1//===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
2//
3// The LLVM Compiler Infrastructure
4//
5// This file is distributed under the University of Illinois Open Source
6// License. See LICENSE.TXT for details.
7//
8//===----------------------------------------------------------------------===//
9//
10// This file contains the implementation of the scalar evolution analysis
11// engine, which is used primarily to analyze expressions involving induction
12// variables in loops.
13//
14// There are several aspects to this library. First is the representation of
15// scalar expressions, which are represented as subclasses of the SCEV class.
16// These classes are used to represent certain types of subexpressions that we
17// can handle. These classes are reference counted, managed by the const SCEV*
18// class. We only create one SCEV of a particular shape, so pointer-comparisons
19// for equality are legal.
20//
21// One important aspect of the SCEV objects is that they are never cyclic, even
22// if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23// the PHI node is one of the idioms that we can represent (e.g., a polynomial
24// recurrence) then we represent it directly as a recurrence node, otherwise we
25// represent it as a SCEVUnknown node.
26//
27// In addition to being able to represent expressions of various types, we also
28// have folders that are used to build the *canonical* representation for a
29// particular expression. These folders are capable of using a variety of
30// rewrite rules to simplify the expressions.
31//
32// Once the folders are defined, we can implement the more interesting
33// higher-level code, such as the code that recognizes PHI nodes of various
34// types, computes the execution count of a loop, etc.
35//
36// TODO: We should use these routines and value representations to implement
37// dependence analysis!
38//
39//===----------------------------------------------------------------------===//
40//
41// There are several good references for the techniques used in this analysis.
42//
43// Chains of recurrences -- a method to expedite the evaluation
44// of closed-form functions
45// Olaf Bachmann, Paul S. Wang, Eugene V. Zima
46//
47// On computational properties of chains of recurrences
48// Eugene V. Zima
49//
50// Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51// Robert A. van Engelen
52//
53// Efficient Symbolic Analysis for Optimizing Compilers
54// Robert A. van Engelen
55//
56// Using the chains of recurrences algebra for data dependence testing and
57// induction variable substitution
58// MS Thesis, Johnie Birch
59//
60//===----------------------------------------------------------------------===//
61
62#define DEBUG_TYPE "scalar-evolution"
63#include "llvm/Analysis/ScalarEvolutionExpressions.h"
64#include "llvm/Constants.h"
65#include "llvm/DerivedTypes.h"
66#include "llvm/GlobalVariable.h"
67#include "llvm/Instructions.h"
68#include "llvm/Analysis/ConstantFolding.h"
69#include "llvm/Analysis/Dominators.h"
70#include "llvm/Analysis/LoopInfo.h"
71#include "llvm/Analysis/ValueTracking.h"
72#include "llvm/Assembly/Writer.h"
73#include "llvm/Target/TargetData.h"
74#include "llvm/Support/CommandLine.h"
75#include "llvm/Support/Compiler.h"
76#include "llvm/Support/ConstantRange.h"
77#include "llvm/Support/GetElementPtrTypeIterator.h"
78#include "llvm/Support/InstIterator.h"
79#include "llvm/Support/MathExtras.h"
80#include "llvm/Support/raw_ostream.h"
81#include "llvm/ADT/Statistic.h"
82#include "llvm/ADT/STLExtras.h"
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 "
99 "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//
113
114SCEV::~SCEV() {}
115
116void SCEV::dump() const {
117 print(errs());
118 errs() << '\n';
119}
120
121void SCEV::print(std::ostream &o) const {
122 raw_os_ostream OS(o);
123 print(OS);
124}
125
126bool SCEV::isZero() const {
127 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
128 return SC->getValue()->isZero();
129 return false;
130}
131
132bool SCEV::isOne() const {
133 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
134 return SC->getValue()->isOne();
135 return false;
136}
137
138bool SCEV::isAllOnesValue() const {
139 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
140 return SC->getValue()->isAllOnesValue();
141 return false;
142}
143
144SCEVCouldNotCompute::SCEVCouldNotCompute() :
145 SCEV(scCouldNotCompute) {}
146
147void SCEVCouldNotCompute::Profile(FoldingSetNodeID &ID) const {
148 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
149}
150
151bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
152 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
153 return false;
154}
155
156const Type *SCEVCouldNotCompute::getType() const {
157 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
158 return 0;
159}
160
161bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
162 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
163 return false;
164}
165
166const SCEV *
167SCEVCouldNotCompute::replaceSymbolicValuesWithConcrete(
168 const SCEV *Sym,
169 const SCEV *Conc,
170 ScalarEvolution &SE) const {
171 return this;
172}
173
174void SCEVCouldNotCompute::print(raw_ostream &OS) const {
175 OS << "***COULDNOTCOMPUTE***";
176}
177
178bool SCEVCouldNotCompute::classof(const SCEV *S) {
179 return S->getSCEVType() == scCouldNotCompute;
180}
181
182const SCEV* ScalarEvolution::getConstant(ConstantInt *V) {
183 FoldingSetNodeID ID;
184 ID.AddInteger(scConstant);
185 ID.AddPointer(V);
186 void *IP = 0;
187 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
188 SCEV *S = SCEVAllocator.Allocate<SCEVConstant>();
189 new (S) SCEVConstant(V);
190 UniqueSCEVs.InsertNode(S, IP);
191 return S;
192}
193
194const SCEV* ScalarEvolution::getConstant(const APInt& Val) {
195 return getConstant(ConstantInt::get(Val));
196}
197
198const SCEV*
199ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
200 return getConstant(ConstantInt::get(cast<IntegerType>(Ty), V, isSigned));
201}
202
203void SCEVConstant::Profile(FoldingSetNodeID &ID) const {
204 ID.AddInteger(scConstant);
205 ID.AddPointer(V);
206}
207
208const Type *SCEVConstant::getType() const { return V->getType(); }
209
210void SCEVConstant::print(raw_ostream &OS) const {
211 WriteAsOperand(OS, V, false);
212}
213
214SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
215 const SCEV* op, const Type *ty)
216 : SCEV(SCEVTy), Op(op), Ty(ty) {}
217
218void SCEVCastExpr::Profile(FoldingSetNodeID &ID) const {
219 ID.AddInteger(getSCEVType());
220 ID.AddPointer(Op);
221 ID.AddPointer(Ty);
222}
223
224bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
225 return Op->dominates(BB, DT);
226}
227
228SCEVTruncateExpr::SCEVTruncateExpr(const SCEV* op, const Type *ty)
229 : SCEVCastExpr(scTruncate, op, ty) {
230 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
231 (Ty->isInteger() || isa<PointerType>(Ty)) &&
232 "Cannot truncate non-integer value!");
233}
234
235void SCEVTruncateExpr::print(raw_ostream &OS) const {
236 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
237}
238
239SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEV* op, const Type *ty)
240 : SCEVCastExpr(scZeroExtend, op, ty) {
241 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
242 (Ty->isInteger() || isa<PointerType>(Ty)) &&
243 "Cannot zero extend non-integer value!");
244}
245
246void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
247 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
248}
249
250SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEV* op, const Type *ty)
251 : SCEVCastExpr(scSignExtend, op, ty) {
252 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
253 (Ty->isInteger() || isa<PointerType>(Ty)) &&
254 "Cannot sign extend non-integer value!");
255}
256
257void SCEVSignExtendExpr::print(raw_ostream &OS) const {
258 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
259}
260
261void SCEVCommutativeExpr::print(raw_ostream &OS) const {
262 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
263 const char *OpStr = getOperationStr();
264 OS << "(" << *Operands[0];
265 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
266 OS << OpStr << *Operands[i];
267 OS << ")";
268}
269
270const SCEV *
271SCEVCommutativeExpr::replaceSymbolicValuesWithConcrete(
272 const SCEV *Sym,
273 const SCEV *Conc,
274 ScalarEvolution &SE) const {
275 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
276 const SCEV* H =
277 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
278 if (H != getOperand(i)) {
279 SmallVector<const SCEV*, 8> NewOps;
280 NewOps.reserve(getNumOperands());
281 for (unsigned j = 0; j != i; ++j)
282 NewOps.push_back(getOperand(j));
283 NewOps.push_back(H);
284 for (++i; i != e; ++i)
285 NewOps.push_back(getOperand(i)->
286 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
287
288 if (isa<SCEVAddExpr>(this))
289 return SE.getAddExpr(NewOps);
290 else if (isa<SCEVMulExpr>(this))
291 return SE.getMulExpr(NewOps);
292 else if (isa<SCEVSMaxExpr>(this))
293 return SE.getSMaxExpr(NewOps);
294 else if (isa<SCEVUMaxExpr>(this))
295 return SE.getUMaxExpr(NewOps);
296 else
297 assert(0 && "Unknown commutative expr!");
298 }
299 }
300 return this;
301}
302
303void SCEVNAryExpr::Profile(FoldingSetNodeID &ID) const {
304 ID.AddInteger(getSCEVType());
305 ID.AddInteger(Operands.size());
306 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
307 ID.AddPointer(Operands[i]);
308}
309
310bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
311 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
312 if (!getOperand(i)->dominates(BB, DT))
313 return false;
314 }
315 return true;
316}
317
318void SCEVUDivExpr::Profile(FoldingSetNodeID &ID) const {
319 ID.AddInteger(scUDivExpr);
320 ID.AddPointer(LHS);
321 ID.AddPointer(RHS);
322}
323
324bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
325 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
326}
327
328void SCEVUDivExpr::print(raw_ostream &OS) const {
329 OS << "(" << *LHS << " /u " << *RHS << ")";
330}
331
332const Type *SCEVUDivExpr::getType() const {
333 // In most cases the types of LHS and RHS will be the same, but in some
334 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
335 // depend on the type for correctness, but handling types carefully can
336 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
337 // a pointer type than the RHS, so use the RHS' type here.
338 return RHS->getType();
339}
340
341void SCEVAddRecExpr::Profile(FoldingSetNodeID &ID) const {
342 ID.AddInteger(scAddRecExpr);
343 ID.AddInteger(Operands.size());
344 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
345 ID.AddPointer(Operands[i]);
346 ID.AddPointer(L);
347}
348
349const SCEV *
350SCEVAddRecExpr::replaceSymbolicValuesWithConcrete(const SCEV *Sym,
351 const SCEV *Conc,
352 ScalarEvolution &SE) const {
353 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
354 const SCEV* H =
355 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
356 if (H != getOperand(i)) {
357 SmallVector<const SCEV*, 8> NewOps;
358 NewOps.reserve(getNumOperands());
359 for (unsigned j = 0; j != i; ++j)
360 NewOps.push_back(getOperand(j));
361 NewOps.push_back(H);
362 for (++i; i != e; ++i)
363 NewOps.push_back(getOperand(i)->
364 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
365
366 return SE.getAddRecExpr(NewOps, L);
367 }
368 }
369 return this;
370}
371
372
373bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
374 // Add recurrences are never invariant in the function-body (null loop).
375 if (!QueryLoop)
376 return false;
377
378 // This recurrence is variant w.r.t. QueryLoop if QueryLoop contains L.
379 if (QueryLoop->contains(L->getHeader()))
380 return false;
381
382 // This recurrence is variant w.r.t. QueryLoop if any of its operands
383 // are variant.
384 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
385 if (!getOperand(i)->isLoopInvariant(QueryLoop))
386 return false;
387
388 // Otherwise it's loop-invariant.
389 return true;
390}
391
392void SCEVAddRecExpr::print(raw_ostream &OS) const {
393 OS << "{" << *Operands[0];
394 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
395 OS << ",+," << *Operands[i];
396 OS << "}<" << L->getHeader()->getName() + ">";
397}
398
399void SCEVUnknown::Profile(FoldingSetNodeID &ID) const {
400 ID.AddInteger(scUnknown);
401 ID.AddPointer(V);
402}
403
404bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
405 // All non-instruction values are loop invariant. All instructions are loop
406 // invariant if they are not contained in the specified loop.
407 // Instructions are never considered invariant in the function body
408 // (null loop) because they are defined within the "loop".
409 if (Instruction *I = dyn_cast<Instruction>(V))
410 return L && !L->contains(I->getParent());
411 return true;
412}
413
414bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
415 if (Instruction *I = dyn_cast<Instruction>(getValue()))
416 return DT->dominates(I->getParent(), BB);
417 return true;
418}
419
420const Type *SCEVUnknown::getType() const {
421 return V->getType();
422}
423
424void SCEVUnknown::print(raw_ostream &OS) const {
425 WriteAsOperand(OS, V, false);
426}
427
428//===----------------------------------------------------------------------===//
429// SCEV Utilities
430//===----------------------------------------------------------------------===//
431
432namespace {
433 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
434 /// than the complexity of the RHS. This comparator is used to canonicalize
435 /// expressions.
436 class VISIBILITY_HIDDEN SCEVComplexityCompare {
437 LoopInfo *LI;
438 public:
439 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
440
441 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
442 // Primarily, sort the SCEVs by their getSCEVType().
443 if (LHS->getSCEVType() != RHS->getSCEVType())
444 return LHS->getSCEVType() < RHS->getSCEVType();
445
446 // Aside from the getSCEVType() ordering, the particular ordering
447 // isn't very important except that it's beneficial to be consistent,
448 // so that (a + b) and (b + a) don't end up as different expressions.
449
450 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
451 // not as complete as it could be.
452 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
453 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
454
455 // Order pointer values after integer values. This helps SCEVExpander
456 // form GEPs.
457 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
458 return false;
459 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
460 return true;
461
462 // Compare getValueID values.
463 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
464 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
465
466 // Sort arguments by their position.
467 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
468 const Argument *RA = cast<Argument>(RU->getValue());
469 return LA->getArgNo() < RA->getArgNo();
470 }
471
472 // For instructions, compare their loop depth, and their opcode.
473 // This is pretty loose.
474 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
475 Instruction *RV = cast<Instruction>(RU->getValue());
476
477 // Compare loop depths.
478 if (LI->getLoopDepth(LV->getParent()) !=
479 LI->getLoopDepth(RV->getParent()))
480 return LI->getLoopDepth(LV->getParent()) <
481 LI->getLoopDepth(RV->getParent());
482
483 // Compare opcodes.
484 if (LV->getOpcode() != RV->getOpcode())
485 return LV->getOpcode() < RV->getOpcode();
486
487 // Compare the number of operands.
488 if (LV->getNumOperands() != RV->getNumOperands())
489 return LV->getNumOperands() < RV->getNumOperands();
490 }
491
492 return false;
493 }
494
495 // Compare constant values.
496 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
497 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
498 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
499 }
500
501 // Compare addrec loop depths.
502 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
503 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
504 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
505 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
506 }
507
508 // Lexicographically compare n-ary expressions.
509 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
510 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
511 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
512 if (i >= RC->getNumOperands())
513 return false;
514 if (operator()(LC->getOperand(i), RC->getOperand(i)))
515 return true;
516 if (operator()(RC->getOperand(i), LC->getOperand(i)))
517 return false;
518 }
519 return LC->getNumOperands() < RC->getNumOperands();
520 }
521
522 // Lexicographically compare udiv expressions.
523 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
524 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
525 if (operator()(LC->getLHS(), RC->getLHS()))
526 return true;
527 if (operator()(RC->getLHS(), LC->getLHS()))
528 return false;
529 if (operator()(LC->getRHS(), RC->getRHS()))
530 return true;
531 if (operator()(RC->getRHS(), LC->getRHS()))
532 return false;
533 return false;
534 }
535
536 // Compare cast expressions by operand.
537 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
538 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
539 return operator()(LC->getOperand(), RC->getOperand());
540 }
541
542 assert(0 && "Unknown SCEV kind!");
543 return false;
544 }
545 };
546}
547
548/// GroupByComplexity - Given a list of SCEV objects, order them by their
549/// complexity, and group objects of the same complexity together by value.
550/// When this routine is finished, we know that any duplicates in the vector are
551/// consecutive and that complexity is monotonically increasing.
552///
553/// Note that we go take special precautions to ensure that we get determinstic
554/// results from this routine. In other words, we don't want the results of
555/// this to depend on where the addresses of various SCEV objects happened to
556/// land in memory.
557///
558static void GroupByComplexity(SmallVectorImpl<const SCEV*> &Ops,
559 LoopInfo *LI) {
560 if (Ops.size() < 2) return; // Noop
561 if (Ops.size() == 2) {
562 // This is the common case, which also happens to be trivially simple.
563 // Special case it.
564 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
565 std::swap(Ops[0], Ops[1]);
566 return;
567 }
568
569 // Do the rough sort by complexity.
570 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
571
572 // Now that we are sorted by complexity, group elements of the same
573 // complexity. Note that this is, at worst, N^2, but the vector is likely to
574 // be extremely short in practice. Note that we take this approach because we
575 // do not want to depend on the addresses of the objects we are grouping.
576 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
577 const SCEV *S = Ops[i];
578 unsigned Complexity = S->getSCEVType();
579
580 // If there are any objects of the same complexity and same value as this
581 // one, group them.
582 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
583 if (Ops[j] == S) { // Found a duplicate.
584 // Move it to immediately after i'th element.
585 std::swap(Ops[i+1], Ops[j]);
586 ++i; // no need to rescan it.
587 if (i == e-2) return; // Done!
588 }
589 }
590 }
591}
592
593
594
595//===----------------------------------------------------------------------===//
596// Simple SCEV method implementations
597//===----------------------------------------------------------------------===//
598
599/// BinomialCoefficient - Compute BC(It, K). The result has width W.
600/// Assume, K > 0.
601static const SCEV* BinomialCoefficient(const SCEV* It, unsigned K,
602 ScalarEvolution &SE,
603 const Type* ResultTy) {
604 // Handle the simplest case efficiently.
605 if (K == 1)
606 return SE.getTruncateOrZeroExtend(It, ResultTy);
607
608 // We are using the following formula for BC(It, K):
609 //
610 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
611 //
612 // Suppose, W is the bitwidth of the return value. We must be prepared for
613 // overflow. Hence, we must assure that the result of our computation is
614 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
615 // safe in modular arithmetic.
616 //
617 // However, this code doesn't use exactly that formula; the formula it uses
618 // is something like the following, where T is the number of factors of 2 in
619 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
620 // exponentiation:
621 //
622 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
623 //
624 // This formula is trivially equivalent to the previous formula. However,
625 // this formula can be implemented much more efficiently. The trick is that
626 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
627 // arithmetic. To do exact division in modular arithmetic, all we have
628 // to do is multiply by the inverse. Therefore, this step can be done at
629 // width W.
630 //
631 // The next issue is how to safely do the division by 2^T. The way this
632 // is done is by doing the multiplication step at a width of at least W + T
633 // bits. This way, the bottom W+T bits of the product are accurate. Then,
634 // when we perform the division by 2^T (which is equivalent to a right shift
635 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
636 // truncated out after the division by 2^T.
637 //
638 // In comparison to just directly using the first formula, this technique
639 // is much more efficient; using the first formula requires W * K bits,
640 // but this formula less than W + K bits. Also, the first formula requires
641 // a division step, whereas this formula only requires multiplies and shifts.
642 //
643 // It doesn't matter whether the subtraction step is done in the calculation
644 // width or the input iteration count's width; if the subtraction overflows,
645 // the result must be zero anyway. We prefer here to do it in the width of
646 // the induction variable because it helps a lot for certain cases; CodeGen
647 // isn't smart enough to ignore the overflow, which leads to much less
648 // efficient code if the width of the subtraction is wider than the native
649 // register width.
650 //
651 // (It's possible to not widen at all by pulling out factors of 2 before
652 // the multiplication; for example, K=2 can be calculated as
653 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
654 // extra arithmetic, so it's not an obvious win, and it gets
655 // much more complicated for K > 3.)
656
657 // Protection from insane SCEVs; this bound is conservative,
658 // but it probably doesn't matter.
659 if (K > 1000)
660 return SE.getCouldNotCompute();
661
662 unsigned W = SE.getTypeSizeInBits(ResultTy);
663
664 // Calculate K! / 2^T and T; we divide out the factors of two before
665 // multiplying for calculating K! / 2^T to avoid overflow.
666 // Other overflow doesn't matter because we only care about the bottom
667 // W bits of the result.
668 APInt OddFactorial(W, 1);
669 unsigned T = 1;
670 for (unsigned i = 3; i <= K; ++i) {
671 APInt Mult(W, i);
672 unsigned TwoFactors = Mult.countTrailingZeros();
673 T += TwoFactors;
674 Mult = Mult.lshr(TwoFactors);
675 OddFactorial *= Mult;
676 }
677
678 // We need at least W + T bits for the multiplication step
679 unsigned CalculationBits = W + T;
680
681 // Calcuate 2^T, at width T+W.
682 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
683
684 // Calculate the multiplicative inverse of K! / 2^T;
685 // this multiplication factor will perform the exact division by
686 // K! / 2^T.
687 APInt Mod = APInt::getSignedMinValue(W+1);
688 APInt MultiplyFactor = OddFactorial.zext(W+1);
689 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
690 MultiplyFactor = MultiplyFactor.trunc(W);
691
692 // Calculate the product, at width T+W
693 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
694 const SCEV* Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
695 for (unsigned i = 1; i != K; ++i) {
696 const SCEV* S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
697 Dividend = SE.getMulExpr(Dividend,
698 SE.getTruncateOrZeroExtend(S, CalculationTy));
699 }
700
701 // Divide by 2^T
702 const SCEV* DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
703
704 // Truncate the result, and divide by K! / 2^T.
705
706 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
707 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
708}
709
710/// evaluateAtIteration - Return the value of this chain of recurrences at
711/// the specified iteration number. We can evaluate this recurrence by
712/// multiplying each element in the chain by the binomial coefficient
713/// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
714///
715/// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
716///
717/// where BC(It, k) stands for binomial coefficient.
718///
719const SCEV* SCEVAddRecExpr::evaluateAtIteration(const SCEV* It,
720 ScalarEvolution &SE) const {
721 const SCEV* Result = getStart();
722 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
723 // The computation is correct in the face of overflow provided that the
724 // multiplication is performed _after_ the evaluation of the binomial
725 // coefficient.
726 const SCEV* Coeff = BinomialCoefficient(It, i, SE, getType());
727 if (isa<SCEVCouldNotCompute>(Coeff))
728 return Coeff;
729
730 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
731 }
732 return Result;
733}
734
735//===----------------------------------------------------------------------===//
736// SCEV Expression folder implementations
737//===----------------------------------------------------------------------===//
738
739const SCEV* ScalarEvolution::getTruncateExpr(const SCEV* Op,
740 const Type *Ty) {
741 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
742 "This is not a truncating conversion!");
743 assert(isSCEVable(Ty) &&
744 "This is not a conversion to a SCEVable type!");
745 Ty = getEffectiveSCEVType(Ty);
746
747 // Fold if the operand is constant.
748 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
749 return getConstant(
750 cast<ConstantInt>(ConstantExpr::getTrunc(SC->getValue(), Ty)));
751
752 // trunc(trunc(x)) --> trunc(x)
753 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
754 return getTruncateExpr(ST->getOperand(), Ty);
755
756 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
757 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
758 return getTruncateOrSignExtend(SS->getOperand(), Ty);
759
760 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
761 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
762 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
763
764 // If the input value is a chrec scev, truncate the chrec's operands.
765 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
766 SmallVector<const SCEV*, 4> Operands;
767 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
768 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
769 return getAddRecExpr(Operands, AddRec->getLoop());
770 }
771
772 FoldingSetNodeID ID;
773 ID.AddInteger(scTruncate);
774 ID.AddPointer(Op);
775 ID.AddPointer(Ty);
776 void *IP = 0;
777 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
778 SCEV *S = SCEVAllocator.Allocate<SCEVTruncateExpr>();
779 new (S) SCEVTruncateExpr(Op, Ty);
780 UniqueSCEVs.InsertNode(S, IP);
781 return S;
782}
783
784const SCEV* ScalarEvolution::getZeroExtendExpr(const SCEV* Op,
785 const Type *Ty) {
786 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
787 "This is not an extending conversion!");
788 assert(isSCEVable(Ty) &&
789 "This is not a conversion to a SCEVable type!");
790 Ty = getEffectiveSCEVType(Ty);
791
792 // Fold if the operand is constant.
793 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
794 const Type *IntTy = getEffectiveSCEVType(Ty);
795 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
796 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
797 return getConstant(cast<ConstantInt>(C));
798 }
799
800 // zext(zext(x)) --> zext(x)
801 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
802 return getZeroExtendExpr(SZ->getOperand(), Ty);
803
804 // If the input value is a chrec scev, and we can prove that the value
805 // did not overflow the old, smaller, value, we can zero extend all of the
806 // operands (often constants). This allows analysis of something like
807 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
808 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
809 if (AR->isAffine()) {
810 // Check whether the backedge-taken count is SCEVCouldNotCompute.
811 // Note that this serves two purposes: It filters out loops that are
812 // simply not analyzable, and it covers the case where this code is
813 // being called from within backedge-taken count analysis, such that
814 // attempting to ask for the backedge-taken count would likely result
815 // in infinite recursion. In the later case, the analysis code will
816 // cope with a conservative value, and it will take care to purge
817 // that value once it has finished.
818 const SCEV* MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
819 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
820 // Manually compute the final value for AR, checking for
821 // overflow.
822 const SCEV* Start = AR->getStart();
823 const SCEV* Step = AR->getStepRecurrence(*this);
824
825 // Check whether the backedge-taken count can be losslessly casted to
826 // the addrec's type. The count is always unsigned.
827 const SCEV* CastedMaxBECount =
828 getTruncateOrZeroExtend(MaxBECount, Start->getType());
829 const SCEV* RecastedMaxBECount =
830 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
831 if (MaxBECount == RecastedMaxBECount) {
832 const Type *WideTy =
833 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
834 // Check whether Start+Step*MaxBECount has no unsigned overflow.
835 const SCEV* ZMul =
836 getMulExpr(CastedMaxBECount,
837 getTruncateOrZeroExtend(Step, Start->getType()));
838 const SCEV* Add = getAddExpr(Start, ZMul);
839 const SCEV* OperandExtendedAdd =
840 getAddExpr(getZeroExtendExpr(Start, WideTy),
841 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
842 getZeroExtendExpr(Step, WideTy)));
843 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
844 // Return the expression with the addrec on the outside.
845 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
846 getZeroExtendExpr(Step, Ty),
847 AR->getLoop());
848
849 // Similar to above, only this time treat the step value as signed.
850 // This covers loops that count down.
851 const SCEV* SMul =
852 getMulExpr(CastedMaxBECount,
853 getTruncateOrSignExtend(Step, Start->getType()));
854 Add = getAddExpr(Start, SMul);
855 OperandExtendedAdd =
856 getAddExpr(getZeroExtendExpr(Start, WideTy),
857 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
858 getSignExtendExpr(Step, WideTy)));
859 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
860 // Return the expression with the addrec on the outside.
861 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
862 getSignExtendExpr(Step, Ty),
863 AR->getLoop());
864 }
865 }
866 }
867
868 FoldingSetNodeID ID;
869 ID.AddInteger(scZeroExtend);
870 ID.AddPointer(Op);
871 ID.AddPointer(Ty);
872 void *IP = 0;
873 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
874 SCEV *S = SCEVAllocator.Allocate<SCEVZeroExtendExpr>();
875 new (S) SCEVZeroExtendExpr(Op, Ty);
876 UniqueSCEVs.InsertNode(S, IP);
877 return S;
878}
879
880const SCEV* ScalarEvolution::getSignExtendExpr(const SCEV* Op,
881 const Type *Ty) {
882 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
883 "This is not an extending conversion!");
884 assert(isSCEVable(Ty) &&
885 "This is not a conversion to a SCEVable type!");
886 Ty = getEffectiveSCEVType(Ty);
887
888 // Fold if the operand is constant.
889 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
890 const Type *IntTy = getEffectiveSCEVType(Ty);
891 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
892 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
893 return getConstant(cast<ConstantInt>(C));
894 }
895
896 // sext(sext(x)) --> sext(x)
897 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
898 return getSignExtendExpr(SS->getOperand(), Ty);
899
900 // If the input value is a chrec scev, and we can prove that the value
901 // did not overflow the old, smaller, value, we can sign extend all of the
902 // operands (often constants). This allows analysis of something like
903 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
904 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
905 if (AR->isAffine()) {
906 // Check whether the backedge-taken count is SCEVCouldNotCompute.
907 // Note that this serves two purposes: It filters out loops that are
908 // simply not analyzable, and it covers the case where this code is
909 // being called from within backedge-taken count analysis, such that
910 // attempting to ask for the backedge-taken count would likely result
911 // in infinite recursion. In the later case, the analysis code will
912 // cope with a conservative value, and it will take care to purge
913 // that value once it has finished.
914 const SCEV* MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
915 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
916 // Manually compute the final value for AR, checking for
917 // overflow.
918 const SCEV* Start = AR->getStart();
919 const SCEV* Step = AR->getStepRecurrence(*this);
920
921 // Check whether the backedge-taken count can be losslessly casted to
922 // the addrec's type. The count is always unsigned.
923 const SCEV* CastedMaxBECount =
924 getTruncateOrZeroExtend(MaxBECount, Start->getType());
925 const SCEV* RecastedMaxBECount =
926 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
927 if (MaxBECount == RecastedMaxBECount) {
928 const Type *WideTy =
929 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
930 // Check whether Start+Step*MaxBECount has no signed overflow.
931 const SCEV* SMul =
932 getMulExpr(CastedMaxBECount,
933 getTruncateOrSignExtend(Step, Start->getType()));
934 const SCEV* Add = getAddExpr(Start, SMul);
935 const SCEV* OperandExtendedAdd =
936 getAddExpr(getSignExtendExpr(Start, WideTy),
937 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
938 getSignExtendExpr(Step, WideTy)));
939 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
940 // Return the expression with the addrec on the outside.
941 return getAddRecExpr(getSignExtendExpr(Start, Ty),
942 getSignExtendExpr(Step, Ty),
943 AR->getLoop());
944 }
945 }
946 }
947
948 FoldingSetNodeID ID;
949 ID.AddInteger(scSignExtend);
950 ID.AddPointer(Op);
951 ID.AddPointer(Ty);
952 void *IP = 0;
953 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
954 SCEV *S = SCEVAllocator.Allocate<SCEVSignExtendExpr>();
955 new (S) SCEVSignExtendExpr(Op, Ty);
956 UniqueSCEVs.InsertNode(S, IP);
957 return S;
958}
959
960/// getAnyExtendExpr - Return a SCEV for the given operand extended with
961/// unspecified bits out to the given type.
962///
963const SCEV* ScalarEvolution::getAnyExtendExpr(const SCEV* Op,
964 const Type *Ty) {
965 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
966 "This is not an extending conversion!");
967 assert(isSCEVable(Ty) &&
968 "This is not a conversion to a SCEVable type!");
969 Ty = getEffectiveSCEVType(Ty);
970
971 // Sign-extend negative constants.
972 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
973 if (SC->getValue()->getValue().isNegative())
974 return getSignExtendExpr(Op, Ty);
975
976 // Peel off a truncate cast.
977 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
978 const SCEV* NewOp = T->getOperand();
979 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
980 return getAnyExtendExpr(NewOp, Ty);
981 return getTruncateOrNoop(NewOp, Ty);
982 }
983
984 // Next try a zext cast. If the cast is folded, use it.
985 const SCEV* ZExt = getZeroExtendExpr(Op, Ty);
986 if (!isa<SCEVZeroExtendExpr>(ZExt))
987 return ZExt;
988
989 // Next try a sext cast. If the cast is folded, use it.
990 const SCEV* SExt = getSignExtendExpr(Op, Ty);
991 if (!isa<SCEVSignExtendExpr>(SExt))
992 return SExt;
993
994 // If the expression is obviously signed, use the sext cast value.
995 if (isa<SCEVSMaxExpr>(Op))
996 return SExt;
997
998 // Absent any other information, use the zext cast value.
999 return ZExt;
1000}
1001
1002/// CollectAddOperandsWithScales - Process the given Ops list, which is
1003/// a list of operands to be added under the given scale, update the given
1004/// map. This is a helper function for getAddRecExpr. As an example of
1005/// what it does, given a sequence of operands that would form an add
1006/// expression like this:
1007///
1008/// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
1009///
1010/// where A and B are constants, update the map with these values:
1011///
1012/// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
1013///
1014/// and add 13 + A*B*29 to AccumulatedConstant.
1015/// This will allow getAddRecExpr to produce this:
1016///
1017/// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
1018///
1019/// This form often exposes folding opportunities that are hidden in
1020/// the original operand list.
1021///
1022/// Return true iff it appears that any interesting folding opportunities
1023/// may be exposed. This helps getAddRecExpr short-circuit extra work in
1024/// the common case where no interesting opportunities are present, and
1025/// is also used as a check to avoid infinite recursion.
1026///
1027static bool
1028CollectAddOperandsWithScales(DenseMap<const SCEV*, APInt> &M,
1029 SmallVector<const SCEV*, 8> &NewOps,
1030 APInt &AccumulatedConstant,
1031 const SmallVectorImpl<const SCEV*> &Ops,
1032 const APInt &Scale,
1033 ScalarEvolution &SE) {
1034 bool Interesting = false;
1035
1036 // Iterate over the add operands.
1037 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1038 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
1039 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
1040 APInt NewScale =
1041 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
1042 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
1043 // A multiplication of a constant with another add; recurse.
1044 Interesting |=
1045 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1046 cast<SCEVAddExpr>(Mul->getOperand(1))
1047 ->getOperands(),
1048 NewScale, SE);
1049 } else {
1050 // A multiplication of a constant with some other value. Update
1051 // the map.
1052 SmallVector<const SCEV*, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1053 const SCEV* Key = SE.getMulExpr(MulOps);
1054 std::pair<DenseMap<const SCEV*, APInt>::iterator, bool> Pair =
1055 M.insert(std::make_pair(Key, NewScale));
1056 if (Pair.second) {
1057 NewOps.push_back(Pair.first->first);
1058 } else {
1059 Pair.first->second += NewScale;
1060 // The map already had an entry for this value, which may indicate
1061 // a folding opportunity.
1062 Interesting = true;
1063 }
1064 }
1065 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1066 // Pull a buried constant out to the outside.
1067 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
1068 Interesting = true;
1069 AccumulatedConstant += Scale * C->getValue()->getValue();
1070 } else {
1071 // An ordinary operand. Update the map.
1072 std::pair<DenseMap<const SCEV*, APInt>::iterator, bool> Pair =
1073 M.insert(std::make_pair(Ops[i], Scale));
1074 if (Pair.second) {
1075 NewOps.push_back(Pair.first->first);
1076 } else {
1077 Pair.first->second += Scale;
1078 // The map already had an entry for this value, which may indicate
1079 // a folding opportunity.
1080 Interesting = true;
1081 }
1082 }
1083 }
1084
1085 return Interesting;
1086}
1087
1088namespace {
1089 struct APIntCompare {
1090 bool operator()(const APInt &LHS, const APInt &RHS) const {
1091 return LHS.ult(RHS);
1092 }
1093 };
1094}
1095
1096/// getAddExpr - Get a canonical add expression, or something simpler if
1097/// possible.
1098const SCEV* ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV*> &Ops) {
1099 assert(!Ops.empty() && "Cannot get empty add!");
1100 if (Ops.size() == 1) return Ops[0];
1101#ifndef NDEBUG
1102 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1103 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1104 getEffectiveSCEVType(Ops[0]->getType()) &&
1105 "SCEVAddExpr operand types don't match!");
1106#endif
1107
1108 // Sort by complexity, this groups all similar expression types together.
1109 GroupByComplexity(Ops, LI);
1110
1111 // If there are any constants, fold them together.
1112 unsigned Idx = 0;
1113 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1114 ++Idx;
1115 assert(Idx < Ops.size());
1116 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1117 // We found two constants, fold them together!
1118 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1119 RHSC->getValue()->getValue());
1120 if (Ops.size() == 2) return Ops[0];
1121 Ops.erase(Ops.begin()+1); // Erase the folded element
1122 LHSC = cast<SCEVConstant>(Ops[0]);
1123 }
1124
1125 // If we are left with a constant zero being added, strip it off.
1126 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1127 Ops.erase(Ops.begin());
1128 --Idx;
1129 }
1130 }
1131
1132 if (Ops.size() == 1) return Ops[0];
1133
1134 // Okay, check to see if the same value occurs in the operand list twice. If
1135 // so, merge them together into an multiply expression. Since we sorted the
1136 // list, these values are required to be adjacent.
1137 const Type *Ty = Ops[0]->getType();
1138 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1139 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1140 // Found a match, merge the two values into a multiply, and add any
1141 // remaining values to the result.
1142 const SCEV* Two = getIntegerSCEV(2, Ty);
1143 const SCEV* Mul = getMulExpr(Ops[i], Two);
1144 if (Ops.size() == 2)
1145 return Mul;
1146 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1147 Ops.push_back(Mul);
1148 return getAddExpr(Ops);
1149 }
1150
1151 // Check for truncates. If all the operands are truncated from the same
1152 // type, see if factoring out the truncate would permit the result to be
1153 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1154 // if the contents of the resulting outer trunc fold to something simple.
1155 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1156 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1157 const Type *DstType = Trunc->getType();
1158 const Type *SrcType = Trunc->getOperand()->getType();
1159 SmallVector<const SCEV*, 8> LargeOps;
1160 bool Ok = true;
1161 // Check all the operands to see if they can be represented in the
1162 // source type of the truncate.
1163 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1164 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1165 if (T->getOperand()->getType() != SrcType) {
1166 Ok = false;
1167 break;
1168 }
1169 LargeOps.push_back(T->getOperand());
1170 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1171 // This could be either sign or zero extension, but sign extension
1172 // is much more likely to be foldable here.
1173 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1174 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1175 SmallVector<const SCEV*, 8> LargeMulOps;
1176 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1177 if (const SCEVTruncateExpr *T =
1178 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1179 if (T->getOperand()->getType() != SrcType) {
1180 Ok = false;
1181 break;
1182 }
1183 LargeMulOps.push_back(T->getOperand());
1184 } else if (const SCEVConstant *C =
1185 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1186 // This could be either sign or zero extension, but sign extension
1187 // is much more likely to be foldable here.
1188 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1189 } else {
1190 Ok = false;
1191 break;
1192 }
1193 }
1194 if (Ok)
1195 LargeOps.push_back(getMulExpr(LargeMulOps));
1196 } else {
1197 Ok = false;
1198 break;
1199 }
1200 }
1201 if (Ok) {
1202 // Evaluate the expression in the larger type.
1203 const SCEV* Fold = getAddExpr(LargeOps);
1204 // If it folds to something simple, use it. Otherwise, don't.
1205 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1206 return getTruncateExpr(Fold, DstType);
1207 }
1208 }
1209
1210 // Skip past any other cast SCEVs.
1211 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1212 ++Idx;
1213
1214 // If there are add operands they would be next.
1215 if (Idx < Ops.size()) {
1216 bool DeletedAdd = false;
1217 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1218 // If we have an add, expand the add operands onto the end of the operands
1219 // list.
1220 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1221 Ops.erase(Ops.begin()+Idx);
1222 DeletedAdd = true;
1223 }
1224
1225 // If we deleted at least one add, we added operands to the end of the list,
1226 // and they are not necessarily sorted. Recurse to resort and resimplify
1227 // any operands we just aquired.
1228 if (DeletedAdd)
1229 return getAddExpr(Ops);
1230 }
1231
1232 // Skip over the add expression until we get to a multiply.
1233 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1234 ++Idx;
1235
1236 // Check to see if there are any folding opportunities present with
1237 // operands multiplied by constant values.
1238 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1239 uint64_t BitWidth = getTypeSizeInBits(Ty);
1240 DenseMap<const SCEV*, APInt> M;
1241 SmallVector<const SCEV*, 8> NewOps;
1242 APInt AccumulatedConstant(BitWidth, 0);
1243 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1244 Ops, APInt(BitWidth, 1), *this)) {
1245 // Some interesting folding opportunity is present, so its worthwhile to
1246 // re-generate the operands list. Group the operands by constant scale,
1247 // to avoid multiplying by the same constant scale multiple times.
1248 std::map<APInt, SmallVector<const SCEV*, 4>, APIntCompare> MulOpLists;
1249 for (SmallVector<const SCEV*, 8>::iterator I = NewOps.begin(),
1250 E = NewOps.end(); I != E; ++I)
1251 MulOpLists[M.find(*I)->second].push_back(*I);
1252 // Re-generate the operands list.
1253 Ops.clear();
1254 if (AccumulatedConstant != 0)
1255 Ops.push_back(getConstant(AccumulatedConstant));
1256 for (std::map<APInt, SmallVector<const SCEV *, 4>, APIntCompare>::iterator
1257 I = MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1258 if (I->first != 0)
1259 Ops.push_back(getMulExpr(getConstant(I->first),
1260 getAddExpr(I->second)));
1261 if (Ops.empty())
1262 return getIntegerSCEV(0, Ty);
1263 if (Ops.size() == 1)
1264 return Ops[0];
1265 return getAddExpr(Ops);
1266 }
1267 }
1268
1269 // If we are adding something to a multiply expression, make sure the
1270 // something is not already an operand of the multiply. If so, merge it into
1271 // the multiply.
1272 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1273 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1274 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1275 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1276 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1277 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1278 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1279 const SCEV* InnerMul = Mul->getOperand(MulOp == 0);
1280 if (Mul->getNumOperands() != 2) {
1281 // If the multiply has more than two operands, we must get the
1282 // Y*Z term.
1283 SmallVector<const SCEV*, 4> MulOps(Mul->op_begin(), Mul->op_end());
1284 MulOps.erase(MulOps.begin()+MulOp);
1285 InnerMul = getMulExpr(MulOps);
1286 }
1287 const SCEV* One = getIntegerSCEV(1, Ty);
1288 const SCEV* AddOne = getAddExpr(InnerMul, One);
1289 const SCEV* OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1290 if (Ops.size() == 2) return OuterMul;
1291 if (AddOp < Idx) {
1292 Ops.erase(Ops.begin()+AddOp);
1293 Ops.erase(Ops.begin()+Idx-1);
1294 } else {
1295 Ops.erase(Ops.begin()+Idx);
1296 Ops.erase(Ops.begin()+AddOp-1);
1297 }
1298 Ops.push_back(OuterMul);
1299 return getAddExpr(Ops);
1300 }
1301
1302 // Check this multiply against other multiplies being added together.
1303 for (unsigned OtherMulIdx = Idx+1;
1304 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1305 ++OtherMulIdx) {
1306 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1307 // If MulOp occurs in OtherMul, we can fold the two multiplies
1308 // together.
1309 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1310 OMulOp != e; ++OMulOp)
1311 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1312 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1313 const SCEV* InnerMul1 = Mul->getOperand(MulOp == 0);
1314 if (Mul->getNumOperands() != 2) {
1315 SmallVector<const SCEV *, 4> MulOps(Mul->op_begin(),
1316 Mul->op_end());
1317 MulOps.erase(MulOps.begin()+MulOp);
1318 InnerMul1 = getMulExpr(MulOps);
1319 }
1320 const SCEV* InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1321 if (OtherMul->getNumOperands() != 2) {
1322 SmallVector<const SCEV *, 4> MulOps(OtherMul->op_begin(),
1323 OtherMul->op_end());
1324 MulOps.erase(MulOps.begin()+OMulOp);
1325 InnerMul2 = getMulExpr(MulOps);
1326 }
1327 const SCEV* InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1328 const SCEV* OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1329 if (Ops.size() == 2) return OuterMul;
1330 Ops.erase(Ops.begin()+Idx);
1331 Ops.erase(Ops.begin()+OtherMulIdx-1);
1332 Ops.push_back(OuterMul);
1333 return getAddExpr(Ops);
1334 }
1335 }
1336 }
1337 }
1338
1339 // If there are any add recurrences in the operands list, see if any other
1340 // added values are loop invariant. If so, we can fold them into the
1341 // recurrence.
1342 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1343 ++Idx;
1344
1345 // Scan over all recurrences, trying to fold loop invariants into them.
1346 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1347 // Scan all of the other operands to this add and add them to the vector if
1348 // they are loop invariant w.r.t. the recurrence.
1349 SmallVector<const SCEV*, 8> LIOps;
1350 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1351 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1352 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1353 LIOps.push_back(Ops[i]);
1354 Ops.erase(Ops.begin()+i);
1355 --i; --e;
1356 }
1357
1358 // If we found some loop invariants, fold them into the recurrence.
1359 if (!LIOps.empty()) {
1360 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1361 LIOps.push_back(AddRec->getStart());
1362
1363 SmallVector<const SCEV*, 4> AddRecOps(AddRec->op_begin(),
1364 AddRec->op_end());
1365 AddRecOps[0] = getAddExpr(LIOps);
1366
1367 const SCEV* NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1368 // If all of the other operands were loop invariant, we are done.
1369 if (Ops.size() == 1) return NewRec;
1370
1371 // Otherwise, add the folded AddRec by the non-liv parts.
1372 for (unsigned i = 0;; ++i)
1373 if (Ops[i] == AddRec) {
1374 Ops[i] = NewRec;
1375 break;
1376 }
1377 return getAddExpr(Ops);
1378 }
1379
1380 // Okay, if there weren't any loop invariants to be folded, check to see if
1381 // there are multiple AddRec's with the same loop induction variable being
1382 // added together. If so, we can fold them.
1383 for (unsigned OtherIdx = Idx+1;
1384 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1385 if (OtherIdx != Idx) {
1386 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1387 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1388 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1389 SmallVector<const SCEV *, 4> NewOps(AddRec->op_begin(),
1390 AddRec->op_end());
1391 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1392 if (i >= NewOps.size()) {
1393 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1394 OtherAddRec->op_end());
1395 break;
1396 }
1397 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1398 }
1399 const SCEV* NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1400
1401 if (Ops.size() == 2) return NewAddRec;
1402
1403 Ops.erase(Ops.begin()+Idx);
1404 Ops.erase(Ops.begin()+OtherIdx-1);
1405 Ops.push_back(NewAddRec);
1406 return getAddExpr(Ops);
1407 }
1408 }
1409
1410 // Otherwise couldn't fold anything into this recurrence. Move onto the
1411 // next one.
1412 }
1413
1414 // Okay, it looks like we really DO need an add expr. Check to see if we
1415 // already have one, otherwise create a new one.
1416 FoldingSetNodeID ID;
1417 ID.AddInteger(scAddExpr);
1418 ID.AddInteger(Ops.size());
1419 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1420 ID.AddPointer(Ops[i]);
1421 void *IP = 0;
1422 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1423 SCEV *S = SCEVAllocator.Allocate<SCEVAddExpr>();
1424 new (S) SCEVAddExpr(Ops);
1425 UniqueSCEVs.InsertNode(S, IP);
1426 return S;
1427}
1428
1429
1430/// getMulExpr - Get a canonical multiply expression, or something simpler if
1431/// possible.
1432const SCEV* ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV*> &Ops) {
1433 assert(!Ops.empty() && "Cannot get empty mul!");
1434#ifndef NDEBUG
1435 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1436 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1437 getEffectiveSCEVType(Ops[0]->getType()) &&
1438 "SCEVMulExpr operand types don't match!");
1439#endif
1440
1441 // Sort by complexity, this groups all similar expression types together.
1442 GroupByComplexity(Ops, LI);
1443
1444 // If there are any constants, fold them together.
1445 unsigned Idx = 0;
1446 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1447
1448 // C1*(C2+V) -> C1*C2 + C1*V
1449 if (Ops.size() == 2)
1450 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1451 if (Add->getNumOperands() == 2 &&
1452 isa<SCEVConstant>(Add->getOperand(0)))
1453 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1454 getMulExpr(LHSC, Add->getOperand(1)));
1455
1456
1457 ++Idx;
1458 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1459 // We found two constants, fold them together!
1460 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1461 RHSC->getValue()->getValue());
1462 Ops[0] = getConstant(Fold);
1463 Ops.erase(Ops.begin()+1); // Erase the folded element
1464 if (Ops.size() == 1) return Ops[0];
1465 LHSC = cast<SCEVConstant>(Ops[0]);
1466 }
1467
1468 // If we are left with a constant one being multiplied, strip it off.
1469 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1470 Ops.erase(Ops.begin());
1471 --Idx;
1472 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1473 // If we have a multiply of zero, it will always be zero.
1474 return Ops[0];
1475 }
1476 }
1477
1478 // Skip over the add expression until we get to a multiply.
1479 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1480 ++Idx;
1481
1482 if (Ops.size() == 1)
1483 return Ops[0];
1484
1485 // If there are mul operands inline them all into this expression.
1486 if (Idx < Ops.size()) {
1487 bool DeletedMul = false;
1488 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1489 // If we have an mul, expand the mul operands onto the end of the operands
1490 // list.
1491 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1492 Ops.erase(Ops.begin()+Idx);
1493 DeletedMul = true;
1494 }
1495
1496 // If we deleted at least one mul, we added operands to the end of the list,
1497 // and they are not necessarily sorted. Recurse to resort and resimplify
1498 // any operands we just aquired.
1499 if (DeletedMul)
1500 return getMulExpr(Ops);
1501 }
1502
1503 // If there are any add recurrences in the operands list, see if any other
1504 // added values are loop invariant. If so, we can fold them into the
1505 // recurrence.
1506 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1507 ++Idx;
1508
1509 // Scan over all recurrences, trying to fold loop invariants into them.
1510 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1511 // Scan all of the other operands to this mul and add them to the vector if
1512 // they are loop invariant w.r.t. the recurrence.
1513 SmallVector<const SCEV*, 8> LIOps;
1514 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1515 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1516 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1517 LIOps.push_back(Ops[i]);
1518 Ops.erase(Ops.begin()+i);
1519 --i; --e;
1520 }
1521
1522 // If we found some loop invariants, fold them into the recurrence.
1523 if (!LIOps.empty()) {
1524 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1525 SmallVector<const SCEV*, 4> NewOps;
1526 NewOps.reserve(AddRec->getNumOperands());
1527 if (LIOps.size() == 1) {
1528 const SCEV *Scale = LIOps[0];
1529 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1530 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1531 } else {
1532 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1533 SmallVector<const SCEV*, 4> MulOps(LIOps.begin(), LIOps.end());
1534 MulOps.push_back(AddRec->getOperand(i));
1535 NewOps.push_back(getMulExpr(MulOps));
1536 }
1537 }
1538
1539 const SCEV* NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1540
1541 // If all of the other operands were loop invariant, we are done.
1542 if (Ops.size() == 1) return NewRec;
1543
1544 // Otherwise, multiply the folded AddRec by the non-liv parts.
1545 for (unsigned i = 0;; ++i)
1546 if (Ops[i] == AddRec) {
1547 Ops[i] = NewRec;
1548 break;
1549 }
1550 return getMulExpr(Ops);
1551 }
1552
1553 // Okay, if there weren't any loop invariants to be folded, check to see if
1554 // there are multiple AddRec's with the same loop induction variable being
1555 // multiplied together. If so, we can fold them.
1556 for (unsigned OtherIdx = Idx+1;
1557 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1558 if (OtherIdx != Idx) {
1559 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1560 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1561 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1562 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1563 const SCEV* NewStart = getMulExpr(F->getStart(),
1564 G->getStart());
1565 const SCEV* B = F->getStepRecurrence(*this);
1566 const SCEV* D = G->getStepRecurrence(*this);
1567 const SCEV* NewStep = getAddExpr(getMulExpr(F, D),
1568 getMulExpr(G, B),
1569 getMulExpr(B, D));
1570 const SCEV* NewAddRec = getAddRecExpr(NewStart, NewStep,
1571 F->getLoop());
1572 if (Ops.size() == 2) return NewAddRec;
1573
1574 Ops.erase(Ops.begin()+Idx);
1575 Ops.erase(Ops.begin()+OtherIdx-1);
1576 Ops.push_back(NewAddRec);
1577 return getMulExpr(Ops);
1578 }
1579 }
1580
1581 // Otherwise couldn't fold anything into this recurrence. Move onto the
1582 // next one.
1583 }
1584
1585 // Okay, it looks like we really DO need an mul expr. Check to see if we
1586 // already have one, otherwise create a new one.
1587 FoldingSetNodeID ID;
1588 ID.AddInteger(scMulExpr);
1589 ID.AddInteger(Ops.size());
1590 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1591 ID.AddPointer(Ops[i]);
1592 void *IP = 0;
1593 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1594 SCEV *S = SCEVAllocator.Allocate<SCEVMulExpr>();
1595 new (S) SCEVMulExpr(Ops);
1596 UniqueSCEVs.InsertNode(S, IP);
1597 return S;
1598}
1599
1600/// getUDivExpr - Get a canonical multiply expression, or something simpler if
1601/// possible.
1602const SCEV *ScalarEvolution::getUDivExpr(const SCEV *LHS,
1603 const SCEV *RHS) {
1604 assert(getEffectiveSCEVType(LHS->getType()) ==
1605 getEffectiveSCEVType(RHS->getType()) &&
1606 "SCEVUDivExpr operand types don't match!");
1607
1608 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1609 if (RHSC->getValue()->equalsInt(1))
1610 return LHS; // X udiv 1 --> x
1611 if (RHSC->isZero())
1612 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1613
1614 // Determine if the division can be folded into the operands of
1615 // its operands.
1616 // TODO: Generalize this to non-constants by using known-bits information.
1617 const Type *Ty = LHS->getType();
1618 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1619 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1620 // For non-power-of-two values, effectively round the value up to the
1621 // nearest power of two.
1622 if (!RHSC->getValue()->getValue().isPowerOf2())
1623 ++MaxShiftAmt;
1624 const IntegerType *ExtTy =
1625 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1626 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1627 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1628 if (const SCEVConstant *Step =
1629 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1630 if (!Step->getValue()->getValue()
1631 .urem(RHSC->getValue()->getValue()) &&
1632 getZeroExtendExpr(AR, ExtTy) ==
1633 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1634 getZeroExtendExpr(Step, ExtTy),
1635 AR->getLoop())) {
1636 SmallVector<const SCEV*, 4> Operands;
1637 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1638 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1639 return getAddRecExpr(Operands, AR->getLoop());
1640 }
1641 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1642 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1643 SmallVector<const SCEV*, 4> Operands;
1644 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1645 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1646 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1647 // Find an operand that's safely divisible.
1648 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1649 const SCEV* Op = M->getOperand(i);
1650 const SCEV* Div = getUDivExpr(Op, RHSC);
1651 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1652 const SmallVectorImpl<const SCEV*> &MOperands = M->getOperands();
1653 Operands = SmallVector<const SCEV*, 4>(MOperands.begin(),
1654 MOperands.end());
1655 Operands[i] = Div;
1656 return getMulExpr(Operands);
1657 }
1658 }
1659 }
1660 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1661 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1662 SmallVector<const SCEV*, 4> Operands;
1663 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1664 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1665 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1666 Operands.clear();
1667 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1668 const SCEV* Op = getUDivExpr(A->getOperand(i), RHS);
1669 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1670 break;
1671 Operands.push_back(Op);
1672 }
1673 if (Operands.size() == A->getNumOperands())
1674 return getAddExpr(Operands);
1675 }
1676 }
1677
1678 // Fold if both operands are constant.
1679 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1680 Constant *LHSCV = LHSC->getValue();
1681 Constant *RHSCV = RHSC->getValue();
1682 return getConstant(cast<ConstantInt>(ConstantExpr::getUDiv(LHSCV,
1683 RHSCV)));
1684 }
1685 }
1686
1687 FoldingSetNodeID ID;
1688 ID.AddInteger(scUDivExpr);
1689 ID.AddPointer(LHS);
1690 ID.AddPointer(RHS);
1691 void *IP = 0;
1692 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1693 SCEV *S = SCEVAllocator.Allocate<SCEVUDivExpr>();
1694 new (S) SCEVUDivExpr(LHS, RHS);
1695 UniqueSCEVs.InsertNode(S, IP);
1696 return S;
1697}
1698
1699
1700/// getAddRecExpr - Get an add recurrence expression for the specified loop.
1701/// Simplify the expression as much as possible.
1702const SCEV* ScalarEvolution::getAddRecExpr(const SCEV* Start,
1703 const SCEV* Step, const Loop *L) {
1704 SmallVector<const SCEV*, 4> Operands;
1705 Operands.push_back(Start);
1706 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1707 if (StepChrec->getLoop() == L) {
1708 Operands.insert(Operands.end(), StepChrec->op_begin(),
1709 StepChrec->op_end());
1710 return getAddRecExpr(Operands, L);
1711 }
1712
1713 Operands.push_back(Step);
1714 return getAddRecExpr(Operands, L);
1715}
1716
1717/// getAddRecExpr - Get an add recurrence expression for the specified loop.
1718/// Simplify the expression as much as possible.
1719const SCEV *
1720ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV*> &Operands,
1721 const Loop *L) {
1722 if (Operands.size() == 1) return Operands[0];
1723#ifndef NDEBUG
1724 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1725 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1726 getEffectiveSCEVType(Operands[0]->getType()) &&
1727 "SCEVAddRecExpr operand types don't match!");
1728#endif
1729
1730 if (Operands.back()->isZero()) {
1731 Operands.pop_back();
1732 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1733 }
1734
1735 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1736 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1737 const Loop* NestedLoop = NestedAR->getLoop();
1738 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1739 SmallVector<const SCEV*, 4> NestedOperands(NestedAR->op_begin(),
1740 NestedAR->op_end());
1741 Operands[0] = NestedAR->getStart();
1742 // AddRecs require their operands be loop-invariant with respect to their
1743 // loops. Don't perform this transformation if it would break this
1744 // requirement.
1745 bool AllInvariant = true;
1746 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1747 if (!Operands[i]->isLoopInvariant(L)) {
1748 AllInvariant = false;
1749 break;
1750 }
1751 if (AllInvariant) {
1752 NestedOperands[0] = getAddRecExpr(Operands, L);
1753 AllInvariant = true;
1754 for (unsigned i = 0, e = NestedOperands.size(); i != e; ++i)
1755 if (!NestedOperands[i]->isLoopInvariant(NestedLoop)) {
1756 AllInvariant = false;
1757 break;
1758 }
1759 if (AllInvariant)
1760 // Ok, both add recurrences are valid after the transformation.
1761 return getAddRecExpr(NestedOperands, NestedLoop);
1762 }
1763 // Reset Operands to its original state.
1764 Operands[0] = NestedAR;
1765 }
1766 }
1767
1768 FoldingSetNodeID ID;
1769 ID.AddInteger(scAddRecExpr);
1770 ID.AddInteger(Operands.size());
1771 for (unsigned i = 0, e = Operands.size(); i != e; ++i)
1772 ID.AddPointer(Operands[i]);
1773 ID.AddPointer(L);
1774 void *IP = 0;
1775 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1776 SCEV *S = SCEVAllocator.Allocate<SCEVAddRecExpr>();
1777 new (S) SCEVAddRecExpr(Operands, L);
1778 UniqueSCEVs.InsertNode(S, IP);
1779 return S;
1780}
1781
1782const SCEV *ScalarEvolution::getSMaxExpr(const SCEV *LHS,
1783 const SCEV *RHS) {
1784 SmallVector<const SCEV*, 2> Ops;
1785 Ops.push_back(LHS);
1786 Ops.push_back(RHS);
1787 return getSMaxExpr(Ops);
1788}
1789
1790const SCEV*
1791ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV*> &Ops) {
1792 assert(!Ops.empty() && "Cannot get empty smax!");
1793 if (Ops.size() == 1) return Ops[0];
1794#ifndef NDEBUG
1795 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1796 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1797 getEffectiveSCEVType(Ops[0]->getType()) &&
1798 "SCEVSMaxExpr operand types don't match!");
1799#endif
1800
1801 // Sort by complexity, this groups all similar expression types together.
1802 GroupByComplexity(Ops, LI);
1803
1804 // If there are any constants, fold them together.
1805 unsigned Idx = 0;
1806 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1807 ++Idx;
1808 assert(Idx < Ops.size());
1809 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1810 // We found two constants, fold them together!
1811 ConstantInt *Fold = ConstantInt::get(
1812 APIntOps::smax(LHSC->getValue()->getValue(),
1813 RHSC->getValue()->getValue()));
1814 Ops[0] = getConstant(Fold);
1815 Ops.erase(Ops.begin()+1); // Erase the folded element
1816 if (Ops.size() == 1) return Ops[0];
1817 LHSC = cast<SCEVConstant>(Ops[0]);
1818 }
1819
1820 // If we are left with a constant minimum-int, strip it off.
1821 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1822 Ops.erase(Ops.begin());
1823 --Idx;
1824 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(true)) {
1825 // If we have an smax with a constant maximum-int, it will always be
1826 // maximum-int.
1827 return Ops[0];
1828 }
1829 }
1830
1831 if (Ops.size() == 1) return Ops[0];
1832
1833 // Find the first SMax
1834 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1835 ++Idx;
1836
1837 // Check to see if one of the operands is an SMax. If so, expand its operands
1838 // onto our operand list, and recurse to simplify.
1839 if (Idx < Ops.size()) {
1840 bool DeletedSMax = false;
1841 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1842 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1843 Ops.erase(Ops.begin()+Idx);
1844 DeletedSMax = true;
1845 }
1846
1847 if (DeletedSMax)
1848 return getSMaxExpr(Ops);
1849 }
1850
1851 // Okay, check to see if the same value occurs in the operand list twice. If
1852 // so, delete one. Since we sorted the list, these values are required to
1853 // be adjacent.
1854 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1855 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1856 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1857 --i; --e;
1858 }
1859
1860 if (Ops.size() == 1) return Ops[0];
1861
1862 assert(!Ops.empty() && "Reduced smax down to nothing!");
1863
1864 // Okay, it looks like we really DO need an smax expr. Check to see if we
1865 // already have one, otherwise create a new one.
1866 FoldingSetNodeID ID;
1867 ID.AddInteger(scSMaxExpr);
1868 ID.AddInteger(Ops.size());
1869 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1870 ID.AddPointer(Ops[i]);
1871 void *IP = 0;
1872 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1873 SCEV *S = SCEVAllocator.Allocate<SCEVSMaxExpr>();
1874 new (S) SCEVSMaxExpr(Ops);
1875 UniqueSCEVs.InsertNode(S, IP);
1876 return S;
1877}
1878
1879const SCEV *ScalarEvolution::getUMaxExpr(const SCEV *LHS,
1880 const SCEV *RHS) {
1881 SmallVector<const SCEV*, 2> Ops;
1882 Ops.push_back(LHS);
1883 Ops.push_back(RHS);
1884 return getUMaxExpr(Ops);
1885}
1886
1887const SCEV*
1888ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV*> &Ops) {
1889 assert(!Ops.empty() && "Cannot get empty umax!");
1890 if (Ops.size() == 1) return Ops[0];
1891#ifndef NDEBUG
1892 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1893 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1894 getEffectiveSCEVType(Ops[0]->getType()) &&
1895 "SCEVUMaxExpr operand types don't match!");
1896#endif
1897
1898 // Sort by complexity, this groups all similar expression types together.
1899 GroupByComplexity(Ops, LI);
1900
1901 // If there are any constants, fold them together.
1902 unsigned Idx = 0;
1903 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1904 ++Idx;
1905 assert(Idx < Ops.size());
1906 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1907 // We found two constants, fold them together!
1908 ConstantInt *Fold = ConstantInt::get(
1909 APIntOps::umax(LHSC->getValue()->getValue(),
1910 RHSC->getValue()->getValue()));
1911 Ops[0] = getConstant(Fold);
1912 Ops.erase(Ops.begin()+1); // Erase the folded element
1913 if (Ops.size() == 1) return Ops[0];
1914 LHSC = cast<SCEVConstant>(Ops[0]);
1915 }
1916
1917 // If we are left with a constant minimum-int, strip it off.
1918 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1919 Ops.erase(Ops.begin());
1920 --Idx;
1921 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isMaxValue(false)) {
1922 // If we have an umax with a constant maximum-int, it will always be
1923 // maximum-int.
1924 return Ops[0];
1925 }
1926 }
1927
1928 if (Ops.size() == 1) return Ops[0];
1929
1930 // Find the first UMax
1931 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1932 ++Idx;
1933
1934 // Check to see if one of the operands is a UMax. If so, expand its operands
1935 // onto our operand list, and recurse to simplify.
1936 if (Idx < Ops.size()) {
1937 bool DeletedUMax = false;
1938 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1939 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1940 Ops.erase(Ops.begin()+Idx);
1941 DeletedUMax = true;
1942 }
1943
1944 if (DeletedUMax)
1945 return getUMaxExpr(Ops);
1946 }
1947
1948 // Okay, check to see if the same value occurs in the operand list twice. If
1949 // so, delete one. Since we sorted the list, these values are required to
1950 // be adjacent.
1951 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1952 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1953 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1954 --i; --e;
1955 }
1956
1957 if (Ops.size() == 1) return Ops[0];
1958
1959 assert(!Ops.empty() && "Reduced umax down to nothing!");
1960
1961 // Okay, it looks like we really DO need a umax expr. Check to see if we
1962 // already have one, otherwise create a new one.
1963 FoldingSetNodeID ID;
1964 ID.AddInteger(scUMaxExpr);
1965 ID.AddInteger(Ops.size());
1966 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1967 ID.AddPointer(Ops[i]);
1968 void *IP = 0;
1969 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1970 SCEV *S = SCEVAllocator.Allocate<SCEVUMaxExpr>();
1971 new (S) SCEVUMaxExpr(Ops);
1972 UniqueSCEVs.InsertNode(S, IP);
1973 return S;
1974}
1975
1976const SCEV *ScalarEvolution::getSMinExpr(const SCEV *LHS,
1977 const SCEV *RHS) {
1978 // ~smax(~x, ~y) == smin(x, y).
1979 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
1980}
1981
1982const SCEV *ScalarEvolution::getUMinExpr(const SCEV *LHS,
1983 const SCEV *RHS) {
1984 // ~umax(~x, ~y) == umin(x, y)
1985 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
1986}
1987
1988const SCEV* ScalarEvolution::getUnknown(Value *V) {
1989 // Don't attempt to do anything other than create a SCEVUnknown object
1990 // here. createSCEV only calls getUnknown after checking for all other
1991 // interesting possibilities, and any other code that calls getUnknown
1992 // is doing so in order to hide a value from SCEV canonicalization.
1993
1994 FoldingSetNodeID ID;
1995 ID.AddInteger(scUnknown);
1996 ID.AddPointer(V);
1997 void *IP = 0;
1998 if (const SCEV *S = UniqueSCEVs.FindNodeOrInsertPos(ID, IP)) return S;
1999 SCEV *S = SCEVAllocator.Allocate<SCEVUnknown>();
2000 new (S) SCEVUnknown(V);
2001 UniqueSCEVs.InsertNode(S, IP);
2002 return S;
2003}
2004
2005//===----------------------------------------------------------------------===//
2006// Basic SCEV Analysis and PHI Idiom Recognition Code
2007//
2008
2009/// isSCEVable - Test if values of the given type are analyzable within
2010/// the SCEV framework. This primarily includes integer types, and it
2011/// can optionally include pointer types if the ScalarEvolution class
2012/// has access to target-specific information.
2013bool ScalarEvolution::isSCEVable(const Type *Ty) const {
2014 // Integers are always SCEVable.
2015 if (Ty->isInteger())
2016 return true;
2017
2018 // Pointers are SCEVable if TargetData information is available
2019 // to provide pointer size information.
2020 if (isa<PointerType>(Ty))
2021 return TD != NULL;
2022
2023 // Otherwise it's not SCEVable.
2024 return false;
2025}
2026
2027/// getTypeSizeInBits - Return the size in bits of the specified type,
2028/// for which isSCEVable must return true.
2029uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
2030 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2031
2032 // If we have a TargetData, use it!
2033 if (TD)
2034 return TD->getTypeSizeInBits(Ty);
2035
2036 // Otherwise, we support only integer types.
2037 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
2038 return Ty->getPrimitiveSizeInBits();
2039}
2040
2041/// getEffectiveSCEVType - Return a type with the same bitwidth as
2042/// the given type and which represents how SCEV will treat the given
2043/// type, for which isSCEVable must return true. For pointer types,
2044/// this is the pointer-sized integer type.
2045const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
2046 assert(isSCEVable(Ty) && "Type is not SCEVable!");
2047
2048 if (Ty->isInteger())
2049 return Ty;
2050
2051 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
2052 return TD->getIntPtrType();
2053}
2054
2055const SCEV* ScalarEvolution::getCouldNotCompute() {
2056 return &CouldNotCompute;
2057}
2058
2059/// hasSCEV - Return true if the SCEV for this value has already been
2060/// computed.
2061bool ScalarEvolution::hasSCEV(Value *V) const {
2062 return Scalars.count(V);
2063}
2064
2065/// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
2066/// expression and create a new one.
2067const SCEV* ScalarEvolution::getSCEV(Value *V) {
2068 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
2069
2070 std::map<SCEVCallbackVH, const SCEV*>::iterator I = Scalars.find(V);
2071 if (I != Scalars.end()) return I->second;
2072 const SCEV* S = createSCEV(V);
2073 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
2074 return S;
2075}
2076
2077/// getIntegerSCEV - Given a SCEVable type, create a constant for the
2078/// specified signed integer value and return a SCEV for the constant.
2079const SCEV* ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
2080 const IntegerType *ITy = cast<IntegerType>(getEffectiveSCEVType(Ty));
2081 return getConstant(ConstantInt::get(ITy, Val));
2082}
2083
2084/// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
2085///
2086const SCEV* ScalarEvolution::getNegativeSCEV(const SCEV* V) {
2087 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2088 return getConstant(cast<ConstantInt>(ConstantExpr::getNeg(VC->getValue())));
2089
2090 const Type *Ty = V->getType();
2091 Ty = getEffectiveSCEVType(Ty);
2092 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
2093}
2094
2095/// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
2096const SCEV* ScalarEvolution::getNotSCEV(const SCEV* V) {
2097 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
2098 return getConstant(cast<ConstantInt>(ConstantExpr::getNot(VC->getValue())));
2099
2100 const Type *Ty = V->getType();
2101 Ty = getEffectiveSCEVType(Ty);
2102 const SCEV* AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
2103 return getMinusSCEV(AllOnes, V);
2104}
2105
2106/// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
2107///
2108const SCEV *ScalarEvolution::getMinusSCEV(const SCEV *LHS,
2109 const SCEV *RHS) {
2110 // X - Y --> X + -Y
2111 return getAddExpr(LHS, getNegativeSCEV(RHS));
2112}
2113
2114/// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
2115/// input value to the specified type. If the type must be extended, it is zero
2116/// extended.
2117const SCEV*
2118ScalarEvolution::getTruncateOrZeroExtend(const SCEV* V,
2119 const Type *Ty) {
2120 const Type *SrcTy = V->getType();
2121 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2122 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2123 "Cannot truncate or zero extend with non-integer arguments!");
2124 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2125 return V; // No conversion
2126 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2127 return getTruncateExpr(V, Ty);
2128 return getZeroExtendExpr(V, Ty);
2129}
2130
2131/// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2132/// input value to the specified type. If the type must be extended, it is sign
2133/// extended.
2134const SCEV*
2135ScalarEvolution::getTruncateOrSignExtend(const SCEV* V,
2136 const Type *Ty) {
2137 const Type *SrcTy = V->getType();
2138 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2139 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2140 "Cannot truncate or zero extend with non-integer arguments!");
2141 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2142 return V; // No conversion
2143 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2144 return getTruncateExpr(V, Ty);
2145 return getSignExtendExpr(V, Ty);
2146}
2147
2148/// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2149/// input value to the specified type. If the type must be extended, it is zero
2150/// extended. The conversion must not be narrowing.
2151const SCEV*
2152ScalarEvolution::getNoopOrZeroExtend(const SCEV* V, const Type *Ty) {
2153 const Type *SrcTy = V->getType();
2154 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2155 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2156 "Cannot noop or zero extend with non-integer arguments!");
2157 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2158 "getNoopOrZeroExtend cannot truncate!");
2159 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2160 return V; // No conversion
2161 return getZeroExtendExpr(V, Ty);
2162}
2163
2164/// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2165/// input value to the specified type. If the type must be extended, it is sign
2166/// extended. The conversion must not be narrowing.
2167const SCEV*
2168ScalarEvolution::getNoopOrSignExtend(const SCEV* V, const Type *Ty) {
2169 const Type *SrcTy = V->getType();
2170 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2171 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2172 "Cannot noop or sign extend with non-integer arguments!");
2173 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2174 "getNoopOrSignExtend cannot truncate!");
2175 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2176 return V; // No conversion
2177 return getSignExtendExpr(V, Ty);
2178}
2179
2180/// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2181/// the input value to the specified type. If the type must be extended,
2182/// it is extended with unspecified bits. The conversion must not be
2183/// narrowing.
2184const SCEV*
2185ScalarEvolution::getNoopOrAnyExtend(const SCEV* V, const Type *Ty) {
2186 const Type *SrcTy = V->getType();
2187 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2188 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2189 "Cannot noop or any extend with non-integer arguments!");
2190 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2191 "getNoopOrAnyExtend cannot truncate!");
2192 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2193 return V; // No conversion
2194 return getAnyExtendExpr(V, Ty);
2195}
2196
2197/// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2198/// input value to the specified type. The conversion must not be widening.
2199const SCEV*
2200ScalarEvolution::getTruncateOrNoop(const SCEV* V, const Type *Ty) {
2201 const Type *SrcTy = V->getType();
2202 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2203 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2204 "Cannot truncate or noop with non-integer arguments!");
2205 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2206 "getTruncateOrNoop cannot extend!");
2207 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2208 return V; // No conversion
2209 return getTruncateExpr(V, Ty);
2210}
2211
2212/// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2213/// the types using zero-extension, and then perform a umax operation
2214/// with them.
2215const SCEV *ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV *LHS,
2216 const SCEV *RHS) {
2217 const SCEV* PromotedLHS = LHS;
2218 const SCEV* PromotedRHS = RHS;
2219
2220 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2221 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2222 else
2223 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2224
2225 return getUMaxExpr(PromotedLHS, PromotedRHS);
2226}
2227
2228/// getUMinFromMismatchedTypes - Promote the operands to the wider of
2229/// the types using zero-extension, and then perform a umin operation
2230/// with them.
2231const SCEV *ScalarEvolution::getUMinFromMismatchedTypes(const SCEV *LHS,
2232 const SCEV *RHS) {
2233 const SCEV* PromotedLHS = LHS;
2234 const SCEV* PromotedRHS = RHS;
2235
2236 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2237 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2238 else
2239 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2240
2241 return getUMinExpr(PromotedLHS, PromotedRHS);
2242}
2243
2244/// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
2245/// the specified instruction and replaces any references to the symbolic value
2246/// SymName with the specified value. This is used during PHI resolution.
2247void
2248ScalarEvolution::ReplaceSymbolicValueWithConcrete(Instruction *I,
2249 const SCEV *SymName,
2250 const SCEV *NewVal) {
2251 std::map<SCEVCallbackVH, const SCEV*>::iterator SI =
2252 Scalars.find(SCEVCallbackVH(I, this));
2253 if (SI == Scalars.end()) return;
2254
2255 const SCEV* NV =
2256 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
2257 if (NV == SI->second) return; // No change.
2258
2259 SI->second = NV; // Update the scalars map!
2260
2261 // Any instruction values that use this instruction might also need to be
2262 // updated!
2263 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
2264 UI != E; ++UI)
2265 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
2266}
2267
2268/// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2269/// a loop header, making it a potential recurrence, or it doesn't.
2270///
2271const SCEV* ScalarEvolution::createNodeForPHI(PHINode *PN) {
2272 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2273 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2274 if (L->getHeader() == PN->getParent()) {
2275 // If it lives in the loop header, it has two incoming values, one
2276 // from outside the loop, and one from inside.
2277 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2278 unsigned BackEdge = IncomingEdge^1;
2279
2280 // While we are analyzing this PHI node, handle its value symbolically.
2281 const SCEV* SymbolicName = getUnknown(PN);
2282 assert(Scalars.find(PN) == Scalars.end() &&
2283 "PHI node already processed?");
2284 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2285
2286 // Using this symbolic name for the PHI, analyze the value coming around
2287 // the back-edge.
2288 const SCEV* BEValue = getSCEV(PN->getIncomingValue(BackEdge));
2289
2290 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2291 // has a special value for the first iteration of the loop.
2292
2293 // If the value coming around the backedge is an add with the symbolic
2294 // value we just inserted, then we found a simple induction variable!
2295 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2296 // If there is a single occurrence of the symbolic value, replace it
2297 // with a recurrence.
2298 unsigned FoundIndex = Add->getNumOperands();
2299 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2300 if (Add->getOperand(i) == SymbolicName)
2301 if (FoundIndex == e) {
2302 FoundIndex = i;
2303 break;
2304 }
2305
2306 if (FoundIndex != Add->getNumOperands()) {
2307 // Create an add with everything but the specified operand.
2308 SmallVector<const SCEV*, 8> Ops;
2309 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2310 if (i != FoundIndex)
2311 Ops.push_back(Add->getOperand(i));
2312 const SCEV* Accum = getAddExpr(Ops);
2313
2314 // This is not a valid addrec if the step amount is varying each
2315 // loop iteration, but is not itself an addrec in this loop.
2316 if (Accum->isLoopInvariant(L) ||
2317 (isa<SCEVAddRecExpr>(Accum) &&
2318 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2319 const SCEV *StartVal =
2320 getSCEV(PN->getIncomingValue(IncomingEdge));
2321 const SCEV *PHISCEV =
2322 getAddRecExpr(StartVal, Accum, L);
2323
2324 // Okay, for the entire analysis of this edge we assumed the PHI
2325 // to be symbolic. We now need to go back and update all of the
2326 // entries for the scalars that use the PHI (except for the PHI
2327 // itself) to use the new analyzed value instead of the "symbolic"
2328 // value.
2329 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2330 return PHISCEV;
2331 }
2332 }
2333 } else if (const SCEVAddRecExpr *AddRec =
2334 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2335 // Otherwise, this could be a loop like this:
2336 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2337 // In this case, j = {1,+,1} and BEValue is j.
2338 // Because the other in-value of i (0) fits the evolution of BEValue
2339 // i really is an addrec evolution.
2340 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2341 const SCEV* StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2342
2343 // If StartVal = j.start - j.stride, we can use StartVal as the
2344 // initial step of the addrec evolution.
2345 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2346 AddRec->getOperand(1))) {
2347 const SCEV* PHISCEV =
2348 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2349
2350 // Okay, for the entire analysis of this edge we assumed the PHI
2351 // to be symbolic. We now need to go back and update all of the
2352 // entries for the scalars that use the PHI (except for the PHI
2353 // itself) to use the new analyzed value instead of the "symbolic"
2354 // value.
2355 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2356 return PHISCEV;
2357 }
2358 }
2359 }
2360
2361 return SymbolicName;
2362 }
2363
2364 // If it's not a loop phi, we can't handle it yet.
2365 return getUnknown(PN);
2366}
2367
2368/// createNodeForGEP - Expand GEP instructions into add and multiply
2369/// operations. This allows them to be analyzed by regular SCEV code.
2370///
2371const SCEV* ScalarEvolution::createNodeForGEP(User *GEP) {
2372
2373 const Type *IntPtrTy = TD->getIntPtrType();
2374 Value *Base = GEP->getOperand(0);
2375 // Don't attempt to analyze GEPs over unsized objects.
2376 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2377 return getUnknown(GEP);
2378 const SCEV* TotalOffset = getIntegerSCEV(0, IntPtrTy);
2379 gep_type_iterator GTI = gep_type_begin(GEP);
2380 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2381 E = GEP->op_end();
2382 I != E; ++I) {
2383 Value *Index = *I;
2384 // Compute the (potentially symbolic) offset in bytes for this index.
2385 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2386 // For a struct, add the member offset.
2387 const StructLayout &SL = *TD->getStructLayout(STy);
2388 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2389 uint64_t Offset = SL.getElementOffset(FieldNo);
2390 TotalOffset = getAddExpr(TotalOffset,
2391 getIntegerSCEV(Offset, IntPtrTy));
2392 } else {
2393 // For an array, add the element offset, explicitly scaled.
2394 const SCEV* LocalOffset = getSCEV(Index);
2395 if (!isa<PointerType>(LocalOffset->getType()))
2396 // Getelementptr indicies are signed.
2397 LocalOffset = getTruncateOrSignExtend(LocalOffset,
2398 IntPtrTy);
2399 LocalOffset =
2400 getMulExpr(LocalOffset,
2401 getIntegerSCEV(TD->getTypeAllocSize(*GTI),
2402 IntPtrTy));
2403 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2404 }
2405 }
2406 return getAddExpr(getSCEV(Base), TotalOffset);
2407}
2408
2409/// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2410/// guaranteed to end in (at every loop iteration). It is, at the same time,
2411/// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2412/// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2413uint32_t
2414ScalarEvolution::GetMinTrailingZeros(const SCEV* S) {
2415 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2416 return C->getValue()->getValue().countTrailingZeros();
2417
2418 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2419 return std::min(GetMinTrailingZeros(T->getOperand()),
2420 (uint32_t)getTypeSizeInBits(T->getType()));
2421
2422 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2423 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2424 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2425 getTypeSizeInBits(E->getType()) : OpRes;
2426 }
2427
2428 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2429 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2430 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2431 getTypeSizeInBits(E->getType()) : OpRes;
2432 }
2433
2434 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2435 // The result is the min of all operands results.
2436 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2437 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2438 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2439 return MinOpRes;
2440 }
2441
2442 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2443 // The result is the sum of all operands results.
2444 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2445 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2446 for (unsigned i = 1, e = M->getNumOperands();
2447 SumOpRes != BitWidth && i != e; ++i)
2448 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2449 BitWidth);
2450 return SumOpRes;
2451 }
2452
2453 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2454 // The result is the min of all operands results.
2455 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2456 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2457 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2458 return MinOpRes;
2459 }
2460
2461 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2462 // The result is the min of all operands results.
2463 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2464 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2465 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2466 return MinOpRes;
2467 }
2468
2469 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2470 // The result is the min of all operands results.
2471 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2472 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2473 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2474 return MinOpRes;
2475 }
2476
2477 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2478 // For a SCEVUnknown, ask ValueTracking.
2479 unsigned BitWidth = getTypeSizeInBits(U->getType());
2480 APInt Mask = APInt::getAllOnesValue(BitWidth);
2481 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2482 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2483 return Zeros.countTrailingOnes();
2484 }
2485
2486 // SCEVUDivExpr
2487 return 0;
2488}
2489
2490uint32_t
2491ScalarEvolution::GetMinLeadingZeros(const SCEV* S) {
2492 // TODO: Handle other SCEV expression types here.
2493
2494 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2495 return C->getValue()->getValue().countLeadingZeros();
2496
2497 if (const SCEVZeroExtendExpr *C = dyn_cast<SCEVZeroExtendExpr>(S)) {
2498 // A zero-extension cast adds zero bits.
2499 return GetMinLeadingZeros(C->getOperand()) +
2500 (getTypeSizeInBits(C->getType()) -
2501 getTypeSizeInBits(C->getOperand()->getType()));
2502 }
2503
2504 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2505 // For a SCEVUnknown, ask ValueTracking.
2506 unsigned BitWidth = getTypeSizeInBits(U->getType());
2507 APInt Mask = APInt::getAllOnesValue(BitWidth);
2508 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2509 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
2510 return Zeros.countLeadingOnes();
2511 }
2512
2513 return 1;
2514}
2515
2516uint32_t
2517ScalarEvolution::GetMinSignBits(const SCEV* S) {
2518 // TODO: Handle other SCEV expression types here.
2519
2520 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
2521 const APInt &A = C->getValue()->getValue();
2522 return A.isNegative() ? A.countLeadingOnes() :
2523 A.countLeadingZeros();
2524 }
2525
2526 if (const SCEVSignExtendExpr *C = dyn_cast<SCEVSignExtendExpr>(S)) {
2527 // A sign-extension cast adds sign bits.
2528 return GetMinSignBits(C->getOperand()) +
2529 (getTypeSizeInBits(C->getType()) -
2530 getTypeSizeInBits(C->getOperand()->getType()));
2531 }
2532
2533 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2534 unsigned BitWidth = getTypeSizeInBits(A->getType());
2535
2536 // Special case decrementing a value (ADD X, -1):
2537 if (const SCEVConstant *CRHS = dyn_cast<SCEVConstant>(A->getOperand(0)))
2538 if (CRHS->isAllOnesValue()) {
2539 SmallVector<const SCEV *, 4> OtherOps(A->op_begin() + 1, A->op_end());
2540 const SCEV *OtherOpsAdd = getAddExpr(OtherOps);
2541 unsigned LZ = GetMinLeadingZeros(OtherOpsAdd);
2542
2543 // If the input is known to be 0 or 1, the output is 0/-1, which is all
2544 // sign bits set.
2545 if (LZ == BitWidth - 1)
2546 return BitWidth;
2547
2548 // If we are subtracting one from a positive number, there is no carry
2549 // out of the result.
2550 if (LZ > 0)
2551 return GetMinSignBits(OtherOpsAdd);
2552 }
2553
2554 // Add can have at most one carry bit. Thus we know that the output
2555 // is, at worst, one more bit than the inputs.
2556 unsigned Min = BitWidth;
2557 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
2558 unsigned N = GetMinSignBits(A->getOperand(i));
2559 Min = std::min(Min, N) - 1;
2560 if (Min == 0) return 1;
2561 }
2562 return 1;
2563 }
2564
2565 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2566 // For a SCEVUnknown, ask ValueTracking.
2567 return ComputeNumSignBits(U->getValue(), TD);
2568 }
2569
2570 return 1;
2571}
2572
2573/// createSCEV - We know that there is no SCEV for the specified value.
2574/// Analyze the expression.
2575///
2576const SCEV* ScalarEvolution::createSCEV(Value *V) {
2577 if (!isSCEVable(V->getType()))
2578 return getUnknown(V);
2579
2580 unsigned Opcode = Instruction::UserOp1;
2581 if (Instruction *I = dyn_cast<Instruction>(V))
2582 Opcode = I->getOpcode();
2583 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2584 Opcode = CE->getOpcode();
2585 else if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
2586 return getConstant(CI);
2587 else if (isa<ConstantPointerNull>(V))
2588 return getIntegerSCEV(0, V->getType());
2589 else if (isa<UndefValue>(V))
2590 return getIntegerSCEV(0, V->getType());
2591 else
2592 return getUnknown(V);
2593
2594 User *U = cast<User>(V);
2595 switch (Opcode) {
2596 case Instruction::Add:
2597 return getAddExpr(getSCEV(U->getOperand(0)),
2598 getSCEV(U->getOperand(1)));
2599 case Instruction::Mul:
2600 return getMulExpr(getSCEV(U->getOperand(0)),
2601 getSCEV(U->getOperand(1)));
2602 case Instruction::UDiv:
2603 return getUDivExpr(getSCEV(U->getOperand(0)),
2604 getSCEV(U->getOperand(1)));
2605 case Instruction::Sub:
2606 return getMinusSCEV(getSCEV(U->getOperand(0)),
2607 getSCEV(U->getOperand(1)));
2608 case Instruction::And:
2609 // For an expression like x&255 that merely masks off the high bits,
2610 // use zext(trunc(x)) as the SCEV expression.
2611 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2612 if (CI->isNullValue())
2613 return getSCEV(U->getOperand(1));
2614 if (CI->isAllOnesValue())
2615 return getSCEV(U->getOperand(0));
2616 const APInt &A = CI->getValue();
2617
2618 // Instcombine's ShrinkDemandedConstant may strip bits out of
2619 // constants, obscuring what would otherwise be a low-bits mask.
2620 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
2621 // knew about to reconstruct a low-bits mask value.
2622 unsigned LZ = A.countLeadingZeros();
2623 unsigned BitWidth = A.getBitWidth();
2624 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
2625 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
2626 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
2627
2628 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
2629
2630 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
2631 return
2632 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2633 IntegerType::get(BitWidth - LZ)),
2634 U->getType());
2635 }
2636 break;
2637
2638 case Instruction::Or:
2639 // If the RHS of the Or is a constant, we may have something like:
2640 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2641 // optimizations will transparently handle this case.
2642 //
2643 // In order for this transformation to be safe, the LHS must be of the
2644 // form X*(2^n) and the Or constant must be less than 2^n.
2645 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2646 const SCEV* LHS = getSCEV(U->getOperand(0));
2647 const APInt &CIVal = CI->getValue();
2648 if (GetMinTrailingZeros(LHS) >=
2649 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2650 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2651 }
2652 break;
2653 case Instruction::Xor:
2654 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2655 // If the RHS of the xor is a signbit, then this is just an add.
2656 // Instcombine turns add of signbit into xor as a strength reduction step.
2657 if (CI->getValue().isSignBit())
2658 return getAddExpr(getSCEV(U->getOperand(0)),
2659 getSCEV(U->getOperand(1)));
2660
2661 // If the RHS of xor is -1, then this is a not operation.
2662 if (CI->isAllOnesValue())
2663 return getNotSCEV(getSCEV(U->getOperand(0)));
2664
2665 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2666 // This is a variant of the check for xor with -1, and it handles
2667 // the case where instcombine has trimmed non-demanded bits out
2668 // of an xor with -1.
2669 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2670 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2671 if (BO->getOpcode() == Instruction::And &&
2672 LCI->getValue() == CI->getValue())
2673 if (const SCEVZeroExtendExpr *Z =
2674 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
2675 const Type *UTy = U->getType();
2676 const SCEV* Z0 = Z->getOperand();
2677 const Type *Z0Ty = Z0->getType();
2678 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
2679
2680 // If C is a low-bits mask, the zero extend is zerving to
2681 // mask off the high bits. Complement the operand and
2682 // re-apply the zext.
2683 if (APIntOps::isMask(Z0TySize, CI->getValue()))
2684 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
2685
2686 // If C is a single bit, it may be in the sign-bit position
2687 // before the zero-extend. In this case, represent the xor
2688 // using an add, which is equivalent, and re-apply the zext.
2689 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
2690 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
2691 Trunc.isSignBit())
2692 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
2693 UTy);
2694 }
2695 }
2696 break;
2697
2698 case Instruction::Shl:
2699 // Turn shift left of a constant amount into a multiply.
2700 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2701 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2702 Constant *X = ConstantInt::get(
2703 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2704 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2705 }
2706 break;
2707
2708 case Instruction::LShr:
2709 // Turn logical shift right of a constant into a unsigned divide.
2710 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2711 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2712 Constant *X = ConstantInt::get(
2713 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2714 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2715 }
2716 break;
2717
2718 case Instruction::AShr:
2719 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2720 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2721 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2722 if (L->getOpcode() == Instruction::Shl &&
2723 L->getOperand(1) == U->getOperand(1)) {
2724 unsigned BitWidth = getTypeSizeInBits(U->getType());
2725 uint64_t Amt = BitWidth - CI->getZExtValue();
2726 if (Amt == BitWidth)
2727 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2728 if (Amt > BitWidth)
2729 return getIntegerSCEV(0, U->getType()); // value is undefined
2730 return
2731 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2732 IntegerType::get(Amt)),
2733 U->getType());
2734 }
2735 break;
2736
2737 case Instruction::Trunc:
2738 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2739
2740 case Instruction::ZExt:
2741 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2742
2743 case Instruction::SExt:
2744 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2745
2746 case Instruction::BitCast:
2747 // BitCasts are no-op casts so we just eliminate the cast.
2748 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2749 return getSCEV(U->getOperand(0));
2750 break;
2751
2752 case Instruction::IntToPtr:
2753 if (!TD) break; // Without TD we can't analyze pointers.
2754 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2755 TD->getIntPtrType());
2756
2757 case Instruction::PtrToInt:
2758 if (!TD) break; // Without TD we can't analyze pointers.
2759 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2760 U->getType());
2761
2762 case Instruction::GetElementPtr:
2763 if (!TD) break; // Without TD we can't analyze pointers.
2764 return createNodeForGEP(U);
2765
2766 case Instruction::PHI:
2767 return createNodeForPHI(cast<PHINode>(U));
2768
2769 case Instruction::Select:
2770 // This could be a smax or umax that was lowered earlier.
2771 // Try to recover it.
2772 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2773 Value *LHS = ICI->getOperand(0);
2774 Value *RHS = ICI->getOperand(1);
2775 switch (ICI->getPredicate()) {
2776 case ICmpInst::ICMP_SLT:
2777 case ICmpInst::ICMP_SLE:
2778 std::swap(LHS, RHS);
2779 // fall through
2780 case ICmpInst::ICMP_SGT:
2781 case ICmpInst::ICMP_SGE:
2782 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2783 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2784 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2785 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
2786 break;
2787 case ICmpInst::ICMP_ULT:
2788 case ICmpInst::ICMP_ULE:
2789 std::swap(LHS, RHS);
2790 // fall through
2791 case ICmpInst::ICMP_UGT:
2792 case ICmpInst::ICMP_UGE:
2793 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2794 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2795 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2796 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
2797 break;
2798 case ICmpInst::ICMP_NE:
2799 // n != 0 ? n : 1 -> umax(n, 1)
2800 if (LHS == U->getOperand(1) &&
2801 isa<ConstantInt>(U->getOperand(2)) &&
2802 cast<ConstantInt>(U->getOperand(2))->isOne() &&
2803 isa<ConstantInt>(RHS) &&
2804 cast<ConstantInt>(RHS)->isZero())
2805 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
2806 break;
2807 case ICmpInst::ICMP_EQ:
2808 // n == 0 ? 1 : n -> umax(n, 1)
2809 if (LHS == U->getOperand(2) &&
2810 isa<ConstantInt>(U->getOperand(1)) &&
2811 cast<ConstantInt>(U->getOperand(1))->isOne() &&
2812 isa<ConstantInt>(RHS) &&
2813 cast<ConstantInt>(RHS)->isZero())
2814 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
2815 break;
2816 default:
2817 break;
2818 }
2819 }
2820
2821 default: // We cannot analyze this expression.
2822 break;
2823 }
2824
2825 return getUnknown(V);
2826}
2827
2828
2829
2830//===----------------------------------------------------------------------===//
2831// Iteration Count Computation Code
2832//
2833
2834/// getBackedgeTakenCount - If the specified loop has a predictable
2835/// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2836/// object. The backedge-taken count is the number of times the loop header
2837/// will be branched to from within the loop. This is one less than the
2838/// trip count of the loop, since it doesn't count the first iteration,
2839/// when the header is branched to from outside the loop.
2840///
2841/// Note that it is not valid to call this method on a loop without a
2842/// loop-invariant backedge-taken count (see
2843/// hasLoopInvariantBackedgeTakenCount).
2844///
2845const SCEV* ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2846 return getBackedgeTakenInfo(L).Exact;
2847}
2848
2849/// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2850/// return the least SCEV value that is known never to be less than the
2851/// actual backedge taken count.
2852const SCEV* ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2853 return getBackedgeTakenInfo(L).Max;
2854}
2855
2856const ScalarEvolution::BackedgeTakenInfo &
2857ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2858 // Initially insert a CouldNotCompute for this loop. If the insertion
2859 // succeeds, procede to actually compute a backedge-taken count and
2860 // update the value. The temporary CouldNotCompute value tells SCEV
2861 // code elsewhere that it shouldn't attempt to request a new
2862 // backedge-taken count, which could result in infinite recursion.
2863 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2864 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2865 if (Pair.second) {
2866 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2867 if (ItCount.Exact != getCouldNotCompute()) {
2868 assert(ItCount.Exact->isLoopInvariant(L) &&
2869 ItCount.Max->isLoopInvariant(L) &&
2870 "Computed trip count isn't loop invariant for loop!");
2871 ++NumTripCountsComputed;
2872
2873 // Update the value in the map.
2874 Pair.first->second = ItCount;
2875 } else {
2876 if (ItCount.Max != getCouldNotCompute())
2877 // Update the value in the map.
2878 Pair.first->second = ItCount;
2879 if (isa<PHINode>(L->getHeader()->begin()))
2880 // Only count loops that have phi nodes as not being computable.
2881 ++NumTripCountsNotComputed;
2882 }
2883
2884 // Now that we know more about the trip count for this loop, forget any
2885 // existing SCEV values for PHI nodes in this loop since they are only
2886 // conservative estimates made without the benefit
2887 // of trip count information.
2888 if (ItCount.hasAnyInfo())
2889 forgetLoopPHIs(L);
2890 }
2891 return Pair.first->second;
2892}
2893
2894/// forgetLoopBackedgeTakenCount - This method should be called by the
2895/// client when it has changed a loop in a way that may effect
2896/// ScalarEvolution's ability to compute a trip count, or if the loop
2897/// is deleted.
2898void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2899 BackedgeTakenCounts.erase(L);
2900 forgetLoopPHIs(L);
2901}
2902
2903/// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2904/// PHI nodes in the given loop. This is used when the trip count of
2905/// the loop may have changed.
2906void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2907 BasicBlock *Header = L->getHeader();
2908
2909 // Push all Loop-header PHIs onto the Worklist stack, except those
2910 // that are presently represented via a SCEVUnknown. SCEVUnknown for
2911 // a PHI either means that it has an unrecognized structure, or it's
2912 // a PHI that's in the progress of being computed by createNodeForPHI.
2913 // In the former case, additional loop trip count information isn't
2914 // going to change anything. In the later case, createNodeForPHI will
2915 // perform the necessary updates on its own when it gets to that point.
2916 SmallVector<Instruction *, 16> Worklist;
2917 for (BasicBlock::iterator I = Header->begin();
2918 PHINode *PN = dyn_cast<PHINode>(I); ++I) {
2919 std::map<SCEVCallbackVH, const SCEV*>::iterator It =
2920 Scalars.find((Value*)I);
2921 if (It != Scalars.end() && !isa<SCEVUnknown>(It->second))
2922 Worklist.push_back(PN);
2923 }
2924
2925 while (!Worklist.empty()) {
2926 Instruction *I = Worklist.pop_back_val();
2927 if (Scalars.erase(I))
2928 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2929 UI != UE; ++UI)
2930 Worklist.push_back(cast<Instruction>(UI));
2931 }
2932}
2933
2934/// ComputeBackedgeTakenCount - Compute the number of times the backedge
2935/// of the specified loop will execute.
2936ScalarEvolution::BackedgeTakenInfo
2937ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2938 SmallVector<BasicBlock*, 8> ExitingBlocks;
2939 L->getExitingBlocks(ExitingBlocks);
2940
2941 // Examine all exits and pick the most conservative values.
2942 const SCEV* BECount = getCouldNotCompute();
2943 const SCEV* MaxBECount = getCouldNotCompute();
2944 bool CouldNotComputeBECount = false;
2945 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
2946 BackedgeTakenInfo NewBTI =
2947 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
2948
2949 if (NewBTI.Exact == getCouldNotCompute()) {
2950 // We couldn't compute an exact value for this exit, so
2951 // we won't be able to compute an exact value for the loop.
2952 CouldNotComputeBECount = true;
2953 BECount = getCouldNotCompute();
2954 } else if (!CouldNotComputeBECount) {
2955 if (BECount == getCouldNotCompute())
2956 BECount = NewBTI.Exact;
2957 else
2958 BECount = getUMinFromMismatchedTypes(BECount, NewBTI.Exact);
2959 }
2960 if (MaxBECount == getCouldNotCompute())
2961 MaxBECount = NewBTI.Max;
2962 else if (NewBTI.Max != getCouldNotCompute())
2963 MaxBECount = getUMinFromMismatchedTypes(MaxBECount, NewBTI.Max);
2964 }
2965
2966 return BackedgeTakenInfo(BECount, MaxBECount);
2967}
2968
2969/// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
2970/// of the specified loop will execute if it exits via the specified block.
2971ScalarEvolution::BackedgeTakenInfo
2972ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
2973 BasicBlock *ExitingBlock) {
2974
2975 // Okay, we've chosen an exiting block. See what condition causes us to
2976 // exit at this block.
2977 //
2978 // FIXME: we should be able to handle switch instructions (with a single exit)
2979 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2980 if (ExitBr == 0) return getCouldNotCompute();
2981 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2982
2983 // At this point, we know we have a conditional branch that determines whether
2984 // the loop is exited. However, we don't know if the branch is executed each
2985 // time through the loop. If not, then the execution count of the branch will
2986 // not be equal to the trip count of the loop.
2987 //
2988 // Currently we check for this by checking to see if the Exit branch goes to
2989 // the loop header. If so, we know it will always execute the same number of
2990 // times as the loop. We also handle the case where the exit block *is* the
2991 // loop header. This is common for un-rotated loops.
2992 //
2993 // If both of those tests fail, walk up the unique predecessor chain to the
2994 // header, stopping if there is an edge that doesn't exit the loop. If the
2995 // header is reached, the execution count of the branch will be equal to the
2996 // trip count of the loop.
2997 //
2998 // More extensive analysis could be done to handle more cases here.
2999 //
3000 if (ExitBr->getSuccessor(0) != L->getHeader() &&
3001 ExitBr->getSuccessor(1) != L->getHeader() &&
3002 ExitBr->getParent() != L->getHeader()) {
3003 // The simple checks failed, try climbing the unique predecessor chain
3004 // up to the header.
3005 bool Ok = false;
3006 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
3007 BasicBlock *Pred = BB->getUniquePredecessor();
3008 if (!Pred)
3009 return getCouldNotCompute();
3010 TerminatorInst *PredTerm = Pred->getTerminator();
3011 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
3012 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
3013 if (PredSucc == BB)
3014 continue;
3015 // If the predecessor has a successor that isn't BB and isn't
3016 // outside the loop, assume the worst.
3017 if (L->contains(PredSucc))
3018 return getCouldNotCompute();
3019 }
3020 if (Pred == L->getHeader()) {
3021 Ok = true;
3022 break;
3023 }
3024 BB = Pred;
3025 }
3026 if (!Ok)
3027 return getCouldNotCompute();
3028 }
3029
3030 // Procede to the next level to examine the exit condition expression.
3031 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
3032 ExitBr->getSuccessor(0),
3033 ExitBr->getSuccessor(1));
3034}
3035
3036/// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
3037/// backedge of the specified loop will execute if its exit condition
3038/// were a conditional branch of ExitCond, TBB, and FBB.
3039ScalarEvolution::BackedgeTakenInfo
3040ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
3041 Value *ExitCond,
3042 BasicBlock *TBB,
3043 BasicBlock *FBB) {
3044 // Check if the controlling expression for this loop is an And or Or.
3045 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
3046 if (BO->getOpcode() == Instruction::And) {
3047 // Recurse on the operands of the and.
3048 BackedgeTakenInfo BTI0 =
3049 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3050 BackedgeTakenInfo BTI1 =
3051 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3052 const SCEV* BECount = getCouldNotCompute();
3053 const SCEV* MaxBECount = getCouldNotCompute();
3054 if (L->contains(TBB)) {
3055 // Both conditions must be true for the loop to continue executing.
3056 // Choose the less conservative count.
3057 if (BTI0.Exact == getCouldNotCompute() ||
3058 BTI1.Exact == getCouldNotCompute())
3059 BECount = getCouldNotCompute();
3060 else
3061 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3062 if (BTI0.Max == getCouldNotCompute())
3063 MaxBECount = BTI1.Max;
3064 else if (BTI1.Max == getCouldNotCompute())
3065 MaxBECount = BTI0.Max;
3066 else
3067 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3068 } else {
3069 // Both conditions must be true for the loop to exit.
3070 assert(L->contains(FBB) && "Loop block has no successor in loop!");
3071 if (BTI0.Exact != getCouldNotCompute() &&
3072 BTI1.Exact != getCouldNotCompute())
3073 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3074 if (BTI0.Max != getCouldNotCompute() &&
3075 BTI1.Max != getCouldNotCompute())
3076 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3077 }
3078
3079 return BackedgeTakenInfo(BECount, MaxBECount);
3080 }
3081 if (BO->getOpcode() == Instruction::Or) {
3082 // Recurse on the operands of the or.
3083 BackedgeTakenInfo BTI0 =
3084 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
3085 BackedgeTakenInfo BTI1 =
3086 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
3087 const SCEV* BECount = getCouldNotCompute();
3088 const SCEV* MaxBECount = getCouldNotCompute();
3089 if (L->contains(FBB)) {
3090 // Both conditions must be false for the loop to continue executing.
3091 // Choose the less conservative count.
3092 if (BTI0.Exact == getCouldNotCompute() ||
3093 BTI1.Exact == getCouldNotCompute())
3094 BECount = getCouldNotCompute();
3095 else
3096 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3097 if (BTI0.Max == getCouldNotCompute())
3098 MaxBECount = BTI1.Max;
3099 else if (BTI1.Max == getCouldNotCompute())
3100 MaxBECount = BTI0.Max;
3101 else
3102 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
3103 } else {
3104 // Both conditions must be false for the loop to exit.
3105 assert(L->contains(TBB) && "Loop block has no successor in loop!");
3106 if (BTI0.Exact != getCouldNotCompute() &&
3107 BTI1.Exact != getCouldNotCompute())
3108 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
3109 if (BTI0.Max != getCouldNotCompute() &&
3110 BTI1.Max != getCouldNotCompute())
3111 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
3112 }
3113
3114 return BackedgeTakenInfo(BECount, MaxBECount);
3115 }
3116 }
3117
3118 // With an icmp, it may be feasible to compute an exact backedge-taken count.
3119 // Procede to the next level to examine the icmp.
3120 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
3121 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
3122
3123 // If it's not an integer or pointer comparison then compute it the hard way.
3124 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3125}
3126
3127/// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
3128/// backedge of the specified loop will execute if its exit condition
3129/// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
3130ScalarEvolution::BackedgeTakenInfo
3131ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
3132 ICmpInst *ExitCond,
3133 BasicBlock *TBB,
3134 BasicBlock *FBB) {
3135
3136 // If the condition was exit on true, convert the condition to exit on false
3137 ICmpInst::Predicate Cond;
3138 if (!L->contains(FBB))
3139 Cond = ExitCond->getPredicate();
3140 else
3141 Cond = ExitCond->getInversePredicate();
3142
3143 // Handle common loops like: for (X = "string"; *X; ++X)
3144 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
3145 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3146 const SCEV* ItCnt =
3147 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3148 if (!isa<SCEVCouldNotCompute>(ItCnt)) {
3149 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType());
3150 return BackedgeTakenInfo(ItCnt,
3151 isa<SCEVConstant>(ItCnt) ? ItCnt :
3152 getConstant(APInt::getMaxValue(BitWidth)-1));
3153 }
3154 }
3155
3156 const SCEV* LHS = getSCEV(ExitCond->getOperand(0));
3157 const SCEV* RHS = getSCEV(ExitCond->getOperand(1));
3158
3159 // Try to evaluate any dependencies out of the loop.
3160 LHS = getSCEVAtScope(LHS, L);
3161 RHS = getSCEVAtScope(RHS, L);
3162
3163 // At this point, we would like to compute how many iterations of the
3164 // loop the predicate will return true for these inputs.
3165 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3166 // If there is a loop-invariant, force it into the RHS.
3167 std::swap(LHS, RHS);
3168 Cond = ICmpInst::getSwappedPredicate(Cond);
3169 }
3170
3171 // If we have a comparison of a chrec against a constant, try to use value
3172 // ranges to answer this query.
3173 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3174 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3175 if (AddRec->getLoop() == L) {
3176 // Form the constant range.
3177 ConstantRange CompRange(
3178 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3179
3180 const SCEV* Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3181 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3182 }
3183
3184 switch (Cond) {
3185 case ICmpInst::ICMP_NE: { // while (X != Y)
3186 // Convert to: while (X-Y != 0)
3187 const SCEV* TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3188 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3189 break;
3190 }
3191 case ICmpInst::ICMP_EQ: {
3192 // Convert to: while (X-Y == 0) // while (X == Y)
3193 const SCEV* TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3194 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3195 break;
3196 }
3197 case ICmpInst::ICMP_SLT: {
3198 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3199 if (BTI.hasAnyInfo()) return BTI;
3200 break;
3201 }
3202 case ICmpInst::ICMP_SGT: {
3203 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3204 getNotSCEV(RHS), L, true);
3205 if (BTI.hasAnyInfo()) return BTI;
3206 break;
3207 }
3208 case ICmpInst::ICMP_ULT: {
3209 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3210 if (BTI.hasAnyInfo()) return BTI;
3211 break;
3212 }
3213 case ICmpInst::ICMP_UGT: {
3214 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3215 getNotSCEV(RHS), L, false);
3216 if (BTI.hasAnyInfo()) return BTI;
3217 break;
3218 }
3219 default:
3220#if 0
3221 errs() << "ComputeBackedgeTakenCount ";
3222 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3223 errs() << "[unsigned] ";
3224 errs() << *LHS << " "
3225 << Instruction::getOpcodeName(Instruction::ICmp)
3226 << " " << *RHS << "\n";
3227#endif
3228 break;
3229 }
3230 return
3231 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3232}
3233
3234static ConstantInt *
3235EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3236 ScalarEvolution &SE) {
3237 const SCEV* InVal = SE.getConstant(C);
3238 const SCEV* Val = AddRec->evaluateAtIteration(InVal, SE);
3239 assert(isa<SCEVConstant>(Val) &&
3240 "Evaluation of SCEV at constant didn't fold correctly?");
3241 return cast<SCEVConstant>(Val)->getValue();
3242}
3243
3244/// GetAddressedElementFromGlobal - Given a global variable with an initializer
3245/// and a GEP expression (missing the pointer index) indexing into it, return
3246/// the addressed element of the initializer or null if the index expression is
3247/// invalid.
3248static Constant *
3249GetAddressedElementFromGlobal(GlobalVariable *GV,
3250 const std::vector<ConstantInt*> &Indices) {
3251 Constant *Init = GV->getInitializer();
3252 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3253 uint64_t Idx = Indices[i]->getZExtValue();
3254 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3255 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3256 Init = cast<Constant>(CS->getOperand(Idx));
3257 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3258 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3259 Init = cast<Constant>(CA->getOperand(Idx));
3260 } else if (isa<ConstantAggregateZero>(Init)) {
3261 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3262 assert(Idx < STy->getNumElements() && "Bad struct index!");
3263 Init = Constant::getNullValue(STy->getElementType(Idx));
3264 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3265 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3266 Init = Constant::getNullValue(ATy->getElementType());
3267 } else {
3268 assert(0 && "Unknown constant aggregate type!");
3269 }
3270 return 0;
3271 } else {
3272 return 0; // Unknown initializer type
3273 }
3274 }
3275 return Init;
3276}
3277
3278/// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3279/// 'icmp op load X, cst', try to see if we can compute the backedge
3280/// execution count.
3281const SCEV *
3282ScalarEvolution::ComputeLoadConstantCompareBackedgeTakenCount(
3283 LoadInst *LI,
3284 Constant *RHS,
3285 const Loop *L,
3286 ICmpInst::Predicate predicate) {
3287 if (LI->isVolatile()) return getCouldNotCompute();
3288
3289 // Check to see if the loaded pointer is a getelementptr of a global.
3290 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3291 if (!GEP) return getCouldNotCompute();
3292
3293 // Make sure that it is really a constant global we are gepping, with an
3294 // initializer, and make sure the first IDX is really 0.
3295 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3296 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
3297 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3298 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3299 return getCouldNotCompute();
3300
3301 // Okay, we allow one non-constant index into the GEP instruction.
3302 Value *VarIdx = 0;
3303 std::vector<ConstantInt*> Indexes;
3304 unsigned VarIdxNum = 0;
3305 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3306 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3307 Indexes.push_back(CI);
3308 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3309 if (VarIdx) return getCouldNotCompute(); // Multiple non-constant idx's.
3310 VarIdx = GEP->getOperand(i);
3311 VarIdxNum = i-2;
3312 Indexes.push_back(0);
3313 }
3314
3315 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3316 // Check to see if X is a loop variant variable value now.
3317 const SCEV* Idx = getSCEV(VarIdx);
3318 Idx = getSCEVAtScope(Idx, L);
3319
3320 // We can only recognize very limited forms of loop index expressions, in
3321 // particular, only affine AddRec's like {C1,+,C2}.
3322 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3323 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3324 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3325 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
3326 return getCouldNotCompute();
3327
3328 unsigned MaxSteps = MaxBruteForceIterations;
3329 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3330 ConstantInt *ItCst =
3331 ConstantInt::get(cast<IntegerType>(IdxExpr->getType()), IterationNum);
3332 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
3333
3334 // Form the GEP offset.
3335 Indexes[VarIdxNum] = Val;
3336
3337 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
3338 if (Result == 0) break; // Cannot compute!
3339
3340 // Evaluate the condition for this iteration.
3341 Result = ConstantExpr::getICmp(predicate, Result, RHS);
3342 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
3343 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
3344#if 0
3345 errs() << "\n***\n*** Computed loop count " << *ItCst
3346 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
3347 << "***\n";
3348#endif
3349 ++NumArrayLenItCounts;
3350 return getConstant(ItCst); // Found terminating iteration!
3351 }
3352 }
3353 return getCouldNotCompute();
3354}
3355
3356
3357/// CanConstantFold - Return true if we can constant fold an instruction of the
3358/// specified type, assuming that all operands were constants.
3359static bool CanConstantFold(const Instruction *I) {
3360 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
3361 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
3362 return true;
3363
3364 if (const CallInst *CI = dyn_cast<CallInst>(I))
3365 if (const Function *F = CI->getCalledFunction())
3366 return canConstantFoldCallTo(F);
3367 return false;
3368}
3369
3370/// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
3371/// in the loop that V is derived from. We allow arbitrary operations along the
3372/// way, but the operands of an operation must either be constants or a value
3373/// derived from a constant PHI. If this expression does not fit with these
3374/// constraints, return null.
3375static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
3376 // If this is not an instruction, or if this is an instruction outside of the
3377 // loop, it can't be derived from a loop PHI.
3378 Instruction *I = dyn_cast<Instruction>(V);
3379 if (I == 0 || !L->contains(I->getParent())) return 0;
3380
3381 if (PHINode *PN = dyn_cast<PHINode>(I)) {
3382 if (L->getHeader() == I->getParent())
3383 return PN;
3384 else
3385 // We don't currently keep track of the control flow needed to evaluate
3386 // PHIs, so we cannot handle PHIs inside of loops.
3387 return 0;
3388 }
3389
3390 // If we won't be able to constant fold this expression even if the operands
3391 // are constants, return early.
3392 if (!CanConstantFold(I)) return 0;
3393
3394 // Otherwise, we can evaluate this instruction if all of its operands are
3395 // constant or derived from a PHI node themselves.
3396 PHINode *PHI = 0;
3397 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
3398 if (!(isa<Constant>(I->getOperand(Op)) ||
3399 isa<GlobalValue>(I->getOperand(Op)))) {
3400 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
3401 if (P == 0) return 0; // Not evolving from PHI
3402 if (PHI == 0)
3403 PHI = P;
3404 else if (PHI != P)
3405 return 0; // Evolving from multiple different PHIs.
3406 }
3407
3408 // This is a expression evolving from a constant PHI!
3409 return PHI;
3410}
3411
3412/// EvaluateExpression - Given an expression that passes the
3413/// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
3414/// in the loop has the value PHIVal. If we can't fold this expression for some
3415/// reason, return null.
3416static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
3417 if (isa<PHINode>(V)) return PHIVal;
3418 if (Constant *C = dyn_cast<Constant>(V)) return C;
3419 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
3420 Instruction *I = cast<Instruction>(V);
3421
3422 std::vector<Constant*> Operands;
3423 Operands.resize(I->getNumOperands());
3424
3425 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3426 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
3427 if (Operands[i] == 0) return 0;
3428 }
3429
3430 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3431 return ConstantFoldCompareInstOperands(CI->getPredicate(),
3432 &Operands[0], Operands.size());
3433 else
3434 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3435 &Operands[0], Operands.size());
3436}
3437
3438/// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
3439/// in the header of its containing loop, we know the loop executes a
3440/// constant number of times, and the PHI node is just a recurrence
3441/// involving constants, fold it.
3442Constant *
3443ScalarEvolution::getConstantEvolutionLoopExitValue(PHINode *PN,
3444 const APInt& BEs,
3445 const Loop *L) {
3446 std::map<PHINode*, Constant*>::iterator I =
3447 ConstantEvolutionLoopExitValue.find(PN);
3448 if (I != ConstantEvolutionLoopExitValue.end())
3449 return I->second;
3450
3451 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
3452 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
3453
3454 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
3455
3456 // Since the loop is canonicalized, the PHI node must have two entries. One
3457 // entry must be a constant (coming in from outside of the loop), and the
3458 // second must be derived from the same PHI.
3459 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3460 Constant *StartCST =
3461 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3462 if (StartCST == 0)
3463 return RetVal = 0; // Must be a constant.
3464
3465 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3466 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3467 if (PN2 != PN)
3468 return RetVal = 0; // Not derived from same PHI.
3469
3470 // Execute the loop symbolically to determine the exit value.
3471 if (BEs.getActiveBits() >= 32)
3472 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
3473
3474 unsigned NumIterations = BEs.getZExtValue(); // must be in range
3475 unsigned IterationNum = 0;
3476 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
3477 if (IterationNum == NumIterations)
3478 return RetVal = PHIVal; // Got exit value!
3479
3480 // Compute the value of the PHI node for the next iteration.
3481 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3482 if (NextPHI == PHIVal)
3483 return RetVal = NextPHI; // Stopped evolving!
3484 if (NextPHI == 0)
3485 return 0; // Couldn't evaluate!
3486 PHIVal = NextPHI;
3487 }
3488}
3489
3490/// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
3491/// constant number of times (the condition evolves only from constants),
3492/// try to evaluate a few iterations of the loop until we get the exit
3493/// condition gets a value of ExitWhen (true or false). If we cannot
3494/// evaluate the trip count of the loop, return getCouldNotCompute().
3495const SCEV *
3496ScalarEvolution::ComputeBackedgeTakenCountExhaustively(const Loop *L,
3497 Value *Cond,
3498 bool ExitWhen) {
3499 PHINode *PN = getConstantEvolvingPHI(Cond, L);
3500 if (PN == 0) return getCouldNotCompute();
3501
3502 // Since the loop is canonicalized, the PHI node must have two entries. One
3503 // entry must be a constant (coming in from outside of the loop), and the
3504 // second must be derived from the same PHI.
3505 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3506 Constant *StartCST =
3507 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3508 if (StartCST == 0) return getCouldNotCompute(); // Must be a constant.
3509
3510 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3511 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3512 if (PN2 != PN) return getCouldNotCompute(); // Not derived from same PHI.
3513
3514 // Okay, we find a PHI node that defines the trip count of this loop. Execute
3515 // the loop symbolically to determine when the condition gets a value of
3516 // "ExitWhen".
3517 unsigned IterationNum = 0;
3518 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
3519 for (Constant *PHIVal = StartCST;
3520 IterationNum != MaxIterations; ++IterationNum) {
3521 ConstantInt *CondVal =
3522 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
3523
3524 // Couldn't symbolically evaluate.
3525 if (!CondVal) return getCouldNotCompute();
3526
3527 if (CondVal->getValue() == uint64_t(ExitWhen)) {
3528 ++NumBruteForceTripCountsComputed;
3529 return getConstant(Type::Int32Ty, IterationNum);
3530 }
3531
3532 // Compute the value of the PHI node for the next iteration.
3533 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3534 if (NextPHI == 0 || NextPHI == PHIVal)
3535 return getCouldNotCompute();// Couldn't evaluate or not making progress...
3536 PHIVal = NextPHI;
3537 }
3538
3539 // Too many iterations were needed to evaluate.
3540 return getCouldNotCompute();
3541}
3542
3543/// getSCEVAtScope - Return a SCEV expression handle for the specified value
3544/// at the specified scope in the program. The L value specifies a loop
3545/// nest to evaluate the expression at, where null is the top-level or a
3546/// specified loop is immediately inside of the loop.
3547///
3548/// This method can be used to compute the exit value for a variable defined
3549/// in a loop by querying what the value will hold in the parent loop.
3550///
3551/// In the case that a relevant loop exit value cannot be computed, the
3552/// original value V is returned.
3553const SCEV* ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
3554 // FIXME: this should be turned into a virtual method on SCEV!
3555
3556 if (isa<SCEVConstant>(V)) return V;
3557
3558 // If this instruction is evolved from a constant-evolving PHI, compute the
3559 // exit value from the loop without using SCEVs.
3560 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
3561 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
3562 const Loop *LI = (*this->LI)[I->getParent()];
3563 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
3564 if (PHINode *PN = dyn_cast<PHINode>(I))
3565 if (PN->getParent() == LI->getHeader()) {
3566 // Okay, there is no closed form solution for the PHI node. Check
3567 // to see if the loop that contains it has a known backedge-taken
3568 // count. If so, we may be able to force computation of the exit
3569 // value.
3570 const SCEV* BackedgeTakenCount = getBackedgeTakenCount(LI);
3571 if (const SCEVConstant *BTCC =
3572 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
3573 // Okay, we know how many times the containing loop executes. If
3574 // this is a constant evolving PHI node, get the final value at
3575 // the specified iteration number.
3576 Constant *RV = getConstantEvolutionLoopExitValue(PN,
3577 BTCC->getValue()->getValue(),
3578 LI);
3579 if (RV) return getSCEV(RV);
3580 }
3581 }
3582
3583 // Okay, this is an expression that we cannot symbolically evaluate
3584 // into a SCEV. Check to see if it's possible to symbolically evaluate
3585 // the arguments into constants, and if so, try to constant propagate the
3586 // result. This is particularly useful for computing loop exit values.
3587 if (CanConstantFold(I)) {
3588 // Check to see if we've folded this instruction at this loop before.
3589 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
3590 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
3591 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
3592 if (!Pair.second)
3593 return Pair.first->second ? &*getSCEV(Pair.first->second) : V;
3594
3595 std::vector<Constant*> Operands;
3596 Operands.reserve(I->getNumOperands());
3597 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3598 Value *Op = I->getOperand(i);
3599 if (Constant *C = dyn_cast<Constant>(Op)) {
3600 Operands.push_back(C);
3601 } else {
3602 // If any of the operands is non-constant and if they are
3603 // non-integer and non-pointer, don't even try to analyze them
3604 // with scev techniques.
3605 if (!isSCEVable(Op->getType()))
3606 return V;
3607
3608 const SCEV* OpV = getSCEVAtScope(getSCEV(Op), L);
3609 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
3610 Constant *C = SC->getValue();
3611 if (C->getType() != Op->getType())
3612 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3613 Op->getType(),
3614 false),
3615 C, Op->getType());
3616 Operands.push_back(C);
3617 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
3618 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
3619 if (C->getType() != Op->getType())
3620 C =
3621 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3622 Op->getType(),
3623 false),
3624 C, Op->getType());
3625 Operands.push_back(C);
3626 } else
3627 return V;
3628 } else {
3629 return V;
3630 }
3631 }
3632 }
3633
3634 Constant *C;
3635 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3636 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
3637 &Operands[0], Operands.size());
3638 else
3639 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3640 &Operands[0], Operands.size());
3641 Pair.first->second = C;
3642 return getSCEV(C);
3643 }
3644 }
3645
3646 // This is some other type of SCEVUnknown, just return it.
3647 return V;
3648 }
3649
3650 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3651 // Avoid performing the look-up in the common case where the specified
3652 // expression has no loop-variant portions.
3653 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3654 const SCEV* OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3655 if (OpAtScope != Comm->getOperand(i)) {
3656 // Okay, at least one of these operands is loop variant but might be
3657 // foldable. Build a new instance of the folded commutative expression.
3658 SmallVector<const SCEV *, 8> NewOps(Comm->op_begin(),
3659 Comm->op_begin()+i);
3660 NewOps.push_back(OpAtScope);
3661
3662 for (++i; i != e; ++i) {
3663 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3664 NewOps.push_back(OpAtScope);
3665 }
3666 if (isa<SCEVAddExpr>(Comm))
3667 return getAddExpr(NewOps);
3668 if (isa<SCEVMulExpr>(Comm))
3669 return getMulExpr(NewOps);
3670 if (isa<SCEVSMaxExpr>(Comm))
3671 return getSMaxExpr(NewOps);
3672 if (isa<SCEVUMaxExpr>(Comm))
3673 return getUMaxExpr(NewOps);
3674 assert(0 && "Unknown commutative SCEV type!");
3675 }
3676 }
3677 // If we got here, all operands are loop invariant.
3678 return Comm;
3679 }
3680
3681 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3682 const SCEV* LHS = getSCEVAtScope(Div->getLHS(), L);
3683 const SCEV* RHS = getSCEVAtScope(Div->getRHS(), L);
3684 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3685 return Div; // must be loop invariant
3686 return getUDivExpr(LHS, RHS);
3687 }
3688
3689 // If this is a loop recurrence for a loop that does not contain L, then we
3690 // are dealing with the final value computed by the loop.
3691 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3692 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3693 // To evaluate this recurrence, we need to know how many times the AddRec
3694 // loop iterates. Compute this now.
3695 const SCEV* BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3696 if (BackedgeTakenCount == getCouldNotCompute()) return AddRec;
3697
3698 // Then, evaluate the AddRec.
3699 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3700 }
3701 return AddRec;
3702 }
3703
3704 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3705 const SCEV* Op = getSCEVAtScope(Cast->getOperand(), L);
3706 if (Op == Cast->getOperand())
3707 return Cast; // must be loop invariant
3708 return getZeroExtendExpr(Op, Cast->getType());
3709 }
3710
3711 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3712 const SCEV* Op = getSCEVAtScope(Cast->getOperand(), L);
3713 if (Op == Cast->getOperand())
3714 return Cast; // must be loop invariant
3715 return getSignExtendExpr(Op, Cast->getType());
3716 }
3717
3718 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3719 const SCEV* Op = getSCEVAtScope(Cast->getOperand(), L);
3720 if (Op == Cast->getOperand())
3721 return Cast; // must be loop invariant
3722 return getTruncateExpr(Op, Cast->getType());
3723 }
3724
3725 assert(0 && "Unknown SCEV type!");
3726 return 0;
3727}
3728
3729/// getSCEVAtScope - This is a convenience function which does
3730/// getSCEVAtScope(getSCEV(V), L).
3731const SCEV* ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3732 return getSCEVAtScope(getSCEV(V), L);
3733}
3734
3735/// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3736/// following equation:
3737///
3738/// A * X = B (mod N)
3739///
3740/// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3741/// A and B isn't important.
3742///
3743/// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3744static const SCEV* SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3745 ScalarEvolution &SE) {
3746 uint32_t BW = A.getBitWidth();
3747 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3748 assert(A != 0 && "A must be non-zero.");
3749
3750 // 1. D = gcd(A, N)
3751 //
3752 // The gcd of A and N may have only one prime factor: 2. The number of
3753 // trailing zeros in A is its multiplicity
3754 uint32_t Mult2 = A.countTrailingZeros();
3755 // D = 2^Mult2
3756
3757 // 2. Check if B is divisible by D.
3758 //
3759 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3760 // is not less than multiplicity of this prime factor for D.
3761 if (B.countTrailingZeros() < Mult2)
3762 return SE.getCouldNotCompute();
3763
3764 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3765 // modulo (N / D).
3766 //
3767 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3768 // bit width during computations.
3769 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3770 APInt Mod(BW + 1, 0);
3771 Mod.set(BW - Mult2); // Mod = N / D
3772 APInt I = AD.multiplicativeInverse(Mod);
3773
3774 // 4. Compute the minimum unsigned root of the equation:
3775 // I * (B / D) mod (N / D)
3776 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3777
3778 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3779 // bits.
3780 return SE.getConstant(Result.trunc(BW));
3781}
3782
3783/// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3784/// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
3785/// might be the same) or two SCEVCouldNotCompute objects.
3786///
3787static std::pair<const SCEV*,const SCEV*>
3788SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
3789 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
3790 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
3791 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
3792 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
3793
3794 // We currently can only solve this if the coefficients are constants.
3795 if (!LC || !MC || !NC) {
3796 const SCEV *CNC = SE.getCouldNotCompute();
3797 return std::make_pair(CNC, CNC);
3798 }
3799
3800 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
3801 const APInt &L = LC->getValue()->getValue();
3802 const APInt &M = MC->getValue()->getValue();
3803 const APInt &N = NC->getValue()->getValue();
3804 APInt Two(BitWidth, 2);
3805 APInt Four(BitWidth, 4);
3806
3807 {
3808 using namespace APIntOps;
3809 const APInt& C = L;
3810 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
3811 // The B coefficient is M-N/2
3812 APInt B(M);
3813 B -= sdiv(N,Two);
3814
3815 // The A coefficient is N/2
3816 APInt A(N.sdiv(Two));
3817
3818 // Compute the B^2-4ac term.
3819 APInt SqrtTerm(B);
3820 SqrtTerm *= B;
3821 SqrtTerm -= Four * (A * C);
3822
3823 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
3824 // integer value or else APInt::sqrt() will assert.
3825 APInt SqrtVal(SqrtTerm.sqrt());
3826
3827 // Compute the two solutions for the quadratic formula.
3828 // The divisions must be performed as signed divisions.
3829 APInt NegB(-B);
3830 APInt TwoA( A << 1 );
3831 if (TwoA.isMinValue()) {
3832 const SCEV *CNC = SE.getCouldNotCompute();
3833 return std::make_pair(CNC, CNC);
3834 }
3835
3836 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
3837 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
3838
3839 return std::make_pair(SE.getConstant(Solution1),
3840 SE.getConstant(Solution2));
3841 } // end APIntOps namespace
3842}
3843
3844/// HowFarToZero - Return the number of times a backedge comparing the specified
3845/// value to zero will execute. If not computable, return CouldNotCompute.
3846const SCEV* ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
3847 // If the value is a constant
3848 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3849 // If the value is already zero, the branch will execute zero times.
3850 if (C->getValue()->isZero()) return C;
3851 return getCouldNotCompute(); // Otherwise it will loop infinitely.
3852 }
3853
3854 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
3855 if (!AddRec || AddRec->getLoop() != L)
3856 return getCouldNotCompute();
3857
3858 if (AddRec->isAffine()) {
3859 // If this is an affine expression, the execution count of this branch is
3860 // the minimum unsigned root of the following equation:
3861 //
3862 // Start + Step*N = 0 (mod 2^BW)
3863 //
3864 // equivalent to:
3865 //
3866 // Step*N = -Start (mod 2^BW)
3867 //
3868 // where BW is the common bit width of Start and Step.
3869
3870 // Get the initial value for the loop.
3871 const SCEV *Start = getSCEVAtScope(AddRec->getStart(),
3872 L->getParentLoop());
3873 const SCEV *Step = getSCEVAtScope(AddRec->getOperand(1),
3874 L->getParentLoop());
3875
3876 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
3877 // For now we handle only constant steps.
3878
3879 // First, handle unitary steps.
3880 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
3881 return getNegativeSCEV(Start); // N = -Start (as unsigned)
3882 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
3883 return Start; // N = Start (as unsigned)
3884
3885 // Then, try to solve the above equation provided that Start is constant.
3886 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
3887 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
3888 -StartC->getValue()->getValue(),
3889 *this);
3890 }
3891 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
3892 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
3893 // the quadratic equation to solve it.
3894 std::pair<const SCEV*,const SCEV*> Roots = SolveQuadraticEquation(AddRec,
3895 *this);
3896 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3897 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3898 if (R1) {
3899#if 0
3900 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
3901 << " sol#2: " << *R2 << "\n";
3902#endif
3903 // Pick the smallest positive root value.
3904 if (ConstantInt *CB =
3905 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3906 R1->getValue(), R2->getValue()))) {
3907 if (CB->getZExtValue() == false)
3908 std::swap(R1, R2); // R1 is the minimum root now.
3909
3910 // We can only use this value if the chrec ends up with an exact zero
3911 // value at this index. When solving for "X*X != 5", for example, we
3912 // should not accept a root of 2.
3913 const SCEV* Val = AddRec->evaluateAtIteration(R1, *this);
3914 if (Val->isZero())
3915 return R1; // We found a quadratic root!
3916 }
3917 }
3918 }
3919
3920 return getCouldNotCompute();
3921}
3922
3923/// HowFarToNonZero - Return the number of times a backedge checking the
3924/// specified value for nonzero will execute. If not computable, return
3925/// CouldNotCompute
3926const SCEV* ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
3927 // Loops that look like: while (X == 0) are very strange indeed. We don't
3928 // handle them yet except for the trivial case. This could be expanded in the
3929 // future as needed.
3930
3931 // If the value is a constant, check to see if it is known to be non-zero
3932 // already. If so, the backedge will execute zero times.
3933 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3934 if (!C->getValue()->isNullValue())
3935 return getIntegerSCEV(0, C->getType());
3936 return getCouldNotCompute(); // Otherwise it will loop infinitely.
3937 }
3938
3939 // We could implement others, but I really doubt anyone writes loops like
3940 // this, and if they did, they would already be constant folded.
3941 return getCouldNotCompute();
3942}
3943
3944/// getLoopPredecessor - If the given loop's header has exactly one unique
3945/// predecessor outside the loop, return it. Otherwise return null.
3946///
3947BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
3948 BasicBlock *Header = L->getHeader();
3949 BasicBlock *Pred = 0;
3950 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
3951 PI != E; ++PI)
3952 if (!L->contains(*PI)) {
3953 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
3954 Pred = *PI;
3955 }
3956 return Pred;
3957}
3958
3959/// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3960/// (which may not be an immediate predecessor) which has exactly one
3961/// successor from which BB is reachable, or null if no such block is
3962/// found.
3963///
3964BasicBlock *
3965ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3966 // If the block has a unique predecessor, then there is no path from the
3967 // predecessor to the block that does not go through the direct edge
3968 // from the predecessor to the block.
3969 if (BasicBlock *Pred = BB->getSinglePredecessor())
3970 return Pred;
3971
3972 // A loop's header is defined to be a block that dominates the loop.
3973 // If the header has a unique predecessor outside the loop, it must be
3974 // a block that has exactly one successor that can reach the loop.
3975 if (Loop *L = LI->getLoopFor(BB))
3976 return getLoopPredecessor(L);
3977
3978 return 0;
3979}
3980
3981/// HasSameValue - SCEV structural equivalence is usually sufficient for
3982/// testing whether two expressions are equal, however for the purposes of
3983/// looking for a condition guarding a loop, it can be useful to be a little
3984/// more general, since a front-end may have replicated the controlling
3985/// expression.
3986///
3987static bool HasSameValue(const SCEV* A, const SCEV* B) {
3988 // Quick check to see if they are the same SCEV.
3989 if (A == B) return true;
3990
3991 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
3992 // two different instructions with the same value. Check for this case.
3993 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
3994 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
3995 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
3996 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
3997 if (AI->isIdenticalTo(BI))
3998 return true;
3999
4000 // Otherwise assume they may have a different value.
4001 return false;
4002}
4003
4004/// isLoopGuardedByCond - Test whether entry to the loop is protected by
4005/// a conditional between LHS and RHS. This is used to help avoid max
4006/// expressions in loop trip counts.
4007bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
4008 ICmpInst::Predicate Pred,
4009 const SCEV *LHS, const SCEV *RHS) {
4010 // Interpret a null as meaning no loop, where there is obviously no guard
4011 // (interprocedural conditions notwithstanding).
4012 if (!L) return false;
4013
4014 BasicBlock *Predecessor = getLoopPredecessor(L);
4015 BasicBlock *PredecessorDest = L->getHeader();
4016
4017 // Starting at the loop predecessor, climb up the predecessor chain, as long
4018 // as there are predecessors that can be found that have unique successors
4019 // leading to the original header.
4020 for (; Predecessor;
4021 PredecessorDest = Predecessor,
4022 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
4023
4024 BranchInst *LoopEntryPredicate =
4025 dyn_cast<BranchInst>(Predecessor->getTerminator());
4026 if (!LoopEntryPredicate ||
4027 LoopEntryPredicate->isUnconditional())
4028 continue;
4029
4030 if (isNecessaryCond(LoopEntryPredicate->getCondition(), Pred, LHS, RHS,
4031 LoopEntryPredicate->getSuccessor(0) != PredecessorDest))
4032 return true;
4033 }
4034
4035 return false;
4036}
4037
4038/// isNecessaryCond - Test whether the given CondValue value is a condition
4039/// which is at least as strict as the one described by Pred, LHS, and RHS.
4040bool ScalarEvolution::isNecessaryCond(Value *CondValue,
4041 ICmpInst::Predicate Pred,
4042 const SCEV *LHS, const SCEV *RHS,
4043 bool Inverse) {
4044 // Recursivly handle And and Or conditions.
4045 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(CondValue)) {
4046 if (BO->getOpcode() == Instruction::And) {
4047 if (!Inverse)
4048 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4049 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4050 } else if (BO->getOpcode() == Instruction::Or) {
4051 if (Inverse)
4052 return isNecessaryCond(BO->getOperand(0), Pred, LHS, RHS, Inverse) ||
4053 isNecessaryCond(BO->getOperand(1), Pred, LHS, RHS, Inverse);
4054 }
4055 }
4056
4057 ICmpInst *ICI = dyn_cast<ICmpInst>(CondValue);
4058 if (!ICI) return false;
4059
4060 // Now that we found a conditional branch that dominates the loop, check to
4061 // see if it is the comparison we are looking for.
4062 Value *PreCondLHS = ICI->getOperand(0);
4063 Value *PreCondRHS = ICI->getOperand(1);
4064 ICmpInst::Predicate Cond;
4065 if (Inverse)
4066 Cond = ICI->getInversePredicate();
4067 else
4068 Cond = ICI->getPredicate();
4069
4070 if (Cond == Pred)
4071 ; // An exact match.
4072 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
4073 ; // The actual condition is beyond sufficient.
4074 else
4075 // Check a few special cases.
4076 switch (Cond) {
4077 case ICmpInst::ICMP_UGT:
4078 if (Pred == ICmpInst::ICMP_ULT) {
4079 std::swap(PreCondLHS, PreCondRHS);
4080 Cond = ICmpInst::ICMP_ULT;
4081 break;
4082 }
4083 return false;
4084 case ICmpInst::ICMP_SGT:
4085 if (Pred == ICmpInst::ICMP_SLT) {
4086 std::swap(PreCondLHS, PreCondRHS);
4087 Cond = ICmpInst::ICMP_SLT;
4088 break;
4089 }
4090 return false;
4091 case ICmpInst::ICMP_NE:
4092 // Expressions like (x >u 0) are often canonicalized to (x != 0),
4093 // so check for this case by checking if the NE is comparing against
4094 // a minimum or maximum constant.
4095 if (!ICmpInst::isTrueWhenEqual(Pred))
4096 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
4097 const APInt &A = CI->getValue();
4098 switch (Pred) {
4099 case ICmpInst::ICMP_SLT:
4100 if (A.isMaxSignedValue()) break;
4101 return false;
4102 case ICmpInst::ICMP_SGT:
4103 if (A.isMinSignedValue()) break;
4104 return false;
4105 case ICmpInst::ICMP_ULT:
4106 if (A.isMaxValue()) break;
4107 return false;
4108 case ICmpInst::ICMP_UGT:
4109 if (A.isMinValue()) break;
4110 return false;
4111 default:
4112 return false;
4113 }
4114 Cond = ICmpInst::ICMP_NE;
4115 // NE is symmetric but the original comparison may not be. Swap
4116 // the operands if necessary so that they match below.
4117 if (isa<SCEVConstant>(LHS))
4118 std::swap(PreCondLHS, PreCondRHS);
4119 break;
4120 }
4121 return false;
4122 default:
4123 // We weren't able to reconcile the condition.
4124 return false;
4125 }
4126
4127 if (!PreCondLHS->getType()->isInteger()) return false;
4128
4129 const SCEV *PreCondLHSSCEV = getSCEV(PreCondLHS);
4130 const SCEV *PreCondRHSSCEV = getSCEV(PreCondRHS);
4131 return (HasSameValue(LHS, PreCondLHSSCEV) &&
4132 HasSameValue(RHS, PreCondRHSSCEV)) ||
4133 (HasSameValue(LHS, getNotSCEV(PreCondRHSSCEV)) &&
4134 HasSameValue(RHS, getNotSCEV(PreCondLHSSCEV)));
4135}
4136
4137/// getBECount - Subtract the end and start values and divide by the step,
4138/// rounding up, to get the number of times the backedge is executed. Return
4139/// CouldNotCompute if an intermediate computation overflows.
4140const SCEV* ScalarEvolution::getBECount(const SCEV* Start,
4141 const SCEV* End,
4142 const SCEV* Step) {
4143 const Type *Ty = Start->getType();
4144 const SCEV* NegOne = getIntegerSCEV(-1, Ty);
4145 const SCEV* Diff = getMinusSCEV(End, Start);
4146 const SCEV* RoundUp = getAddExpr(Step, NegOne);
4147
4148 // Add an adjustment to the difference between End and Start so that
4149 // the division will effectively round up.
4150 const SCEV* Add = getAddExpr(Diff, RoundUp);
4151
4152 // Check Add for unsigned overflow.
4153 // TODO: More sophisticated things could be done here.
4154 const Type *WideTy = IntegerType::get(getTypeSizeInBits(Ty) + 1);
4155 const SCEV* OperandExtendedAdd =
4156 getAddExpr(getZeroExtendExpr(Diff, WideTy),
4157 getZeroExtendExpr(RoundUp, WideTy));
4158 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
4159 return getCouldNotCompute();
4160
4161 return getUDivExpr(Add, Step);
4162}
4163
4164/// HowManyLessThans - Return the number of times a backedge containing the
4165/// specified less-than comparison will execute. If not computable, return
4166/// CouldNotCompute.
4167ScalarEvolution::BackedgeTakenInfo
4168ScalarEvolution::HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
4169 const Loop *L, bool isSigned) {
4170 // Only handle: "ADDREC < LoopInvariant".
4171 if (!RHS->isLoopInvariant(L)) return getCouldNotCompute();
4172
4173 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
4174 if (!AddRec || AddRec->getLoop() != L)
4175 return getCouldNotCompute();
4176
4177 if (AddRec->isAffine()) {
4178 // FORNOW: We only support unit strides.
4179 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
4180 const SCEV* Step = AddRec->getStepRecurrence(*this);
4181
4182 // TODO: handle non-constant strides.
4183 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
4184 if (!CStep || CStep->isZero())
4185 return getCouldNotCompute();
4186 if (CStep->isOne()) {
4187 // With unit stride, the iteration never steps past the limit value.
4188 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
4189 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
4190 // Test whether a positive iteration iteration can step past the limit
4191 // value and past the maximum value for its type in a single step.
4192 if (isSigned) {
4193 APInt Max = APInt::getSignedMaxValue(BitWidth);
4194 if ((Max - CStep->getValue()->getValue())
4195 .slt(CLimit->getValue()->getValue()))
4196 return getCouldNotCompute();
4197 } else {
4198 APInt Max = APInt::getMaxValue(BitWidth);
4199 if ((Max - CStep->getValue()->getValue())
4200 .ult(CLimit->getValue()->getValue()))
4201 return getCouldNotCompute();
4202 }
4203 } else
4204 // TODO: handle non-constant limit values below.
4205 return getCouldNotCompute();
4206 } else
4207 // TODO: handle negative strides below.
4208 return getCouldNotCompute();
4209
4210 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
4211 // m. So, we count the number of iterations in which {n,+,s} < m is true.
4212 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
4213 // treat m-n as signed nor unsigned due to overflow possibility.
4214
4215 // First, we get the value of the LHS in the first iteration: n
4216 const SCEV* Start = AddRec->getOperand(0);
4217
4218 // Determine the minimum constant start value.
4219 const SCEV *MinStart = isa<SCEVConstant>(Start) ? Start :
4220 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
4221 APInt::getMinValue(BitWidth));
4222
4223 // If we know that the condition is true in order to enter the loop,
4224 // then we know that it will run exactly (m-n)/s times. Otherwise, we
4225 // only know that it will execute (max(m,n)-n)/s times. In both cases,
4226 // the division must round up.
4227 const SCEV* End = RHS;
4228 if (!isLoopGuardedByCond(L,
4229 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
4230 getMinusSCEV(Start, Step), RHS))
4231 End = isSigned ? getSMaxExpr(RHS, Start)
4232 : getUMaxExpr(RHS, Start);
4233
4234 // Determine the maximum constant end value.
4235 const SCEV* MaxEnd =
4236 isa<SCEVConstant>(End) ? End :
4237 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth)
4238 .ashr(GetMinSignBits(End) - 1) :
4239 APInt::getMaxValue(BitWidth)
4240 .lshr(GetMinLeadingZeros(End)));
4241
4242 // Finally, we subtract these two values and divide, rounding up, to get
4243 // the number of times the backedge is executed.
4244 const SCEV* BECount = getBECount(Start, End, Step);
4245
4246 // The maximum backedge count is similar, except using the minimum start
4247 // value and the maximum end value.
4248 const SCEV* MaxBECount = getBECount(MinStart, MaxEnd, Step);
4249
4250 return BackedgeTakenInfo(BECount, MaxBECount);
4251 }
4252
4253 return getCouldNotCompute();
4254}
4255
4256/// getNumIterationsInRange - Return the number of iterations of this loop that
4257/// produce values in the specified constant range. Another way of looking at
4258/// this is that it returns the first iteration number where the value is not in
4259/// the condition, thus computing the exit count. If the iteration count can't
4260/// be computed, an instance of SCEVCouldNotCompute is returned.
4261const SCEV* SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
4262 ScalarEvolution &SE) const {
4263 if (Range.isFullSet()) // Infinite loop.
4264 return SE.getCouldNotCompute();
4265
4266 // If the start is a non-zero constant, shift the range to simplify things.
4267 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
4268 if (!SC->getValue()->isZero()) {
4269 SmallVector<const SCEV*, 4> Operands(op_begin(), op_end());
4270 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
4271 const SCEV* Shifted = SE.getAddRecExpr(Operands, getLoop());
4272 if (const SCEVAddRecExpr *ShiftedAddRec =
4273 dyn_cast<SCEVAddRecExpr>(Shifted))
4274 return ShiftedAddRec->getNumIterationsInRange(
4275 Range.subtract(SC->getValue()->getValue()), SE);
4276 // This is strange and shouldn't happen.
4277 return SE.getCouldNotCompute();
4278 }
4279
4280 // The only time we can solve this is when we have all constant indices.
4281 // Otherwise, we cannot determine the overflow conditions.
4282 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
4283 if (!isa<SCEVConstant>(getOperand(i)))
4284 return SE.getCouldNotCompute();
4285
4286
4287 // Okay at this point we know that all elements of the chrec are constants and
4288 // that the start element is zero.
4289
4290 // First check to see if the range contains zero. If not, the first
4291 // iteration exits.
4292 unsigned BitWidth = SE.getTypeSizeInBits(getType());
4293 if (!Range.contains(APInt(BitWidth, 0)))
4294 return SE.getIntegerSCEV(0, getType());
4295
4296 if (isAffine()) {
4297 // If this is an affine expression then we have this situation:
4298 // Solve {0,+,A} in Range === Ax in Range
4299
4300 // We know that zero is in the range. If A is positive then we know that
4301 // the upper value of the range must be the first possible exit value.
4302 // If A is negative then the lower of the range is the last possible loop
4303 // value. Also note that we already checked for a full range.
4304 APInt One(BitWidth,1);
4305 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
4306 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
4307
4308 // The exit value should be (End+A)/A.
4309 APInt ExitVal = (End + A).udiv(A);
4310 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
4311
4312 // Evaluate at the exit value. If we really did fall out of the valid
4313 // range, then we computed our trip count, otherwise wrap around or other
4314 // things must have happened.
4315 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
4316 if (Range.contains(Val->getValue()))
4317 return SE.getCouldNotCompute(); // Something strange happened
4318
4319 // Ensure that the previous value is in the range. This is a sanity check.
4320 assert(Range.contains(
4321 EvaluateConstantChrecAtConstant(this,
4322 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
4323 "Linear scev computation is off in a bad way!");
4324 return SE.getConstant(ExitValue);
4325 } else if (isQuadratic()) {
4326 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
4327 // quadratic equation to solve it. To do this, we must frame our problem in
4328 // terms of figuring out when zero is crossed, instead of when
4329 // Range.getUpper() is crossed.
4330 SmallVector<const SCEV*, 4> NewOps(op_begin(), op_end());
4331 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
4332 const SCEV* NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
4333
4334 // Next, solve the constructed addrec
4335 std::pair<const SCEV*,const SCEV*> Roots =
4336 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
4337 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4338 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4339 if (R1) {
4340 // Pick the smallest positive root value.
4341 if (ConstantInt *CB =
4342 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4343 R1->getValue(), R2->getValue()))) {
4344 if (CB->getZExtValue() == false)
4345 std::swap(R1, R2); // R1 is the minimum root now.
4346
4347 // Make sure the root is not off by one. The returned iteration should
4348 // not be in the range, but the previous one should be. When solving
4349 // for "X*X < 5", for example, we should not return a root of 2.
4350 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
4351 R1->getValue(),
4352 SE);
4353 if (Range.contains(R1Val->getValue())) {
4354 // The next iteration must be out of the range...
4355 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
4356
4357 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4358 if (!Range.contains(R1Val->getValue()))
4359 return SE.getConstant(NextVal);
4360 return SE.getCouldNotCompute(); // Something strange happened
4361 }
4362
4363 // If R1 was not in the range, then it is a good return value. Make
4364 // sure that R1-1 WAS in the range though, just in case.
4365 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
4366 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4367 if (Range.contains(R1Val->getValue()))
4368 return R1;
4369 return SE.getCouldNotCompute(); // Something strange happened
4370 }
4371 }
4372 }
4373
4374 return SE.getCouldNotCompute();
4375}
4376
4377
4378
4379//===----------------------------------------------------------------------===//
4380// SCEVCallbackVH Class Implementation
4381//===----------------------------------------------------------------------===//
4382
4383void ScalarEvolution::SCEVCallbackVH::deleted() {
4384 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
4385 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
4386 SE->ConstantEvolutionLoopExitValue.erase(PN);
4387 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
4388 SE->ValuesAtScopes.erase(I);
4389 SE->Scalars.erase(getValPtr());
4390 // this now dangles!
4391}
4392
4393void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
4394 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
4395
4396 // Forget all the expressions associated with users of the old value,
4397 // so that future queries will recompute the expressions using the new
4398 // value.
4399 SmallVector<User *, 16> Worklist;
4400 Value *Old = getValPtr();
4401 bool DeleteOld = false;
4402 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
4403 UI != UE; ++UI)
4404 Worklist.push_back(*UI);
4405 while (!Worklist.empty()) {
4406 User *U = Worklist.pop_back_val();
4407 // Deleting the Old value will cause this to dangle. Postpone
4408 // that until everything else is done.
4409 if (U == Old) {
4410 DeleteOld = true;
4411 continue;
4412 }
4413 if (PHINode *PN = dyn_cast<PHINode>(U))
4414 SE->ConstantEvolutionLoopExitValue.erase(PN);
4415 if (Instruction *I = dyn_cast<Instruction>(U))
4416 SE->ValuesAtScopes.erase(I);
4417 if (SE->Scalars.erase(U))
4418 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
4419 UI != UE; ++UI)
4420 Worklist.push_back(*UI);
4421 }
4422 if (DeleteOld) {
4423 if (PHINode *PN = dyn_cast<PHINode>(Old))
4424 SE->ConstantEvolutionLoopExitValue.erase(PN);
4425 if (Instruction *I = dyn_cast<Instruction>(Old))
4426 SE->ValuesAtScopes.erase(I);
4427 SE->Scalars.erase(Old);
4428 // this now dangles!
4429 }
4430 // this may dangle!
4431}
4432
4433ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
4434 : CallbackVH(V), SE(se) {}
4435
4436//===----------------------------------------------------------------------===//
4437// ScalarEvolution Class Implementation
4438//===----------------------------------------------------------------------===//
4439
4440ScalarEvolution::ScalarEvolution()
4441 : FunctionPass(&ID) {
4442}
4443
4444bool ScalarEvolution::runOnFunction(Function &F) {
4445 this->F = &F;
4446 LI = &getAnalysis<LoopInfo>();
4447 TD = getAnalysisIfAvailable<TargetData>();
4448 return false;
4449}
4450
4451void ScalarEvolution::releaseMemory() {
4452 Scalars.clear();
4453 BackedgeTakenCounts.clear();
4454 ConstantEvolutionLoopExitValue.clear();
4455 ValuesAtScopes.clear();
4456 UniqueSCEVs.clear();
4457 SCEVAllocator.Reset();
4458}
4459
4460void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
4461 AU.setPreservesAll();
4462 AU.addRequiredTransitive<LoopInfo>();
4463}
4464
4465bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
4466 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
4467}
4468
4469static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
4470 const Loop *L) {
4471 // Print all inner loops first
4472 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4473 PrintLoopInfo(OS, SE, *I);
4474
4475 OS << "Loop " << L->getHeader()->getName() << ": ";
4476
4477 SmallVector<BasicBlock*, 8> ExitBlocks;
4478 L->getExitBlocks(ExitBlocks);
4479 if (ExitBlocks.size() != 1)
4480 OS << "<multiple exits> ";
4481
4482 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
4483 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
4484 } else {
4485 OS << "Unpredictable backedge-taken count. ";
4486 }
4487
4488 OS << "\n";
4489 OS << "Loop " << L->getHeader()->getName() << ": ";
4490
4491 if (!isa<SCEVCouldNotCompute>(SE->getMaxBackedgeTakenCount(L))) {
4492 OS << "max backedge-taken count is " << *SE->getMaxBackedgeTakenCount(L);
4493 } else {
4494 OS << "Unpredictable max backedge-taken count. ";
4495 }
4496
4497 OS << "\n";
4498}
4499
4500void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
4501 // ScalarEvolution's implementaiton of the print method is to print
4502 // out SCEV values of all instructions that are interesting. Doing
4503 // this potentially causes it to create new SCEV objects though,
4504 // which technically conflicts with the const qualifier. This isn't
4505 // observable from outside the class though (the hasSCEV function
4506 // notwithstanding), so casting away the const isn't dangerous.
4507 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
4508
4509 OS << "Classifying expressions for: " << F->getName() << "\n";
4510 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
4511 if (isSCEVable(I->getType())) {
4512 OS << *I;
4513 OS << " --> ";
4514 const SCEV* SV = SE.getSCEV(&*I);
4515 SV->print(OS);
4516
4517 const Loop *L = LI->getLoopFor((*I).getParent());
4518
4519 const SCEV* AtUse = SE.getSCEVAtScope(SV, L);
4520 if (AtUse != SV) {
4521 OS << " --> ";
4522 AtUse->print(OS);
4523 }
4524
4525 if (L) {
4526 OS << "\t\t" "Exits: ";
4527 const SCEV* ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
4528 if (!ExitValue->isLoopInvariant(L)) {
4529 OS << "<<Unknown>>";
4530 } else {
4531 OS << *ExitValue;
4532 }
4533 }
4534
4535 OS << "\n";
4536 }
4537
4538 OS << "Determining loop execution counts for: " << F->getName() << "\n";
4539 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
4540 PrintLoopInfo(OS, &SE, *I);
4541}
4542
4543void ScalarEvolution::print(std::ostream &o, const Module *M) const {
4544 raw_os_ostream OS(o);
4545 print(OS, M);
4546}