502 return UnknownValue;
3503
3504 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3505 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3506 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3507 // treat m-n as signed nor unsigned due to overflow possibility.
3508
3509 // First, we get the value of the LHS in the first iteration: n
3510 SCEVHandle Start = AddRec->getOperand(0);
3511
3512 // Determine the minimum constant start value.
3513 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3514 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3515 APInt::getMinValue(BitWidth));
3516
3517 // If we know that the condition is true in order to enter the loop,
3518 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3519 // only know that it will execute (max(m,n)-n)/s times. In both cases,
3520 // the division must round up.
3521 SCEVHandle End = RHS;
3522 if (!isLoopGuardedByCond(L,
3523 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3524 getMinusSCEV(Start, Step), RHS))
3525 End = isSigned ? getSMaxExpr(RHS, Start)
3526 : getUMaxExpr(RHS, Start);
3527
3528 // Determine the maximum constant end value.
3529 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3530 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3531 APInt::getMaxValue(BitWidth));
3532
3533 // Finally, we subtract these two values and divide, rounding up, to get
3534 // the number of times the backedge is executed.
3535 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3536 getAddExpr(Step, NegOne)),
3537 Step);
3538
3539 // The maximum backedge count is similar, except using the minimum start
3540 // value and the maximum end value.
3541 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3542 MinStart),
3543 getAddExpr(Step, NegOne)),
3544 Step);
3545
3546 return BackedgeTakenInfo(BECount, MaxBECount);
3547 }
3548
3549 return UnknownValue;
3550}
3551
3552/// getNumIterationsInRange - Return the number of iterations of this loop that
3553/// produce values in the specified constant range. Another way of looking at
3554/// this is that it returns the first iteration number where the value is not in
3555/// the condition, thus computing the exit count. If the iteration count can't
3556/// be computed, an instance of SCEVCouldNotCompute is returned.
3557SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3558 ScalarEvolution &SE) const {
3559 if (Range.isFullSet()) // Infinite loop.
3560 return SE.getCouldNotCompute();
3561
3562 // If the start is a non-zero constant, shift the range to simplify things.
3563 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3564 if (!SC->getValue()->isZero()) {
3565 std::vector<SCEVHandle> Operands(op_begin(), op_end());
3566 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3567 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3568 if (const SCEVAddRecExpr *ShiftedAddRec =
3569 dyn_cast<SCEVAddRecExpr>(Shifted))
3570 return ShiftedAddRec->getNumIterationsInRange(
3571 Range.subtract(SC->getValue()->getValue()), SE);
3572 // This is strange and shouldn't happen.
3573 return SE.getCouldNotCompute();
3574 }
3575
3576 // The only time we can solve this is when we have all constant indices.
3577 // Otherwise, we cannot determine the overflow conditions.
3578 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3579 if (!isa<SCEVConstant>(getOperand(i)))
3580 return SE.getCouldNotCompute();
3581
3582
3583 // Okay at this point we know that all elements of the chrec are constants and
3584 // that the start element is zero.
3585
3586 // First check to see if the range contains zero. If not, the first
3587 // iteration exits.
3588 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3589 if (!Range.contains(APInt(BitWidth, 0)))
3590 return SE.getConstant(ConstantInt::get(getType(),0));
3591
3592 if (isAffine()) {
3593 // If this is an affine expression then we have this situation:
3594 // Solve {0,+,A} in Range === Ax in Range
3595
3596 // We know that zero is in the range. If A is positive then we know that
3597 // the upper value of the range must be the first possible exit value.
3598 // If A is negative then the lower of the range is the last possible loop
3599 // value. Also note that we already checked for a full range.
3600 APInt One(BitWidth,1);
3601 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3602 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3603
3604 // The exit value should be (End+A)/A.
3605 APInt ExitVal = (End + A).udiv(A);
3606 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3607
3608 // Evaluate at the exit value. If we really did fall out of the valid
3609 // range, then we computed our trip count, otherwise wrap around or other
3610 // things must have happened.
3611 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3612 if (Range.contains(Val->getValue()))
3613 return SE.getCouldNotCompute(); // Something strange happened
3614
3615 // Ensure that the previous value is in the range. This is a sanity check.
3616 assert(Range.contains(
3617 EvaluateConstantChrecAtConstant(this,
3618 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3619 "Linear scev computation is off in a bad way!");
3620 return SE.getConstant(ExitValue);
3621 } else if (isQuadratic()) {
3622 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3623 // quadratic equation to solve it. To do this, we must frame our problem in
3624 // terms of figuring out when zero is crossed, instead of when
3625 // Range.getUpper() is crossed.
3626 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3627 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3628 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3629
3630 // Next, solve the constructed addrec
3631 std::pair<SCEVHandle,SCEVHandle> Roots =
3632 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3633 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3634 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3635 if (R1) {
3636 // Pick the smallest positive root value.
3637 if (ConstantInt *CB =
3638 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3639 R1->getValue(), R2->getValue()))) {
3640 if (CB->getZExtValue() == false)
3641 std::swap(R1, R2); // R1 is the minimum root now.
3642
3643 // Make sure the root is not off by one. The returned iteration should
3644 // not be in the range, but the previous one should be. When solving
3645 // for "X*X < 5", for example, we should not return a root of 2.
3646 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3647 R1->getValue(),
3648 SE);
3649 if (Range.contains(R1Val->getValue())) {
3650 // The next iteration must be out of the range...
3651 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3652
3653 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3654 if (!Range.contains(R1Val->getValue()))
3655 return SE.getConstant(NextVal);
3656 return SE.getCouldNotCompute(); // Something strange happened
3657 }
3658
3659 // If R1 was not in the range, then it is a good return value. Make
3660 // sure that R1-1 WAS in the range though, just in case.
3661 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3662 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3663 if (Range.contains(R1Val->getValue()))
3664 return R1;
3665 return SE.getCouldNotCompute(); // Something strange happened
3666 }
3667 }
3668 }
3669
3670 return SE.getCouldNotCompute();
3671}
3672
3673
3674
3675//===----------------------------------------------------------------------===//
3676// SCEVCallbackVH Class Implementation
3677//===----------------------------------------------------------------------===//
3678
3679void ScalarEvolution::SCEVCallbackVH::deleted() {
3680 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3681 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
3682 SE->ConstantEvolutionLoopExitValue.erase(PN);
3683 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
3684 SE->ValuesAtScopes.erase(I);
3685 SE->Scalars.erase(getValPtr());
3686 // this now dangles!
3687}
3688
3689void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
3690 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3691
3692 // Forget all the expressions associated with users of the old value,
3693 // so that future queries will recompute the expressions using the new
3694 // value.
3695 SmallVector<User *, 16> Worklist;
3696 Value *Old = getValPtr();
3697 bool DeleteOld = false;
3698 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
3699 UI != UE; ++UI)
3700 Worklist.push_back(*UI);
3701 while (!Worklist.empty()) {
3702 User *U = Worklist.pop_back_val();
3703 // Deleting the Old value will cause this to dangle. Postpone
3704 // that until everything else is done.
3705 if (U == Old) {
3706 DeleteOld = true;
3707 continue;
3708 }
3709 if (PHINode *PN = dyn_cast<PHINode>(U))
3710 SE->ConstantEvolutionLoopExitValue.erase(PN);
3711 if (Instruction *I = dyn_cast<Instruction>(U))
3712 SE->ValuesAtScopes.erase(I);
3713 if (SE->Scalars.erase(U))
3714 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
3715 UI != UE; ++UI)
3716 Worklist.push_back(*UI);
3717 }
3718 if (DeleteOld) {
3719 if (PHINode *PN = dyn_cast<PHINode>(Old))
3720 SE->ConstantEvolutionLoopExitValue.erase(PN);
3721 if (Instruction *I = dyn_cast<Instruction>(Old))
3722 SE->ValuesAtScopes.erase(I);
3723 SE->Scalars.erase(Old);
3724 // this now dangles!
3725 }
3726 // this may dangle!
3727}
3728
3729ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
3730 : CallbackVH(V), SE(se) {}
3731
3732//===----------------------------------------------------------------------===//
3733// ScalarEvolution Class Implementation
3734//===----------------------------------------------------------------------===//
3735
3736ScalarEvolution::ScalarEvolution()
3737 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) {
3738}
3739
3740bool ScalarEvolution::runOnFunction(Function &F) {
3741 this->F = &F;
3742 LI = &getAnalysis<LoopInfo>();
3743 TD = getAnalysisIfAvailable<TargetData>();
3744 return false;
3745}
3746
3747void ScalarEvolution::releaseMemory() {
3748 Scalars.clear();
3749 BackedgeTakenCounts.clear();
3750 ConstantEvolutionLoopExitValue.clear();
3751 ValuesAtScopes.clear();
3752}
3753
3754void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3755 AU.setPreservesAll();
3756 AU.addRequiredTransitive<LoopInfo>();
3757}
3758
3759bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3760 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3761}
3762
3763static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3764 const Loop *L) {
3765 // Print all inner loops first
3766 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3767 PrintLoopInfo(OS, SE, *I);
3768
3769 OS << "Loop " << L->getHeader()->getName() << ": ";
3770
3771 SmallVector<BasicBlock*, 8> ExitBlocks;
3772 L->getExitBlocks(ExitBlocks);
3773 if (ExitBlocks.size() != 1)
3774 OS << "<multiple exits> ";
3775
3776 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3777 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3778 } else {
3779 OS << "Unpredictable backedge-taken count. ";
3780 }
3781
3782 OS << "\n";
3783}
3784
3785void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3786 // ScalarEvolution's implementaiton of the print method is to print
3787 // out SCEV values of all instructions that are interesting. Doing
3788 // this potentially causes it to create new SCEV objects though,
3789 // which technically conflicts with the const qualifier. This isn't
3790 // observable from outside the class though (the hasSCEV function
3791 // notwithstanding), so casting away the const isn't dangerous.
3792 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3793
3794 OS << "Classifying expressions for: " << F->getName() << "\n";
3795 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3796 if (isSCEVable(I->getType())) {
3797 OS << *I;
3798 OS << " --> ";
3799 SCEVHandle SV = SE.getSCEV(&*I);
3800 SV->print(OS);
3801 OS << "\t\t";
3802
3803 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3804 OS << "Exits: ";
3805 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3806 if (!ExitValue->isLoopInvariant(L)) {
3807 OS << "<<Unknown>>";
3808 } else {
3809 OS << *ExitValue;
3810 }
3811 }
3812
3813 OS << "\n";
3814 }
3815
3816 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3817 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3818 PrintLoopInfo(OS, &SE, *I);
3819}
3820
3821void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3822 raw_os_ostream OS(o);
3823 print(OS, M);
3824}
| 2475 // Okay, we've computed the exiting block. See what condition causes us to
2476 // exit.
2477 //
2478 // FIXME: we should be able to handle switch instructions (with a single exit)
2479 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2480 if (ExitBr == 0) return UnknownValue;
2481 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2482
2483 // At this point, we know we have a conditional branch that determines whether
2484 // the loop is exited. However, we don't know if the branch is executed each
2485 // time through the loop. If not, then the execution count of the branch will
2486 // not be equal to the trip count of the loop.
2487 //
2488 // Currently we check for this by checking to see if the Exit branch goes to
2489 // the loop header. If so, we know it will always execute the same number of
2490 // times as the loop. We also handle the case where the exit block *is* the
2491 // loop header. This is common for un-rotated loops. More extensive analysis
2492 // could be done to handle more cases here.
2493 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2494 ExitBr->getSuccessor(1) != L->getHeader() &&
2495 ExitBr->getParent() != L->getHeader())
2496 return UnknownValue;
2497
2498 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2499
2500 // If it's not an integer or pointer comparison then compute it the hard way.
2501 if (ExitCond == 0)
2502 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2503 ExitBr->getSuccessor(0) == ExitBlock);
2504
2505 // If the condition was exit on true, convert the condition to exit on false
2506 ICmpInst::Predicate Cond;
2507 if (ExitBr->getSuccessor(1) == ExitBlock)
2508 Cond = ExitCond->getPredicate();
2509 else
2510 Cond = ExitCond->getInversePredicate();
2511
2512 // Handle common loops like: for (X = "string"; *X; ++X)
2513 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2514 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2515 SCEVHandle ItCnt =
2516 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2517 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2518 }
2519
2520 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2521 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2522
2523 // Try to evaluate any dependencies out of the loop.
2524 LHS = getSCEVAtScope(LHS, L);
2525 RHS = getSCEVAtScope(RHS, L);
2526
2527 // At this point, we would like to compute how many iterations of the
2528 // loop the predicate will return true for these inputs.
2529 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2530 // If there is a loop-invariant, force it into the RHS.
2531 std::swap(LHS, RHS);
2532 Cond = ICmpInst::getSwappedPredicate(Cond);
2533 }
2534
2535 // If we have a comparison of a chrec against a constant, try to use value
2536 // ranges to answer this query.
2537 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2538 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2539 if (AddRec->getLoop() == L) {
2540 // Form the constant range.
2541 ConstantRange CompRange(
2542 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
2543
2544 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2545 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2546 }
2547
2548 switch (Cond) {
2549 case ICmpInst::ICMP_NE: { // while (X != Y)
2550 // Convert to: while (X-Y != 0)
2551 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2552 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2553 break;
2554 }
2555 case ICmpInst::ICMP_EQ: {
2556 // Convert to: while (X-Y == 0) // while (X == Y)
2557 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2558 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2559 break;
2560 }
2561 case ICmpInst::ICMP_SLT: {
2562 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2563 if (BTI.hasAnyInfo()) return BTI;
2564 break;
2565 }
2566 case ICmpInst::ICMP_SGT: {
2567 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2568 getNotSCEV(RHS), L, true);
2569 if (BTI.hasAnyInfo()) return BTI;
2570 break;
2571 }
2572 case ICmpInst::ICMP_ULT: {
2573 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2574 if (BTI.hasAnyInfo()) return BTI;
2575 break;
2576 }
2577 case ICmpInst::ICMP_UGT: {
2578 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2579 getNotSCEV(RHS), L, false);
2580 if (BTI.hasAnyInfo()) return BTI;
2581 break;
2582 }
2583 default:
2584#if 0
2585 errs() << "ComputeBackedgeTakenCount ";
2586 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2587 errs() << "[unsigned] ";
2588 errs() << *LHS << " "
2589 << Instruction::getOpcodeName(Instruction::ICmp)
2590 << " " << *RHS << "\n";
2591#endif
2592 break;
2593 }
2594 return
2595 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2596 ExitBr->getSuccessor(0) == ExitBlock);
2597}
2598
2599static ConstantInt *
2600EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2601 ScalarEvolution &SE) {
2602 SCEVHandle InVal = SE.getConstant(C);
2603 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2604 assert(isa<SCEVConstant>(Val) &&
2605 "Evaluation of SCEV at constant didn't fold correctly?");
2606 return cast<SCEVConstant>(Val)->getValue();
2607}
2608
2609/// GetAddressedElementFromGlobal - Given a global variable with an initializer
2610/// and a GEP expression (missing the pointer index) indexing into it, return
2611/// the addressed element of the initializer or null if the index expression is
2612/// invalid.
2613static Constant *
2614GetAddressedElementFromGlobal(GlobalVariable *GV,
2615 const std::vector<ConstantInt*> &Indices) {
2616 Constant *Init = GV->getInitializer();
2617 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2618 uint64_t Idx = Indices[i]->getZExtValue();
2619 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2620 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2621 Init = cast<Constant>(CS->getOperand(Idx));
2622 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2623 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2624 Init = cast<Constant>(CA->getOperand(Idx));
2625 } else if (isa<ConstantAggregateZero>(Init)) {
2626 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2627 assert(Idx < STy->getNumElements() && "Bad struct index!");
2628 Init = Constant::getNullValue(STy->getElementType(Idx));
2629 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2630 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2631 Init = Constant::getNullValue(ATy->getElementType());
2632 } else {
2633 assert(0 && "Unknown constant aggregate type!");
2634 }
2635 return 0;
2636 } else {
2637 return 0; // Unknown initializer type
2638 }
2639 }
2640 return Init;
2641}
2642
2643/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2644/// 'icmp op load X, cst', try to see if we can compute the backedge
2645/// execution count.
2646SCEVHandle ScalarEvolution::
2647ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2648 const Loop *L,
2649 ICmpInst::Predicate predicate) {
2650 if (LI->isVolatile()) return UnknownValue;
2651
2652 // Check to see if the loaded pointer is a getelementptr of a global.
2653 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2654 if (!GEP) return UnknownValue;
2655
2656 // Make sure that it is really a constant global we are gepping, with an
2657 // initializer, and make sure the first IDX is really 0.
2658 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2659 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2660 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2661 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2662 return UnknownValue;
2663
2664 // Okay, we allow one non-constant index into the GEP instruction.
2665 Value *VarIdx = 0;
2666 std::vector<ConstantInt*> Indexes;
2667 unsigned VarIdxNum = 0;
2668 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2669 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2670 Indexes.push_back(CI);
2671 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2672 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2673 VarIdx = GEP->getOperand(i);
2674 VarIdxNum = i-2;
2675 Indexes.push_back(0);
2676 }
2677
2678 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2679 // Check to see if X is a loop variant variable value now.
2680 SCEVHandle Idx = getSCEV(VarIdx);
2681 Idx = getSCEVAtScope(Idx, L);
2682
2683 // We can only recognize very limited forms of loop index expressions, in
2684 // particular, only affine AddRec's like {C1,+,C2}.
2685 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2686 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2687 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2688 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2689 return UnknownValue;
2690
2691 unsigned MaxSteps = MaxBruteForceIterations;
2692 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2693 ConstantInt *ItCst =
2694 ConstantInt::get(IdxExpr->getType(), IterationNum);
2695 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2696
2697 // Form the GEP offset.
2698 Indexes[VarIdxNum] = Val;
2699
2700 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2701 if (Result == 0) break; // Cannot compute!
2702
2703 // Evaluate the condition for this iteration.
2704 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2705 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2706 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2707#if 0
2708 errs() << "\n***\n*** Computed loop count " << *ItCst
2709 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2710 << "***\n";
2711#endif
2712 ++NumArrayLenItCounts;
2713 return getConstant(ItCst); // Found terminating iteration!
2714 }
2715 }
2716 return UnknownValue;
2717}
2718
2719
2720/// CanConstantFold - Return true if we can constant fold an instruction of the
2721/// specified type, assuming that all operands were constants.
2722static bool CanConstantFold(const Instruction *I) {
2723 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2724 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2725 return true;
2726
2727 if (const CallInst *CI = dyn_cast<CallInst>(I))
2728 if (const Function *F = CI->getCalledFunction())
2729 return canConstantFoldCallTo(F);
2730 return false;
2731}
2732
2733/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2734/// in the loop that V is derived from. We allow arbitrary operations along the
2735/// way, but the operands of an operation must either be constants or a value
2736/// derived from a constant PHI. If this expression does not fit with these
2737/// constraints, return null.
2738static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2739 // If this is not an instruction, or if this is an instruction outside of the
2740 // loop, it can't be derived from a loop PHI.
2741 Instruction *I = dyn_cast<Instruction>(V);
2742 if (I == 0 || !L->contains(I->getParent())) return 0;
2743
2744 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2745 if (L->getHeader() == I->getParent())
2746 return PN;
2747 else
2748 // We don't currently keep track of the control flow needed to evaluate
2749 // PHIs, so we cannot handle PHIs inside of loops.
2750 return 0;
2751 }
2752
2753 // If we won't be able to constant fold this expression even if the operands
2754 // are constants, return early.
2755 if (!CanConstantFold(I)) return 0;
2756
2757 // Otherwise, we can evaluate this instruction if all of its operands are
2758 // constant or derived from a PHI node themselves.
2759 PHINode *PHI = 0;
2760 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2761 if (!(isa<Constant>(I->getOperand(Op)) ||
2762 isa<GlobalValue>(I->getOperand(Op)))) {
2763 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2764 if (P == 0) return 0; // Not evolving from PHI
2765 if (PHI == 0)
2766 PHI = P;
2767 else if (PHI != P)
2768 return 0; // Evolving from multiple different PHIs.
2769 }
2770
2771 // This is a expression evolving from a constant PHI!
2772 return PHI;
2773}
2774
2775/// EvaluateExpression - Given an expression that passes the
2776/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2777/// in the loop has the value PHIVal. If we can't fold this expression for some
2778/// reason, return null.
2779static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2780 if (isa<PHINode>(V)) return PHIVal;
2781 if (Constant *C = dyn_cast<Constant>(V)) return C;
2782 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2783 Instruction *I = cast<Instruction>(V);
2784
2785 std::vector<Constant*> Operands;
2786 Operands.resize(I->getNumOperands());
2787
2788 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2789 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2790 if (Operands[i] == 0) return 0;
2791 }
2792
2793 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2794 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2795 &Operands[0], Operands.size());
2796 else
2797 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2798 &Operands[0], Operands.size());
2799}
2800
2801/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2802/// in the header of its containing loop, we know the loop executes a
2803/// constant number of times, and the PHI node is just a recurrence
2804/// involving constants, fold it.
2805Constant *ScalarEvolution::
2806getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2807 std::map<PHINode*, Constant*>::iterator I =
2808 ConstantEvolutionLoopExitValue.find(PN);
2809 if (I != ConstantEvolutionLoopExitValue.end())
2810 return I->second;
2811
2812 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2813 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2814
2815 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2816
2817 // Since the loop is canonicalized, the PHI node must have two entries. One
2818 // entry must be a constant (coming in from outside of the loop), and the
2819 // second must be derived from the same PHI.
2820 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2821 Constant *StartCST =
2822 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2823 if (StartCST == 0)
2824 return RetVal = 0; // Must be a constant.
2825
2826 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2827 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2828 if (PN2 != PN)
2829 return RetVal = 0; // Not derived from same PHI.
2830
2831 // Execute the loop symbolically to determine the exit value.
2832 if (BEs.getActiveBits() >= 32)
2833 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2834
2835 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2836 unsigned IterationNum = 0;
2837 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2838 if (IterationNum == NumIterations)
2839 return RetVal = PHIVal; // Got exit value!
2840
2841 // Compute the value of the PHI node for the next iteration.
2842 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2843 if (NextPHI == PHIVal)
2844 return RetVal = NextPHI; // Stopped evolving!
2845 if (NextPHI == 0)
2846 return 0; // Couldn't evaluate!
2847 PHIVal = NextPHI;
2848 }
2849}
2850
2851/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2852/// constant number of times (the condition evolves only from constants),
2853/// try to evaluate a few iterations of the loop until we get the exit
2854/// condition gets a value of ExitWhen (true or false). If we cannot
2855/// evaluate the trip count of the loop, return UnknownValue.
2856SCEVHandle ScalarEvolution::
2857ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2858 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2859 if (PN == 0) return UnknownValue;
2860
2861 // Since the loop is canonicalized, the PHI node must have two entries. One
2862 // entry must be a constant (coming in from outside of the loop), and the
2863 // second must be derived from the same PHI.
2864 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2865 Constant *StartCST =
2866 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2867 if (StartCST == 0) return UnknownValue; // Must be a constant.
2868
2869 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2870 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2871 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2872
2873 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2874 // the loop symbolically to determine when the condition gets a value of
2875 // "ExitWhen".
2876 unsigned IterationNum = 0;
2877 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2878 for (Constant *PHIVal = StartCST;
2879 IterationNum != MaxIterations; ++IterationNum) {
2880 ConstantInt *CondVal =
2881 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2882
2883 // Couldn't symbolically evaluate.
2884 if (!CondVal) return UnknownValue;
2885
2886 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2887 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2888 ++NumBruteForceTripCountsComputed;
2889 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2890 }
2891
2892 // Compute the value of the PHI node for the next iteration.
2893 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2894 if (NextPHI == 0 || NextPHI == PHIVal)
2895 return UnknownValue; // Couldn't evaluate or not making progress...
2896 PHIVal = NextPHI;
2897 }
2898
2899 // Too many iterations were needed to evaluate.
2900 return UnknownValue;
2901}
2902
2903/// getSCEVAtScope - Return a SCEV expression handle for the specified value
2904/// at the specified scope in the program. The L value specifies a loop
2905/// nest to evaluate the expression at, where null is the top-level or a
2906/// specified loop is immediately inside of the loop.
2907///
2908/// This method can be used to compute the exit value for a variable defined
2909/// in a loop by querying what the value will hold in the parent loop.
2910///
2911/// In the case that a relevant loop exit value cannot be computed, the
2912/// original value V is returned.
2913SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
2914 // FIXME: this should be turned into a virtual method on SCEV!
2915
2916 if (isa<SCEVConstant>(V)) return V;
2917
2918 // If this instruction is evolved from a constant-evolving PHI, compute the
2919 // exit value from the loop without using SCEVs.
2920 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2921 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2922 const Loop *LI = (*this->LI)[I->getParent()];
2923 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2924 if (PHINode *PN = dyn_cast<PHINode>(I))
2925 if (PN->getParent() == LI->getHeader()) {
2926 // Okay, there is no closed form solution for the PHI node. Check
2927 // to see if the loop that contains it has a known backedge-taken
2928 // count. If so, we may be able to force computation of the exit
2929 // value.
2930 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2931 if (const SCEVConstant *BTCC =
2932 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2933 // Okay, we know how many times the containing loop executes. If
2934 // this is a constant evolving PHI node, get the final value at
2935 // the specified iteration number.
2936 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2937 BTCC->getValue()->getValue(),
2938 LI);
2939 if (RV) return getUnknown(RV);
2940 }
2941 }
2942
2943 // Okay, this is an expression that we cannot symbolically evaluate
2944 // into a SCEV. Check to see if it's possible to symbolically evaluate
2945 // the arguments into constants, and if so, try to constant propagate the
2946 // result. This is particularly useful for computing loop exit values.
2947 if (CanConstantFold(I)) {
2948 // Check to see if we've folded this instruction at this loop before.
2949 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
2950 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
2951 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
2952 if (!Pair.second)
2953 return Pair.first->second ? &*getUnknown(Pair.first->second) : V;
2954
2955 std::vector<Constant*> Operands;
2956 Operands.reserve(I->getNumOperands());
2957 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2958 Value *Op = I->getOperand(i);
2959 if (Constant *C = dyn_cast<Constant>(Op)) {
2960 Operands.push_back(C);
2961 } else {
2962 // If any of the operands is non-constant and if they are
2963 // non-integer and non-pointer, don't even try to analyze them
2964 // with scev techniques.
2965 if (!isSCEVable(Op->getType()))
2966 return V;
2967
2968 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2969 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
2970 Constant *C = SC->getValue();
2971 if (C->getType() != Op->getType())
2972 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2973 Op->getType(),
2974 false),
2975 C, Op->getType());
2976 Operands.push_back(C);
2977 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2978 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
2979 if (C->getType() != Op->getType())
2980 C =
2981 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2982 Op->getType(),
2983 false),
2984 C, Op->getType());
2985 Operands.push_back(C);
2986 } else
2987 return V;
2988 } else {
2989 return V;
2990 }
2991 }
2992 }
2993
2994 Constant *C;
2995 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2996 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2997 &Operands[0], Operands.size());
2998 else
2999 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3000 &Operands[0], Operands.size());
3001 Pair.first->second = C;
3002 return getUnknown(C);
3003 }
3004 }
3005
3006 // This is some other type of SCEVUnknown, just return it.
3007 return V;
3008 }
3009
3010 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3011 // Avoid performing the look-up in the common case where the specified
3012 // expression has no loop-variant portions.
3013 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3014 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3015 if (OpAtScope != Comm->getOperand(i)) {
3016 // Okay, at least one of these operands is loop variant but might be
3017 // foldable. Build a new instance of the folded commutative expression.
3018 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
3019 NewOps.push_back(OpAtScope);
3020
3021 for (++i; i != e; ++i) {
3022 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3023 NewOps.push_back(OpAtScope);
3024 }
3025 if (isa<SCEVAddExpr>(Comm))
3026 return getAddExpr(NewOps);
3027 if (isa<SCEVMulExpr>(Comm))
3028 return getMulExpr(NewOps);
3029 if (isa<SCEVSMaxExpr>(Comm))
3030 return getSMaxExpr(NewOps);
3031 if (isa<SCEVUMaxExpr>(Comm))
3032 return getUMaxExpr(NewOps);
3033 assert(0 && "Unknown commutative SCEV type!");
3034 }
3035 }
3036 // If we got here, all operands are loop invariant.
3037 return Comm;
3038 }
3039
3040 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3041 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
3042 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
3043 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3044 return Div; // must be loop invariant
3045 return getUDivExpr(LHS, RHS);
3046 }
3047
3048 // If this is a loop recurrence for a loop that does not contain L, then we
3049 // are dealing with the final value computed by the loop.
3050 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3051 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3052 // To evaluate this recurrence, we need to know how many times the AddRec
3053 // loop iterates. Compute this now.
3054 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3055 if (BackedgeTakenCount == UnknownValue) return AddRec;
3056
3057 // Then, evaluate the AddRec.
3058 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3059 }
3060 return AddRec;
3061 }
3062
3063 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3064 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3065 if (Op == Cast->getOperand())
3066 return Cast; // must be loop invariant
3067 return getZeroExtendExpr(Op, Cast->getType());
3068 }
3069
3070 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3071 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3072 if (Op == Cast->getOperand())
3073 return Cast; // must be loop invariant
3074 return getSignExtendExpr(Op, Cast->getType());
3075 }
3076
3077 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3078 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3079 if (Op == Cast->getOperand())
3080 return Cast; // must be loop invariant
3081 return getTruncateExpr(Op, Cast->getType());
3082 }
3083
3084 assert(0 && "Unknown SCEV type!");
3085 return 0;
3086}
3087
3088/// getSCEVAtScope - This is a convenience function which does
3089/// getSCEVAtScope(getSCEV(V), L).
3090SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3091 return getSCEVAtScope(getSCEV(V), L);
3092}
3093
3094/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3095/// following equation:
3096///
3097/// A * X = B (mod N)
3098///
3099/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3100/// A and B isn't important.
3101///
3102/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3103static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3104 ScalarEvolution &SE) {
3105 uint32_t BW = A.getBitWidth();
3106 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3107 assert(A != 0 && "A must be non-zero.");
3108
3109 // 1. D = gcd(A, N)
3110 //
3111 // The gcd of A and N may have only one prime factor: 2. The number of
3112 // trailing zeros in A is its multiplicity
3113 uint32_t Mult2 = A.countTrailingZeros();
3114 // D = 2^Mult2
3115
3116 // 2. Check if B is divisible by D.
3117 //
3118 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3119 // is not less than multiplicity of this prime factor for D.
3120 if (B.countTrailingZeros() < Mult2)
3121 return SE.getCouldNotCompute();
3122
3123 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3124 // modulo (N / D).
3125 //
3126 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3127 // bit width during computations.
3128 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3129 APInt Mod(BW + 1, 0);
3130 Mod.set(BW - Mult2); // Mod = N / D
3131 APInt I = AD.multiplicativeInverse(Mod);
3132
3133 // 4. Compute the minimum unsigned root of the equation:
3134 // I * (B / D) mod (N / D)
3135 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3136
3137 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3138 // bits.
3139 return SE.getConstant(Result.trunc(BW));
3140}
3141
3142/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3143/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
3144/// might be the same) or two SCEVCouldNotCompute objects.
3145///
3146static std::pair<SCEVHandle,SCEVHandle>
3147SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
3148 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
3149 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
3150 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
3151 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
3152
3153 // We currently can only solve this if the coefficients are constants.
3154 if (!LC || !MC || !NC) {
3155 const SCEV *CNC = SE.getCouldNotCompute();
3156 return std::make_pair(CNC, CNC);
3157 }
3158
3159 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
3160 const APInt &L = LC->getValue()->getValue();
3161 const APInt &M = MC->getValue()->getValue();
3162 const APInt &N = NC->getValue()->getValue();
3163 APInt Two(BitWidth, 2);
3164 APInt Four(BitWidth, 4);
3165
3166 {
3167 using namespace APIntOps;
3168 const APInt& C = L;
3169 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
3170 // The B coefficient is M-N/2
3171 APInt B(M);
3172 B -= sdiv(N,Two);
3173
3174 // The A coefficient is N/2
3175 APInt A(N.sdiv(Two));
3176
3177 // Compute the B^2-4ac term.
3178 APInt SqrtTerm(B);
3179 SqrtTerm *= B;
3180 SqrtTerm -= Four * (A * C);
3181
3182 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
3183 // integer value or else APInt::sqrt() will assert.
3184 APInt SqrtVal(SqrtTerm.sqrt());
3185
3186 // Compute the two solutions for the quadratic formula.
3187 // The divisions must be performed as signed divisions.
3188 APInt NegB(-B);
3189 APInt TwoA( A << 1 );
3190 if (TwoA.isMinValue()) {
3191 const SCEV *CNC = SE.getCouldNotCompute();
3192 return std::make_pair(CNC, CNC);
3193 }
3194
3195 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
3196 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
3197
3198 return std::make_pair(SE.getConstant(Solution1),
3199 SE.getConstant(Solution2));
3200 } // end APIntOps namespace
3201}
3202
3203/// HowFarToZero - Return the number of times a backedge comparing the specified
3204/// value to zero will execute. If not computable, return UnknownValue.
3205SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
3206 // If the value is a constant
3207 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3208 // If the value is already zero, the branch will execute zero times.
3209 if (C->getValue()->isZero()) return C;
3210 return UnknownValue; // Otherwise it will loop infinitely.
3211 }
3212
3213 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
3214 if (!AddRec || AddRec->getLoop() != L)
3215 return UnknownValue;
3216
3217 if (AddRec->isAffine()) {
3218 // If this is an affine expression, the execution count of this branch is
3219 // the minimum unsigned root of the following equation:
3220 //
3221 // Start + Step*N = 0 (mod 2^BW)
3222 //
3223 // equivalent to:
3224 //
3225 // Step*N = -Start (mod 2^BW)
3226 //
3227 // where BW is the common bit width of Start and Step.
3228
3229 // Get the initial value for the loop.
3230 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
3231 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
3232
3233 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
3234 // For now we handle only constant steps.
3235
3236 // First, handle unitary steps.
3237 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
3238 return getNegativeSCEV(Start); // N = -Start (as unsigned)
3239 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
3240 return Start; // N = Start (as unsigned)
3241
3242 // Then, try to solve the above equation provided that Start is constant.
3243 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
3244 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
3245 -StartC->getValue()->getValue(),
3246 *this);
3247 }
3248 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
3249 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
3250 // the quadratic equation to solve it.
3251 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
3252 *this);
3253 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3254 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3255 if (R1) {
3256#if 0
3257 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
3258 << " sol#2: " << *R2 << "\n";
3259#endif
3260 // Pick the smallest positive root value.
3261 if (ConstantInt *CB =
3262 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3263 R1->getValue(), R2->getValue()))) {
3264 if (CB->getZExtValue() == false)
3265 std::swap(R1, R2); // R1 is the minimum root now.
3266
3267 // We can only use this value if the chrec ends up with an exact zero
3268 // value at this index. When solving for "X*X != 5", for example, we
3269 // should not accept a root of 2.
3270 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
3271 if (Val->isZero())
3272 return R1; // We found a quadratic root!
3273 }
3274 }
3275 }
3276
3277 return UnknownValue;
3278}
3279
3280/// HowFarToNonZero - Return the number of times a backedge checking the
3281/// specified value for nonzero will execute. If not computable, return
3282/// UnknownValue
3283SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
3284 // Loops that look like: while (X == 0) are very strange indeed. We don't
3285 // handle them yet except for the trivial case. This could be expanded in the
3286 // future as needed.
3287
3288 // If the value is a constant, check to see if it is known to be non-zero
3289 // already. If so, the backedge will execute zero times.
3290 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3291 if (!C->getValue()->isNullValue())
3292 return getIntegerSCEV(0, C->getType());
3293 return UnknownValue; // Otherwise it will loop infinitely.
3294 }
3295
3296 // We could implement others, but I really doubt anyone writes loops like
3297 // this, and if they did, they would already be constant folded.
3298 return UnknownValue;
3299}
3300
3301/// getLoopPredecessor - If the given loop's header has exactly one unique
3302/// predecessor outside the loop, return it. Otherwise return null.
3303///
3304BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
3305 BasicBlock *Header = L->getHeader();
3306 BasicBlock *Pred = 0;
3307 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
3308 PI != E; ++PI)
3309 if (!L->contains(*PI)) {
3310 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
3311 Pred = *PI;
3312 }
3313 return Pred;
3314}
3315
3316/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3317/// (which may not be an immediate predecessor) which has exactly one
3318/// successor from which BB is reachable, or null if no such block is
3319/// found.
3320///
3321BasicBlock *
3322ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3323 // If the block has a unique predecessor, then there is no path from the
3324 // predecessor to the block that does not go through the direct edge
3325 // from the predecessor to the block.
3326 if (BasicBlock *Pred = BB->getSinglePredecessor())
3327 return Pred;
3328
3329 // A loop's header is defined to be a block that dominates the loop.
3330 // If the header has a unique predecessor outside the loop, it must be
3331 // a block that has exactly one successor that can reach the loop.
3332 if (Loop *L = LI->getLoopFor(BB))
3333 return getLoopPredecessor(L);
3334
3335 return 0;
3336}
3337
3338/// isLoopGuardedByCond - Test whether entry to the loop is protected by
3339/// a conditional between LHS and RHS. This is used to help avoid max
3340/// expressions in loop trip counts.
3341bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3342 ICmpInst::Predicate Pred,
3343 const SCEV *LHS, const SCEV *RHS) {
3344 // Interpret a null as meaning no loop, where there is obviously no guard
3345 // (interprocedural conditions notwithstanding).
3346 if (!L) return false;
3347
3348 BasicBlock *Predecessor = getLoopPredecessor(L);
3349 BasicBlock *PredecessorDest = L->getHeader();
3350
3351 // Starting at the loop predecessor, climb up the predecessor chain, as long
3352 // as there are predecessors that can be found that have unique successors
3353 // leading to the original header.
3354 for (; Predecessor;
3355 PredecessorDest = Predecessor,
3356 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
3357
3358 BranchInst *LoopEntryPredicate =
3359 dyn_cast<BranchInst>(Predecessor->getTerminator());
3360 if (!LoopEntryPredicate ||
3361 LoopEntryPredicate->isUnconditional())
3362 continue;
3363
3364 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3365 if (!ICI) continue;
3366
3367 // Now that we found a conditional branch that dominates the loop, check to
3368 // see if it is the comparison we are looking for.
3369 Value *PreCondLHS = ICI->getOperand(0);
3370 Value *PreCondRHS = ICI->getOperand(1);
3371 ICmpInst::Predicate Cond;
3372 if (LoopEntryPredicate->getSuccessor(0) == PredecessorDest)
3373 Cond = ICI->getPredicate();
3374 else
3375 Cond = ICI->getInversePredicate();
3376
3377 if (Cond == Pred)
3378 ; // An exact match.
3379 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3380 ; // The actual condition is beyond sufficient.
3381 else
3382 // Check a few special cases.
3383 switch (Cond) {
3384 case ICmpInst::ICMP_UGT:
3385 if (Pred == ICmpInst::ICMP_ULT) {
3386 std::swap(PreCondLHS, PreCondRHS);
3387 Cond = ICmpInst::ICMP_ULT;
3388 break;
3389 }
3390 continue;
3391 case ICmpInst::ICMP_SGT:
3392 if (Pred == ICmpInst::ICMP_SLT) {
3393 std::swap(PreCondLHS, PreCondRHS);
3394 Cond = ICmpInst::ICMP_SLT;
3395 break;
3396 }
3397 continue;
3398 case ICmpInst::ICMP_NE:
3399 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3400 // so check for this case by checking if the NE is comparing against
3401 // a minimum or maximum constant.
3402 if (!ICmpInst::isTrueWhenEqual(Pred))
3403 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3404 const APInt &A = CI->getValue();
3405 switch (Pred) {
3406 case ICmpInst::ICMP_SLT:
3407 if (A.isMaxSignedValue()) break;
3408 continue;
3409 case ICmpInst::ICMP_SGT:
3410 if (A.isMinSignedValue()) break;
3411 continue;
3412 case ICmpInst::ICMP_ULT:
3413 if (A.isMaxValue()) break;
3414 continue;
3415 case ICmpInst::ICMP_UGT:
3416 if (A.isMinValue()) break;
3417 continue;
3418 default:
3419 continue;
3420 }
3421 Cond = ICmpInst::ICMP_NE;
3422 // NE is symmetric but the original comparison may not be. Swap
3423 // the operands if necessary so that they match below.
3424 if (isa<SCEVConstant>(LHS))
3425 std::swap(PreCondLHS, PreCondRHS);
3426 break;
3427 }
3428 continue;
3429 default:
3430 // We weren't able to reconcile the condition.
3431 continue;
3432 }
3433
3434 if (!PreCondLHS->getType()->isInteger()) continue;
3435
3436 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3437 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3438 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3439 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3440 RHS == getNotSCEV(PreCondLHSSCEV)))
3441 return true;
3442 }
3443
3444 return false;
3445}
3446
3447/// HowManyLessThans - Return the number of times a backedge containing the
3448/// specified less-than comparison will execute. If not computable, return
3449/// UnknownValue.
3450ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3451HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
3452 const Loop *L, bool isSigned) {
3453 // Only handle: "ADDREC < LoopInvariant".
3454 if (!RHS->isLoopInvariant(L)) return UnknownValue;
3455
3456 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3457 if (!AddRec || AddRec->getLoop() != L)
3458 return UnknownValue;
3459
3460 if (AddRec->isAffine()) {
3461 // FORNOW: We only support unit strides.
3462 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3463 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3464 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3465
3466 // TODO: handle non-constant strides.
3467 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3468 if (!CStep || CStep->isZero())
3469 return UnknownValue;
3470 if (CStep->isOne()) {
3471 // With unit stride, the iteration never steps past the limit value.
3472 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3473 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3474 // Test whether a positive iteration iteration can step past the limit
3475 // value and past the maximum value for its type in a single step.
3476 if (isSigned) {
3477 APInt Max = APInt::getSignedMaxValue(BitWidth);
3478 if ((Max - CStep->getValue()->getValue())
3479 .slt(CLimit->getValue()->getValue()))
3480 return UnknownValue;
3481 } else {
3482 APInt Max = APInt::getMaxValue(BitWidth);
3483 if ((Max - CStep->getValue()->getValue())
3484 .ult(CLimit->getValue()->getValue()))
3485 return UnknownValue;
3486 }
3487 } else
3488 // TODO: handle non-constant limit values below.
3489 return UnknownValue;
3490 } else
3491 // TODO: handle negative strides below.
3492 return UnknownValue;
3493
3494 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3495 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3496 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3497 // treat m-n as signed nor unsigned due to overflow possibility.
3498
3499 // First, we get the value of the LHS in the first iteration: n
3500 SCEVHandle Start = AddRec->getOperand(0);
3501
3502 // Determine the minimum constant start value.
3503 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3504 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3505 APInt::getMinValue(BitWidth));
3506
3507 // If we know that the condition is true in order to enter the loop,
3508 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3509 // only know that it will execute (max(m,n)-n)/s times. In both cases,
3510 // the division must round up.
3511 SCEVHandle End = RHS;
3512 if (!isLoopGuardedByCond(L,
3513 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3514 getMinusSCEV(Start, Step), RHS))
3515 End = isSigned ? getSMaxExpr(RHS, Start)
3516 : getUMaxExpr(RHS, Start);
3517
3518 // Determine the maximum constant end value.
3519 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3520 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3521 APInt::getMaxValue(BitWidth));
3522
3523 // Finally, we subtract these two values and divide, rounding up, to get
3524 // the number of times the backedge is executed.
3525 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3526 getAddExpr(Step, NegOne)),
3527 Step);
3528
3529 // The maximum backedge count is similar, except using the minimum start
3530 // value and the maximum end value.
3531 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3532 MinStart),
3533 getAddExpr(Step, NegOne)),
3534 Step);
3535
3536 return BackedgeTakenInfo(BECount, MaxBECount);
3537 }
3538
3539 return UnknownValue;
3540}
3541
3542/// getNumIterationsInRange - Return the number of iterations of this loop that
3543/// produce values in the specified constant range. Another way of looking at
3544/// this is that it returns the first iteration number where the value is not in
3545/// the condition, thus computing the exit count. If the iteration count can't
3546/// be computed, an instance of SCEVCouldNotCompute is returned.
3547SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3548 ScalarEvolution &SE) const {
3549 if (Range.isFullSet()) // Infinite loop.
3550 return SE.getCouldNotCompute();
3551
3552 // If the start is a non-zero constant, shift the range to simplify things.
3553 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3554 if (!SC->getValue()->isZero()) {
3555 std::vector<SCEVHandle> Operands(op_begin(), op_end());
3556 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3557 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3558 if (const SCEVAddRecExpr *ShiftedAddRec =
3559 dyn_cast<SCEVAddRecExpr>(Shifted))
3560 return ShiftedAddRec->getNumIterationsInRange(
3561 Range.subtract(SC->getValue()->getValue()), SE);
3562 // This is strange and shouldn't happen.
3563 return SE.getCouldNotCompute();
3564 }
3565
3566 // The only time we can solve this is when we have all constant indices.
3567 // Otherwise, we cannot determine the overflow conditions.
3568 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3569 if (!isa<SCEVConstant>(getOperand(i)))
3570 return SE.getCouldNotCompute();
3571
3572
3573 // Okay at this point we know that all elements of the chrec are constants and
3574 // that the start element is zero.
3575
3576 // First check to see if the range contains zero. If not, the first
3577 // iteration exits.
3578 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3579 if (!Range.contains(APInt(BitWidth, 0)))
3580 return SE.getConstant(ConstantInt::get(getType(),0));
3581
3582 if (isAffine()) {
3583 // If this is an affine expression then we have this situation:
3584 // Solve {0,+,A} in Range === Ax in Range
3585
3586 // We know that zero is in the range. If A is positive then we know that
3587 // the upper value of the range must be the first possible exit value.
3588 // If A is negative then the lower of the range is the last possible loop
3589 // value. Also note that we already checked for a full range.
3590 APInt One(BitWidth,1);
3591 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3592 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3593
3594 // The exit value should be (End+A)/A.
3595 APInt ExitVal = (End + A).udiv(A);
3596 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3597
3598 // Evaluate at the exit value. If we really did fall out of the valid
3599 // range, then we computed our trip count, otherwise wrap around or other
3600 // things must have happened.
3601 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3602 if (Range.contains(Val->getValue()))
3603 return SE.getCouldNotCompute(); // Something strange happened
3604
3605 // Ensure that the previous value is in the range. This is a sanity check.
3606 assert(Range.contains(
3607 EvaluateConstantChrecAtConstant(this,
3608 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3609 "Linear scev computation is off in a bad way!");
3610 return SE.getConstant(ExitValue);
3611 } else if (isQuadratic()) {
3612 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3613 // quadratic equation to solve it. To do this, we must frame our problem in
3614 // terms of figuring out when zero is crossed, instead of when
3615 // Range.getUpper() is crossed.
3616 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3617 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3618 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3619
3620 // Next, solve the constructed addrec
3621 std::pair<SCEVHandle,SCEVHandle> Roots =
3622 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3623 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3624 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3625 if (R1) {
3626 // Pick the smallest positive root value.
3627 if (ConstantInt *CB =
3628 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3629 R1->getValue(), R2->getValue()))) {
3630 if (CB->getZExtValue() == false)
3631 std::swap(R1, R2); // R1 is the minimum root now.
3632
3633 // Make sure the root is not off by one. The returned iteration should
3634 // not be in the range, but the previous one should be. When solving
3635 // for "X*X < 5", for example, we should not return a root of 2.
3636 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3637 R1->getValue(),
3638 SE);
3639 if (Range.contains(R1Val->getValue())) {
3640 // The next iteration must be out of the range...
3641 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3642
3643 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3644 if (!Range.contains(R1Val->getValue()))
3645 return SE.getConstant(NextVal);
3646 return SE.getCouldNotCompute(); // Something strange happened
3647 }
3648
3649 // If R1 was not in the range, then it is a good return value. Make
3650 // sure that R1-1 WAS in the range though, just in case.
3651 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3652 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3653 if (Range.contains(R1Val->getValue()))
3654 return R1;
3655 return SE.getCouldNotCompute(); // Something strange happened
3656 }
3657 }
3658 }
3659
3660 return SE.getCouldNotCompute();
3661}
3662
3663
3664
3665//===----------------------------------------------------------------------===//
3666// SCEVCallbackVH Class Implementation
3667//===----------------------------------------------------------------------===//
3668
3669void ScalarEvolution::SCEVCallbackVH::deleted() {
3670 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3671 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
3672 SE->ConstantEvolutionLoopExitValue.erase(PN);
3673 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
3674 SE->ValuesAtScopes.erase(I);
3675 SE->Scalars.erase(getValPtr());
3676 // this now dangles!
3677}
3678
3679void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
3680 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3681
3682 // Forget all the expressions associated with users of the old value,
3683 // so that future queries will recompute the expressions using the new
3684 // value.
3685 SmallVector<User *, 16> Worklist;
3686 Value *Old = getValPtr();
3687 bool DeleteOld = false;
3688 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
3689 UI != UE; ++UI)
3690 Worklist.push_back(*UI);
3691 while (!Worklist.empty()) {
3692 User *U = Worklist.pop_back_val();
3693 // Deleting the Old value will cause this to dangle. Postpone
3694 // that until everything else is done.
3695 if (U == Old) {
3696 DeleteOld = true;
3697 continue;
3698 }
3699 if (PHINode *PN = dyn_cast<PHINode>(U))
3700 SE->ConstantEvolutionLoopExitValue.erase(PN);
3701 if (Instruction *I = dyn_cast<Instruction>(U))
3702 SE->ValuesAtScopes.erase(I);
3703 if (SE->Scalars.erase(U))
3704 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
3705 UI != UE; ++UI)
3706 Worklist.push_back(*UI);
3707 }
3708 if (DeleteOld) {
3709 if (PHINode *PN = dyn_cast<PHINode>(Old))
3710 SE->ConstantEvolutionLoopExitValue.erase(PN);
3711 if (Instruction *I = dyn_cast<Instruction>(Old))
3712 SE->ValuesAtScopes.erase(I);
3713 SE->Scalars.erase(Old);
3714 // this now dangles!
3715 }
3716 // this may dangle!
3717}
3718
3719ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
3720 : CallbackVH(V), SE(se) {}
3721
3722//===----------------------------------------------------------------------===//
3723// ScalarEvolution Class Implementation
3724//===----------------------------------------------------------------------===//
3725
3726ScalarEvolution::ScalarEvolution()
3727 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) {
3728}
3729
3730bool ScalarEvolution::runOnFunction(Function &F) {
3731 this->F = &F;
3732 LI = &getAnalysis<LoopInfo>();
3733 TD = getAnalysisIfAvailable<TargetData>();
3734 return false;
3735}
3736
3737void ScalarEvolution::releaseMemory() {
3738 Scalars.clear();
3739 BackedgeTakenCounts.clear();
3740 ConstantEvolutionLoopExitValue.clear();
3741 ValuesAtScopes.clear();
3742}
3743
3744void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3745 AU.setPreservesAll();
3746 AU.addRequiredTransitive<LoopInfo>();
3747}
3748
3749bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3750 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3751}
3752
3753static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3754 const Loop *L) {
3755 // Print all inner loops first
3756 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3757 PrintLoopInfo(OS, SE, *I);
3758
3759 OS << "Loop " << L->getHeader()->getName() << ": ";
3760
3761 SmallVector<BasicBlock*, 8> ExitBlocks;
3762 L->getExitBlocks(ExitBlocks);
3763 if (ExitBlocks.size() != 1)
3764 OS << "<multiple exits> ";
3765
3766 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3767 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3768 } else {
3769 OS << "Unpredictable backedge-taken count. ";
3770 }
3771
3772 OS << "\n";
3773}
3774
3775void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3776 // ScalarEvolution's implementaiton of the print method is to print
3777 // out SCEV values of all instructions that are interesting. Doing
3778 // this potentially causes it to create new SCEV objects though,
3779 // which technically conflicts with the const qualifier. This isn't
3780 // observable from outside the class though (the hasSCEV function
3781 // notwithstanding), so casting away the const isn't dangerous.
3782 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3783
3784 OS << "Classifying expressions for: " << F->getName() << "\n";
3785 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3786 if (isSCEVable(I->getType())) {
3787 OS << *I;
3788 OS << " --> ";
3789 SCEVHandle SV = SE.getSCEV(&*I);
3790 SV->print(OS);
3791 OS << "\t\t";
3792
3793 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3794 OS << "Exits: ";
3795 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3796 if (!ExitValue->isLoopInvariant(L)) {
3797 OS << "<<Unknown>>";
3798 } else {
3799 OS << *ExitValue;
3800 }
3801 }
3802
3803 OS << "\n";
3804 }
3805
3806 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3807 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3808 PrintLoopInfo(OS, &SE, *I);
3809}
3810
3811void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3812 raw_os_ostream OS(o);
3813 print(OS, M);
3814}
|