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"
87 STATISTIC(NumArrayLenItCounts,
88 "Number of trip counts computed with array length");
89 STATISTIC(NumTripCountsComputed,
90 "Number of loops with predictable loop counts");
91 STATISTIC(NumTripCountsNotComputed,
92 "Number of loops without predictable loop counts");
93 STATISTIC(NumBruteForceTripCountsComputed,
94 "Number of loops with trip counts computed by force");
96 static cl::opt<unsigned>
97 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
98 cl::desc("Maximum number of iterations SCEV will "
99 "symbolically execute a constant derived loop"),
102 static RegisterPass<ScalarEvolution>
103 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
104 char ScalarEvolution::ID = 0;
106 //===----------------------------------------------------------------------===//
107 // SCEV class definitions
108 //===----------------------------------------------------------------------===//
110 //===----------------------------------------------------------------------===//
111 // Implementation of the SCEV class.
114 void SCEV::dump() const {
119 void SCEV::print(std::ostream &o) const {
120 raw_os_ostream OS(o);
124 bool SCEV::isZero() const {
125 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
126 return SC->getValue()->isZero();
130 bool SCEV::isOne() const {
131 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
132 return SC->getValue()->isOne();
136 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
137 SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
139 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
140 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
144 const Type *SCEVCouldNotCompute::getType() const {
145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
149 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
150 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
154 SCEVHandle SCEVCouldNotCompute::
155 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
156 const SCEVHandle &Conc,
157 ScalarEvolution &SE) const {
161 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
162 OS << "***COULDNOTCOMPUTE***";
165 bool SCEVCouldNotCompute::classof(const SCEV *S) {
166 return S->getSCEVType() == scCouldNotCompute;
170 // SCEVConstants - Only allow the creation of one SCEVConstant for any
171 // particular value. Don't use a SCEVHandle here, or else the object will
173 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
176 SCEVConstant::~SCEVConstant() {
177 SCEVConstants->erase(V);
180 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
181 SCEVConstant *&R = (*SCEVConstants)[V];
182 if (R == 0) R = new SCEVConstant(V);
186 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
187 return getConstant(ConstantInt::get(Val));
190 const Type *SCEVConstant::getType() const { return V->getType(); }
192 void SCEVConstant::print(raw_ostream &OS) const {
193 WriteAsOperand(OS, V, false);
196 SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
197 const SCEVHandle &op, const Type *ty)
198 : SCEV(SCEVTy), Op(op), Ty(ty) {}
200 SCEVCastExpr::~SCEVCastExpr() {}
202 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
203 return Op->dominates(BB, DT);
206 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
207 // particular input. Don't use a SCEVHandle here, or else the object will
209 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
210 SCEVTruncateExpr*> > SCEVTruncates;
212 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
213 : SCEVCastExpr(scTruncate, op, ty) {
214 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
215 (Ty->isInteger() || isa<PointerType>(Ty)) &&
216 "Cannot truncate non-integer value!");
219 SCEVTruncateExpr::~SCEVTruncateExpr() {
220 SCEVTruncates->erase(std::make_pair(Op, Ty));
223 void SCEVTruncateExpr::print(raw_ostream &OS) const {
224 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
227 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
228 // particular input. Don't use a SCEVHandle here, or else the object will never
230 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
231 SCEVZeroExtendExpr*> > SCEVZeroExtends;
233 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
234 : SCEVCastExpr(scZeroExtend, op, ty) {
235 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
236 (Ty->isInteger() || isa<PointerType>(Ty)) &&
237 "Cannot zero extend non-integer value!");
240 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
241 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
244 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
245 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
248 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
249 // particular input. Don't use a SCEVHandle here, or else the object will never
251 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
252 SCEVSignExtendExpr*> > SCEVSignExtends;
254 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
255 : SCEVCastExpr(scSignExtend, op, ty) {
256 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
257 (Ty->isInteger() || isa<PointerType>(Ty)) &&
258 "Cannot sign extend non-integer value!");
261 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
262 SCEVSignExtends->erase(std::make_pair(Op, Ty));
265 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
266 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
269 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
270 // particular input. Don't use a SCEVHandle here, or else the object will never
272 static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >,
273 SCEVCommutativeExpr*> > SCEVCommExprs;
275 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
276 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
277 SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps));
280 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
281 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
282 const char *OpStr = getOperationStr();
283 OS << "(" << *Operands[0];
284 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
285 OS << OpStr << *Operands[i];
289 SCEVHandle SCEVCommutativeExpr::
290 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
291 const SCEVHandle &Conc,
292 ScalarEvolution &SE) const {
293 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
295 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
296 if (H != getOperand(i)) {
297 std::vector<SCEVHandle> NewOps;
298 NewOps.reserve(getNumOperands());
299 for (unsigned j = 0; j != i; ++j)
300 NewOps.push_back(getOperand(j));
302 for (++i; i != e; ++i)
303 NewOps.push_back(getOperand(i)->
304 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
306 if (isa<SCEVAddExpr>(this))
307 return SE.getAddExpr(NewOps);
308 else if (isa<SCEVMulExpr>(this))
309 return SE.getMulExpr(NewOps);
310 else if (isa<SCEVSMaxExpr>(this))
311 return SE.getSMaxExpr(NewOps);
312 else if (isa<SCEVUMaxExpr>(this))
313 return SE.getUMaxExpr(NewOps);
315 assert(0 && "Unknown commutative expr!");
321 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
322 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
323 if (!getOperand(i)->dominates(BB, DT))
330 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
331 // input. Don't use a SCEVHandle here, or else the object will never be
333 static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>,
334 SCEVUDivExpr*> > SCEVUDivs;
336 SCEVUDivExpr::~SCEVUDivExpr() {
337 SCEVUDivs->erase(std::make_pair(LHS, RHS));
340 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
341 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
344 void SCEVUDivExpr::print(raw_ostream &OS) const {
345 OS << "(" << *LHS << " /u " << *RHS << ")";
348 const Type *SCEVUDivExpr::getType() const {
349 return LHS->getType();
352 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
353 // particular input. Don't use a SCEVHandle here, or else the object will never
355 static ManagedStatic<std::map<std::pair<const Loop *,
356 std::vector<const SCEV*> >,
357 SCEVAddRecExpr*> > SCEVAddRecExprs;
359 SCEVAddRecExpr::~SCEVAddRecExpr() {
360 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
361 SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps));
364 SCEVHandle SCEVAddRecExpr::
365 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
366 const SCEVHandle &Conc,
367 ScalarEvolution &SE) const {
368 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
370 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
371 if (H != getOperand(i)) {
372 std::vector<SCEVHandle> NewOps;
373 NewOps.reserve(getNumOperands());
374 for (unsigned j = 0; j != i; ++j)
375 NewOps.push_back(getOperand(j));
377 for (++i; i != e; ++i)
378 NewOps.push_back(getOperand(i)->
379 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
381 return SE.getAddRecExpr(NewOps, L);
388 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
389 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
390 // contain L and if the start is invariant.
391 return !QueryLoop->contains(L->getHeader()) &&
392 getOperand(0)->isLoopInvariant(QueryLoop);
396 void SCEVAddRecExpr::print(raw_ostream &OS) const {
397 OS << "{" << *Operands[0];
398 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
399 OS << ",+," << *Operands[i];
400 OS << "}<" << L->getHeader()->getName() + ">";
403 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
404 // value. Don't use a SCEVHandle here, or else the object will never be
406 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
408 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
410 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
411 // All non-instruction values are loop invariant. All instructions are loop
412 // invariant if they are not contained in the specified loop.
413 if (Instruction *I = dyn_cast<Instruction>(V))
414 return !L->contains(I->getParent());
418 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
419 if (Instruction *I = dyn_cast<Instruction>(getValue()))
420 return DT->dominates(I->getParent(), BB);
424 const Type *SCEVUnknown::getType() const {
428 void SCEVUnknown::print(raw_ostream &OS) const {
429 WriteAsOperand(OS, V, false);
432 //===----------------------------------------------------------------------===//
434 //===----------------------------------------------------------------------===//
437 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
438 /// than the complexity of the RHS. This comparator is used to canonicalize
440 class VISIBILITY_HIDDEN SCEVComplexityCompare {
443 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
445 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
446 // Primarily, sort the SCEVs by their getSCEVType().
447 if (LHS->getSCEVType() != RHS->getSCEVType())
448 return LHS->getSCEVType() < RHS->getSCEVType();
450 // Aside from the getSCEVType() ordering, the particular ordering
451 // isn't very important except that it's beneficial to be consistent,
452 // so that (a + b) and (b + a) don't end up as different expressions.
454 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
455 // not as complete as it could be.
456 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
457 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
459 // Order pointer values after integer values. This helps SCEVExpander
461 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
463 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
466 // Compare getValueID values.
467 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
468 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
470 // Sort arguments by their position.
471 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
472 const Argument *RA = cast<Argument>(RU->getValue());
473 return LA->getArgNo() < RA->getArgNo();
476 // For instructions, compare their loop depth, and their opcode.
477 // This is pretty loose.
478 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
479 Instruction *RV = cast<Instruction>(RU->getValue());
481 // Compare loop depths.
482 if (LI->getLoopDepth(LV->getParent()) !=
483 LI->getLoopDepth(RV->getParent()))
484 return LI->getLoopDepth(LV->getParent()) <
485 LI->getLoopDepth(RV->getParent());
488 if (LV->getOpcode() != RV->getOpcode())
489 return LV->getOpcode() < RV->getOpcode();
491 // Compare the number of operands.
492 if (LV->getNumOperands() != RV->getNumOperands())
493 return LV->getNumOperands() < RV->getNumOperands();
499 // Constant sorting doesn't matter since they'll be folded.
500 if (isa<SCEVConstant>(LHS))
503 // Lexicographically compare n-ary expressions.
504 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
505 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
506 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
507 if (i >= RC->getNumOperands())
509 if (operator()(LC->getOperand(i), RC->getOperand(i)))
511 if (operator()(RC->getOperand(i), LC->getOperand(i)))
514 return LC->getNumOperands() < RC->getNumOperands();
517 // Lexicographically compare udiv expressions.
518 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
519 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
520 if (operator()(LC->getLHS(), RC->getLHS()))
522 if (operator()(RC->getLHS(), LC->getLHS()))
524 if (operator()(LC->getRHS(), RC->getRHS()))
526 if (operator()(RC->getRHS(), LC->getRHS()))
531 // Compare cast expressions by operand.
532 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
533 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
534 return operator()(LC->getOperand(), RC->getOperand());
537 assert(0 && "Unknown SCEV kind!");
543 /// GroupByComplexity - Given a list of SCEV objects, order them by their
544 /// complexity, and group objects of the same complexity together by value.
545 /// When this routine is finished, we know that any duplicates in the vector are
546 /// consecutive and that complexity is monotonically increasing.
548 /// Note that we go take special precautions to ensure that we get determinstic
549 /// results from this routine. In other words, we don't want the results of
550 /// this to depend on where the addresses of various SCEV objects happened to
553 static void GroupByComplexity(std::vector<SCEVHandle> &Ops,
555 if (Ops.size() < 2) return; // Noop
556 if (Ops.size() == 2) {
557 // This is the common case, which also happens to be trivially simple.
559 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
560 std::swap(Ops[0], Ops[1]);
564 // Do the rough sort by complexity.
565 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
567 // Now that we are sorted by complexity, group elements of the same
568 // complexity. Note that this is, at worst, N^2, but the vector is likely to
569 // be extremely short in practice. Note that we take this approach because we
570 // do not want to depend on the addresses of the objects we are grouping.
571 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
572 const SCEV *S = Ops[i];
573 unsigned Complexity = S->getSCEVType();
575 // If there are any objects of the same complexity and same value as this
577 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
578 if (Ops[j] == S) { // Found a duplicate.
579 // Move it to immediately after i'th element.
580 std::swap(Ops[i+1], Ops[j]);
581 ++i; // no need to rescan it.
582 if (i == e-2) return; // Done!
590 //===----------------------------------------------------------------------===//
591 // Simple SCEV method implementations
592 //===----------------------------------------------------------------------===//
594 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
596 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
598 const Type* ResultTy) {
599 // Handle the simplest case efficiently.
601 return SE.getTruncateOrZeroExtend(It, ResultTy);
603 // We are using the following formula for BC(It, K):
605 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
607 // Suppose, W is the bitwidth of the return value. We must be prepared for
608 // overflow. Hence, we must assure that the result of our computation is
609 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
610 // safe in modular arithmetic.
612 // However, this code doesn't use exactly that formula; the formula it uses
613 // is something like the following, where T is the number of factors of 2 in
614 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
617 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
619 // This formula is trivially equivalent to the previous formula. However,
620 // this formula can be implemented much more efficiently. The trick is that
621 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
622 // arithmetic. To do exact division in modular arithmetic, all we have
623 // to do is multiply by the inverse. Therefore, this step can be done at
626 // The next issue is how to safely do the division by 2^T. The way this
627 // is done is by doing the multiplication step at a width of at least W + T
628 // bits. This way, the bottom W+T bits of the product are accurate. Then,
629 // when we perform the division by 2^T (which is equivalent to a right shift
630 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
631 // truncated out after the division by 2^T.
633 // In comparison to just directly using the first formula, this technique
634 // is much more efficient; using the first formula requires W * K bits,
635 // but this formula less than W + K bits. Also, the first formula requires
636 // a division step, whereas this formula only requires multiplies and shifts.
638 // It doesn't matter whether the subtraction step is done in the calculation
639 // width or the input iteration count's width; if the subtraction overflows,
640 // the result must be zero anyway. We prefer here to do it in the width of
641 // the induction variable because it helps a lot for certain cases; CodeGen
642 // isn't smart enough to ignore the overflow, which leads to much less
643 // efficient code if the width of the subtraction is wider than the native
646 // (It's possible to not widen at all by pulling out factors of 2 before
647 // the multiplication; for example, K=2 can be calculated as
648 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
649 // extra arithmetic, so it's not an obvious win, and it gets
650 // much more complicated for K > 3.)
652 // Protection from insane SCEVs; this bound is conservative,
653 // but it probably doesn't matter.
655 return SE.getCouldNotCompute();
657 unsigned W = SE.getTypeSizeInBits(ResultTy);
659 // Calculate K! / 2^T and T; we divide out the factors of two before
660 // multiplying for calculating K! / 2^T to avoid overflow.
661 // Other overflow doesn't matter because we only care about the bottom
662 // W bits of the result.
663 APInt OddFactorial(W, 1);
665 for (unsigned i = 3; i <= K; ++i) {
667 unsigned TwoFactors = Mult.countTrailingZeros();
669 Mult = Mult.lshr(TwoFactors);
670 OddFactorial *= Mult;
673 // We need at least W + T bits for the multiplication step
674 unsigned CalculationBits = W + T;
676 // Calcuate 2^T, at width T+W.
677 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
679 // Calculate the multiplicative inverse of K! / 2^T;
680 // this multiplication factor will perform the exact division by
682 APInt Mod = APInt::getSignedMinValue(W+1);
683 APInt MultiplyFactor = OddFactorial.zext(W+1);
684 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
685 MultiplyFactor = MultiplyFactor.trunc(W);
687 // Calculate the product, at width T+W
688 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
689 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
690 for (unsigned i = 1; i != K; ++i) {
691 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
692 Dividend = SE.getMulExpr(Dividend,
693 SE.getTruncateOrZeroExtend(S, CalculationTy));
697 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
699 // Truncate the result, and divide by K! / 2^T.
701 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
702 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
705 /// evaluateAtIteration - Return the value of this chain of recurrences at
706 /// the specified iteration number. We can evaluate this recurrence by
707 /// multiplying each element in the chain by the binomial coefficient
708 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
710 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
712 /// where BC(It, k) stands for binomial coefficient.
714 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
715 ScalarEvolution &SE) const {
716 SCEVHandle Result = getStart();
717 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
718 // The computation is correct in the face of overflow provided that the
719 // multiplication is performed _after_ the evaluation of the binomial
721 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
722 if (isa<SCEVCouldNotCompute>(Coeff))
725 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
730 //===----------------------------------------------------------------------===//
731 // SCEV Expression folder implementations
732 //===----------------------------------------------------------------------===//
734 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op,
736 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
737 "This is not a truncating conversion!");
738 assert(isSCEVable(Ty) &&
739 "This is not a conversion to a SCEVable type!");
740 Ty = getEffectiveSCEVType(Ty);
742 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
744 ConstantExpr::getTrunc(SC->getValue(), Ty));
746 // trunc(trunc(x)) --> trunc(x)
747 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
748 return getTruncateExpr(ST->getOperand(), Ty);
750 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
751 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
752 return getTruncateOrSignExtend(SS->getOperand(), Ty);
754 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
755 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
756 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
758 // If the input value is a chrec scev made out of constants, truncate
759 // all of the constants.
760 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
761 std::vector<SCEVHandle> Operands;
762 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
763 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
764 return getAddRecExpr(Operands, AddRec->getLoop());
767 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
768 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
772 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
774 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
775 "This is not an extending conversion!");
776 assert(isSCEVable(Ty) &&
777 "This is not a conversion to a SCEVable type!");
778 Ty = getEffectiveSCEVType(Ty);
780 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
781 const Type *IntTy = getEffectiveSCEVType(Ty);
782 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
783 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
784 return getUnknown(C);
787 // zext(zext(x)) --> zext(x)
788 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
789 return getZeroExtendExpr(SZ->getOperand(), Ty);
791 // If the input value is a chrec scev, and we can prove that the value
792 // did not overflow the old, smaller, value, we can zero extend all of the
793 // operands (often constants). This allows analysis of something like
794 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
795 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
796 if (AR->isAffine()) {
797 // Check whether the backedge-taken count is SCEVCouldNotCompute.
798 // Note that this serves two purposes: It filters out loops that are
799 // simply not analyzable, and it covers the case where this code is
800 // being called from within backedge-taken count analysis, such that
801 // attempting to ask for the backedge-taken count would likely result
802 // in infinite recursion. In the later case, the analysis code will
803 // cope with a conservative value, and it will take care to purge
804 // that value once it has finished.
805 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
806 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
807 // Manually compute the final value for AR, checking for
809 SCEVHandle Start = AR->getStart();
810 SCEVHandle Step = AR->getStepRecurrence(*this);
812 // Check whether the backedge-taken count can be losslessly casted to
813 // the addrec's type. The count is always unsigned.
814 SCEVHandle CastedMaxBECount =
815 getTruncateOrZeroExtend(MaxBECount, Start->getType());
816 SCEVHandle RecastedMaxBECount =
817 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
818 if (MaxBECount == RecastedMaxBECount) {
820 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
821 // Check whether Start+Step*MaxBECount has no unsigned overflow.
823 getMulExpr(CastedMaxBECount,
824 getTruncateOrZeroExtend(Step, Start->getType()));
825 SCEVHandle Add = getAddExpr(Start, ZMul);
826 SCEVHandle OperandExtendedAdd =
827 getAddExpr(getZeroExtendExpr(Start, WideTy),
828 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
829 getZeroExtendExpr(Step, WideTy)));
830 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
831 // Return the expression with the addrec on the outside.
832 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
833 getZeroExtendExpr(Step, Ty),
836 // Similar to above, only this time treat the step value as signed.
837 // This covers loops that count down.
839 getMulExpr(CastedMaxBECount,
840 getTruncateOrSignExtend(Step, Start->getType()));
841 Add = getAddExpr(Start, SMul);
843 getAddExpr(getZeroExtendExpr(Start, WideTy),
844 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
845 getSignExtendExpr(Step, WideTy)));
846 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
847 // Return the expression with the addrec on the outside.
848 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
849 getSignExtendExpr(Step, Ty),
855 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
856 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
860 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
862 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
863 "This is not an extending conversion!");
864 assert(isSCEVable(Ty) &&
865 "This is not a conversion to a SCEVable type!");
866 Ty = getEffectiveSCEVType(Ty);
868 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
869 const Type *IntTy = getEffectiveSCEVType(Ty);
870 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
871 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
872 return getUnknown(C);
875 // sext(sext(x)) --> sext(x)
876 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
877 return getSignExtendExpr(SS->getOperand(), Ty);
879 // If the input value is a chrec scev, and we can prove that the value
880 // did not overflow the old, smaller, value, we can sign extend all of the
881 // operands (often constants). This allows analysis of something like
882 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
883 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
884 if (AR->isAffine()) {
885 // Check whether the backedge-taken count is SCEVCouldNotCompute.
886 // Note that this serves two purposes: It filters out loops that are
887 // simply not analyzable, and it covers the case where this code is
888 // being called from within backedge-taken count analysis, such that
889 // attempting to ask for the backedge-taken count would likely result
890 // in infinite recursion. In the later case, the analysis code will
891 // cope with a conservative value, and it will take care to purge
892 // that value once it has finished.
893 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
894 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
895 // Manually compute the final value for AR, checking for
897 SCEVHandle Start = AR->getStart();
898 SCEVHandle Step = AR->getStepRecurrence(*this);
900 // Check whether the backedge-taken count can be losslessly casted to
901 // the addrec's type. The count is always unsigned.
902 SCEVHandle CastedMaxBECount =
903 getTruncateOrZeroExtend(MaxBECount, Start->getType());
904 SCEVHandle RecastedMaxBECount =
905 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
906 if (MaxBECount == RecastedMaxBECount) {
908 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
909 // Check whether Start+Step*MaxBECount has no signed overflow.
911 getMulExpr(CastedMaxBECount,
912 getTruncateOrSignExtend(Step, Start->getType()));
913 SCEVHandle Add = getAddExpr(Start, SMul);
914 SCEVHandle OperandExtendedAdd =
915 getAddExpr(getSignExtendExpr(Start, WideTy),
916 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
917 getSignExtendExpr(Step, WideTy)));
918 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
919 // Return the expression with the addrec on the outside.
920 return getAddRecExpr(getSignExtendExpr(Start, Ty),
921 getSignExtendExpr(Step, Ty),
927 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
928 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
932 // get - Get a canonical add expression, or something simpler if possible.
933 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
934 assert(!Ops.empty() && "Cannot get empty add!");
935 if (Ops.size() == 1) return Ops[0];
937 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
938 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
939 getEffectiveSCEVType(Ops[0]->getType()) &&
940 "SCEVAddExpr operand types don't match!");
943 // Sort by complexity, this groups all similar expression types together.
944 GroupByComplexity(Ops, LI);
946 // If there are any constants, fold them together.
948 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
950 assert(Idx < Ops.size());
951 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
952 // We found two constants, fold them together!
953 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
954 RHSC->getValue()->getValue());
955 Ops[0] = getConstant(Fold);
956 Ops.erase(Ops.begin()+1); // Erase the folded element
957 if (Ops.size() == 1) return Ops[0];
958 LHSC = cast<SCEVConstant>(Ops[0]);
961 // If we are left with a constant zero being added, strip it off.
962 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
963 Ops.erase(Ops.begin());
968 if (Ops.size() == 1) return Ops[0];
970 // Okay, check to see if the same value occurs in the operand list twice. If
971 // so, merge them together into an multiply expression. Since we sorted the
972 // list, these values are required to be adjacent.
973 const Type *Ty = Ops[0]->getType();
974 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
975 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
976 // Found a match, merge the two values into a multiply, and add any
977 // remaining values to the result.
978 SCEVHandle Two = getIntegerSCEV(2, Ty);
979 SCEVHandle Mul = getMulExpr(Ops[i], Two);
982 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
984 return getAddExpr(Ops);
987 // Check for truncates. If all the operands are truncated from the same
988 // type, see if factoring out the truncate would permit the result to be
989 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
990 // if the contents of the resulting outer trunc fold to something simple.
991 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
992 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
993 const Type *DstType = Trunc->getType();
994 const Type *SrcType = Trunc->getOperand()->getType();
995 std::vector<SCEVHandle> LargeOps;
997 // Check all the operands to see if they can be represented in the
998 // source type of the truncate.
999 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1000 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1001 if (T->getOperand()->getType() != SrcType) {
1005 LargeOps.push_back(T->getOperand());
1006 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1007 // This could be either sign or zero extension, but sign extension
1008 // is much more likely to be foldable here.
1009 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1010 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1011 std::vector<SCEVHandle> LargeMulOps;
1012 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1013 if (const SCEVTruncateExpr *T =
1014 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1015 if (T->getOperand()->getType() != SrcType) {
1019 LargeMulOps.push_back(T->getOperand());
1020 } else if (const SCEVConstant *C =
1021 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1022 // This could be either sign or zero extension, but sign extension
1023 // is much more likely to be foldable here.
1024 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1031 LargeOps.push_back(getMulExpr(LargeMulOps));
1038 // Evaluate the expression in the larger type.
1039 SCEVHandle Fold = getAddExpr(LargeOps);
1040 // If it folds to something simple, use it. Otherwise, don't.
1041 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1042 return getTruncateExpr(Fold, DstType);
1046 // Skip past any other cast SCEVs.
1047 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1050 // If there are add operands they would be next.
1051 if (Idx < Ops.size()) {
1052 bool DeletedAdd = false;
1053 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1054 // If we have an add, expand the add operands onto the end of the operands
1056 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1057 Ops.erase(Ops.begin()+Idx);
1061 // If we deleted at least one add, we added operands to the end of the list,
1062 // and they are not necessarily sorted. Recurse to resort and resimplify
1063 // any operands we just aquired.
1065 return getAddExpr(Ops);
1068 // Skip over the add expression until we get to a multiply.
1069 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1072 // If we are adding something to a multiply expression, make sure the
1073 // something is not already an operand of the multiply. If so, merge it into
1075 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1076 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1077 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1078 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1079 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1080 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
1081 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1082 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
1083 if (Mul->getNumOperands() != 2) {
1084 // If the multiply has more than two operands, we must get the
1086 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1087 MulOps.erase(MulOps.begin()+MulOp);
1088 InnerMul = getMulExpr(MulOps);
1090 SCEVHandle One = getIntegerSCEV(1, Ty);
1091 SCEVHandle AddOne = getAddExpr(InnerMul, One);
1092 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1093 if (Ops.size() == 2) return OuterMul;
1095 Ops.erase(Ops.begin()+AddOp);
1096 Ops.erase(Ops.begin()+Idx-1);
1098 Ops.erase(Ops.begin()+Idx);
1099 Ops.erase(Ops.begin()+AddOp-1);
1101 Ops.push_back(OuterMul);
1102 return getAddExpr(Ops);
1105 // Check this multiply against other multiplies being added together.
1106 for (unsigned OtherMulIdx = Idx+1;
1107 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1109 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1110 // If MulOp occurs in OtherMul, we can fold the two multiplies
1112 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1113 OMulOp != e; ++OMulOp)
1114 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1115 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1116 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
1117 if (Mul->getNumOperands() != 2) {
1118 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1119 MulOps.erase(MulOps.begin()+MulOp);
1120 InnerMul1 = getMulExpr(MulOps);
1122 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1123 if (OtherMul->getNumOperands() != 2) {
1124 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
1125 OtherMul->op_end());
1126 MulOps.erase(MulOps.begin()+OMulOp);
1127 InnerMul2 = getMulExpr(MulOps);
1129 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1130 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1131 if (Ops.size() == 2) return OuterMul;
1132 Ops.erase(Ops.begin()+Idx);
1133 Ops.erase(Ops.begin()+OtherMulIdx-1);
1134 Ops.push_back(OuterMul);
1135 return getAddExpr(Ops);
1141 // If there are any add recurrences in the operands list, see if any other
1142 // added values are loop invariant. If so, we can fold them into the
1144 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1147 // Scan over all recurrences, trying to fold loop invariants into them.
1148 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1149 // Scan all of the other operands to this add and add them to the vector if
1150 // they are loop invariant w.r.t. the recurrence.
1151 std::vector<SCEVHandle> LIOps;
1152 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1153 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1154 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1155 LIOps.push_back(Ops[i]);
1156 Ops.erase(Ops.begin()+i);
1160 // If we found some loop invariants, fold them into the recurrence.
1161 if (!LIOps.empty()) {
1162 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1163 LIOps.push_back(AddRec->getStart());
1165 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
1166 AddRecOps[0] = getAddExpr(LIOps);
1168 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1169 // If all of the other operands were loop invariant, we are done.
1170 if (Ops.size() == 1) return NewRec;
1172 // Otherwise, add the folded AddRec by the non-liv parts.
1173 for (unsigned i = 0;; ++i)
1174 if (Ops[i] == AddRec) {
1178 return getAddExpr(Ops);
1181 // Okay, if there weren't any loop invariants to be folded, check to see if
1182 // there are multiple AddRec's with the same loop induction variable being
1183 // added together. If so, we can fold them.
1184 for (unsigned OtherIdx = Idx+1;
1185 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1186 if (OtherIdx != Idx) {
1187 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1188 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1189 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1190 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
1191 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1192 if (i >= NewOps.size()) {
1193 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1194 OtherAddRec->op_end());
1197 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1199 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1201 if (Ops.size() == 2) return NewAddRec;
1203 Ops.erase(Ops.begin()+Idx);
1204 Ops.erase(Ops.begin()+OtherIdx-1);
1205 Ops.push_back(NewAddRec);
1206 return getAddExpr(Ops);
1210 // Otherwise couldn't fold anything into this recurrence. Move onto the
1214 // Okay, it looks like we really DO need an add expr. Check to see if we
1215 // already have one, otherwise create a new one.
1216 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1217 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
1219 if (Result == 0) Result = new SCEVAddExpr(Ops);
1224 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
1225 assert(!Ops.empty() && "Cannot get empty mul!");
1227 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1228 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1229 getEffectiveSCEVType(Ops[0]->getType()) &&
1230 "SCEVMulExpr operand types don't match!");
1233 // Sort by complexity, this groups all similar expression types together.
1234 GroupByComplexity(Ops, LI);
1236 // If there are any constants, fold them together.
1238 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1240 // C1*(C2+V) -> C1*C2 + C1*V
1241 if (Ops.size() == 2)
1242 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1243 if (Add->getNumOperands() == 2 &&
1244 isa<SCEVConstant>(Add->getOperand(0)))
1245 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1246 getMulExpr(LHSC, Add->getOperand(1)));
1250 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1251 // We found two constants, fold them together!
1252 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1253 RHSC->getValue()->getValue());
1254 Ops[0] = getConstant(Fold);
1255 Ops.erase(Ops.begin()+1); // Erase the folded element
1256 if (Ops.size() == 1) return Ops[0];
1257 LHSC = cast<SCEVConstant>(Ops[0]);
1260 // If we are left with a constant one being multiplied, strip it off.
1261 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1262 Ops.erase(Ops.begin());
1264 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1265 // If we have a multiply of zero, it will always be zero.
1270 // Skip over the add expression until we get to a multiply.
1271 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1274 if (Ops.size() == 1)
1277 // If there are mul operands inline them all into this expression.
1278 if (Idx < Ops.size()) {
1279 bool DeletedMul = false;
1280 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1281 // If we have an mul, expand the mul operands onto the end of the operands
1283 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1284 Ops.erase(Ops.begin()+Idx);
1288 // If we deleted at least one mul, we added operands to the end of the list,
1289 // and they are not necessarily sorted. Recurse to resort and resimplify
1290 // any operands we just aquired.
1292 return getMulExpr(Ops);
1295 // If there are any add recurrences in the operands list, see if any other
1296 // added values are loop invariant. If so, we can fold them into the
1298 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1301 // Scan over all recurrences, trying to fold loop invariants into them.
1302 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1303 // Scan all of the other operands to this mul and add them to the vector if
1304 // they are loop invariant w.r.t. the recurrence.
1305 std::vector<SCEVHandle> LIOps;
1306 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1307 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1308 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1309 LIOps.push_back(Ops[i]);
1310 Ops.erase(Ops.begin()+i);
1314 // If we found some loop invariants, fold them into the recurrence.
1315 if (!LIOps.empty()) {
1316 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1317 std::vector<SCEVHandle> NewOps;
1318 NewOps.reserve(AddRec->getNumOperands());
1319 if (LIOps.size() == 1) {
1320 const SCEV *Scale = LIOps[0];
1321 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1322 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1324 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1325 std::vector<SCEVHandle> MulOps(LIOps);
1326 MulOps.push_back(AddRec->getOperand(i));
1327 NewOps.push_back(getMulExpr(MulOps));
1331 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1333 // If all of the other operands were loop invariant, we are done.
1334 if (Ops.size() == 1) return NewRec;
1336 // Otherwise, multiply the folded AddRec by the non-liv parts.
1337 for (unsigned i = 0;; ++i)
1338 if (Ops[i] == AddRec) {
1342 return getMulExpr(Ops);
1345 // Okay, if there weren't any loop invariants to be folded, check to see if
1346 // there are multiple AddRec's with the same loop induction variable being
1347 // multiplied together. If so, we can fold them.
1348 for (unsigned OtherIdx = Idx+1;
1349 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1350 if (OtherIdx != Idx) {
1351 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1352 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1353 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1354 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1355 SCEVHandle NewStart = getMulExpr(F->getStart(),
1357 SCEVHandle B = F->getStepRecurrence(*this);
1358 SCEVHandle D = G->getStepRecurrence(*this);
1359 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1362 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1364 if (Ops.size() == 2) return NewAddRec;
1366 Ops.erase(Ops.begin()+Idx);
1367 Ops.erase(Ops.begin()+OtherIdx-1);
1368 Ops.push_back(NewAddRec);
1369 return getMulExpr(Ops);
1373 // Otherwise couldn't fold anything into this recurrence. Move onto the
1377 // Okay, it looks like we really DO need an mul expr. Check to see if we
1378 // already have one, otherwise create a new one.
1379 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1380 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1383 Result = new SCEVMulExpr(Ops);
1387 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS,
1388 const SCEVHandle &RHS) {
1389 assert(getEffectiveSCEVType(LHS->getType()) ==
1390 getEffectiveSCEVType(RHS->getType()) &&
1391 "SCEVUDivExpr operand types don't match!");
1393 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1394 if (RHSC->getValue()->equalsInt(1))
1395 return LHS; // X udiv 1 --> x
1397 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1399 // Determine if the division can be folded into the operands of
1401 // TODO: Generalize this to non-constants by using known-bits information.
1402 const Type *Ty = LHS->getType();
1403 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1404 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1405 // For non-power-of-two values, effectively round the value up to the
1406 // nearest power of two.
1407 if (!RHSC->getValue()->getValue().isPowerOf2())
1409 const IntegerType *ExtTy =
1410 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1411 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1412 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1413 if (const SCEVConstant *Step =
1414 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1415 if (!Step->getValue()->getValue()
1416 .urem(RHSC->getValue()->getValue()) &&
1417 getZeroExtendExpr(AR, ExtTy) ==
1418 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1419 getZeroExtendExpr(Step, ExtTy),
1421 std::vector<SCEVHandle> Operands;
1422 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1423 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1424 return getAddRecExpr(Operands, AR->getLoop());
1426 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1427 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1428 std::vector<SCEVHandle> Operands;
1429 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1430 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1431 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1432 // Find an operand that's safely divisible.
1433 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1434 SCEVHandle Op = M->getOperand(i);
1435 SCEVHandle Div = getUDivExpr(Op, RHSC);
1436 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1437 Operands = M->getOperands();
1439 return getMulExpr(Operands);
1443 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1444 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1445 std::vector<SCEVHandle> Operands;
1446 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1447 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1448 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1450 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1451 SCEVHandle Op = getUDivExpr(A->getOperand(i), RHS);
1452 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1454 Operands.push_back(Op);
1456 if (Operands.size() == A->getNumOperands())
1457 return getAddExpr(Operands);
1461 // Fold if both operands are constant.
1462 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1463 Constant *LHSCV = LHSC->getValue();
1464 Constant *RHSCV = RHSC->getValue();
1465 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1469 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1470 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1475 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1476 /// specified loop. Simplify the expression as much as possible.
1477 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1478 const SCEVHandle &Step, const Loop *L) {
1479 std::vector<SCEVHandle> Operands;
1480 Operands.push_back(Start);
1481 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1482 if (StepChrec->getLoop() == L) {
1483 Operands.insert(Operands.end(), StepChrec->op_begin(),
1484 StepChrec->op_end());
1485 return getAddRecExpr(Operands, L);
1488 Operands.push_back(Step);
1489 return getAddRecExpr(Operands, L);
1492 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1493 /// specified loop. Simplify the expression as much as possible.
1494 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1496 if (Operands.size() == 1) return Operands[0];
1498 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1499 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1500 getEffectiveSCEVType(Operands[0]->getType()) &&
1501 "SCEVAddRecExpr operand types don't match!");
1504 if (Operands.back()->isZero()) {
1505 Operands.pop_back();
1506 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1509 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1510 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1511 const Loop* NestedLoop = NestedAR->getLoop();
1512 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1513 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1514 NestedAR->op_end());
1515 SCEVHandle NestedARHandle(NestedAR);
1516 Operands[0] = NestedAR->getStart();
1517 NestedOperands[0] = getAddRecExpr(Operands, L);
1518 return getAddRecExpr(NestedOperands, NestedLoop);
1522 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
1523 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)];
1524 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1528 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1529 const SCEVHandle &RHS) {
1530 std::vector<SCEVHandle> Ops;
1533 return getSMaxExpr(Ops);
1536 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1537 assert(!Ops.empty() && "Cannot get empty smax!");
1538 if (Ops.size() == 1) return Ops[0];
1540 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1541 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1542 getEffectiveSCEVType(Ops[0]->getType()) &&
1543 "SCEVSMaxExpr operand types don't match!");
1546 // Sort by complexity, this groups all similar expression types together.
1547 GroupByComplexity(Ops, LI);
1549 // If there are any constants, fold them together.
1551 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1553 assert(Idx < Ops.size());
1554 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1555 // We found two constants, fold them together!
1556 ConstantInt *Fold = ConstantInt::get(
1557 APIntOps::smax(LHSC->getValue()->getValue(),
1558 RHSC->getValue()->getValue()));
1559 Ops[0] = getConstant(Fold);
1560 Ops.erase(Ops.begin()+1); // Erase the folded element
1561 if (Ops.size() == 1) return Ops[0];
1562 LHSC = cast<SCEVConstant>(Ops[0]);
1565 // If we are left with a constant -inf, strip it off.
1566 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1567 Ops.erase(Ops.begin());
1572 if (Ops.size() == 1) return Ops[0];
1574 // Find the first SMax
1575 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1578 // Check to see if one of the operands is an SMax. If so, expand its operands
1579 // onto our operand list, and recurse to simplify.
1580 if (Idx < Ops.size()) {
1581 bool DeletedSMax = false;
1582 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1583 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1584 Ops.erase(Ops.begin()+Idx);
1589 return getSMaxExpr(Ops);
1592 // Okay, check to see if the same value occurs in the operand list twice. If
1593 // so, delete one. Since we sorted the list, these values are required to
1595 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1596 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1597 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1601 if (Ops.size() == 1) return Ops[0];
1603 assert(!Ops.empty() && "Reduced smax down to nothing!");
1605 // Okay, it looks like we really DO need an smax expr. Check to see if we
1606 // already have one, otherwise create a new one.
1607 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1608 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1610 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1614 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1615 const SCEVHandle &RHS) {
1616 std::vector<SCEVHandle> Ops;
1619 return getUMaxExpr(Ops);
1622 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1623 assert(!Ops.empty() && "Cannot get empty umax!");
1624 if (Ops.size() == 1) return Ops[0];
1626 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1627 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1628 getEffectiveSCEVType(Ops[0]->getType()) &&
1629 "SCEVUMaxExpr operand types don't match!");
1632 // Sort by complexity, this groups all similar expression types together.
1633 GroupByComplexity(Ops, LI);
1635 // If there are any constants, fold them together.
1637 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1639 assert(Idx < Ops.size());
1640 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1641 // We found two constants, fold them together!
1642 ConstantInt *Fold = ConstantInt::get(
1643 APIntOps::umax(LHSC->getValue()->getValue(),
1644 RHSC->getValue()->getValue()));
1645 Ops[0] = getConstant(Fold);
1646 Ops.erase(Ops.begin()+1); // Erase the folded element
1647 if (Ops.size() == 1) return Ops[0];
1648 LHSC = cast<SCEVConstant>(Ops[0]);
1651 // If we are left with a constant zero, strip it off.
1652 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1653 Ops.erase(Ops.begin());
1658 if (Ops.size() == 1) return Ops[0];
1660 // Find the first UMax
1661 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1664 // Check to see if one of the operands is a UMax. If so, expand its operands
1665 // onto our operand list, and recurse to simplify.
1666 if (Idx < Ops.size()) {
1667 bool DeletedUMax = false;
1668 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1669 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1670 Ops.erase(Ops.begin()+Idx);
1675 return getUMaxExpr(Ops);
1678 // Okay, check to see if the same value occurs in the operand list twice. If
1679 // so, delete one. Since we sorted the list, these values are required to
1681 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1682 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1683 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1687 if (Ops.size() == 1) return Ops[0];
1689 assert(!Ops.empty() && "Reduced umax down to nothing!");
1691 // Okay, it looks like we really DO need a umax expr. Check to see if we
1692 // already have one, otherwise create a new one.
1693 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1694 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1696 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1700 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1701 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1702 return getConstant(CI);
1703 if (isa<ConstantPointerNull>(V))
1704 return getIntegerSCEV(0, V->getType());
1705 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1706 if (Result == 0) Result = new SCEVUnknown(V);
1710 //===----------------------------------------------------------------------===//
1711 // Basic SCEV Analysis and PHI Idiom Recognition Code
1714 /// isSCEVable - Test if values of the given type are analyzable within
1715 /// the SCEV framework. This primarily includes integer types, and it
1716 /// can optionally include pointer types if the ScalarEvolution class
1717 /// has access to target-specific information.
1718 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1719 // Integers are always SCEVable.
1720 if (Ty->isInteger())
1723 // Pointers are SCEVable if TargetData information is available
1724 // to provide pointer size information.
1725 if (isa<PointerType>(Ty))
1728 // Otherwise it's not SCEVable.
1732 /// getTypeSizeInBits - Return the size in bits of the specified type,
1733 /// for which isSCEVable must return true.
1734 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1735 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1737 // If we have a TargetData, use it!
1739 return TD->getTypeSizeInBits(Ty);
1741 // Otherwise, we support only integer types.
1742 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1743 return Ty->getPrimitiveSizeInBits();
1746 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1747 /// the given type and which represents how SCEV will treat the given
1748 /// type, for which isSCEVable must return true. For pointer types,
1749 /// this is the pointer-sized integer type.
1750 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1751 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1753 if (Ty->isInteger())
1756 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1757 return TD->getIntPtrType();
1760 SCEVHandle ScalarEvolution::getCouldNotCompute() {
1761 return UnknownValue;
1764 /// hasSCEV - Return true if the SCEV for this value has already been
1766 bool ScalarEvolution::hasSCEV(Value *V) const {
1767 return Scalars.count(V);
1770 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1771 /// expression and create a new one.
1772 SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1773 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1775 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
1776 if (I != Scalars.end()) return I->second;
1777 SCEVHandle S = createSCEV(V);
1778 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
1782 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1783 /// specified signed integer value and return a SCEV for the constant.
1784 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1785 Ty = getEffectiveSCEVType(Ty);
1788 C = Constant::getNullValue(Ty);
1789 else if (Ty->isFloatingPoint())
1790 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1791 APFloat::IEEEdouble, Val));
1793 C = ConstantInt::get(Ty, Val);
1794 return getUnknown(C);
1797 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1799 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1800 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1801 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1803 const Type *Ty = V->getType();
1804 Ty = getEffectiveSCEVType(Ty);
1805 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1808 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1809 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1810 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1811 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1813 const Type *Ty = V->getType();
1814 Ty = getEffectiveSCEVType(Ty);
1815 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1816 return getMinusSCEV(AllOnes, V);
1819 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1821 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1822 const SCEVHandle &RHS) {
1824 return getAddExpr(LHS, getNegativeSCEV(RHS));
1827 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1828 /// input value to the specified type. If the type must be extended, it is zero
1831 ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1833 const Type *SrcTy = V->getType();
1834 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1835 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1836 "Cannot truncate or zero extend with non-integer arguments!");
1837 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1838 return V; // No conversion
1839 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1840 return getTruncateExpr(V, Ty);
1841 return getZeroExtendExpr(V, Ty);
1844 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1845 /// input value to the specified type. If the type must be extended, it is sign
1848 ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1850 const Type *SrcTy = V->getType();
1851 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1852 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1853 "Cannot truncate or zero extend with non-integer arguments!");
1854 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1855 return V; // No conversion
1856 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1857 return getTruncateExpr(V, Ty);
1858 return getSignExtendExpr(V, Ty);
1861 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
1862 /// input value to the specified type. If the type must be extended, it is zero
1863 /// extended. The conversion must not be narrowing.
1865 ScalarEvolution::getNoopOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
1866 const Type *SrcTy = V->getType();
1867 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1868 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1869 "Cannot noop or zero extend with non-integer arguments!");
1870 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1871 "getNoopOrZeroExtend cannot truncate!");
1872 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1873 return V; // No conversion
1874 return getZeroExtendExpr(V, Ty);
1877 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
1878 /// input value to the specified type. If the type must be extended, it is sign
1879 /// extended. The conversion must not be narrowing.
1881 ScalarEvolution::getNoopOrSignExtend(const SCEVHandle &V, const Type *Ty) {
1882 const Type *SrcTy = V->getType();
1883 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1884 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1885 "Cannot noop or sign extend with non-integer arguments!");
1886 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1887 "getNoopOrSignExtend cannot truncate!");
1888 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1889 return V; // No conversion
1890 return getSignExtendExpr(V, Ty);
1893 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
1894 /// input value to the specified type. The conversion must not be widening.
1896 ScalarEvolution::getTruncateOrNoop(const SCEVHandle &V, const Type *Ty) {
1897 const Type *SrcTy = V->getType();
1898 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1899 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1900 "Cannot truncate or noop with non-integer arguments!");
1901 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
1902 "getTruncateOrNoop cannot extend!");
1903 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1904 return V; // No conversion
1905 return getTruncateExpr(V, Ty);
1908 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1909 /// the specified instruction and replaces any references to the symbolic value
1910 /// SymName with the specified value. This is used during PHI resolution.
1911 void ScalarEvolution::
1912 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1913 const SCEVHandle &NewVal) {
1914 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
1915 Scalars.find(SCEVCallbackVH(I, this));
1916 if (SI == Scalars.end()) return;
1919 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
1920 if (NV == SI->second) return; // No change.
1922 SI->second = NV; // Update the scalars map!
1924 // Any instruction values that use this instruction might also need to be
1926 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1928 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1931 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1932 /// a loop header, making it a potential recurrence, or it doesn't.
1934 SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
1935 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1936 if (const Loop *L = LI->getLoopFor(PN->getParent()))
1937 if (L->getHeader() == PN->getParent()) {
1938 // If it lives in the loop header, it has two incoming values, one
1939 // from outside the loop, and one from inside.
1940 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1941 unsigned BackEdge = IncomingEdge^1;
1943 // While we are analyzing this PHI node, handle its value symbolically.
1944 SCEVHandle SymbolicName = getUnknown(PN);
1945 assert(Scalars.find(PN) == Scalars.end() &&
1946 "PHI node already processed?");
1947 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
1949 // Using this symbolic name for the PHI, analyze the value coming around
1951 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1953 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1954 // has a special value for the first iteration of the loop.
1956 // If the value coming around the backedge is an add with the symbolic
1957 // value we just inserted, then we found a simple induction variable!
1958 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1959 // If there is a single occurrence of the symbolic value, replace it
1960 // with a recurrence.
1961 unsigned FoundIndex = Add->getNumOperands();
1962 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1963 if (Add->getOperand(i) == SymbolicName)
1964 if (FoundIndex == e) {
1969 if (FoundIndex != Add->getNumOperands()) {
1970 // Create an add with everything but the specified operand.
1971 std::vector<SCEVHandle> Ops;
1972 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1973 if (i != FoundIndex)
1974 Ops.push_back(Add->getOperand(i));
1975 SCEVHandle Accum = getAddExpr(Ops);
1977 // This is not a valid addrec if the step amount is varying each
1978 // loop iteration, but is not itself an addrec in this loop.
1979 if (Accum->isLoopInvariant(L) ||
1980 (isa<SCEVAddRecExpr>(Accum) &&
1981 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1982 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1983 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
1985 // Okay, for the entire analysis of this edge we assumed the PHI
1986 // to be symbolic. We now need to go back and update all of the
1987 // entries for the scalars that use the PHI (except for the PHI
1988 // itself) to use the new analyzed value instead of the "symbolic"
1990 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1994 } else if (const SCEVAddRecExpr *AddRec =
1995 dyn_cast<SCEVAddRecExpr>(BEValue)) {
1996 // Otherwise, this could be a loop like this:
1997 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1998 // In this case, j = {1,+,1} and BEValue is j.
1999 // Because the other in-value of i (0) fits the evolution of BEValue
2000 // i really is an addrec evolution.
2001 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2002 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2004 // If StartVal = j.start - j.stride, we can use StartVal as the
2005 // initial step of the addrec evolution.
2006 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2007 AddRec->getOperand(1))) {
2008 SCEVHandle PHISCEV =
2009 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2011 // Okay, for the entire analysis of this edge we assumed the PHI
2012 // to be symbolic. We now need to go back and update all of the
2013 // entries for the scalars that use the PHI (except for the PHI
2014 // itself) to use the new analyzed value instead of the "symbolic"
2016 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2022 return SymbolicName;
2025 // If it's not a loop phi, we can't handle it yet.
2026 return getUnknown(PN);
2029 /// createNodeForGEP - Expand GEP instructions into add and multiply
2030 /// operations. This allows them to be analyzed by regular SCEV code.
2032 SCEVHandle ScalarEvolution::createNodeForGEP(User *GEP) {
2034 const Type *IntPtrTy = TD->getIntPtrType();
2035 Value *Base = GEP->getOperand(0);
2036 // Don't attempt to analyze GEPs over unsized objects.
2037 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2038 return getUnknown(GEP);
2039 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
2040 gep_type_iterator GTI = gep_type_begin(GEP);
2041 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2045 // Compute the (potentially symbolic) offset in bytes for this index.
2046 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2047 // For a struct, add the member offset.
2048 const StructLayout &SL = *TD->getStructLayout(STy);
2049 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2050 uint64_t Offset = SL.getElementOffset(FieldNo);
2051 TotalOffset = getAddExpr(TotalOffset,
2052 getIntegerSCEV(Offset, IntPtrTy));
2054 // For an array, add the element offset, explicitly scaled.
2055 SCEVHandle LocalOffset = getSCEV(Index);
2056 if (!isa<PointerType>(LocalOffset->getType()))
2057 // Getelementptr indicies are signed.
2058 LocalOffset = getTruncateOrSignExtend(LocalOffset,
2061 getMulExpr(LocalOffset,
2062 getIntegerSCEV(TD->getTypeAllocSize(*GTI),
2064 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2067 return getAddExpr(getSCEV(Base), TotalOffset);
2070 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2071 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2072 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2073 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2074 static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
2075 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2076 return C->getValue()->getValue().countTrailingZeros();
2078 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2079 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
2080 (uint32_t)SE.getTypeSizeInBits(T->getType()));
2082 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2083 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2084 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2085 SE.getTypeSizeInBits(E->getType()) : OpRes;
2088 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2089 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2090 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2091 SE.getTypeSizeInBits(E->getType()) : OpRes;
2094 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2095 // The result is the min of all operands results.
2096 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2097 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2098 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2102 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2103 // The result is the sum of all operands results.
2104 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2105 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
2106 for (unsigned i = 1, e = M->getNumOperands();
2107 SumOpRes != BitWidth && i != e; ++i)
2108 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
2113 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2114 // The result is the min of all operands results.
2115 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2116 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2117 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2121 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2122 // The result is the min of all operands results.
2123 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2124 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2125 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2129 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2130 // The result is the min of all operands results.
2131 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2132 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2133 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2137 // SCEVUDivExpr, SCEVUnknown
2141 /// createSCEV - We know that there is no SCEV for the specified value.
2142 /// Analyze the expression.
2144 SCEVHandle ScalarEvolution::createSCEV(Value *V) {
2145 if (!isSCEVable(V->getType()))
2146 return getUnknown(V);
2148 unsigned Opcode = Instruction::UserOp1;
2149 if (Instruction *I = dyn_cast<Instruction>(V))
2150 Opcode = I->getOpcode();
2151 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2152 Opcode = CE->getOpcode();
2154 return getUnknown(V);
2156 User *U = cast<User>(V);
2158 case Instruction::Add:
2159 return getAddExpr(getSCEV(U->getOperand(0)),
2160 getSCEV(U->getOperand(1)));
2161 case Instruction::Mul:
2162 return getMulExpr(getSCEV(U->getOperand(0)),
2163 getSCEV(U->getOperand(1)));
2164 case Instruction::UDiv:
2165 return getUDivExpr(getSCEV(U->getOperand(0)),
2166 getSCEV(U->getOperand(1)));
2167 case Instruction::Sub:
2168 return getMinusSCEV(getSCEV(U->getOperand(0)),
2169 getSCEV(U->getOperand(1)));
2170 case Instruction::And:
2171 // For an expression like x&255 that merely masks off the high bits,
2172 // use zext(trunc(x)) as the SCEV expression.
2173 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2174 if (CI->isNullValue())
2175 return getSCEV(U->getOperand(1));
2176 if (CI->isAllOnesValue())
2177 return getSCEV(U->getOperand(0));
2178 const APInt &A = CI->getValue();
2179 unsigned Ones = A.countTrailingOnes();
2180 if (APIntOps::isMask(Ones, A))
2182 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2183 IntegerType::get(Ones)),
2187 case Instruction::Or:
2188 // If the RHS of the Or is a constant, we may have something like:
2189 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2190 // optimizations will transparently handle this case.
2192 // In order for this transformation to be safe, the LHS must be of the
2193 // form X*(2^n) and the Or constant must be less than 2^n.
2194 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2195 SCEVHandle LHS = getSCEV(U->getOperand(0));
2196 const APInt &CIVal = CI->getValue();
2197 if (GetMinTrailingZeros(LHS, *this) >=
2198 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2199 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2202 case Instruction::Xor:
2203 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2204 // If the RHS of the xor is a signbit, then this is just an add.
2205 // Instcombine turns add of signbit into xor as a strength reduction step.
2206 if (CI->getValue().isSignBit())
2207 return getAddExpr(getSCEV(U->getOperand(0)),
2208 getSCEV(U->getOperand(1)));
2210 // If the RHS of xor is -1, then this is a not operation.
2211 if (CI->isAllOnesValue())
2212 return getNotSCEV(getSCEV(U->getOperand(0)));
2214 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2215 // This is a variant of the check for xor with -1, and it handles
2216 // the case where instcombine has trimmed non-demanded bits out
2217 // of an xor with -1.
2218 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2219 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2220 if (BO->getOpcode() == Instruction::And &&
2221 LCI->getValue() == CI->getValue())
2222 if (const SCEVZeroExtendExpr *Z =
2223 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0))))
2224 return getZeroExtendExpr(getNotSCEV(Z->getOperand()),
2229 case Instruction::Shl:
2230 // Turn shift left of a constant amount into a multiply.
2231 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2232 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2233 Constant *X = ConstantInt::get(
2234 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2235 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2239 case Instruction::LShr:
2240 // Turn logical shift right of a constant into a unsigned divide.
2241 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2242 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2243 Constant *X = ConstantInt::get(
2244 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2245 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2249 case Instruction::AShr:
2250 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2251 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2252 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2253 if (L->getOpcode() == Instruction::Shl &&
2254 L->getOperand(1) == U->getOperand(1)) {
2255 unsigned BitWidth = getTypeSizeInBits(U->getType());
2256 uint64_t Amt = BitWidth - CI->getZExtValue();
2257 if (Amt == BitWidth)
2258 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2260 return getIntegerSCEV(0, U->getType()); // value is undefined
2262 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2263 IntegerType::get(Amt)),
2268 case Instruction::Trunc:
2269 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2271 case Instruction::ZExt:
2272 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2274 case Instruction::SExt:
2275 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2277 case Instruction::BitCast:
2278 // BitCasts are no-op casts so we just eliminate the cast.
2279 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2280 return getSCEV(U->getOperand(0));
2283 case Instruction::IntToPtr:
2284 if (!TD) break; // Without TD we can't analyze pointers.
2285 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2286 TD->getIntPtrType());
2288 case Instruction::PtrToInt:
2289 if (!TD) break; // Without TD we can't analyze pointers.
2290 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2293 case Instruction::GetElementPtr:
2294 if (!TD) break; // Without TD we can't analyze pointers.
2295 return createNodeForGEP(U);
2297 case Instruction::PHI:
2298 return createNodeForPHI(cast<PHINode>(U));
2300 case Instruction::Select:
2301 // This could be a smax or umax that was lowered earlier.
2302 // Try to recover it.
2303 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2304 Value *LHS = ICI->getOperand(0);
2305 Value *RHS = ICI->getOperand(1);
2306 switch (ICI->getPredicate()) {
2307 case ICmpInst::ICMP_SLT:
2308 case ICmpInst::ICMP_SLE:
2309 std::swap(LHS, RHS);
2311 case ICmpInst::ICMP_SGT:
2312 case ICmpInst::ICMP_SGE:
2313 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2314 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2315 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2316 // ~smax(~x, ~y) == smin(x, y).
2317 return getNotSCEV(getSMaxExpr(
2318 getNotSCEV(getSCEV(LHS)),
2319 getNotSCEV(getSCEV(RHS))));
2321 case ICmpInst::ICMP_ULT:
2322 case ICmpInst::ICMP_ULE:
2323 std::swap(LHS, RHS);
2325 case ICmpInst::ICMP_UGT:
2326 case ICmpInst::ICMP_UGE:
2327 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2328 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2329 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2330 // ~umax(~x, ~y) == umin(x, y)
2331 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2332 getNotSCEV(getSCEV(RHS))));
2339 default: // We cannot analyze this expression.
2343 return getUnknown(V);
2348 //===----------------------------------------------------------------------===//
2349 // Iteration Count Computation Code
2352 /// getBackedgeTakenCount - If the specified loop has a predictable
2353 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2354 /// object. The backedge-taken count is the number of times the loop header
2355 /// will be branched to from within the loop. This is one less than the
2356 /// trip count of the loop, since it doesn't count the first iteration,
2357 /// when the header is branched to from outside the loop.
2359 /// Note that it is not valid to call this method on a loop without a
2360 /// loop-invariant backedge-taken count (see
2361 /// hasLoopInvariantBackedgeTakenCount).
2363 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2364 return getBackedgeTakenInfo(L).Exact;
2367 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2368 /// return the least SCEV value that is known never to be less than the
2369 /// actual backedge taken count.
2370 SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2371 return getBackedgeTakenInfo(L).Max;
2374 const ScalarEvolution::BackedgeTakenInfo &
2375 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2376 // Initially insert a CouldNotCompute for this loop. If the insertion
2377 // succeeds, procede to actually compute a backedge-taken count and
2378 // update the value. The temporary CouldNotCompute value tells SCEV
2379 // code elsewhere that it shouldn't attempt to request a new
2380 // backedge-taken count, which could result in infinite recursion.
2381 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2382 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2384 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2385 if (ItCount.Exact != UnknownValue) {
2386 assert(ItCount.Exact->isLoopInvariant(L) &&
2387 ItCount.Max->isLoopInvariant(L) &&
2388 "Computed trip count isn't loop invariant for loop!");
2389 ++NumTripCountsComputed;
2391 // Update the value in the map.
2392 Pair.first->second = ItCount;
2393 } else if (isa<PHINode>(L->getHeader()->begin())) {
2394 // Only count loops that have phi nodes as not being computable.
2395 ++NumTripCountsNotComputed;
2398 // Now that we know more about the trip count for this loop, forget any
2399 // existing SCEV values for PHI nodes in this loop since they are only
2400 // conservative estimates made without the benefit
2401 // of trip count information.
2402 if (ItCount.hasAnyInfo())
2405 return Pair.first->second;
2408 /// forgetLoopBackedgeTakenCount - This method should be called by the
2409 /// client when it has changed a loop in a way that may effect
2410 /// ScalarEvolution's ability to compute a trip count, or if the loop
2412 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2413 BackedgeTakenCounts.erase(L);
2417 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2418 /// PHI nodes in the given loop. This is used when the trip count of
2419 /// the loop may have changed.
2420 void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2421 BasicBlock *Header = L->getHeader();
2423 // Push all Loop-header PHIs onto the Worklist stack, except those
2424 // that are presently represented via a SCEVUnknown. SCEVUnknown for
2425 // a PHI either means that it has an unrecognized structure, or it's
2426 // a PHI that's in the progress of being computed by createNodeForPHI.
2427 // In the former case, additional loop trip count information isn't
2428 // going to change anything. In the later case, createNodeForPHI will
2429 // perform the necessary updates on its own when it gets to that point.
2430 SmallVector<Instruction *, 16> Worklist;
2431 for (BasicBlock::iterator I = Header->begin();
2432 PHINode *PN = dyn_cast<PHINode>(I); ++I) {
2433 std::map<SCEVCallbackVH, SCEVHandle>::iterator It = Scalars.find((Value*)I);
2434 if (It != Scalars.end() && !isa<SCEVUnknown>(It->second))
2435 Worklist.push_back(PN);
2438 while (!Worklist.empty()) {
2439 Instruction *I = Worklist.pop_back_val();
2440 if (Scalars.erase(I))
2441 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2443 Worklist.push_back(cast<Instruction>(UI));
2447 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2448 /// of the specified loop will execute.
2449 ScalarEvolution::BackedgeTakenInfo
2450 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2451 // If the loop has a non-one exit block count, we can't analyze it.
2452 SmallVector<BasicBlock*, 8> ExitBlocks;
2453 L->getExitBlocks(ExitBlocks);
2454 if (ExitBlocks.size() != 1) return UnknownValue;
2456 // Okay, there is one exit block. Try to find the condition that causes the
2457 // loop to be exited.
2458 BasicBlock *ExitBlock = ExitBlocks[0];
2460 BasicBlock *ExitingBlock = 0;
2461 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
2463 if (L->contains(*PI)) {
2464 if (ExitingBlock == 0)
2467 return UnknownValue; // More than one block exiting!
2469 assert(ExitingBlock && "No exits from loop, something is broken!");
2471 // Okay, we've computed the exiting block. See what condition causes us to
2474 // FIXME: we should be able to handle switch instructions (with a single exit)
2475 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2476 if (ExitBr == 0) return UnknownValue;
2477 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2479 // At this point, we know we have a conditional branch that determines whether
2480 // the loop is exited. However, we don't know if the branch is executed each
2481 // time through the loop. If not, then the execution count of the branch will
2482 // not be equal to the trip count of the loop.
2484 // Currently we check for this by checking to see if the Exit branch goes to
2485 // the loop header. If so, we know it will always execute the same number of
2486 // times as the loop. We also handle the case where the exit block *is* the
2487 // loop header. This is common for un-rotated loops. More extensive analysis
2488 // could be done to handle more cases here.
2489 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2490 ExitBr->getSuccessor(1) != L->getHeader() &&
2491 ExitBr->getParent() != L->getHeader())
2492 return UnknownValue;
2494 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2496 // If it's not an integer or pointer comparison then compute it the hard way.
2498 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2499 ExitBr->getSuccessor(0) == ExitBlock);
2501 // If the condition was exit on true, convert the condition to exit on false
2502 ICmpInst::Predicate Cond;
2503 if (ExitBr->getSuccessor(1) == ExitBlock)
2504 Cond = ExitCond->getPredicate();
2506 Cond = ExitCond->getInversePredicate();
2508 // Handle common loops like: for (X = "string"; *X; ++X)
2509 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2510 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2512 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2513 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2516 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2517 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2519 // Try to evaluate any dependencies out of the loop.
2520 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
2521 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
2522 Tmp = getSCEVAtScope(RHS, L);
2523 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
2525 // At this point, we would like to compute how many iterations of the
2526 // loop the predicate will return true for these inputs.
2527 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2528 // If there is a loop-invariant, force it into the RHS.
2529 std::swap(LHS, RHS);
2530 Cond = ICmpInst::getSwappedPredicate(Cond);
2533 // If we have a comparison of a chrec against a constant, try to use value
2534 // ranges to answer this query.
2535 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2536 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2537 if (AddRec->getLoop() == L) {
2538 // Form the constant range.
2539 ConstantRange CompRange(
2540 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
2542 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2543 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2547 case ICmpInst::ICMP_NE: { // while (X != Y)
2548 // Convert to: while (X-Y != 0)
2549 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2550 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2553 case ICmpInst::ICMP_EQ: {
2554 // Convert to: while (X-Y == 0) // while (X == Y)
2555 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2556 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2559 case ICmpInst::ICMP_SLT: {
2560 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2561 if (BTI.hasAnyInfo()) return BTI;
2564 case ICmpInst::ICMP_SGT: {
2565 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2566 getNotSCEV(RHS), L, true);
2567 if (BTI.hasAnyInfo()) return BTI;
2570 case ICmpInst::ICMP_ULT: {
2571 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2572 if (BTI.hasAnyInfo()) return BTI;
2575 case ICmpInst::ICMP_UGT: {
2576 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2577 getNotSCEV(RHS), L, false);
2578 if (BTI.hasAnyInfo()) return BTI;
2583 errs() << "ComputeBackedgeTakenCount ";
2584 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2585 errs() << "[unsigned] ";
2586 errs() << *LHS << " "
2587 << Instruction::getOpcodeName(Instruction::ICmp)
2588 << " " << *RHS << "\n";
2593 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2594 ExitBr->getSuccessor(0) == ExitBlock);
2597 static ConstantInt *
2598 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2599 ScalarEvolution &SE) {
2600 SCEVHandle InVal = SE.getConstant(C);
2601 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2602 assert(isa<SCEVConstant>(Val) &&
2603 "Evaluation of SCEV at constant didn't fold correctly?");
2604 return cast<SCEVConstant>(Val)->getValue();
2607 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2608 /// and a GEP expression (missing the pointer index) indexing into it, return
2609 /// the addressed element of the initializer or null if the index expression is
2612 GetAddressedElementFromGlobal(GlobalVariable *GV,
2613 const std::vector<ConstantInt*> &Indices) {
2614 Constant *Init = GV->getInitializer();
2615 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2616 uint64_t Idx = Indices[i]->getZExtValue();
2617 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2618 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2619 Init = cast<Constant>(CS->getOperand(Idx));
2620 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2621 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2622 Init = cast<Constant>(CA->getOperand(Idx));
2623 } else if (isa<ConstantAggregateZero>(Init)) {
2624 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2625 assert(Idx < STy->getNumElements() && "Bad struct index!");
2626 Init = Constant::getNullValue(STy->getElementType(Idx));
2627 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2628 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2629 Init = Constant::getNullValue(ATy->getElementType());
2631 assert(0 && "Unknown constant aggregate type!");
2635 return 0; // Unknown initializer type
2641 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2642 /// 'icmp op load X, cst', try to see if we can compute the backedge
2643 /// execution count.
2644 SCEVHandle ScalarEvolution::
2645 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2647 ICmpInst::Predicate predicate) {
2648 if (LI->isVolatile()) return UnknownValue;
2650 // Check to see if the loaded pointer is a getelementptr of a global.
2651 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2652 if (!GEP) return UnknownValue;
2654 // Make sure that it is really a constant global we are gepping, with an
2655 // initializer, and make sure the first IDX is really 0.
2656 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2657 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2658 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2659 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2660 return UnknownValue;
2662 // Okay, we allow one non-constant index into the GEP instruction.
2664 std::vector<ConstantInt*> Indexes;
2665 unsigned VarIdxNum = 0;
2666 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2667 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2668 Indexes.push_back(CI);
2669 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2670 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2671 VarIdx = GEP->getOperand(i);
2673 Indexes.push_back(0);
2676 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2677 // Check to see if X is a loop variant variable value now.
2678 SCEVHandle Idx = getSCEV(VarIdx);
2679 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2680 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2682 // We can only recognize very limited forms of loop index expressions, in
2683 // particular, only affine AddRec's like {C1,+,C2}.
2684 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2685 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2686 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2687 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2688 return UnknownValue;
2690 unsigned MaxSteps = MaxBruteForceIterations;
2691 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2692 ConstantInt *ItCst =
2693 ConstantInt::get(IdxExpr->getType(), IterationNum);
2694 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2696 // Form the GEP offset.
2697 Indexes[VarIdxNum] = Val;
2699 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2700 if (Result == 0) break; // Cannot compute!
2702 // Evaluate the condition for this iteration.
2703 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2704 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2705 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2707 errs() << "\n***\n*** Computed loop count " << *ItCst
2708 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2711 ++NumArrayLenItCounts;
2712 return getConstant(ItCst); // Found terminating iteration!
2715 return UnknownValue;
2719 /// CanConstantFold - Return true if we can constant fold an instruction of the
2720 /// specified type, assuming that all operands were constants.
2721 static bool CanConstantFold(const Instruction *I) {
2722 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2723 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2726 if (const CallInst *CI = dyn_cast<CallInst>(I))
2727 if (const Function *F = CI->getCalledFunction())
2728 return canConstantFoldCallTo(F);
2732 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2733 /// in the loop that V is derived from. We allow arbitrary operations along the
2734 /// way, but the operands of an operation must either be constants or a value
2735 /// derived from a constant PHI. If this expression does not fit with these
2736 /// constraints, return null.
2737 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2738 // If this is not an instruction, or if this is an instruction outside of the
2739 // loop, it can't be derived from a loop PHI.
2740 Instruction *I = dyn_cast<Instruction>(V);
2741 if (I == 0 || !L->contains(I->getParent())) return 0;
2743 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2744 if (L->getHeader() == I->getParent())
2747 // We don't currently keep track of the control flow needed to evaluate
2748 // PHIs, so we cannot handle PHIs inside of loops.
2752 // If we won't be able to constant fold this expression even if the operands
2753 // are constants, return early.
2754 if (!CanConstantFold(I)) return 0;
2756 // Otherwise, we can evaluate this instruction if all of its operands are
2757 // constant or derived from a PHI node themselves.
2759 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2760 if (!(isa<Constant>(I->getOperand(Op)) ||
2761 isa<GlobalValue>(I->getOperand(Op)))) {
2762 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2763 if (P == 0) return 0; // Not evolving from PHI
2767 return 0; // Evolving from multiple different PHIs.
2770 // This is a expression evolving from a constant PHI!
2774 /// EvaluateExpression - Given an expression that passes the
2775 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2776 /// in the loop has the value PHIVal. If we can't fold this expression for some
2777 /// reason, return null.
2778 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2779 if (isa<PHINode>(V)) return PHIVal;
2780 if (Constant *C = dyn_cast<Constant>(V)) return C;
2781 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2782 Instruction *I = cast<Instruction>(V);
2784 std::vector<Constant*> Operands;
2785 Operands.resize(I->getNumOperands());
2787 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2788 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2789 if (Operands[i] == 0) return 0;
2792 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2793 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2794 &Operands[0], Operands.size());
2796 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2797 &Operands[0], Operands.size());
2800 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2801 /// in the header of its containing loop, we know the loop executes a
2802 /// constant number of times, and the PHI node is just a recurrence
2803 /// involving constants, fold it.
2804 Constant *ScalarEvolution::
2805 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2806 std::map<PHINode*, Constant*>::iterator I =
2807 ConstantEvolutionLoopExitValue.find(PN);
2808 if (I != ConstantEvolutionLoopExitValue.end())
2811 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2812 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2814 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2816 // Since the loop is canonicalized, the PHI node must have two entries. One
2817 // entry must be a constant (coming in from outside of the loop), and the
2818 // second must be derived from the same PHI.
2819 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2820 Constant *StartCST =
2821 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2823 return RetVal = 0; // Must be a constant.
2825 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2826 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2828 return RetVal = 0; // Not derived from same PHI.
2830 // Execute the loop symbolically to determine the exit value.
2831 if (BEs.getActiveBits() >= 32)
2832 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2834 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2835 unsigned IterationNum = 0;
2836 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2837 if (IterationNum == NumIterations)
2838 return RetVal = PHIVal; // Got exit value!
2840 // Compute the value of the PHI node for the next iteration.
2841 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2842 if (NextPHI == PHIVal)
2843 return RetVal = NextPHI; // Stopped evolving!
2845 return 0; // Couldn't evaluate!
2850 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2851 /// constant number of times (the condition evolves only from constants),
2852 /// try to evaluate a few iterations of the loop until we get the exit
2853 /// condition gets a value of ExitWhen (true or false). If we cannot
2854 /// evaluate the trip count of the loop, return UnknownValue.
2855 SCEVHandle ScalarEvolution::
2856 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2857 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2858 if (PN == 0) return UnknownValue;
2860 // Since the loop is canonicalized, the PHI node must have two entries. One
2861 // entry must be a constant (coming in from outside of the loop), and the
2862 // second must be derived from the same PHI.
2863 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2864 Constant *StartCST =
2865 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2866 if (StartCST == 0) return UnknownValue; // Must be a constant.
2868 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2869 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2870 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2872 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2873 // the loop symbolically to determine when the condition gets a value of
2875 unsigned IterationNum = 0;
2876 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2877 for (Constant *PHIVal = StartCST;
2878 IterationNum != MaxIterations; ++IterationNum) {
2879 ConstantInt *CondVal =
2880 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2882 // Couldn't symbolically evaluate.
2883 if (!CondVal) return UnknownValue;
2885 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2886 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2887 ++NumBruteForceTripCountsComputed;
2888 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2891 // Compute the value of the PHI node for the next iteration.
2892 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2893 if (NextPHI == 0 || NextPHI == PHIVal)
2894 return UnknownValue; // Couldn't evaluate or not making progress...
2898 // Too many iterations were needed to evaluate.
2899 return UnknownValue;
2902 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
2903 /// at the specified scope in the program. The L value specifies a loop
2904 /// nest to evaluate the expression at, where null is the top-level or a
2905 /// specified loop is immediately inside of the loop.
2907 /// This method can be used to compute the exit value for a variable defined
2908 /// in a loop by querying what the value will hold in the parent loop.
2910 /// If this value is not computable at this scope, a SCEVCouldNotCompute
2911 /// object is returned.
2912 SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
2913 // FIXME: this should be turned into a virtual method on SCEV!
2915 if (isa<SCEVConstant>(V)) return V;
2917 // If this instruction is evolved from a constant-evolving PHI, compute the
2918 // exit value from the loop without using SCEVs.
2919 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2920 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2921 const Loop *LI = (*this->LI)[I->getParent()];
2922 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2923 if (PHINode *PN = dyn_cast<PHINode>(I))
2924 if (PN->getParent() == LI->getHeader()) {
2925 // Okay, there is no closed form solution for the PHI node. Check
2926 // to see if the loop that contains it has a known backedge-taken
2927 // count. If so, we may be able to force computation of the exit
2929 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2930 if (const SCEVConstant *BTCC =
2931 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2932 // Okay, we know how many times the containing loop executes. If
2933 // this is a constant evolving PHI node, get the final value at
2934 // the specified iteration number.
2935 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2936 BTCC->getValue()->getValue(),
2938 if (RV) return getUnknown(RV);
2942 // Okay, this is an expression that we cannot symbolically evaluate
2943 // into a SCEV. Check to see if it's possible to symbolically evaluate
2944 // the arguments into constants, and if so, try to constant propagate the
2945 // result. This is particularly useful for computing loop exit values.
2946 if (CanConstantFold(I)) {
2947 // Check to see if we've folded this instruction at this loop before.
2948 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
2949 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
2950 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
2952 return Pair.first->second ? &*getUnknown(Pair.first->second) : V;
2954 std::vector<Constant*> Operands;
2955 Operands.reserve(I->getNumOperands());
2956 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2957 Value *Op = I->getOperand(i);
2958 if (Constant *C = dyn_cast<Constant>(Op)) {
2959 Operands.push_back(C);
2961 // If any of the operands is non-constant and if they are
2962 // non-integer and non-pointer, don't even try to analyze them
2963 // with scev techniques.
2964 if (!isSCEVable(Op->getType()))
2967 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2968 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
2969 Constant *C = SC->getValue();
2970 if (C->getType() != Op->getType())
2971 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2975 Operands.push_back(C);
2976 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2977 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
2978 if (C->getType() != Op->getType())
2980 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2984 Operands.push_back(C);
2994 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2995 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2996 &Operands[0], Operands.size());
2998 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2999 &Operands[0], Operands.size());
3000 Pair.first->second = C;
3001 return getUnknown(C);
3005 // This is some other type of SCEVUnknown, just return it.
3009 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3010 // Avoid performing the look-up in the common case where the specified
3011 // expression has no loop-variant portions.
3012 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3013 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3014 if (OpAtScope != Comm->getOperand(i)) {
3015 if (OpAtScope == UnknownValue) return UnknownValue;
3016 // Okay, at least one of these operands is loop variant but might be
3017 // foldable. Build a new instance of the folded commutative expression.
3018 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
3019 NewOps.push_back(OpAtScope);
3021 for (++i; i != e; ++i) {
3022 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3023 if (OpAtScope == UnknownValue) return UnknownValue;
3024 NewOps.push_back(OpAtScope);
3026 if (isa<SCEVAddExpr>(Comm))
3027 return getAddExpr(NewOps);
3028 if (isa<SCEVMulExpr>(Comm))
3029 return getMulExpr(NewOps);
3030 if (isa<SCEVSMaxExpr>(Comm))
3031 return getSMaxExpr(NewOps);
3032 if (isa<SCEVUMaxExpr>(Comm))
3033 return getUMaxExpr(NewOps);
3034 assert(0 && "Unknown commutative SCEV type!");
3037 // If we got here, all operands are loop invariant.
3041 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3042 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
3043 if (LHS == UnknownValue) return LHS;
3044 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
3045 if (RHS == UnknownValue) return RHS;
3046 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3047 return Div; // must be loop invariant
3048 return getUDivExpr(LHS, RHS);
3051 // If this is a loop recurrence for a loop that does not contain L, then we
3052 // are dealing with the final value computed by the loop.
3053 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3054 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3055 // To evaluate this recurrence, we need to know how many times the AddRec
3056 // loop iterates. Compute this now.
3057 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3058 if (BackedgeTakenCount == UnknownValue) return UnknownValue;
3060 // Then, evaluate the AddRec.
3061 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3063 return UnknownValue;
3066 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3067 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3068 if (Op == UnknownValue) return Op;
3069 if (Op == Cast->getOperand())
3070 return Cast; // must be loop invariant
3071 return getZeroExtendExpr(Op, Cast->getType());
3074 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3075 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3076 if (Op == UnknownValue) return Op;
3077 if (Op == Cast->getOperand())
3078 return Cast; // must be loop invariant
3079 return getSignExtendExpr(Op, Cast->getType());
3082 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3083 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3084 if (Op == UnknownValue) return Op;
3085 if (Op == Cast->getOperand())
3086 return Cast; // must be loop invariant
3087 return getTruncateExpr(Op, Cast->getType());
3090 assert(0 && "Unknown SCEV type!");
3094 /// getSCEVAtScope - This is a convenience function which does
3095 /// getSCEVAtScope(getSCEV(V), L).
3096 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3097 return getSCEVAtScope(getSCEV(V), L);
3100 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3101 /// following equation:
3103 /// A * X = B (mod N)
3105 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3106 /// A and B isn't important.
3108 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3109 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3110 ScalarEvolution &SE) {
3111 uint32_t BW = A.getBitWidth();
3112 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3113 assert(A != 0 && "A must be non-zero.");
3117 // The gcd of A and N may have only one prime factor: 2. The number of
3118 // trailing zeros in A is its multiplicity
3119 uint32_t Mult2 = A.countTrailingZeros();
3122 // 2. Check if B is divisible by D.
3124 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3125 // is not less than multiplicity of this prime factor for D.
3126 if (B.countTrailingZeros() < Mult2)
3127 return SE.getCouldNotCompute();
3129 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3132 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3133 // bit width during computations.
3134 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3135 APInt Mod(BW + 1, 0);
3136 Mod.set(BW - Mult2); // Mod = N / D
3137 APInt I = AD.multiplicativeInverse(Mod);
3139 // 4. Compute the minimum unsigned root of the equation:
3140 // I * (B / D) mod (N / D)
3141 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3143 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3145 return SE.getConstant(Result.trunc(BW));
3148 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3149 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
3150 /// might be the same) or two SCEVCouldNotCompute objects.
3152 static std::pair<SCEVHandle,SCEVHandle>
3153 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
3154 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
3155 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
3156 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
3157 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
3159 // We currently can only solve this if the coefficients are constants.
3160 if (!LC || !MC || !NC) {
3161 const SCEV *CNC = SE.getCouldNotCompute();
3162 return std::make_pair(CNC, CNC);
3165 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
3166 const APInt &L = LC->getValue()->getValue();
3167 const APInt &M = MC->getValue()->getValue();
3168 const APInt &N = NC->getValue()->getValue();
3169 APInt Two(BitWidth, 2);
3170 APInt Four(BitWidth, 4);
3173 using namespace APIntOps;
3175 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
3176 // The B coefficient is M-N/2
3180 // The A coefficient is N/2
3181 APInt A(N.sdiv(Two));
3183 // Compute the B^2-4ac term.
3186 SqrtTerm -= Four * (A * C);
3188 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
3189 // integer value or else APInt::sqrt() will assert.
3190 APInt SqrtVal(SqrtTerm.sqrt());
3192 // Compute the two solutions for the quadratic formula.
3193 // The divisions must be performed as signed divisions.
3195 APInt TwoA( A << 1 );
3196 if (TwoA.isMinValue()) {
3197 const SCEV *CNC = SE.getCouldNotCompute();
3198 return std::make_pair(CNC, CNC);
3201 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
3202 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
3204 return std::make_pair(SE.getConstant(Solution1),
3205 SE.getConstant(Solution2));
3206 } // end APIntOps namespace
3209 /// HowFarToZero - Return the number of times a backedge comparing the specified
3210 /// value to zero will execute. If not computable, return UnknownValue
3211 SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
3212 // If the value is a constant
3213 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3214 // If the value is already zero, the branch will execute zero times.
3215 if (C->getValue()->isZero()) return C;
3216 return UnknownValue; // Otherwise it will loop infinitely.
3219 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
3220 if (!AddRec || AddRec->getLoop() != L)
3221 return UnknownValue;
3223 if (AddRec->isAffine()) {
3224 // If this is an affine expression, the execution count of this branch is
3225 // the minimum unsigned root of the following equation:
3227 // Start + Step*N = 0 (mod 2^BW)
3231 // Step*N = -Start (mod 2^BW)
3233 // where BW is the common bit width of Start and Step.
3235 // Get the initial value for the loop.
3236 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
3237 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
3239 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
3241 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
3242 // For now we handle only constant steps.
3244 // First, handle unitary steps.
3245 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
3246 return getNegativeSCEV(Start); // N = -Start (as unsigned)
3247 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
3248 return Start; // N = Start (as unsigned)
3250 // Then, try to solve the above equation provided that Start is constant.
3251 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
3252 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
3253 -StartC->getValue()->getValue(),
3256 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
3257 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
3258 // the quadratic equation to solve it.
3259 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
3261 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3262 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3265 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
3266 << " sol#2: " << *R2 << "\n";
3268 // Pick the smallest positive root value.
3269 if (ConstantInt *CB =
3270 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3271 R1->getValue(), R2->getValue()))) {
3272 if (CB->getZExtValue() == false)
3273 std::swap(R1, R2); // R1 is the minimum root now.
3275 // We can only use this value if the chrec ends up with an exact zero
3276 // value at this index. When solving for "X*X != 5", for example, we
3277 // should not accept a root of 2.
3278 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
3280 return R1; // We found a quadratic root!
3285 return UnknownValue;
3288 /// HowFarToNonZero - Return the number of times a backedge checking the
3289 /// specified value for nonzero will execute. If not computable, return
3291 SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
3292 // Loops that look like: while (X == 0) are very strange indeed. We don't
3293 // handle them yet except for the trivial case. This could be expanded in the
3294 // future as needed.
3296 // If the value is a constant, check to see if it is known to be non-zero
3297 // already. If so, the backedge will execute zero times.
3298 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3299 if (!C->getValue()->isNullValue())
3300 return getIntegerSCEV(0, C->getType());
3301 return UnknownValue; // Otherwise it will loop infinitely.
3304 // We could implement others, but I really doubt anyone writes loops like
3305 // this, and if they did, they would already be constant folded.
3306 return UnknownValue;
3309 /// getLoopPredecessor - If the given loop's header has exactly one unique
3310 /// predecessor outside the loop, return it. Otherwise return null.
3312 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
3313 BasicBlock *Header = L->getHeader();
3314 BasicBlock *Pred = 0;
3315 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
3317 if (!L->contains(*PI)) {
3318 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
3324 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3325 /// (which may not be an immediate predecessor) which has exactly one
3326 /// successor from which BB is reachable, or null if no such block is
3330 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3331 // If the block has a unique predecessor, then there is no path from the
3332 // predecessor to the block that does not go through the direct edge
3333 // from the predecessor to the block.
3334 if (BasicBlock *Pred = BB->getSinglePredecessor())
3337 // A loop's header is defined to be a block that dominates the loop.
3338 // If the header has a unique predecessor outside the loop, it must be
3339 // a block that has exactly one successor that can reach the loop.
3340 if (Loop *L = LI->getLoopFor(BB))
3341 return getLoopPredecessor(L);
3346 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
3347 /// a conditional between LHS and RHS. This is used to help avoid max
3348 /// expressions in loop trip counts.
3349 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3350 ICmpInst::Predicate Pred,
3351 const SCEV *LHS, const SCEV *RHS) {
3352 // Interpret a null as meaning no loop, where there is obviously no guard
3353 // (interprocedural conditions notwithstanding).
3354 if (!L) return false;
3356 BasicBlock *Predecessor = getLoopPredecessor(L);
3357 BasicBlock *PredecessorDest = L->getHeader();
3359 // Starting at the loop predecessor, climb up the predecessor chain, as long
3360 // as there are predecessors that can be found that have unique successors
3361 // leading to the original header.
3363 PredecessorDest = Predecessor,
3364 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
3366 BranchInst *LoopEntryPredicate =
3367 dyn_cast<BranchInst>(Predecessor->getTerminator());
3368 if (!LoopEntryPredicate ||
3369 LoopEntryPredicate->isUnconditional())
3372 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3375 // Now that we found a conditional branch that dominates the loop, check to
3376 // see if it is the comparison we are looking for.
3377 Value *PreCondLHS = ICI->getOperand(0);
3378 Value *PreCondRHS = ICI->getOperand(1);
3379 ICmpInst::Predicate Cond;
3380 if (LoopEntryPredicate->getSuccessor(0) == PredecessorDest)
3381 Cond = ICI->getPredicate();
3383 Cond = ICI->getInversePredicate();
3386 ; // An exact match.
3387 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3388 ; // The actual condition is beyond sufficient.
3390 // Check a few special cases.
3392 case ICmpInst::ICMP_UGT:
3393 if (Pred == ICmpInst::ICMP_ULT) {
3394 std::swap(PreCondLHS, PreCondRHS);
3395 Cond = ICmpInst::ICMP_ULT;
3399 case ICmpInst::ICMP_SGT:
3400 if (Pred == ICmpInst::ICMP_SLT) {
3401 std::swap(PreCondLHS, PreCondRHS);
3402 Cond = ICmpInst::ICMP_SLT;
3406 case ICmpInst::ICMP_NE:
3407 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3408 // so check for this case by checking if the NE is comparing against
3409 // a minimum or maximum constant.
3410 if (!ICmpInst::isTrueWhenEqual(Pred))
3411 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3412 const APInt &A = CI->getValue();
3414 case ICmpInst::ICMP_SLT:
3415 if (A.isMaxSignedValue()) break;
3417 case ICmpInst::ICMP_SGT:
3418 if (A.isMinSignedValue()) break;
3420 case ICmpInst::ICMP_ULT:
3421 if (A.isMaxValue()) break;
3423 case ICmpInst::ICMP_UGT:
3424 if (A.isMinValue()) break;
3429 Cond = ICmpInst::ICMP_NE;
3430 // NE is symmetric but the original comparison may not be. Swap
3431 // the operands if necessary so that they match below.
3432 if (isa<SCEVConstant>(LHS))
3433 std::swap(PreCondLHS, PreCondRHS);
3438 // We weren't able to reconcile the condition.
3442 if (!PreCondLHS->getType()->isInteger()) continue;
3444 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3445 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3446 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3447 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3448 RHS == getNotSCEV(PreCondLHSSCEV)))
3455 /// HowManyLessThans - Return the number of times a backedge containing the
3456 /// specified less-than comparison will execute. If not computable, return
3458 ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3459 HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
3460 const Loop *L, bool isSigned) {
3461 // Only handle: "ADDREC < LoopInvariant".
3462 if (!RHS->isLoopInvariant(L)) return UnknownValue;
3464 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3465 if (!AddRec || AddRec->getLoop() != L)
3466 return UnknownValue;
3468 if (AddRec->isAffine()) {
3469 // FORNOW: We only support unit strides.
3470 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3471 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3472 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3474 // TODO: handle non-constant strides.
3475 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3476 if (!CStep || CStep->isZero())
3477 return UnknownValue;
3478 if (CStep->isOne()) {
3479 // With unit stride, the iteration never steps past the limit value.
3480 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3481 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3482 // Test whether a positive iteration iteration can step past the limit
3483 // value and past the maximum value for its type in a single step.
3485 APInt Max = APInt::getSignedMaxValue(BitWidth);
3486 if ((Max - CStep->getValue()->getValue())
3487 .slt(CLimit->getValue()->getValue()))
3488 return UnknownValue;
3490 APInt Max = APInt::getMaxValue(BitWidth);
3491 if ((Max - CStep->getValue()->getValue())
3492 .ult(CLimit->getValue()->getValue()))
3493 return UnknownValue;
3496 // TODO: handle non-constant limit values below.
3497 return UnknownValue;
3499 // TODO: handle negative strides below.
3500 return UnknownValue;
3502 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3503 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3504 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3505 // treat m-n as signed nor unsigned due to overflow possibility.
3507 // First, we get the value of the LHS in the first iteration: n
3508 SCEVHandle Start = AddRec->getOperand(0);
3510 // Determine the minimum constant start value.
3511 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3512 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3513 APInt::getMinValue(BitWidth));
3515 // If we know that the condition is true in order to enter the loop,
3516 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3517 // only know if will execute (max(m,n)-n)/s times. In both cases, the
3518 // division must round up.
3519 SCEVHandle End = RHS;
3520 if (!isLoopGuardedByCond(L,
3521 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3522 getMinusSCEV(Start, Step), RHS))
3523 End = isSigned ? getSMaxExpr(RHS, Start)
3524 : getUMaxExpr(RHS, Start);
3526 // Determine the maximum constant end value.
3527 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3528 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3529 APInt::getMaxValue(BitWidth));
3531 // Finally, we subtract these two values and divide, rounding up, to get
3532 // the number of times the backedge is executed.
3533 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3534 getAddExpr(Step, NegOne)),
3537 // The maximum backedge count is similar, except using the minimum start
3538 // value and the maximum end value.
3539 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3541 getAddExpr(Step, NegOne)),
3544 return BackedgeTakenInfo(BECount, MaxBECount);
3547 return UnknownValue;
3550 /// getNumIterationsInRange - Return the number of iterations of this loop that
3551 /// produce values in the specified constant range. Another way of looking at
3552 /// this is that it returns the first iteration number where the value is not in
3553 /// the condition, thus computing the exit count. If the iteration count can't
3554 /// be computed, an instance of SCEVCouldNotCompute is returned.
3555 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3556 ScalarEvolution &SE) const {
3557 if (Range.isFullSet()) // Infinite loop.
3558 return SE.getCouldNotCompute();
3560 // If the start is a non-zero constant, shift the range to simplify things.
3561 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3562 if (!SC->getValue()->isZero()) {
3563 std::vector<SCEVHandle> Operands(op_begin(), op_end());
3564 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3565 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3566 if (const SCEVAddRecExpr *ShiftedAddRec =
3567 dyn_cast<SCEVAddRecExpr>(Shifted))
3568 return ShiftedAddRec->getNumIterationsInRange(
3569 Range.subtract(SC->getValue()->getValue()), SE);
3570 // This is strange and shouldn't happen.
3571 return SE.getCouldNotCompute();
3574 // The only time we can solve this is when we have all constant indices.
3575 // Otherwise, we cannot determine the overflow conditions.
3576 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3577 if (!isa<SCEVConstant>(getOperand(i)))
3578 return SE.getCouldNotCompute();
3581 // Okay at this point we know that all elements of the chrec are constants and
3582 // that the start element is zero.
3584 // First check to see if the range contains zero. If not, the first
3586 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3587 if (!Range.contains(APInt(BitWidth, 0)))
3588 return SE.getConstant(ConstantInt::get(getType(),0));
3591 // If this is an affine expression then we have this situation:
3592 // Solve {0,+,A} in Range === Ax in Range
3594 // We know that zero is in the range. If A is positive then we know that
3595 // the upper value of the range must be the first possible exit value.
3596 // If A is negative then the lower of the range is the last possible loop
3597 // value. Also note that we already checked for a full range.
3598 APInt One(BitWidth,1);
3599 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3600 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3602 // The exit value should be (End+A)/A.
3603 APInt ExitVal = (End + A).udiv(A);
3604 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3606 // Evaluate at the exit value. If we really did fall out of the valid
3607 // range, then we computed our trip count, otherwise wrap around or other
3608 // things must have happened.
3609 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3610 if (Range.contains(Val->getValue()))
3611 return SE.getCouldNotCompute(); // Something strange happened
3613 // Ensure that the previous value is in the range. This is a sanity check.
3614 assert(Range.contains(
3615 EvaluateConstantChrecAtConstant(this,
3616 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3617 "Linear scev computation is off in a bad way!");
3618 return SE.getConstant(ExitValue);
3619 } else if (isQuadratic()) {
3620 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3621 // quadratic equation to solve it. To do this, we must frame our problem in
3622 // terms of figuring out when zero is crossed, instead of when
3623 // Range.getUpper() is crossed.
3624 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3625 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3626 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3628 // Next, solve the constructed addrec
3629 std::pair<SCEVHandle,SCEVHandle> Roots =
3630 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3631 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3632 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3634 // Pick the smallest positive root value.
3635 if (ConstantInt *CB =
3636 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3637 R1->getValue(), R2->getValue()))) {
3638 if (CB->getZExtValue() == false)
3639 std::swap(R1, R2); // R1 is the minimum root now.
3641 // Make sure the root is not off by one. The returned iteration should
3642 // not be in the range, but the previous one should be. When solving
3643 // for "X*X < 5", for example, we should not return a root of 2.
3644 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3647 if (Range.contains(R1Val->getValue())) {
3648 // The next iteration must be out of the range...
3649 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3651 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3652 if (!Range.contains(R1Val->getValue()))
3653 return SE.getConstant(NextVal);
3654 return SE.getCouldNotCompute(); // Something strange happened
3657 // If R1 was not in the range, then it is a good return value. Make
3658 // sure that R1-1 WAS in the range though, just in case.
3659 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3660 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3661 if (Range.contains(R1Val->getValue()))
3663 return SE.getCouldNotCompute(); // Something strange happened
3668 return SE.getCouldNotCompute();
3673 //===----------------------------------------------------------------------===//
3674 // SCEVCallbackVH Class Implementation
3675 //===----------------------------------------------------------------------===//
3677 void ScalarEvolution::SCEVCallbackVH::deleted() {
3678 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3679 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
3680 SE->ConstantEvolutionLoopExitValue.erase(PN);
3681 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
3682 SE->ValuesAtScopes.erase(I);
3683 SE->Scalars.erase(getValPtr());
3684 // this now dangles!
3687 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
3688 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3690 // Forget all the expressions associated with users of the old value,
3691 // so that future queries will recompute the expressions using the new
3693 SmallVector<User *, 16> Worklist;
3694 Value *Old = getValPtr();
3695 bool DeleteOld = false;
3696 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
3698 Worklist.push_back(*UI);
3699 while (!Worklist.empty()) {
3700 User *U = Worklist.pop_back_val();
3701 // Deleting the Old value will cause this to dangle. Postpone
3702 // that until everything else is done.
3707 if (PHINode *PN = dyn_cast<PHINode>(U))
3708 SE->ConstantEvolutionLoopExitValue.erase(PN);
3709 if (Instruction *I = dyn_cast<Instruction>(U))
3710 SE->ValuesAtScopes.erase(I);
3711 if (SE->Scalars.erase(U))
3712 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
3714 Worklist.push_back(*UI);
3717 if (PHINode *PN = dyn_cast<PHINode>(Old))
3718 SE->ConstantEvolutionLoopExitValue.erase(PN);
3719 if (Instruction *I = dyn_cast<Instruction>(Old))
3720 SE->ValuesAtScopes.erase(I);
3721 SE->Scalars.erase(Old);
3722 // this now dangles!
3727 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
3728 : CallbackVH(V), SE(se) {}
3730 //===----------------------------------------------------------------------===//
3731 // ScalarEvolution Class Implementation
3732 //===----------------------------------------------------------------------===//
3734 ScalarEvolution::ScalarEvolution()
3735 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) {
3738 bool ScalarEvolution::runOnFunction(Function &F) {
3740 LI = &getAnalysis<LoopInfo>();
3741 TD = getAnalysisIfAvailable<TargetData>();
3745 void ScalarEvolution::releaseMemory() {
3747 BackedgeTakenCounts.clear();
3748 ConstantEvolutionLoopExitValue.clear();
3749 ValuesAtScopes.clear();
3752 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3753 AU.setPreservesAll();
3754 AU.addRequiredTransitive<LoopInfo>();
3757 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3758 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3761 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3763 // Print all inner loops first
3764 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3765 PrintLoopInfo(OS, SE, *I);
3767 OS << "Loop " << L->getHeader()->getName() << ": ";
3769 SmallVector<BasicBlock*, 8> ExitBlocks;
3770 L->getExitBlocks(ExitBlocks);
3771 if (ExitBlocks.size() != 1)
3772 OS << "<multiple exits> ";
3774 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3775 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3777 OS << "Unpredictable backedge-taken count. ";
3783 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3784 // ScalarEvolution's implementaiton of the print method is to print
3785 // out SCEV values of all instructions that are interesting. Doing
3786 // this potentially causes it to create new SCEV objects though,
3787 // which technically conflicts with the const qualifier. This isn't
3788 // observable from outside the class though (the hasSCEV function
3789 // notwithstanding), so casting away the const isn't dangerous.
3790 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3792 OS << "Classifying expressions for: " << F->getName() << "\n";
3793 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3794 if (isSCEVable(I->getType())) {
3797 SCEVHandle SV = SE.getSCEV(&*I);
3801 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3803 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3804 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3805 OS << "<<Unknown>>";
3815 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3816 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3817 PrintLoopInfo(OS, &SE, *I);
3820 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3821 raw_os_ostream OS(o);