1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/Dominators.h"
70 #include "llvm/Analysis/LoopInfo.h"
71 #include "llvm/Assembly/Writer.h"
72 #include "llvm/Target/TargetData.h"
73 #include "llvm/Support/CommandLine.h"
74 #include "llvm/Support/Compiler.h"
75 #include "llvm/Support/ConstantRange.h"
76 #include "llvm/Support/GetElementPtrTypeIterator.h"
77 #include "llvm/Support/InstIterator.h"
78 #include "llvm/Support/ManagedStatic.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"
86 STATISTIC(NumArrayLenItCounts,
87 "Number of trip counts computed with array length");
88 STATISTIC(NumTripCountsComputed,
89 "Number of loops with predictable loop counts");
90 STATISTIC(NumTripCountsNotComputed,
91 "Number of loops without predictable loop counts");
92 STATISTIC(NumBruteForceTripCountsComputed,
93 "Number of loops with trip counts computed by force");
95 static cl::opt<unsigned>
96 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
97 cl::desc("Maximum number of iterations SCEV will "
98 "symbolically execute a constant derived loop"),
101 static RegisterPass<ScalarEvolution>
102 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
103 char ScalarEvolution::ID = 0;
105 //===----------------------------------------------------------------------===//
106 // SCEV class definitions
107 //===----------------------------------------------------------------------===//
109 //===----------------------------------------------------------------------===//
110 // Implementation of the SCEV class.
113 void SCEV::dump() const {
118 void SCEV::print(std::ostream &o) const {
119 raw_os_ostream OS(o);
123 bool SCEV::isZero() const {
124 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
125 return SC->getValue()->isZero();
129 bool SCEV::isOne() const {
130 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
131 return SC->getValue()->isOne();
135 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
136 SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
138 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
139 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
143 const Type *SCEVCouldNotCompute::getType() const {
144 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
148 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
149 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
153 SCEVHandle SCEVCouldNotCompute::
154 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
155 const SCEVHandle &Conc,
156 ScalarEvolution &SE) const {
160 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
161 OS << "***COULDNOTCOMPUTE***";
164 bool SCEVCouldNotCompute::classof(const SCEV *S) {
165 return S->getSCEVType() == scCouldNotCompute;
169 // SCEVConstants - Only allow the creation of one SCEVConstant for any
170 // particular value. Don't use a SCEVHandle here, or else the object will
172 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
175 SCEVConstant::~SCEVConstant() {
176 SCEVConstants->erase(V);
179 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
180 SCEVConstant *&R = (*SCEVConstants)[V];
181 if (R == 0) R = new SCEVConstant(V);
185 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
186 return getConstant(ConstantInt::get(Val));
189 const Type *SCEVConstant::getType() const { return V->getType(); }
191 void SCEVConstant::print(raw_ostream &OS) const {
192 WriteAsOperand(OS, V, false);
195 SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
196 const SCEVHandle &op, const Type *ty)
197 : SCEV(SCEVTy), Op(op), Ty(ty) {}
199 SCEVCastExpr::~SCEVCastExpr() {}
201 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
202 return Op->dominates(BB, DT);
205 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
206 // particular input. Don't use a SCEVHandle here, or else the object will
208 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
209 SCEVTruncateExpr*> > SCEVTruncates;
211 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
212 : SCEVCastExpr(scTruncate, op, ty) {
213 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
214 (Ty->isInteger() || isa<PointerType>(Ty)) &&
215 "Cannot truncate non-integer value!");
218 SCEVTruncateExpr::~SCEVTruncateExpr() {
219 SCEVTruncates->erase(std::make_pair(Op, Ty));
222 void SCEVTruncateExpr::print(raw_ostream &OS) const {
223 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
226 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
227 // particular input. Don't use a SCEVHandle here, or else the object will never
229 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
230 SCEVZeroExtendExpr*> > SCEVZeroExtends;
232 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
233 : SCEVCastExpr(scZeroExtend, op, ty) {
234 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
235 (Ty->isInteger() || isa<PointerType>(Ty)) &&
236 "Cannot zero extend non-integer value!");
239 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
240 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
243 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
244 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
247 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
248 // particular input. Don't use a SCEVHandle here, or else the object will never
250 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
251 SCEVSignExtendExpr*> > SCEVSignExtends;
253 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
254 : SCEVCastExpr(scSignExtend, op, ty) {
255 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
256 (Ty->isInteger() || isa<PointerType>(Ty)) &&
257 "Cannot sign extend non-integer value!");
260 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
261 SCEVSignExtends->erase(std::make_pair(Op, Ty));
264 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
265 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
268 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
269 // particular input. Don't use a SCEVHandle here, or else the object will never
271 static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >,
272 SCEVCommutativeExpr*> > SCEVCommExprs;
274 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
275 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
276 SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps));
279 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
280 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
281 const char *OpStr = getOperationStr();
282 OS << "(" << *Operands[0];
283 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
284 OS << OpStr << *Operands[i];
288 SCEVHandle SCEVCommutativeExpr::
289 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
290 const SCEVHandle &Conc,
291 ScalarEvolution &SE) const {
292 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
294 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
295 if (H != getOperand(i)) {
296 SmallVector<SCEVHandle, 8> NewOps;
297 NewOps.reserve(getNumOperands());
298 for (unsigned j = 0; j != i; ++j)
299 NewOps.push_back(getOperand(j));
301 for (++i; i != e; ++i)
302 NewOps.push_back(getOperand(i)->
303 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
305 if (isa<SCEVAddExpr>(this))
306 return SE.getAddExpr(NewOps);
307 else if (isa<SCEVMulExpr>(this))
308 return SE.getMulExpr(NewOps);
309 else if (isa<SCEVSMaxExpr>(this))
310 return SE.getSMaxExpr(NewOps);
311 else if (isa<SCEVUMaxExpr>(this))
312 return SE.getUMaxExpr(NewOps);
314 assert(0 && "Unknown commutative expr!");
320 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
321 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
322 if (!getOperand(i)->dominates(BB, DT))
329 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
330 // input. Don't use a SCEVHandle here, or else the object will never be
332 static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>,
333 SCEVUDivExpr*> > SCEVUDivs;
335 SCEVUDivExpr::~SCEVUDivExpr() {
336 SCEVUDivs->erase(std::make_pair(LHS, RHS));
339 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
340 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
343 void SCEVUDivExpr::print(raw_ostream &OS) const {
344 OS << "(" << *LHS << " /u " << *RHS << ")";
347 const Type *SCEVUDivExpr::getType() const {
348 // In most cases the types of LHS and RHS will be the same, but in some
349 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
350 // depend on the type for correctness, but handling types carefully can
351 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
352 // a pointer type than the RHS, so use the RHS' type here.
353 return RHS->getType();
356 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
357 // particular input. Don't use a SCEVHandle here, or else the object will never
359 static ManagedStatic<std::map<std::pair<const Loop *,
360 std::vector<const SCEV*> >,
361 SCEVAddRecExpr*> > SCEVAddRecExprs;
363 SCEVAddRecExpr::~SCEVAddRecExpr() {
364 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
365 SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps));
368 SCEVHandle SCEVAddRecExpr::
369 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
370 const SCEVHandle &Conc,
371 ScalarEvolution &SE) const {
372 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
374 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
375 if (H != getOperand(i)) {
376 SmallVector<SCEVHandle, 8> NewOps;
377 NewOps.reserve(getNumOperands());
378 for (unsigned j = 0; j != i; ++j)
379 NewOps.push_back(getOperand(j));
381 for (++i; i != e; ++i)
382 NewOps.push_back(getOperand(i)->
383 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
385 return SE.getAddRecExpr(NewOps, L);
392 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
393 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
394 // contain L and if the start is invariant.
395 // Add recurrences are never invariant in the function-body (null loop).
397 !QueryLoop->contains(L->getHeader()) &&
398 getOperand(0)->isLoopInvariant(QueryLoop);
402 void SCEVAddRecExpr::print(raw_ostream &OS) const {
403 OS << "{" << *Operands[0];
404 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
405 OS << ",+," << *Operands[i];
406 OS << "}<" << L->getHeader()->getName() + ">";
409 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
410 // value. Don't use a SCEVHandle here, or else the object will never be
412 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
414 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
416 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
417 // All non-instruction values are loop invariant. All instructions are loop
418 // invariant if they are not contained in the specified loop.
419 // Instructions are never considered invariant in the function body
420 // (null loop) because they are defined within the "loop".
421 if (Instruction *I = dyn_cast<Instruction>(V))
422 return L && !L->contains(I->getParent());
426 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
427 if (Instruction *I = dyn_cast<Instruction>(getValue()))
428 return DT->dominates(I->getParent(), BB);
432 const Type *SCEVUnknown::getType() const {
436 void SCEVUnknown::print(raw_ostream &OS) const {
437 WriteAsOperand(OS, V, false);
440 //===----------------------------------------------------------------------===//
442 //===----------------------------------------------------------------------===//
445 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
446 /// than the complexity of the RHS. This comparator is used to canonicalize
448 class VISIBILITY_HIDDEN SCEVComplexityCompare {
451 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
453 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
454 // Primarily, sort the SCEVs by their getSCEVType().
455 if (LHS->getSCEVType() != RHS->getSCEVType())
456 return LHS->getSCEVType() < RHS->getSCEVType();
458 // Aside from the getSCEVType() ordering, the particular ordering
459 // isn't very important except that it's beneficial to be consistent,
460 // so that (a + b) and (b + a) don't end up as different expressions.
462 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
463 // not as complete as it could be.
464 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
465 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
467 // Order pointer values after integer values. This helps SCEVExpander
469 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
471 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
474 // Compare getValueID values.
475 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
476 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
478 // Sort arguments by their position.
479 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
480 const Argument *RA = cast<Argument>(RU->getValue());
481 return LA->getArgNo() < RA->getArgNo();
484 // For instructions, compare their loop depth, and their opcode.
485 // This is pretty loose.
486 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
487 Instruction *RV = cast<Instruction>(RU->getValue());
489 // Compare loop depths.
490 if (LI->getLoopDepth(LV->getParent()) !=
491 LI->getLoopDepth(RV->getParent()))
492 return LI->getLoopDepth(LV->getParent()) <
493 LI->getLoopDepth(RV->getParent());
496 if (LV->getOpcode() != RV->getOpcode())
497 return LV->getOpcode() < RV->getOpcode();
499 // Compare the number of operands.
500 if (LV->getNumOperands() != RV->getNumOperands())
501 return LV->getNumOperands() < RV->getNumOperands();
507 // Compare constant values.
508 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
509 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
510 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
513 // Compare addrec loop depths.
514 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
515 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
516 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
517 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
520 // Lexicographically compare n-ary expressions.
521 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
522 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
523 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
524 if (i >= RC->getNumOperands())
526 if (operator()(LC->getOperand(i), RC->getOperand(i)))
528 if (operator()(RC->getOperand(i), LC->getOperand(i)))
531 return LC->getNumOperands() < RC->getNumOperands();
534 // Lexicographically compare udiv expressions.
535 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
536 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
537 if (operator()(LC->getLHS(), RC->getLHS()))
539 if (operator()(RC->getLHS(), LC->getLHS()))
541 if (operator()(LC->getRHS(), RC->getRHS()))
543 if (operator()(RC->getRHS(), LC->getRHS()))
548 // Compare cast expressions by operand.
549 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
550 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
551 return operator()(LC->getOperand(), RC->getOperand());
554 assert(0 && "Unknown SCEV kind!");
560 /// GroupByComplexity - Given a list of SCEV objects, order them by their
561 /// complexity, and group objects of the same complexity together by value.
562 /// When this routine is finished, we know that any duplicates in the vector are
563 /// consecutive and that complexity is monotonically increasing.
565 /// Note that we go take special precautions to ensure that we get determinstic
566 /// results from this routine. In other words, we don't want the results of
567 /// this to depend on where the addresses of various SCEV objects happened to
570 static void GroupByComplexity(SmallVectorImpl<SCEVHandle> &Ops,
572 if (Ops.size() < 2) return; // Noop
573 if (Ops.size() == 2) {
574 // This is the common case, which also happens to be trivially simple.
576 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
577 std::swap(Ops[0], Ops[1]);
581 // Do the rough sort by complexity.
582 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
584 // Now that we are sorted by complexity, group elements of the same
585 // complexity. Note that this is, at worst, N^2, but the vector is likely to
586 // be extremely short in practice. Note that we take this approach because we
587 // do not want to depend on the addresses of the objects we are grouping.
588 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
589 const SCEV *S = Ops[i];
590 unsigned Complexity = S->getSCEVType();
592 // If there are any objects of the same complexity and same value as this
594 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
595 if (Ops[j] == S) { // Found a duplicate.
596 // Move it to immediately after i'th element.
597 std::swap(Ops[i+1], Ops[j]);
598 ++i; // no need to rescan it.
599 if (i == e-2) return; // Done!
607 //===----------------------------------------------------------------------===//
608 // Simple SCEV method implementations
609 //===----------------------------------------------------------------------===//
611 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
613 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
615 const Type* ResultTy) {
616 // Handle the simplest case efficiently.
618 return SE.getTruncateOrZeroExtend(It, ResultTy);
620 // We are using the following formula for BC(It, K):
622 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
624 // Suppose, W is the bitwidth of the return value. We must be prepared for
625 // overflow. Hence, we must assure that the result of our computation is
626 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
627 // safe in modular arithmetic.
629 // However, this code doesn't use exactly that formula; the formula it uses
630 // is something like the following, where T is the number of factors of 2 in
631 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
634 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
636 // This formula is trivially equivalent to the previous formula. However,
637 // this formula can be implemented much more efficiently. The trick is that
638 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
639 // arithmetic. To do exact division in modular arithmetic, all we have
640 // to do is multiply by the inverse. Therefore, this step can be done at
643 // The next issue is how to safely do the division by 2^T. The way this
644 // is done is by doing the multiplication step at a width of at least W + T
645 // bits. This way, the bottom W+T bits of the product are accurate. Then,
646 // when we perform the division by 2^T (which is equivalent to a right shift
647 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
648 // truncated out after the division by 2^T.
650 // In comparison to just directly using the first formula, this technique
651 // is much more efficient; using the first formula requires W * K bits,
652 // but this formula less than W + K bits. Also, the first formula requires
653 // a division step, whereas this formula only requires multiplies and shifts.
655 // It doesn't matter whether the subtraction step is done in the calculation
656 // width or the input iteration count's width; if the subtraction overflows,
657 // the result must be zero anyway. We prefer here to do it in the width of
658 // the induction variable because it helps a lot for certain cases; CodeGen
659 // isn't smart enough to ignore the overflow, which leads to much less
660 // efficient code if the width of the subtraction is wider than the native
663 // (It's possible to not widen at all by pulling out factors of 2 before
664 // the multiplication; for example, K=2 can be calculated as
665 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
666 // extra arithmetic, so it's not an obvious win, and it gets
667 // much more complicated for K > 3.)
669 // Protection from insane SCEVs; this bound is conservative,
670 // but it probably doesn't matter.
672 return SE.getCouldNotCompute();
674 unsigned W = SE.getTypeSizeInBits(ResultTy);
676 // Calculate K! / 2^T and T; we divide out the factors of two before
677 // multiplying for calculating K! / 2^T to avoid overflow.
678 // Other overflow doesn't matter because we only care about the bottom
679 // W bits of the result.
680 APInt OddFactorial(W, 1);
682 for (unsigned i = 3; i <= K; ++i) {
684 unsigned TwoFactors = Mult.countTrailingZeros();
686 Mult = Mult.lshr(TwoFactors);
687 OddFactorial *= Mult;
690 // We need at least W + T bits for the multiplication step
691 unsigned CalculationBits = W + T;
693 // Calcuate 2^T, at width T+W.
694 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
696 // Calculate the multiplicative inverse of K! / 2^T;
697 // this multiplication factor will perform the exact division by
699 APInt Mod = APInt::getSignedMinValue(W+1);
700 APInt MultiplyFactor = OddFactorial.zext(W+1);
701 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
702 MultiplyFactor = MultiplyFactor.trunc(W);
704 // Calculate the product, at width T+W
705 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
706 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
707 for (unsigned i = 1; i != K; ++i) {
708 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
709 Dividend = SE.getMulExpr(Dividend,
710 SE.getTruncateOrZeroExtend(S, CalculationTy));
714 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
716 // Truncate the result, and divide by K! / 2^T.
718 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
719 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
722 /// evaluateAtIteration - Return the value of this chain of recurrences at
723 /// the specified iteration number. We can evaluate this recurrence by
724 /// multiplying each element in the chain by the binomial coefficient
725 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
727 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
729 /// where BC(It, k) stands for binomial coefficient.
731 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
732 ScalarEvolution &SE) const {
733 SCEVHandle Result = getStart();
734 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
735 // The computation is correct in the face of overflow provided that the
736 // multiplication is performed _after_ the evaluation of the binomial
738 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
739 if (isa<SCEVCouldNotCompute>(Coeff))
742 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
747 //===----------------------------------------------------------------------===//
748 // SCEV Expression folder implementations
749 //===----------------------------------------------------------------------===//
751 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op,
753 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
754 "This is not a truncating conversion!");
755 assert(isSCEVable(Ty) &&
756 "This is not a conversion to a SCEVable type!");
757 Ty = getEffectiveSCEVType(Ty);
759 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
761 ConstantExpr::getTrunc(SC->getValue(), Ty));
763 // trunc(trunc(x)) --> trunc(x)
764 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
765 return getTruncateExpr(ST->getOperand(), Ty);
767 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
768 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
769 return getTruncateOrSignExtend(SS->getOperand(), Ty);
771 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
772 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
773 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
775 // If the input value is a chrec scev made out of constants, truncate
776 // all of the constants.
777 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
778 SmallVector<SCEVHandle, 4> Operands;
779 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
780 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
781 return getAddRecExpr(Operands, AddRec->getLoop());
784 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
785 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
789 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
791 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
792 "This is not an extending conversion!");
793 assert(isSCEVable(Ty) &&
794 "This is not a conversion to a SCEVable type!");
795 Ty = getEffectiveSCEVType(Ty);
797 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
798 const Type *IntTy = getEffectiveSCEVType(Ty);
799 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
800 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
801 return getUnknown(C);
804 // zext(zext(x)) --> zext(x)
805 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
806 return getZeroExtendExpr(SZ->getOperand(), Ty);
808 // If the input value is a chrec scev, and we can prove that the value
809 // did not overflow the old, smaller, value, we can zero extend all of the
810 // operands (often constants). This allows analysis of something like
811 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
812 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
813 if (AR->isAffine()) {
814 // Check whether the backedge-taken count is SCEVCouldNotCompute.
815 // Note that this serves two purposes: It filters out loops that are
816 // simply not analyzable, and it covers the case where this code is
817 // being called from within backedge-taken count analysis, such that
818 // attempting to ask for the backedge-taken count would likely result
819 // in infinite recursion. In the later case, the analysis code will
820 // cope with a conservative value, and it will take care to purge
821 // that value once it has finished.
822 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
823 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
824 // Manually compute the final value for AR, checking for
826 SCEVHandle Start = AR->getStart();
827 SCEVHandle Step = AR->getStepRecurrence(*this);
829 // Check whether the backedge-taken count can be losslessly casted to
830 // the addrec's type. The count is always unsigned.
831 SCEVHandle CastedMaxBECount =
832 getTruncateOrZeroExtend(MaxBECount, Start->getType());
833 SCEVHandle RecastedMaxBECount =
834 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
835 if (MaxBECount == RecastedMaxBECount) {
837 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
838 // Check whether Start+Step*MaxBECount has no unsigned overflow.
840 getMulExpr(CastedMaxBECount,
841 getTruncateOrZeroExtend(Step, Start->getType()));
842 SCEVHandle Add = getAddExpr(Start, ZMul);
843 SCEVHandle OperandExtendedAdd =
844 getAddExpr(getZeroExtendExpr(Start, WideTy),
845 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
846 getZeroExtendExpr(Step, WideTy)));
847 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
848 // Return the expression with the addrec on the outside.
849 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
850 getZeroExtendExpr(Step, Ty),
853 // Similar to above, only this time treat the step value as signed.
854 // This covers loops that count down.
856 getMulExpr(CastedMaxBECount,
857 getTruncateOrSignExtend(Step, Start->getType()));
858 Add = getAddExpr(Start, SMul);
860 getAddExpr(getZeroExtendExpr(Start, WideTy),
861 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
862 getSignExtendExpr(Step, WideTy)));
863 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
864 // Return the expression with the addrec on the outside.
865 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
866 getSignExtendExpr(Step, Ty),
872 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
873 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
877 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
879 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
880 "This is not an extending conversion!");
881 assert(isSCEVable(Ty) &&
882 "This is not a conversion to a SCEVable type!");
883 Ty = getEffectiveSCEVType(Ty);
885 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
886 const Type *IntTy = getEffectiveSCEVType(Ty);
887 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
888 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
889 return getUnknown(C);
892 // sext(sext(x)) --> sext(x)
893 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
894 return getSignExtendExpr(SS->getOperand(), Ty);
896 // If the input value is a chrec scev, and we can prove that the value
897 // did not overflow the old, smaller, value, we can sign extend all of the
898 // operands (often constants). This allows analysis of something like
899 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
900 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
901 if (AR->isAffine()) {
902 // Check whether the backedge-taken count is SCEVCouldNotCompute.
903 // Note that this serves two purposes: It filters out loops that are
904 // simply not analyzable, and it covers the case where this code is
905 // being called from within backedge-taken count analysis, such that
906 // attempting to ask for the backedge-taken count would likely result
907 // in infinite recursion. In the later case, the analysis code will
908 // cope with a conservative value, and it will take care to purge
909 // that value once it has finished.
910 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
911 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
912 // Manually compute the final value for AR, checking for
914 SCEVHandle Start = AR->getStart();
915 SCEVHandle Step = AR->getStepRecurrence(*this);
917 // Check whether the backedge-taken count can be losslessly casted to
918 // the addrec's type. The count is always unsigned.
919 SCEVHandle CastedMaxBECount =
920 getTruncateOrZeroExtend(MaxBECount, Start->getType());
921 SCEVHandle RecastedMaxBECount =
922 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
923 if (MaxBECount == RecastedMaxBECount) {
925 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
926 // Check whether Start+Step*MaxBECount has no signed overflow.
928 getMulExpr(CastedMaxBECount,
929 getTruncateOrSignExtend(Step, Start->getType()));
930 SCEVHandle Add = getAddExpr(Start, SMul);
931 SCEVHandle OperandExtendedAdd =
932 getAddExpr(getSignExtendExpr(Start, WideTy),
933 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
934 getSignExtendExpr(Step, WideTy)));
935 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
936 // Return the expression with the addrec on the outside.
937 return getAddRecExpr(getSignExtendExpr(Start, Ty),
938 getSignExtendExpr(Step, Ty),
944 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
945 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
949 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
950 /// unspecified bits out to the given type.
952 SCEVHandle ScalarEvolution::getAnyExtendExpr(const SCEVHandle &Op,
954 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
955 "This is not an extending conversion!");
956 assert(isSCEVable(Ty) &&
957 "This is not a conversion to a SCEVable type!");
958 Ty = getEffectiveSCEVType(Ty);
960 // Sign-extend negative constants.
961 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
962 if (SC->getValue()->getValue().isNegative())
963 return getSignExtendExpr(Op, Ty);
965 // Peel off a truncate cast.
966 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
967 SCEVHandle NewOp = T->getOperand();
968 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
969 return getAnyExtendExpr(NewOp, Ty);
970 return getTruncateOrNoop(NewOp, Ty);
973 // Next try a zext cast. If the cast is folded, use it.
974 SCEVHandle ZExt = getZeroExtendExpr(Op, Ty);
975 if (!isa<SCEVZeroExtendExpr>(ZExt))
978 // Next try a sext cast. If the cast is folded, use it.
979 SCEVHandle SExt = getSignExtendExpr(Op, Ty);
980 if (!isa<SCEVSignExtendExpr>(SExt))
983 // If the expression is obviously signed, use the sext cast value.
984 if (isa<SCEVSMaxExpr>(Op))
987 // Absent any other information, use the zext cast value.
991 /// getAddExpr - Get a canonical add expression, or something simpler if
993 SCEVHandle ScalarEvolution::getAddExpr(SmallVectorImpl<SCEVHandle> &Ops) {
994 assert(!Ops.empty() && "Cannot get empty add!");
995 if (Ops.size() == 1) return Ops[0];
997 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
998 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
999 getEffectiveSCEVType(Ops[0]->getType()) &&
1000 "SCEVAddExpr operand types don't match!");
1003 // Sort by complexity, this groups all similar expression types together.
1004 GroupByComplexity(Ops, LI);
1006 // If there are any constants, fold them together.
1008 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1010 assert(Idx < Ops.size());
1011 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1012 // We found two constants, fold them together!
1013 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1014 RHSC->getValue()->getValue());
1015 Ops.erase(Ops.begin()+1); // Erase the folded element
1016 if (Ops.size() == 1) return Ops[0];
1017 LHSC = cast<SCEVConstant>(Ops[0]);
1020 // If we are left with a constant zero being added, strip it off.
1021 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1022 Ops.erase(Ops.begin());
1027 if (Ops.size() == 1) return Ops[0];
1029 // Okay, check to see if the same value occurs in the operand list twice. If
1030 // so, merge them together into an multiply expression. Since we sorted the
1031 // list, these values are required to be adjacent.
1032 const Type *Ty = Ops[0]->getType();
1033 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1034 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1035 // Found a match, merge the two values into a multiply, and add any
1036 // remaining values to the result.
1037 SCEVHandle Two = getIntegerSCEV(2, Ty);
1038 SCEVHandle Mul = getMulExpr(Ops[i], Two);
1039 if (Ops.size() == 2)
1041 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1043 return getAddExpr(Ops);
1046 // Check for truncates. If all the operands are truncated from the same
1047 // type, see if factoring out the truncate would permit the result to be
1048 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1049 // if the contents of the resulting outer trunc fold to something simple.
1050 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1051 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1052 const Type *DstType = Trunc->getType();
1053 const Type *SrcType = Trunc->getOperand()->getType();
1054 SmallVector<SCEVHandle, 8> LargeOps;
1056 // Check all the operands to see if they can be represented in the
1057 // source type of the truncate.
1058 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1059 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1060 if (T->getOperand()->getType() != SrcType) {
1064 LargeOps.push_back(T->getOperand());
1065 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1066 // This could be either sign or zero extension, but sign extension
1067 // is much more likely to be foldable here.
1068 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1069 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1070 SmallVector<SCEVHandle, 8> LargeMulOps;
1071 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1072 if (const SCEVTruncateExpr *T =
1073 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1074 if (T->getOperand()->getType() != SrcType) {
1078 LargeMulOps.push_back(T->getOperand());
1079 } else if (const SCEVConstant *C =
1080 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1081 // This could be either sign or zero extension, but sign extension
1082 // is much more likely to be foldable here.
1083 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1090 LargeOps.push_back(getMulExpr(LargeMulOps));
1097 // Evaluate the expression in the larger type.
1098 SCEVHandle Fold = getAddExpr(LargeOps);
1099 // If it folds to something simple, use it. Otherwise, don't.
1100 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1101 return getTruncateExpr(Fold, DstType);
1105 // Skip past any other cast SCEVs.
1106 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1109 // If there are add operands they would be next.
1110 if (Idx < Ops.size()) {
1111 bool DeletedAdd = false;
1112 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1113 // If we have an add, expand the add operands onto the end of the operands
1115 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1116 Ops.erase(Ops.begin()+Idx);
1120 // If we deleted at least one add, we added operands to the end of the list,
1121 // and they are not necessarily sorted. Recurse to resort and resimplify
1122 // any operands we just aquired.
1124 return getAddExpr(Ops);
1127 // Skip over the add expression until we get to a multiply.
1128 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1131 // If we are adding something to a multiply expression, make sure the
1132 // something is not already an operand of the multiply. If so, merge it into
1134 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1135 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1136 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1137 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1138 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1139 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1140 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1141 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
1142 if (Mul->getNumOperands() != 2) {
1143 // If the multiply has more than two operands, we must get the
1145 SmallVector<SCEVHandle, 4> MulOps(Mul->op_begin(), Mul->op_end());
1146 MulOps.erase(MulOps.begin()+MulOp);
1147 InnerMul = getMulExpr(MulOps);
1149 SCEVHandle One = getIntegerSCEV(1, Ty);
1150 SCEVHandle AddOne = getAddExpr(InnerMul, One);
1151 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1152 if (Ops.size() == 2) return OuterMul;
1154 Ops.erase(Ops.begin()+AddOp);
1155 Ops.erase(Ops.begin()+Idx-1);
1157 Ops.erase(Ops.begin()+Idx);
1158 Ops.erase(Ops.begin()+AddOp-1);
1160 Ops.push_back(OuterMul);
1161 return getAddExpr(Ops);
1164 // Check this multiply against other multiplies being added together.
1165 for (unsigned OtherMulIdx = Idx+1;
1166 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1168 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1169 // If MulOp occurs in OtherMul, we can fold the two multiplies
1171 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1172 OMulOp != e; ++OMulOp)
1173 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1174 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1175 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
1176 if (Mul->getNumOperands() != 2) {
1177 SmallVector<SCEVHandle, 4> MulOps(Mul->op_begin(), Mul->op_end());
1178 MulOps.erase(MulOps.begin()+MulOp);
1179 InnerMul1 = getMulExpr(MulOps);
1181 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1182 if (OtherMul->getNumOperands() != 2) {
1183 SmallVector<SCEVHandle, 4> MulOps(OtherMul->op_begin(),
1184 OtherMul->op_end());
1185 MulOps.erase(MulOps.begin()+OMulOp);
1186 InnerMul2 = getMulExpr(MulOps);
1188 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1189 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1190 if (Ops.size() == 2) return OuterMul;
1191 Ops.erase(Ops.begin()+Idx);
1192 Ops.erase(Ops.begin()+OtherMulIdx-1);
1193 Ops.push_back(OuterMul);
1194 return getAddExpr(Ops);
1200 // If there are any add recurrences in the operands list, see if any other
1201 // added values are loop invariant. If so, we can fold them into the
1203 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1206 // Scan over all recurrences, trying to fold loop invariants into them.
1207 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1208 // Scan all of the other operands to this add and add them to the vector if
1209 // they are loop invariant w.r.t. the recurrence.
1210 SmallVector<SCEVHandle, 8> LIOps;
1211 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1212 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1213 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1214 LIOps.push_back(Ops[i]);
1215 Ops.erase(Ops.begin()+i);
1219 // If we found some loop invariants, fold them into the recurrence.
1220 if (!LIOps.empty()) {
1221 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1222 LIOps.push_back(AddRec->getStart());
1224 SmallVector<SCEVHandle, 4> AddRecOps(AddRec->op_begin(),
1226 AddRecOps[0] = getAddExpr(LIOps);
1228 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1229 // If all of the other operands were loop invariant, we are done.
1230 if (Ops.size() == 1) return NewRec;
1232 // Otherwise, add the folded AddRec by the non-liv parts.
1233 for (unsigned i = 0;; ++i)
1234 if (Ops[i] == AddRec) {
1238 return getAddExpr(Ops);
1241 // Okay, if there weren't any loop invariants to be folded, check to see if
1242 // there are multiple AddRec's with the same loop induction variable being
1243 // added together. If so, we can fold them.
1244 for (unsigned OtherIdx = Idx+1;
1245 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1246 if (OtherIdx != Idx) {
1247 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1248 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1249 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1250 SmallVector<SCEVHandle, 4> NewOps(AddRec->op_begin(), AddRec->op_end());
1251 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1252 if (i >= NewOps.size()) {
1253 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1254 OtherAddRec->op_end());
1257 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1259 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1261 if (Ops.size() == 2) return NewAddRec;
1263 Ops.erase(Ops.begin()+Idx);
1264 Ops.erase(Ops.begin()+OtherIdx-1);
1265 Ops.push_back(NewAddRec);
1266 return getAddExpr(Ops);
1270 // Otherwise couldn't fold anything into this recurrence. Move onto the
1274 // Okay, it looks like we really DO need an add expr. Check to see if we
1275 // already have one, otherwise create a new one.
1276 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1277 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
1279 if (Result == 0) Result = new SCEVAddExpr(Ops);
1284 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1286 SCEVHandle ScalarEvolution::getMulExpr(SmallVectorImpl<SCEVHandle> &Ops) {
1287 assert(!Ops.empty() && "Cannot get empty mul!");
1289 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1290 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1291 getEffectiveSCEVType(Ops[0]->getType()) &&
1292 "SCEVMulExpr operand types don't match!");
1295 // Sort by complexity, this groups all similar expression types together.
1296 GroupByComplexity(Ops, LI);
1298 // If there are any constants, fold them together.
1300 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1302 // C1*(C2+V) -> C1*C2 + C1*V
1303 if (Ops.size() == 2)
1304 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1305 if (Add->getNumOperands() == 2 &&
1306 isa<SCEVConstant>(Add->getOperand(0)))
1307 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1308 getMulExpr(LHSC, Add->getOperand(1)));
1312 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1313 // We found two constants, fold them together!
1314 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1315 RHSC->getValue()->getValue());
1316 Ops[0] = getConstant(Fold);
1317 Ops.erase(Ops.begin()+1); // Erase the folded element
1318 if (Ops.size() == 1) return Ops[0];
1319 LHSC = cast<SCEVConstant>(Ops[0]);
1322 // If we are left with a constant one being multiplied, strip it off.
1323 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1324 Ops.erase(Ops.begin());
1326 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1327 // If we have a multiply of zero, it will always be zero.
1332 // Skip over the add expression until we get to a multiply.
1333 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1336 if (Ops.size() == 1)
1339 // If there are mul operands inline them all into this expression.
1340 if (Idx < Ops.size()) {
1341 bool DeletedMul = false;
1342 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1343 // If we have an mul, expand the mul operands onto the end of the operands
1345 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1346 Ops.erase(Ops.begin()+Idx);
1350 // If we deleted at least one mul, we added operands to the end of the list,
1351 // and they are not necessarily sorted. Recurse to resort and resimplify
1352 // any operands we just aquired.
1354 return getMulExpr(Ops);
1357 // If there are any add recurrences in the operands list, see if any other
1358 // added values are loop invariant. If so, we can fold them into the
1360 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1363 // Scan over all recurrences, trying to fold loop invariants into them.
1364 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1365 // Scan all of the other operands to this mul and add them to the vector if
1366 // they are loop invariant w.r.t. the recurrence.
1367 SmallVector<SCEVHandle, 8> LIOps;
1368 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1369 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1370 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1371 LIOps.push_back(Ops[i]);
1372 Ops.erase(Ops.begin()+i);
1376 // If we found some loop invariants, fold them into the recurrence.
1377 if (!LIOps.empty()) {
1378 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1379 SmallVector<SCEVHandle, 4> NewOps;
1380 NewOps.reserve(AddRec->getNumOperands());
1381 if (LIOps.size() == 1) {
1382 const SCEV *Scale = LIOps[0];
1383 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1384 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1386 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1387 SmallVector<SCEVHandle, 4> MulOps(LIOps.begin(), LIOps.end());
1388 MulOps.push_back(AddRec->getOperand(i));
1389 NewOps.push_back(getMulExpr(MulOps));
1393 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1395 // If all of the other operands were loop invariant, we are done.
1396 if (Ops.size() == 1) return NewRec;
1398 // Otherwise, multiply the folded AddRec by the non-liv parts.
1399 for (unsigned i = 0;; ++i)
1400 if (Ops[i] == AddRec) {
1404 return getMulExpr(Ops);
1407 // Okay, if there weren't any loop invariants to be folded, check to see if
1408 // there are multiple AddRec's with the same loop induction variable being
1409 // multiplied together. If so, we can fold them.
1410 for (unsigned OtherIdx = Idx+1;
1411 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1412 if (OtherIdx != Idx) {
1413 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1414 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1415 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1416 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1417 SCEVHandle NewStart = getMulExpr(F->getStart(),
1419 SCEVHandle B = F->getStepRecurrence(*this);
1420 SCEVHandle D = G->getStepRecurrence(*this);
1421 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1424 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1426 if (Ops.size() == 2) return NewAddRec;
1428 Ops.erase(Ops.begin()+Idx);
1429 Ops.erase(Ops.begin()+OtherIdx-1);
1430 Ops.push_back(NewAddRec);
1431 return getMulExpr(Ops);
1435 // Otherwise couldn't fold anything into this recurrence. Move onto the
1439 // Okay, it looks like we really DO need an mul expr. Check to see if we
1440 // already have one, otherwise create a new one.
1441 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1442 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1445 Result = new SCEVMulExpr(Ops);
1449 /// getUDivExpr - Get a canonical multiply expression, or something simpler if
1451 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS,
1452 const SCEVHandle &RHS) {
1453 assert(getEffectiveSCEVType(LHS->getType()) ==
1454 getEffectiveSCEVType(RHS->getType()) &&
1455 "SCEVUDivExpr operand types don't match!");
1457 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1458 if (RHSC->getValue()->equalsInt(1))
1459 return LHS; // X udiv 1 --> x
1461 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1463 // Determine if the division can be folded into the operands of
1465 // TODO: Generalize this to non-constants by using known-bits information.
1466 const Type *Ty = LHS->getType();
1467 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1468 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1469 // For non-power-of-two values, effectively round the value up to the
1470 // nearest power of two.
1471 if (!RHSC->getValue()->getValue().isPowerOf2())
1473 const IntegerType *ExtTy =
1474 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1475 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1476 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1477 if (const SCEVConstant *Step =
1478 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1479 if (!Step->getValue()->getValue()
1480 .urem(RHSC->getValue()->getValue()) &&
1481 getZeroExtendExpr(AR, ExtTy) ==
1482 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1483 getZeroExtendExpr(Step, ExtTy),
1485 SmallVector<SCEVHandle, 4> Operands;
1486 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1487 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1488 return getAddRecExpr(Operands, AR->getLoop());
1490 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1491 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1492 SmallVector<SCEVHandle, 4> Operands;
1493 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1494 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1495 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1496 // Find an operand that's safely divisible.
1497 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1498 SCEVHandle Op = M->getOperand(i);
1499 SCEVHandle Div = getUDivExpr(Op, RHSC);
1500 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1501 const SmallVectorImpl<SCEVHandle> &MOperands = M->getOperands();
1502 Operands = SmallVector<SCEVHandle, 4>(MOperands.begin(),
1505 return getMulExpr(Operands);
1509 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1510 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1511 SmallVector<SCEVHandle, 4> Operands;
1512 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1513 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1514 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1516 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1517 SCEVHandle Op = getUDivExpr(A->getOperand(i), RHS);
1518 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1520 Operands.push_back(Op);
1522 if (Operands.size() == A->getNumOperands())
1523 return getAddExpr(Operands);
1527 // Fold if both operands are constant.
1528 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1529 Constant *LHSCV = LHSC->getValue();
1530 Constant *RHSCV = RHSC->getValue();
1531 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1535 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1536 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1541 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1542 /// Simplify the expression as much as possible.
1543 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1544 const SCEVHandle &Step, const Loop *L) {
1545 SmallVector<SCEVHandle, 4> Operands;
1546 Operands.push_back(Start);
1547 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1548 if (StepChrec->getLoop() == L) {
1549 Operands.insert(Operands.end(), StepChrec->op_begin(),
1550 StepChrec->op_end());
1551 return getAddRecExpr(Operands, L);
1554 Operands.push_back(Step);
1555 return getAddRecExpr(Operands, L);
1558 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1559 /// Simplify the expression as much as possible.
1560 SCEVHandle ScalarEvolution::getAddRecExpr(SmallVectorImpl<SCEVHandle> &Operands,
1562 if (Operands.size() == 1) return Operands[0];
1564 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1565 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1566 getEffectiveSCEVType(Operands[0]->getType()) &&
1567 "SCEVAddRecExpr operand types don't match!");
1570 if (Operands.back()->isZero()) {
1571 Operands.pop_back();
1572 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1575 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1576 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1577 const Loop* NestedLoop = NestedAR->getLoop();
1578 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1579 SmallVector<SCEVHandle, 4> NestedOperands(NestedAR->op_begin(),
1580 NestedAR->op_end());
1581 SCEVHandle NestedARHandle(NestedAR);
1582 Operands[0] = NestedAR->getStart();
1583 NestedOperands[0] = getAddRecExpr(Operands, L);
1584 return getAddRecExpr(NestedOperands, NestedLoop);
1588 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
1589 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)];
1590 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1594 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1595 const SCEVHandle &RHS) {
1596 SmallVector<SCEVHandle, 2> Ops;
1599 return getSMaxExpr(Ops);
1603 ScalarEvolution::getSMaxExpr(SmallVectorImpl<SCEVHandle> &Ops) {
1604 assert(!Ops.empty() && "Cannot get empty smax!");
1605 if (Ops.size() == 1) return Ops[0];
1607 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1608 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1609 getEffectiveSCEVType(Ops[0]->getType()) &&
1610 "SCEVSMaxExpr operand types don't match!");
1613 // Sort by complexity, this groups all similar expression types together.
1614 GroupByComplexity(Ops, LI);
1616 // If there are any constants, fold them together.
1618 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1620 assert(Idx < Ops.size());
1621 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1622 // We found two constants, fold them together!
1623 ConstantInt *Fold = ConstantInt::get(
1624 APIntOps::smax(LHSC->getValue()->getValue(),
1625 RHSC->getValue()->getValue()));
1626 Ops[0] = getConstant(Fold);
1627 Ops.erase(Ops.begin()+1); // Erase the folded element
1628 if (Ops.size() == 1) return Ops[0];
1629 LHSC = cast<SCEVConstant>(Ops[0]);
1632 // If we are left with a constant -inf, strip it off.
1633 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1634 Ops.erase(Ops.begin());
1639 if (Ops.size() == 1) return Ops[0];
1641 // Find the first SMax
1642 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1645 // Check to see if one of the operands is an SMax. If so, expand its operands
1646 // onto our operand list, and recurse to simplify.
1647 if (Idx < Ops.size()) {
1648 bool DeletedSMax = false;
1649 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1650 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1651 Ops.erase(Ops.begin()+Idx);
1656 return getSMaxExpr(Ops);
1659 // Okay, check to see if the same value occurs in the operand list twice. If
1660 // so, delete one. Since we sorted the list, these values are required to
1662 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1663 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1664 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1668 if (Ops.size() == 1) return Ops[0];
1670 assert(!Ops.empty() && "Reduced smax down to nothing!");
1672 // Okay, it looks like we really DO need an smax expr. Check to see if we
1673 // already have one, otherwise create a new one.
1674 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1675 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1677 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1681 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1682 const SCEVHandle &RHS) {
1683 SmallVector<SCEVHandle, 2> Ops;
1686 return getUMaxExpr(Ops);
1690 ScalarEvolution::getUMaxExpr(SmallVectorImpl<SCEVHandle> &Ops) {
1691 assert(!Ops.empty() && "Cannot get empty umax!");
1692 if (Ops.size() == 1) return Ops[0];
1694 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1695 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1696 getEffectiveSCEVType(Ops[0]->getType()) &&
1697 "SCEVUMaxExpr operand types don't match!");
1700 // Sort by complexity, this groups all similar expression types together.
1701 GroupByComplexity(Ops, LI);
1703 // If there are any constants, fold them together.
1705 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1707 assert(Idx < Ops.size());
1708 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1709 // We found two constants, fold them together!
1710 ConstantInt *Fold = ConstantInt::get(
1711 APIntOps::umax(LHSC->getValue()->getValue(),
1712 RHSC->getValue()->getValue()));
1713 Ops[0] = getConstant(Fold);
1714 Ops.erase(Ops.begin()+1); // Erase the folded element
1715 if (Ops.size() == 1) return Ops[0];
1716 LHSC = cast<SCEVConstant>(Ops[0]);
1719 // If we are left with a constant zero, strip it off.
1720 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1721 Ops.erase(Ops.begin());
1726 if (Ops.size() == 1) return Ops[0];
1728 // Find the first UMax
1729 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1732 // Check to see if one of the operands is a UMax. If so, expand its operands
1733 // onto our operand list, and recurse to simplify.
1734 if (Idx < Ops.size()) {
1735 bool DeletedUMax = false;
1736 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1737 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1738 Ops.erase(Ops.begin()+Idx);
1743 return getUMaxExpr(Ops);
1746 // Okay, check to see if the same value occurs in the operand list twice. If
1747 // so, delete one. Since we sorted the list, these values are required to
1749 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1750 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1751 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1755 if (Ops.size() == 1) return Ops[0];
1757 assert(!Ops.empty() && "Reduced umax down to nothing!");
1759 // Okay, it looks like we really DO need a umax expr. Check to see if we
1760 // already have one, otherwise create a new one.
1761 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1762 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1764 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1768 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1769 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1770 return getConstant(CI);
1771 if (isa<ConstantPointerNull>(V))
1772 return getIntegerSCEV(0, V->getType());
1773 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1774 if (Result == 0) Result = new SCEVUnknown(V);
1778 //===----------------------------------------------------------------------===//
1779 // Basic SCEV Analysis and PHI Idiom Recognition Code
1782 /// isSCEVable - Test if values of the given type are analyzable within
1783 /// the SCEV framework. This primarily includes integer types, and it
1784 /// can optionally include pointer types if the ScalarEvolution class
1785 /// has access to target-specific information.
1786 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1787 // Integers are always SCEVable.
1788 if (Ty->isInteger())
1791 // Pointers are SCEVable if TargetData information is available
1792 // to provide pointer size information.
1793 if (isa<PointerType>(Ty))
1796 // Otherwise it's not SCEVable.
1800 /// getTypeSizeInBits - Return the size in bits of the specified type,
1801 /// for which isSCEVable must return true.
1802 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1803 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1805 // If we have a TargetData, use it!
1807 return TD->getTypeSizeInBits(Ty);
1809 // Otherwise, we support only integer types.
1810 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1811 return Ty->getPrimitiveSizeInBits();
1814 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1815 /// the given type and which represents how SCEV will treat the given
1816 /// type, for which isSCEVable must return true. For pointer types,
1817 /// this is the pointer-sized integer type.
1818 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1819 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1821 if (Ty->isInteger())
1824 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1825 return TD->getIntPtrType();
1828 SCEVHandle ScalarEvolution::getCouldNotCompute() {
1829 return CouldNotCompute;
1832 /// hasSCEV - Return true if the SCEV for this value has already been
1834 bool ScalarEvolution::hasSCEV(Value *V) const {
1835 return Scalars.count(V);
1838 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1839 /// expression and create a new one.
1840 SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1841 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1843 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
1844 if (I != Scalars.end()) return I->second;
1845 SCEVHandle S = createSCEV(V);
1846 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
1850 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1851 /// specified signed integer value and return a SCEV for the constant.
1852 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1853 Ty = getEffectiveSCEVType(Ty);
1856 C = Constant::getNullValue(Ty);
1857 else if (Ty->isFloatingPoint())
1858 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1859 APFloat::IEEEdouble, Val));
1861 C = ConstantInt::get(Ty, Val);
1862 return getUnknown(C);
1865 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1867 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1868 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1869 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1871 const Type *Ty = V->getType();
1872 Ty = getEffectiveSCEVType(Ty);
1873 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1876 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1877 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1878 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1879 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1881 const Type *Ty = V->getType();
1882 Ty = getEffectiveSCEVType(Ty);
1883 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1884 return getMinusSCEV(AllOnes, V);
1887 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1889 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1890 const SCEVHandle &RHS) {
1892 return getAddExpr(LHS, getNegativeSCEV(RHS));
1895 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1896 /// input value to the specified type. If the type must be extended, it is zero
1899 ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1901 const Type *SrcTy = V->getType();
1902 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1903 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1904 "Cannot truncate or zero extend with non-integer arguments!");
1905 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1906 return V; // No conversion
1907 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1908 return getTruncateExpr(V, Ty);
1909 return getZeroExtendExpr(V, Ty);
1912 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1913 /// input value to the specified type. If the type must be extended, it is sign
1916 ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1918 const Type *SrcTy = V->getType();
1919 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1920 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1921 "Cannot truncate or zero extend with non-integer arguments!");
1922 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1923 return V; // No conversion
1924 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1925 return getTruncateExpr(V, Ty);
1926 return getSignExtendExpr(V, Ty);
1929 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
1930 /// input value to the specified type. If the type must be extended, it is zero
1931 /// extended. The conversion must not be narrowing.
1933 ScalarEvolution::getNoopOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
1934 const Type *SrcTy = V->getType();
1935 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1936 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1937 "Cannot noop or zero extend with non-integer arguments!");
1938 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1939 "getNoopOrZeroExtend cannot truncate!");
1940 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1941 return V; // No conversion
1942 return getZeroExtendExpr(V, Ty);
1945 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
1946 /// input value to the specified type. If the type must be extended, it is sign
1947 /// extended. The conversion must not be narrowing.
1949 ScalarEvolution::getNoopOrSignExtend(const SCEVHandle &V, const Type *Ty) {
1950 const Type *SrcTy = V->getType();
1951 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1952 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1953 "Cannot noop or sign extend with non-integer arguments!");
1954 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1955 "getNoopOrSignExtend cannot truncate!");
1956 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1957 return V; // No conversion
1958 return getSignExtendExpr(V, Ty);
1961 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
1962 /// the input value to the specified type. If the type must be extended,
1963 /// it is extended with unspecified bits. The conversion must not be
1966 ScalarEvolution::getNoopOrAnyExtend(const SCEVHandle &V, const Type *Ty) {
1967 const Type *SrcTy = V->getType();
1968 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1969 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1970 "Cannot noop or any extend with non-integer arguments!");
1971 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1972 "getNoopOrAnyExtend cannot truncate!");
1973 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1974 return V; // No conversion
1975 return getAnyExtendExpr(V, Ty);
1978 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
1979 /// input value to the specified type. The conversion must not be widening.
1981 ScalarEvolution::getTruncateOrNoop(const SCEVHandle &V, const Type *Ty) {
1982 const Type *SrcTy = V->getType();
1983 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1984 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1985 "Cannot truncate or noop with non-integer arguments!");
1986 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
1987 "getTruncateOrNoop cannot extend!");
1988 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1989 return V; // No conversion
1990 return getTruncateExpr(V, Ty);
1993 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1994 /// the specified instruction and replaces any references to the symbolic value
1995 /// SymName with the specified value. This is used during PHI resolution.
1996 void ScalarEvolution::
1997 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1998 const SCEVHandle &NewVal) {
1999 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
2000 Scalars.find(SCEVCallbackVH(I, this));
2001 if (SI == Scalars.end()) return;
2004 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
2005 if (NV == SI->second) return; // No change.
2007 SI->second = NV; // Update the scalars map!
2009 // Any instruction values that use this instruction might also need to be
2011 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
2013 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
2016 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2017 /// a loop header, making it a potential recurrence, or it doesn't.
2019 SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
2020 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2021 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2022 if (L->getHeader() == PN->getParent()) {
2023 // If it lives in the loop header, it has two incoming values, one
2024 // from outside the loop, and one from inside.
2025 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2026 unsigned BackEdge = IncomingEdge^1;
2028 // While we are analyzing this PHI node, handle its value symbolically.
2029 SCEVHandle SymbolicName = getUnknown(PN);
2030 assert(Scalars.find(PN) == Scalars.end() &&
2031 "PHI node already processed?");
2032 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2034 // Using this symbolic name for the PHI, analyze the value coming around
2036 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
2038 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2039 // has a special value for the first iteration of the loop.
2041 // If the value coming around the backedge is an add with the symbolic
2042 // value we just inserted, then we found a simple induction variable!
2043 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2044 // If there is a single occurrence of the symbolic value, replace it
2045 // with a recurrence.
2046 unsigned FoundIndex = Add->getNumOperands();
2047 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2048 if (Add->getOperand(i) == SymbolicName)
2049 if (FoundIndex == e) {
2054 if (FoundIndex != Add->getNumOperands()) {
2055 // Create an add with everything but the specified operand.
2056 SmallVector<SCEVHandle, 8> Ops;
2057 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2058 if (i != FoundIndex)
2059 Ops.push_back(Add->getOperand(i));
2060 SCEVHandle Accum = getAddExpr(Ops);
2062 // This is not a valid addrec if the step amount is varying each
2063 // loop iteration, but is not itself an addrec in this loop.
2064 if (Accum->isLoopInvariant(L) ||
2065 (isa<SCEVAddRecExpr>(Accum) &&
2066 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2067 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2068 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
2070 // Okay, for the entire analysis of this edge we assumed the PHI
2071 // to be symbolic. We now need to go back and update all of the
2072 // entries for the scalars that use the PHI (except for the PHI
2073 // itself) to use the new analyzed value instead of the "symbolic"
2075 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2079 } else if (const SCEVAddRecExpr *AddRec =
2080 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2081 // Otherwise, this could be a loop like this:
2082 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2083 // In this case, j = {1,+,1} and BEValue is j.
2084 // Because the other in-value of i (0) fits the evolution of BEValue
2085 // i really is an addrec evolution.
2086 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2087 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2089 // If StartVal = j.start - j.stride, we can use StartVal as the
2090 // initial step of the addrec evolution.
2091 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2092 AddRec->getOperand(1))) {
2093 SCEVHandle PHISCEV =
2094 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2096 // Okay, for the entire analysis of this edge we assumed the PHI
2097 // to be symbolic. We now need to go back and update all of the
2098 // entries for the scalars that use the PHI (except for the PHI
2099 // itself) to use the new analyzed value instead of the "symbolic"
2101 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2107 return SymbolicName;
2110 // If it's not a loop phi, we can't handle it yet.
2111 return getUnknown(PN);
2114 /// createNodeForGEP - Expand GEP instructions into add and multiply
2115 /// operations. This allows them to be analyzed by regular SCEV code.
2117 SCEVHandle ScalarEvolution::createNodeForGEP(User *GEP) {
2119 const Type *IntPtrTy = TD->getIntPtrType();
2120 Value *Base = GEP->getOperand(0);
2121 // Don't attempt to analyze GEPs over unsized objects.
2122 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2123 return getUnknown(GEP);
2124 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
2125 gep_type_iterator GTI = gep_type_begin(GEP);
2126 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2130 // Compute the (potentially symbolic) offset in bytes for this index.
2131 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2132 // For a struct, add the member offset.
2133 const StructLayout &SL = *TD->getStructLayout(STy);
2134 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2135 uint64_t Offset = SL.getElementOffset(FieldNo);
2136 TotalOffset = getAddExpr(TotalOffset,
2137 getIntegerSCEV(Offset, IntPtrTy));
2139 // For an array, add the element offset, explicitly scaled.
2140 SCEVHandle LocalOffset = getSCEV(Index);
2141 if (!isa<PointerType>(LocalOffset->getType()))
2142 // Getelementptr indicies are signed.
2143 LocalOffset = getTruncateOrSignExtend(LocalOffset,
2146 getMulExpr(LocalOffset,
2147 getIntegerSCEV(TD->getTypeAllocSize(*GTI),
2149 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2152 return getAddExpr(getSCEV(Base), TotalOffset);
2155 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2156 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2157 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2158 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2159 static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
2160 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2161 return C->getValue()->getValue().countTrailingZeros();
2163 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2164 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
2165 (uint32_t)SE.getTypeSizeInBits(T->getType()));
2167 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2168 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2169 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2170 SE.getTypeSizeInBits(E->getType()) : OpRes;
2173 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2174 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2175 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2176 SE.getTypeSizeInBits(E->getType()) : OpRes;
2179 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2180 // The result is the min of all operands results.
2181 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2182 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2183 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2187 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2188 // The result is the sum of all operands results.
2189 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2190 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
2191 for (unsigned i = 1, e = M->getNumOperands();
2192 SumOpRes != BitWidth && i != e; ++i)
2193 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
2198 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2199 // The result is the min of all operands results.
2200 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2201 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2202 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2206 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2207 // The result is the min of all operands results.
2208 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2209 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2210 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2214 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2215 // The result is the min of all operands results.
2216 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2217 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2218 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2222 // SCEVUDivExpr, SCEVUnknown
2226 /// createSCEV - We know that there is no SCEV for the specified value.
2227 /// Analyze the expression.
2229 SCEVHandle ScalarEvolution::createSCEV(Value *V) {
2230 if (!isSCEVable(V->getType()))
2231 return getUnknown(V);
2233 unsigned Opcode = Instruction::UserOp1;
2234 if (Instruction *I = dyn_cast<Instruction>(V))
2235 Opcode = I->getOpcode();
2236 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2237 Opcode = CE->getOpcode();
2239 return getUnknown(V);
2241 User *U = cast<User>(V);
2243 case Instruction::Add:
2244 return getAddExpr(getSCEV(U->getOperand(0)),
2245 getSCEV(U->getOperand(1)));
2246 case Instruction::Mul:
2247 return getMulExpr(getSCEV(U->getOperand(0)),
2248 getSCEV(U->getOperand(1)));
2249 case Instruction::UDiv:
2250 return getUDivExpr(getSCEV(U->getOperand(0)),
2251 getSCEV(U->getOperand(1)));
2252 case Instruction::Sub:
2253 return getMinusSCEV(getSCEV(U->getOperand(0)),
2254 getSCEV(U->getOperand(1)));
2255 case Instruction::And:
2256 // For an expression like x&255 that merely masks off the high bits,
2257 // use zext(trunc(x)) as the SCEV expression.
2258 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2259 if (CI->isNullValue())
2260 return getSCEV(U->getOperand(1));
2261 if (CI->isAllOnesValue())
2262 return getSCEV(U->getOperand(0));
2263 const APInt &A = CI->getValue();
2264 unsigned Ones = A.countTrailingOnes();
2265 if (APIntOps::isMask(Ones, A))
2267 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2268 IntegerType::get(Ones)),
2272 case Instruction::Or:
2273 // If the RHS of the Or is a constant, we may have something like:
2274 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2275 // optimizations will transparently handle this case.
2277 // In order for this transformation to be safe, the LHS must be of the
2278 // form X*(2^n) and the Or constant must be less than 2^n.
2279 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2280 SCEVHandle LHS = getSCEV(U->getOperand(0));
2281 const APInt &CIVal = CI->getValue();
2282 if (GetMinTrailingZeros(LHS, *this) >=
2283 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2284 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2287 case Instruction::Xor:
2288 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2289 // If the RHS of the xor is a signbit, then this is just an add.
2290 // Instcombine turns add of signbit into xor as a strength reduction step.
2291 if (CI->getValue().isSignBit())
2292 return getAddExpr(getSCEV(U->getOperand(0)),
2293 getSCEV(U->getOperand(1)));
2295 // If the RHS of xor is -1, then this is a not operation.
2296 if (CI->isAllOnesValue())
2297 return getNotSCEV(getSCEV(U->getOperand(0)));
2299 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2300 // This is a variant of the check for xor with -1, and it handles
2301 // the case where instcombine has trimmed non-demanded bits out
2302 // of an xor with -1.
2303 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2304 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2305 if (BO->getOpcode() == Instruction::And &&
2306 LCI->getValue() == CI->getValue())
2307 if (const SCEVZeroExtendExpr *Z =
2308 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0))))
2309 return getZeroExtendExpr(getNotSCEV(Z->getOperand()),
2314 case Instruction::Shl:
2315 // Turn shift left of a constant amount into a multiply.
2316 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2317 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2318 Constant *X = ConstantInt::get(
2319 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2320 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2324 case Instruction::LShr:
2325 // Turn logical shift right of a constant into a unsigned divide.
2326 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2327 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2328 Constant *X = ConstantInt::get(
2329 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2330 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2334 case Instruction::AShr:
2335 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2336 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2337 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2338 if (L->getOpcode() == Instruction::Shl &&
2339 L->getOperand(1) == U->getOperand(1)) {
2340 unsigned BitWidth = getTypeSizeInBits(U->getType());
2341 uint64_t Amt = BitWidth - CI->getZExtValue();
2342 if (Amt == BitWidth)
2343 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2345 return getIntegerSCEV(0, U->getType()); // value is undefined
2347 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2348 IntegerType::get(Amt)),
2353 case Instruction::Trunc:
2354 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2356 case Instruction::ZExt:
2357 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2359 case Instruction::SExt:
2360 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2362 case Instruction::BitCast:
2363 // BitCasts are no-op casts so we just eliminate the cast.
2364 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2365 return getSCEV(U->getOperand(0));
2368 case Instruction::IntToPtr:
2369 if (!TD) break; // Without TD we can't analyze pointers.
2370 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2371 TD->getIntPtrType());
2373 case Instruction::PtrToInt:
2374 if (!TD) break; // Without TD we can't analyze pointers.
2375 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2378 case Instruction::GetElementPtr:
2379 if (!TD) break; // Without TD we can't analyze pointers.
2380 return createNodeForGEP(U);
2382 case Instruction::PHI:
2383 return createNodeForPHI(cast<PHINode>(U));
2385 case Instruction::Select:
2386 // This could be a smax or umax that was lowered earlier.
2387 // Try to recover it.
2388 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2389 Value *LHS = ICI->getOperand(0);
2390 Value *RHS = ICI->getOperand(1);
2391 switch (ICI->getPredicate()) {
2392 case ICmpInst::ICMP_SLT:
2393 case ICmpInst::ICMP_SLE:
2394 std::swap(LHS, RHS);
2396 case ICmpInst::ICMP_SGT:
2397 case ICmpInst::ICMP_SGE:
2398 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2399 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2400 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2401 // ~smax(~x, ~y) == smin(x, y).
2402 return getNotSCEV(getSMaxExpr(
2403 getNotSCEV(getSCEV(LHS)),
2404 getNotSCEV(getSCEV(RHS))));
2406 case ICmpInst::ICMP_ULT:
2407 case ICmpInst::ICMP_ULE:
2408 std::swap(LHS, RHS);
2410 case ICmpInst::ICMP_UGT:
2411 case ICmpInst::ICMP_UGE:
2412 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2413 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2414 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2415 // ~umax(~x, ~y) == umin(x, y)
2416 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2417 getNotSCEV(getSCEV(RHS))));
2424 default: // We cannot analyze this expression.
2428 return getUnknown(V);
2433 //===----------------------------------------------------------------------===//
2434 // Iteration Count Computation Code
2437 /// getBackedgeTakenCount - If the specified loop has a predictable
2438 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2439 /// object. The backedge-taken count is the number of times the loop header
2440 /// will be branched to from within the loop. This is one less than the
2441 /// trip count of the loop, since it doesn't count the first iteration,
2442 /// when the header is branched to from outside the loop.
2444 /// Note that it is not valid to call this method on a loop without a
2445 /// loop-invariant backedge-taken count (see
2446 /// hasLoopInvariantBackedgeTakenCount).
2448 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2449 return getBackedgeTakenInfo(L).Exact;
2452 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2453 /// return the least SCEV value that is known never to be less than the
2454 /// actual backedge taken count.
2455 SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2456 return getBackedgeTakenInfo(L).Max;
2459 const ScalarEvolution::BackedgeTakenInfo &
2460 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2461 // Initially insert a CouldNotCompute for this loop. If the insertion
2462 // succeeds, procede to actually compute a backedge-taken count and
2463 // update the value. The temporary CouldNotCompute value tells SCEV
2464 // code elsewhere that it shouldn't attempt to request a new
2465 // backedge-taken count, which could result in infinite recursion.
2466 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2467 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2469 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2470 if (ItCount.Exact != CouldNotCompute) {
2471 assert(ItCount.Exact->isLoopInvariant(L) &&
2472 ItCount.Max->isLoopInvariant(L) &&
2473 "Computed trip count isn't loop invariant for loop!");
2474 ++NumTripCountsComputed;
2476 // Update the value in the map.
2477 Pair.first->second = ItCount;
2478 } else if (isa<PHINode>(L->getHeader()->begin())) {
2479 // Only count loops that have phi nodes as not being computable.
2480 ++NumTripCountsNotComputed;
2483 // Now that we know more about the trip count for this loop, forget any
2484 // existing SCEV values for PHI nodes in this loop since they are only
2485 // conservative estimates made without the benefit
2486 // of trip count information.
2487 if (ItCount.hasAnyInfo())
2490 return Pair.first->second;
2493 /// forgetLoopBackedgeTakenCount - This method should be called by the
2494 /// client when it has changed a loop in a way that may effect
2495 /// ScalarEvolution's ability to compute a trip count, or if the loop
2497 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2498 BackedgeTakenCounts.erase(L);
2502 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2503 /// PHI nodes in the given loop. This is used when the trip count of
2504 /// the loop may have changed.
2505 void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2506 BasicBlock *Header = L->getHeader();
2508 // Push all Loop-header PHIs onto the Worklist stack, except those
2509 // that are presently represented via a SCEVUnknown. SCEVUnknown for
2510 // a PHI either means that it has an unrecognized structure, or it's
2511 // a PHI that's in the progress of being computed by createNodeForPHI.
2512 // In the former case, additional loop trip count information isn't
2513 // going to change anything. In the later case, createNodeForPHI will
2514 // perform the necessary updates on its own when it gets to that point.
2515 SmallVector<Instruction *, 16> Worklist;
2516 for (BasicBlock::iterator I = Header->begin();
2517 PHINode *PN = dyn_cast<PHINode>(I); ++I) {
2518 std::map<SCEVCallbackVH, SCEVHandle>::iterator It = Scalars.find((Value*)I);
2519 if (It != Scalars.end() && !isa<SCEVUnknown>(It->second))
2520 Worklist.push_back(PN);
2523 while (!Worklist.empty()) {
2524 Instruction *I = Worklist.pop_back_val();
2525 if (Scalars.erase(I))
2526 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2528 Worklist.push_back(cast<Instruction>(UI));
2532 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2533 /// of the specified loop will execute.
2534 ScalarEvolution::BackedgeTakenInfo
2535 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2536 // If the loop has a non-one exit block count, we can't analyze it.
2537 BasicBlock *ExitBlock = L->getExitBlock();
2539 return CouldNotCompute;
2541 // Okay, there is one exit block. Try to find the condition that causes the
2542 // loop to be exited.
2543 BasicBlock *ExitingBlock = L->getExitingBlock();
2545 return CouldNotCompute; // More than one block exiting!
2547 // Okay, we've computed the exiting block. See what condition causes us to
2550 // FIXME: we should be able to handle switch instructions (with a single exit)
2551 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2552 if (ExitBr == 0) return CouldNotCompute;
2553 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2555 // At this point, we know we have a conditional branch that determines whether
2556 // the loop is exited. However, we don't know if the branch is executed each
2557 // time through the loop. If not, then the execution count of the branch will
2558 // not be equal to the trip count of the loop.
2560 // Currently we check for this by checking to see if the Exit branch goes to
2561 // the loop header. If so, we know it will always execute the same number of
2562 // times as the loop. We also handle the case where the exit block *is* the
2563 // loop header. This is common for un-rotated loops. More extensive analysis
2564 // could be done to handle more cases here.
2565 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2566 ExitBr->getSuccessor(1) != L->getHeader() &&
2567 ExitBr->getParent() != L->getHeader())
2568 return CouldNotCompute;
2570 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2572 // If it's not an integer or pointer comparison then compute it the hard way.
2574 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2575 ExitBr->getSuccessor(0) == ExitBlock);
2577 // If the condition was exit on true, convert the condition to exit on false
2578 ICmpInst::Predicate Cond;
2579 if (ExitBr->getSuccessor(1) == ExitBlock)
2580 Cond = ExitCond->getPredicate();
2582 Cond = ExitCond->getInversePredicate();
2584 // Handle common loops like: for (X = "string"; *X; ++X)
2585 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2586 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2588 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2589 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2592 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2593 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2595 // Try to evaluate any dependencies out of the loop.
2596 LHS = getSCEVAtScope(LHS, L);
2597 RHS = getSCEVAtScope(RHS, L);
2599 // At this point, we would like to compute how many iterations of the
2600 // loop the predicate will return true for these inputs.
2601 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2602 // If there is a loop-invariant, force it into the RHS.
2603 std::swap(LHS, RHS);
2604 Cond = ICmpInst::getSwappedPredicate(Cond);
2607 // If we have a comparison of a chrec against a constant, try to use value
2608 // ranges to answer this query.
2609 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2610 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2611 if (AddRec->getLoop() == L) {
2612 // Form the constant range.
2613 ConstantRange CompRange(
2614 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
2616 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2617 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2621 case ICmpInst::ICMP_NE: { // while (X != Y)
2622 // Convert to: while (X-Y != 0)
2623 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2624 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2627 case ICmpInst::ICMP_EQ: {
2628 // Convert to: while (X-Y == 0) // while (X == Y)
2629 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2630 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2633 case ICmpInst::ICMP_SLT: {
2634 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2635 if (BTI.hasAnyInfo()) return BTI;
2638 case ICmpInst::ICMP_SGT: {
2639 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2640 getNotSCEV(RHS), L, true);
2641 if (BTI.hasAnyInfo()) return BTI;
2644 case ICmpInst::ICMP_ULT: {
2645 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2646 if (BTI.hasAnyInfo()) return BTI;
2649 case ICmpInst::ICMP_UGT: {
2650 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2651 getNotSCEV(RHS), L, false);
2652 if (BTI.hasAnyInfo()) return BTI;
2657 errs() << "ComputeBackedgeTakenCount ";
2658 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2659 errs() << "[unsigned] ";
2660 errs() << *LHS << " "
2661 << Instruction::getOpcodeName(Instruction::ICmp)
2662 << " " << *RHS << "\n";
2667 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2668 ExitBr->getSuccessor(0) == ExitBlock);
2671 static ConstantInt *
2672 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2673 ScalarEvolution &SE) {
2674 SCEVHandle InVal = SE.getConstant(C);
2675 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2676 assert(isa<SCEVConstant>(Val) &&
2677 "Evaluation of SCEV at constant didn't fold correctly?");
2678 return cast<SCEVConstant>(Val)->getValue();
2681 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2682 /// and a GEP expression (missing the pointer index) indexing into it, return
2683 /// the addressed element of the initializer or null if the index expression is
2686 GetAddressedElementFromGlobal(GlobalVariable *GV,
2687 const std::vector<ConstantInt*> &Indices) {
2688 Constant *Init = GV->getInitializer();
2689 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2690 uint64_t Idx = Indices[i]->getZExtValue();
2691 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2692 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2693 Init = cast<Constant>(CS->getOperand(Idx));
2694 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2695 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2696 Init = cast<Constant>(CA->getOperand(Idx));
2697 } else if (isa<ConstantAggregateZero>(Init)) {
2698 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2699 assert(Idx < STy->getNumElements() && "Bad struct index!");
2700 Init = Constant::getNullValue(STy->getElementType(Idx));
2701 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2702 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2703 Init = Constant::getNullValue(ATy->getElementType());
2705 assert(0 && "Unknown constant aggregate type!");
2709 return 0; // Unknown initializer type
2715 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2716 /// 'icmp op load X, cst', try to see if we can compute the backedge
2717 /// execution count.
2718 SCEVHandle ScalarEvolution::
2719 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2721 ICmpInst::Predicate predicate) {
2722 if (LI->isVolatile()) return CouldNotCompute;
2724 // Check to see if the loaded pointer is a getelementptr of a global.
2725 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2726 if (!GEP) return CouldNotCompute;
2728 // Make sure that it is really a constant global we are gepping, with an
2729 // initializer, and make sure the first IDX is really 0.
2730 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2731 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2732 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2733 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2734 return CouldNotCompute;
2736 // Okay, we allow one non-constant index into the GEP instruction.
2738 std::vector<ConstantInt*> Indexes;
2739 unsigned VarIdxNum = 0;
2740 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2741 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2742 Indexes.push_back(CI);
2743 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2744 if (VarIdx) return CouldNotCompute; // Multiple non-constant idx's.
2745 VarIdx = GEP->getOperand(i);
2747 Indexes.push_back(0);
2750 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2751 // Check to see if X is a loop variant variable value now.
2752 SCEVHandle Idx = getSCEV(VarIdx);
2753 Idx = getSCEVAtScope(Idx, L);
2755 // We can only recognize very limited forms of loop index expressions, in
2756 // particular, only affine AddRec's like {C1,+,C2}.
2757 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2758 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2759 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2760 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2761 return CouldNotCompute;
2763 unsigned MaxSteps = MaxBruteForceIterations;
2764 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2765 ConstantInt *ItCst =
2766 ConstantInt::get(IdxExpr->getType(), IterationNum);
2767 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2769 // Form the GEP offset.
2770 Indexes[VarIdxNum] = Val;
2772 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2773 if (Result == 0) break; // Cannot compute!
2775 // Evaluate the condition for this iteration.
2776 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2777 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2778 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2780 errs() << "\n***\n*** Computed loop count " << *ItCst
2781 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2784 ++NumArrayLenItCounts;
2785 return getConstant(ItCst); // Found terminating iteration!
2788 return CouldNotCompute;
2792 /// CanConstantFold - Return true if we can constant fold an instruction of the
2793 /// specified type, assuming that all operands were constants.
2794 static bool CanConstantFold(const Instruction *I) {
2795 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2796 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2799 if (const CallInst *CI = dyn_cast<CallInst>(I))
2800 if (const Function *F = CI->getCalledFunction())
2801 return canConstantFoldCallTo(F);
2805 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2806 /// in the loop that V is derived from. We allow arbitrary operations along the
2807 /// way, but the operands of an operation must either be constants or a value
2808 /// derived from a constant PHI. If this expression does not fit with these
2809 /// constraints, return null.
2810 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2811 // If this is not an instruction, or if this is an instruction outside of the
2812 // loop, it can't be derived from a loop PHI.
2813 Instruction *I = dyn_cast<Instruction>(V);
2814 if (I == 0 || !L->contains(I->getParent())) return 0;
2816 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2817 if (L->getHeader() == I->getParent())
2820 // We don't currently keep track of the control flow needed to evaluate
2821 // PHIs, so we cannot handle PHIs inside of loops.
2825 // If we won't be able to constant fold this expression even if the operands
2826 // are constants, return early.
2827 if (!CanConstantFold(I)) return 0;
2829 // Otherwise, we can evaluate this instruction if all of its operands are
2830 // constant or derived from a PHI node themselves.
2832 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2833 if (!(isa<Constant>(I->getOperand(Op)) ||
2834 isa<GlobalValue>(I->getOperand(Op)))) {
2835 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2836 if (P == 0) return 0; // Not evolving from PHI
2840 return 0; // Evolving from multiple different PHIs.
2843 // This is a expression evolving from a constant PHI!
2847 /// EvaluateExpression - Given an expression that passes the
2848 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2849 /// in the loop has the value PHIVal. If we can't fold this expression for some
2850 /// reason, return null.
2851 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2852 if (isa<PHINode>(V)) return PHIVal;
2853 if (Constant *C = dyn_cast<Constant>(V)) return C;
2854 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2855 Instruction *I = cast<Instruction>(V);
2857 std::vector<Constant*> Operands;
2858 Operands.resize(I->getNumOperands());
2860 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2861 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2862 if (Operands[i] == 0) return 0;
2865 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2866 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2867 &Operands[0], Operands.size());
2869 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2870 &Operands[0], Operands.size());
2873 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2874 /// in the header of its containing loop, we know the loop executes a
2875 /// constant number of times, and the PHI node is just a recurrence
2876 /// involving constants, fold it.
2877 Constant *ScalarEvolution::
2878 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2879 std::map<PHINode*, Constant*>::iterator I =
2880 ConstantEvolutionLoopExitValue.find(PN);
2881 if (I != ConstantEvolutionLoopExitValue.end())
2884 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2885 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2887 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2889 // Since the loop is canonicalized, the PHI node must have two entries. One
2890 // entry must be a constant (coming in from outside of the loop), and the
2891 // second must be derived from the same PHI.
2892 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2893 Constant *StartCST =
2894 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2896 return RetVal = 0; // Must be a constant.
2898 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2899 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2901 return RetVal = 0; // Not derived from same PHI.
2903 // Execute the loop symbolically to determine the exit value.
2904 if (BEs.getActiveBits() >= 32)
2905 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2907 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2908 unsigned IterationNum = 0;
2909 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2910 if (IterationNum == NumIterations)
2911 return RetVal = PHIVal; // Got exit value!
2913 // Compute the value of the PHI node for the next iteration.
2914 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2915 if (NextPHI == PHIVal)
2916 return RetVal = NextPHI; // Stopped evolving!
2918 return 0; // Couldn't evaluate!
2923 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2924 /// constant number of times (the condition evolves only from constants),
2925 /// try to evaluate a few iterations of the loop until we get the exit
2926 /// condition gets a value of ExitWhen (true or false). If we cannot
2927 /// evaluate the trip count of the loop, return CouldNotCompute.
2928 SCEVHandle ScalarEvolution::
2929 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2930 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2931 if (PN == 0) return CouldNotCompute;
2933 // Since the loop is canonicalized, the PHI node must have two entries. One
2934 // entry must be a constant (coming in from outside of the loop), and the
2935 // second must be derived from the same PHI.
2936 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2937 Constant *StartCST =
2938 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2939 if (StartCST == 0) return CouldNotCompute; // Must be a constant.
2941 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2942 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2943 if (PN2 != PN) return CouldNotCompute; // Not derived from same PHI.
2945 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2946 // the loop symbolically to determine when the condition gets a value of
2948 unsigned IterationNum = 0;
2949 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2950 for (Constant *PHIVal = StartCST;
2951 IterationNum != MaxIterations; ++IterationNum) {
2952 ConstantInt *CondVal =
2953 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2955 // Couldn't symbolically evaluate.
2956 if (!CondVal) return CouldNotCompute;
2958 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2959 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2960 ++NumBruteForceTripCountsComputed;
2961 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2964 // Compute the value of the PHI node for the next iteration.
2965 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2966 if (NextPHI == 0 || NextPHI == PHIVal)
2967 return CouldNotCompute; // Couldn't evaluate or not making progress...
2971 // Too many iterations were needed to evaluate.
2972 return CouldNotCompute;
2975 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
2976 /// at the specified scope in the program. The L value specifies a loop
2977 /// nest to evaluate the expression at, where null is the top-level or a
2978 /// specified loop is immediately inside of the loop.
2980 /// This method can be used to compute the exit value for a variable defined
2981 /// in a loop by querying what the value will hold in the parent loop.
2983 /// In the case that a relevant loop exit value cannot be computed, the
2984 /// original value V is returned.
2985 SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
2986 // FIXME: this should be turned into a virtual method on SCEV!
2988 if (isa<SCEVConstant>(V)) return V;
2990 // If this instruction is evolved from a constant-evolving PHI, compute the
2991 // exit value from the loop without using SCEVs.
2992 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2993 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2994 const Loop *LI = (*this->LI)[I->getParent()];
2995 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2996 if (PHINode *PN = dyn_cast<PHINode>(I))
2997 if (PN->getParent() == LI->getHeader()) {
2998 // Okay, there is no closed form solution for the PHI node. Check
2999 // to see if the loop that contains it has a known backedge-taken
3000 // count. If so, we may be able to force computation of the exit
3002 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
3003 if (const SCEVConstant *BTCC =
3004 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
3005 // Okay, we know how many times the containing loop executes. If
3006 // this is a constant evolving PHI node, get the final value at
3007 // the specified iteration number.
3008 Constant *RV = getConstantEvolutionLoopExitValue(PN,
3009 BTCC->getValue()->getValue(),
3011 if (RV) return getUnknown(RV);
3015 // Okay, this is an expression that we cannot symbolically evaluate
3016 // into a SCEV. Check to see if it's possible to symbolically evaluate
3017 // the arguments into constants, and if so, try to constant propagate the
3018 // result. This is particularly useful for computing loop exit values.
3019 if (CanConstantFold(I)) {
3020 // Check to see if we've folded this instruction at this loop before.
3021 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
3022 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
3023 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
3025 return Pair.first->second ? &*getUnknown(Pair.first->second) : V;
3027 std::vector<Constant*> Operands;
3028 Operands.reserve(I->getNumOperands());
3029 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3030 Value *Op = I->getOperand(i);
3031 if (Constant *C = dyn_cast<Constant>(Op)) {
3032 Operands.push_back(C);
3034 // If any of the operands is non-constant and if they are
3035 // non-integer and non-pointer, don't even try to analyze them
3036 // with scev techniques.
3037 if (!isSCEVable(Op->getType()))
3040 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
3041 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
3042 Constant *C = SC->getValue();
3043 if (C->getType() != Op->getType())
3044 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3048 Operands.push_back(C);
3049 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
3050 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
3051 if (C->getType() != Op->getType())
3053 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3057 Operands.push_back(C);
3067 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3068 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
3069 &Operands[0], Operands.size());
3071 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3072 &Operands[0], Operands.size());
3073 Pair.first->second = C;
3074 return getUnknown(C);
3078 // This is some other type of SCEVUnknown, just return it.
3082 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3083 // Avoid performing the look-up in the common case where the specified
3084 // expression has no loop-variant portions.
3085 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3086 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3087 if (OpAtScope != Comm->getOperand(i)) {
3088 // Okay, at least one of these operands is loop variant but might be
3089 // foldable. Build a new instance of the folded commutative expression.
3090 SmallVector<SCEVHandle, 8> NewOps(Comm->op_begin(), Comm->op_begin()+i);
3091 NewOps.push_back(OpAtScope);
3093 for (++i; i != e; ++i) {
3094 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3095 NewOps.push_back(OpAtScope);
3097 if (isa<SCEVAddExpr>(Comm))
3098 return getAddExpr(NewOps);
3099 if (isa<SCEVMulExpr>(Comm))
3100 return getMulExpr(NewOps);
3101 if (isa<SCEVSMaxExpr>(Comm))
3102 return getSMaxExpr(NewOps);
3103 if (isa<SCEVUMaxExpr>(Comm))
3104 return getUMaxExpr(NewOps);
3105 assert(0 && "Unknown commutative SCEV type!");
3108 // If we got here, all operands are loop invariant.
3112 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3113 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
3114 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
3115 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3116 return Div; // must be loop invariant
3117 return getUDivExpr(LHS, RHS);
3120 // If this is a loop recurrence for a loop that does not contain L, then we
3121 // are dealing with the final value computed by the loop.
3122 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3123 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3124 // To evaluate this recurrence, we need to know how many times the AddRec
3125 // loop iterates. Compute this now.
3126 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3127 if (BackedgeTakenCount == CouldNotCompute) return AddRec;
3129 // Then, evaluate the AddRec.
3130 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3135 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3136 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3137 if (Op == Cast->getOperand())
3138 return Cast; // must be loop invariant
3139 return getZeroExtendExpr(Op, Cast->getType());
3142 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3143 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3144 if (Op == Cast->getOperand())
3145 return Cast; // must be loop invariant
3146 return getSignExtendExpr(Op, Cast->getType());
3149 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3150 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3151 if (Op == Cast->getOperand())
3152 return Cast; // must be loop invariant
3153 return getTruncateExpr(Op, Cast->getType());
3156 assert(0 && "Unknown SCEV type!");
3160 /// getSCEVAtScope - This is a convenience function which does
3161 /// getSCEVAtScope(getSCEV(V), L).
3162 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3163 return getSCEVAtScope(getSCEV(V), L);
3166 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3167 /// following equation:
3169 /// A * X = B (mod N)
3171 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3172 /// A and B isn't important.
3174 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3175 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3176 ScalarEvolution &SE) {
3177 uint32_t BW = A.getBitWidth();
3178 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3179 assert(A != 0 && "A must be non-zero.");
3183 // The gcd of A and N may have only one prime factor: 2. The number of
3184 // trailing zeros in A is its multiplicity
3185 uint32_t Mult2 = A.countTrailingZeros();
3188 // 2. Check if B is divisible by D.
3190 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3191 // is not less than multiplicity of this prime factor for D.
3192 if (B.countTrailingZeros() < Mult2)
3193 return SE.getCouldNotCompute();
3195 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3198 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3199 // bit width during computations.
3200 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3201 APInt Mod(BW + 1, 0);
3202 Mod.set(BW - Mult2); // Mod = N / D
3203 APInt I = AD.multiplicativeInverse(Mod);
3205 // 4. Compute the minimum unsigned root of the equation:
3206 // I * (B / D) mod (N / D)
3207 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3209 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3211 return SE.getConstant(Result.trunc(BW));
3214 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3215 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
3216 /// might be the same) or two SCEVCouldNotCompute objects.
3218 static std::pair<SCEVHandle,SCEVHandle>
3219 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
3220 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
3221 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
3222 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
3223 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
3225 // We currently can only solve this if the coefficients are constants.
3226 if (!LC || !MC || !NC) {
3227 const SCEV *CNC = SE.getCouldNotCompute();
3228 return std::make_pair(CNC, CNC);
3231 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
3232 const APInt &L = LC->getValue()->getValue();
3233 const APInt &M = MC->getValue()->getValue();
3234 const APInt &N = NC->getValue()->getValue();
3235 APInt Two(BitWidth, 2);
3236 APInt Four(BitWidth, 4);
3239 using namespace APIntOps;
3241 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
3242 // The B coefficient is M-N/2
3246 // The A coefficient is N/2
3247 APInt A(N.sdiv(Two));
3249 // Compute the B^2-4ac term.
3252 SqrtTerm -= Four * (A * C);
3254 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
3255 // integer value or else APInt::sqrt() will assert.
3256 APInt SqrtVal(SqrtTerm.sqrt());
3258 // Compute the two solutions for the quadratic formula.
3259 // The divisions must be performed as signed divisions.
3261 APInt TwoA( A << 1 );
3262 if (TwoA.isMinValue()) {
3263 const SCEV *CNC = SE.getCouldNotCompute();
3264 return std::make_pair(CNC, CNC);
3267 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
3268 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
3270 return std::make_pair(SE.getConstant(Solution1),
3271 SE.getConstant(Solution2));
3272 } // end APIntOps namespace
3275 /// HowFarToZero - Return the number of times a backedge comparing the specified
3276 /// value to zero will execute. If not computable, return CouldNotCompute.
3277 SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
3278 // If the value is a constant
3279 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3280 // If the value is already zero, the branch will execute zero times.
3281 if (C->getValue()->isZero()) return C;
3282 return CouldNotCompute; // Otherwise it will loop infinitely.
3285 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
3286 if (!AddRec || AddRec->getLoop() != L)
3287 return CouldNotCompute;
3289 if (AddRec->isAffine()) {
3290 // If this is an affine expression, the execution count of this branch is
3291 // the minimum unsigned root of the following equation:
3293 // Start + Step*N = 0 (mod 2^BW)
3297 // Step*N = -Start (mod 2^BW)
3299 // where BW is the common bit width of Start and Step.
3301 // Get the initial value for the loop.
3302 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
3303 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
3305 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
3306 // For now we handle only constant steps.
3308 // First, handle unitary steps.
3309 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
3310 return getNegativeSCEV(Start); // N = -Start (as unsigned)
3311 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
3312 return Start; // N = Start (as unsigned)
3314 // Then, try to solve the above equation provided that Start is constant.
3315 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
3316 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
3317 -StartC->getValue()->getValue(),
3320 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
3321 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
3322 // the quadratic equation to solve it.
3323 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
3325 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3326 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3329 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
3330 << " sol#2: " << *R2 << "\n";
3332 // Pick the smallest positive root value.
3333 if (ConstantInt *CB =
3334 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3335 R1->getValue(), R2->getValue()))) {
3336 if (CB->getZExtValue() == false)
3337 std::swap(R1, R2); // R1 is the minimum root now.
3339 // We can only use this value if the chrec ends up with an exact zero
3340 // value at this index. When solving for "X*X != 5", for example, we
3341 // should not accept a root of 2.
3342 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
3344 return R1; // We found a quadratic root!
3349 return CouldNotCompute;
3352 /// HowFarToNonZero - Return the number of times a backedge checking the
3353 /// specified value for nonzero will execute. If not computable, return
3355 SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
3356 // Loops that look like: while (X == 0) are very strange indeed. We don't
3357 // handle them yet except for the trivial case. This could be expanded in the
3358 // future as needed.
3360 // If the value is a constant, check to see if it is known to be non-zero
3361 // already. If so, the backedge will execute zero times.
3362 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3363 if (!C->getValue()->isNullValue())
3364 return getIntegerSCEV(0, C->getType());
3365 return CouldNotCompute; // Otherwise it will loop infinitely.
3368 // We could implement others, but I really doubt anyone writes loops like
3369 // this, and if they did, they would already be constant folded.
3370 return CouldNotCompute;
3373 /// getLoopPredecessor - If the given loop's header has exactly one unique
3374 /// predecessor outside the loop, return it. Otherwise return null.
3376 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
3377 BasicBlock *Header = L->getHeader();
3378 BasicBlock *Pred = 0;
3379 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
3381 if (!L->contains(*PI)) {
3382 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
3388 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3389 /// (which may not be an immediate predecessor) which has exactly one
3390 /// successor from which BB is reachable, or null if no such block is
3394 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3395 // If the block has a unique predecessor, then there is no path from the
3396 // predecessor to the block that does not go through the direct edge
3397 // from the predecessor to the block.
3398 if (BasicBlock *Pred = BB->getSinglePredecessor())
3401 // A loop's header is defined to be a block that dominates the loop.
3402 // If the header has a unique predecessor outside the loop, it must be
3403 // a block that has exactly one successor that can reach the loop.
3404 if (Loop *L = LI->getLoopFor(BB))
3405 return getLoopPredecessor(L);
3410 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
3411 /// a conditional between LHS and RHS. This is used to help avoid max
3412 /// expressions in loop trip counts.
3413 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3414 ICmpInst::Predicate Pred,
3415 const SCEV *LHS, const SCEV *RHS) {
3416 // Interpret a null as meaning no loop, where there is obviously no guard
3417 // (interprocedural conditions notwithstanding).
3418 if (!L) return false;
3420 BasicBlock *Predecessor = getLoopPredecessor(L);
3421 BasicBlock *PredecessorDest = L->getHeader();
3423 // Starting at the loop predecessor, climb up the predecessor chain, as long
3424 // as there are predecessors that can be found that have unique successors
3425 // leading to the original header.
3427 PredecessorDest = Predecessor,
3428 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
3430 BranchInst *LoopEntryPredicate =
3431 dyn_cast<BranchInst>(Predecessor->getTerminator());
3432 if (!LoopEntryPredicate ||
3433 LoopEntryPredicate->isUnconditional())
3436 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3439 // Now that we found a conditional branch that dominates the loop, check to
3440 // see if it is the comparison we are looking for.
3441 Value *PreCondLHS = ICI->getOperand(0);
3442 Value *PreCondRHS = ICI->getOperand(1);
3443 ICmpInst::Predicate Cond;
3444 if (LoopEntryPredicate->getSuccessor(0) == PredecessorDest)
3445 Cond = ICI->getPredicate();
3447 Cond = ICI->getInversePredicate();
3450 ; // An exact match.
3451 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3452 ; // The actual condition is beyond sufficient.
3454 // Check a few special cases.
3456 case ICmpInst::ICMP_UGT:
3457 if (Pred == ICmpInst::ICMP_ULT) {
3458 std::swap(PreCondLHS, PreCondRHS);
3459 Cond = ICmpInst::ICMP_ULT;
3463 case ICmpInst::ICMP_SGT:
3464 if (Pred == ICmpInst::ICMP_SLT) {
3465 std::swap(PreCondLHS, PreCondRHS);
3466 Cond = ICmpInst::ICMP_SLT;
3470 case ICmpInst::ICMP_NE:
3471 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3472 // so check for this case by checking if the NE is comparing against
3473 // a minimum or maximum constant.
3474 if (!ICmpInst::isTrueWhenEqual(Pred))
3475 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3476 const APInt &A = CI->getValue();
3478 case ICmpInst::ICMP_SLT:
3479 if (A.isMaxSignedValue()) break;
3481 case ICmpInst::ICMP_SGT:
3482 if (A.isMinSignedValue()) break;
3484 case ICmpInst::ICMP_ULT:
3485 if (A.isMaxValue()) break;
3487 case ICmpInst::ICMP_UGT:
3488 if (A.isMinValue()) break;
3493 Cond = ICmpInst::ICMP_NE;
3494 // NE is symmetric but the original comparison may not be. Swap
3495 // the operands if necessary so that they match below.
3496 if (isa<SCEVConstant>(LHS))
3497 std::swap(PreCondLHS, PreCondRHS);
3502 // We weren't able to reconcile the condition.
3506 if (!PreCondLHS->getType()->isInteger()) continue;
3508 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3509 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3510 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3511 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3512 RHS == getNotSCEV(PreCondLHSSCEV)))
3519 /// HowManyLessThans - Return the number of times a backedge containing the
3520 /// specified less-than comparison will execute. If not computable, return
3521 /// CouldNotCompute.
3522 ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3523 HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
3524 const Loop *L, bool isSigned) {
3525 // Only handle: "ADDREC < LoopInvariant".
3526 if (!RHS->isLoopInvariant(L)) return CouldNotCompute;
3528 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3529 if (!AddRec || AddRec->getLoop() != L)
3530 return CouldNotCompute;
3532 if (AddRec->isAffine()) {
3533 // FORNOW: We only support unit strides.
3534 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3535 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3536 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3538 // TODO: handle non-constant strides.
3539 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3540 if (!CStep || CStep->isZero())
3541 return CouldNotCompute;
3542 if (CStep->isOne()) {
3543 // With unit stride, the iteration never steps past the limit value.
3544 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3545 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3546 // Test whether a positive iteration iteration can step past the limit
3547 // value and past the maximum value for its type in a single step.
3549 APInt Max = APInt::getSignedMaxValue(BitWidth);
3550 if ((Max - CStep->getValue()->getValue())
3551 .slt(CLimit->getValue()->getValue()))
3552 return CouldNotCompute;
3554 APInt Max = APInt::getMaxValue(BitWidth);
3555 if ((Max - CStep->getValue()->getValue())
3556 .ult(CLimit->getValue()->getValue()))
3557 return CouldNotCompute;
3560 // TODO: handle non-constant limit values below.
3561 return CouldNotCompute;
3563 // TODO: handle negative strides below.
3564 return CouldNotCompute;
3566 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3567 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3568 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3569 // treat m-n as signed nor unsigned due to overflow possibility.
3571 // First, we get the value of the LHS in the first iteration: n
3572 SCEVHandle Start = AddRec->getOperand(0);
3574 // Determine the minimum constant start value.
3575 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3576 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3577 APInt::getMinValue(BitWidth));
3579 // If we know that the condition is true in order to enter the loop,
3580 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3581 // only know that it will execute (max(m,n)-n)/s times. In both cases,
3582 // the division must round up.
3583 SCEVHandle End = RHS;
3584 if (!isLoopGuardedByCond(L,
3585 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3586 getMinusSCEV(Start, Step), RHS))
3587 End = isSigned ? getSMaxExpr(RHS, Start)
3588 : getUMaxExpr(RHS, Start);
3590 // Determine the maximum constant end value.
3591 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3592 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3593 APInt::getMaxValue(BitWidth));
3595 // Finally, we subtract these two values and divide, rounding up, to get
3596 // the number of times the backedge is executed.
3597 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3598 getAddExpr(Step, NegOne)),
3601 // The maximum backedge count is similar, except using the minimum start
3602 // value and the maximum end value.
3603 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3605 getAddExpr(Step, NegOne)),
3608 return BackedgeTakenInfo(BECount, MaxBECount);
3611 return CouldNotCompute;
3614 /// getNumIterationsInRange - Return the number of iterations of this loop that
3615 /// produce values in the specified constant range. Another way of looking at
3616 /// this is that it returns the first iteration number where the value is not in
3617 /// the condition, thus computing the exit count. If the iteration count can't
3618 /// be computed, an instance of SCEVCouldNotCompute is returned.
3619 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3620 ScalarEvolution &SE) const {
3621 if (Range.isFullSet()) // Infinite loop.
3622 return SE.getCouldNotCompute();
3624 // If the start is a non-zero constant, shift the range to simplify things.
3625 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3626 if (!SC->getValue()->isZero()) {
3627 SmallVector<SCEVHandle, 4> Operands(op_begin(), op_end());
3628 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3629 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3630 if (const SCEVAddRecExpr *ShiftedAddRec =
3631 dyn_cast<SCEVAddRecExpr>(Shifted))
3632 return ShiftedAddRec->getNumIterationsInRange(
3633 Range.subtract(SC->getValue()->getValue()), SE);
3634 // This is strange and shouldn't happen.
3635 return SE.getCouldNotCompute();
3638 // The only time we can solve this is when we have all constant indices.
3639 // Otherwise, we cannot determine the overflow conditions.
3640 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3641 if (!isa<SCEVConstant>(getOperand(i)))
3642 return SE.getCouldNotCompute();
3645 // Okay at this point we know that all elements of the chrec are constants and
3646 // that the start element is zero.
3648 // First check to see if the range contains zero. If not, the first
3650 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3651 if (!Range.contains(APInt(BitWidth, 0)))
3652 return SE.getConstant(ConstantInt::get(getType(),0));
3655 // If this is an affine expression then we have this situation:
3656 // Solve {0,+,A} in Range === Ax in Range
3658 // We know that zero is in the range. If A is positive then we know that
3659 // the upper value of the range must be the first possible exit value.
3660 // If A is negative then the lower of the range is the last possible loop
3661 // value. Also note that we already checked for a full range.
3662 APInt One(BitWidth,1);
3663 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3664 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3666 // The exit value should be (End+A)/A.
3667 APInt ExitVal = (End + A).udiv(A);
3668 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3670 // Evaluate at the exit value. If we really did fall out of the valid
3671 // range, then we computed our trip count, otherwise wrap around or other
3672 // things must have happened.
3673 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3674 if (Range.contains(Val->getValue()))
3675 return SE.getCouldNotCompute(); // Something strange happened
3677 // Ensure that the previous value is in the range. This is a sanity check.
3678 assert(Range.contains(
3679 EvaluateConstantChrecAtConstant(this,
3680 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3681 "Linear scev computation is off in a bad way!");
3682 return SE.getConstant(ExitValue);
3683 } else if (isQuadratic()) {
3684 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3685 // quadratic equation to solve it. To do this, we must frame our problem in
3686 // terms of figuring out when zero is crossed, instead of when
3687 // Range.getUpper() is crossed.
3688 SmallVector<SCEVHandle, 4> NewOps(op_begin(), op_end());
3689 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3690 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3692 // Next, solve the constructed addrec
3693 std::pair<SCEVHandle,SCEVHandle> Roots =
3694 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3695 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3696 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3698 // Pick the smallest positive root value.
3699 if (ConstantInt *CB =
3700 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3701 R1->getValue(), R2->getValue()))) {
3702 if (CB->getZExtValue() == false)
3703 std::swap(R1, R2); // R1 is the minimum root now.
3705 // Make sure the root is not off by one. The returned iteration should
3706 // not be in the range, but the previous one should be. When solving
3707 // for "X*X < 5", for example, we should not return a root of 2.
3708 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3711 if (Range.contains(R1Val->getValue())) {
3712 // The next iteration must be out of the range...
3713 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3715 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3716 if (!Range.contains(R1Val->getValue()))
3717 return SE.getConstant(NextVal);
3718 return SE.getCouldNotCompute(); // Something strange happened
3721 // If R1 was not in the range, then it is a good return value. Make
3722 // sure that R1-1 WAS in the range though, just in case.
3723 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3724 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3725 if (Range.contains(R1Val->getValue()))
3727 return SE.getCouldNotCompute(); // Something strange happened
3732 return SE.getCouldNotCompute();
3737 //===----------------------------------------------------------------------===//
3738 // SCEVCallbackVH Class Implementation
3739 //===----------------------------------------------------------------------===//
3741 void ScalarEvolution::SCEVCallbackVH::deleted() {
3742 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3743 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
3744 SE->ConstantEvolutionLoopExitValue.erase(PN);
3745 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
3746 SE->ValuesAtScopes.erase(I);
3747 SE->Scalars.erase(getValPtr());
3748 // this now dangles!
3751 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
3752 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3754 // Forget all the expressions associated with users of the old value,
3755 // so that future queries will recompute the expressions using the new
3757 SmallVector<User *, 16> Worklist;
3758 Value *Old = getValPtr();
3759 bool DeleteOld = false;
3760 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
3762 Worklist.push_back(*UI);
3763 while (!Worklist.empty()) {
3764 User *U = Worklist.pop_back_val();
3765 // Deleting the Old value will cause this to dangle. Postpone
3766 // that until everything else is done.
3771 if (PHINode *PN = dyn_cast<PHINode>(U))
3772 SE->ConstantEvolutionLoopExitValue.erase(PN);
3773 if (Instruction *I = dyn_cast<Instruction>(U))
3774 SE->ValuesAtScopes.erase(I);
3775 if (SE->Scalars.erase(U))
3776 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
3778 Worklist.push_back(*UI);
3781 if (PHINode *PN = dyn_cast<PHINode>(Old))
3782 SE->ConstantEvolutionLoopExitValue.erase(PN);
3783 if (Instruction *I = dyn_cast<Instruction>(Old))
3784 SE->ValuesAtScopes.erase(I);
3785 SE->Scalars.erase(Old);
3786 // this now dangles!
3791 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
3792 : CallbackVH(V), SE(se) {}
3794 //===----------------------------------------------------------------------===//
3795 // ScalarEvolution Class Implementation
3796 //===----------------------------------------------------------------------===//
3798 ScalarEvolution::ScalarEvolution()
3799 : FunctionPass(&ID), CouldNotCompute(new SCEVCouldNotCompute()) {
3802 bool ScalarEvolution::runOnFunction(Function &F) {
3804 LI = &getAnalysis<LoopInfo>();
3805 TD = getAnalysisIfAvailable<TargetData>();
3809 void ScalarEvolution::releaseMemory() {
3811 BackedgeTakenCounts.clear();
3812 ConstantEvolutionLoopExitValue.clear();
3813 ValuesAtScopes.clear();
3816 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3817 AU.setPreservesAll();
3818 AU.addRequiredTransitive<LoopInfo>();
3821 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3822 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3825 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3827 // Print all inner loops first
3828 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3829 PrintLoopInfo(OS, SE, *I);
3831 OS << "Loop " << L->getHeader()->getName() << ": ";
3833 SmallVector<BasicBlock*, 8> ExitBlocks;
3834 L->getExitBlocks(ExitBlocks);
3835 if (ExitBlocks.size() != 1)
3836 OS << "<multiple exits> ";
3838 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3839 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3841 OS << "Unpredictable backedge-taken count. ";
3847 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3848 // ScalarEvolution's implementaiton of the print method is to print
3849 // out SCEV values of all instructions that are interesting. Doing
3850 // this potentially causes it to create new SCEV objects though,
3851 // which technically conflicts with the const qualifier. This isn't
3852 // observable from outside the class though (the hasSCEV function
3853 // notwithstanding), so casting away the const isn't dangerous.
3854 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3856 OS << "Classifying expressions for: " << F->getName() << "\n";
3857 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3858 if (isSCEVable(I->getType())) {
3861 SCEVHandle SV = SE.getSCEV(&*I);
3865 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3867 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3868 if (!ExitValue->isLoopInvariant(L)) {
3869 OS << "<<Unknown>>";
3878 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3879 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3880 PrintLoopInfo(OS, &SE, *I);
3883 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3884 raw_os_ostream OS(o);