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();
131 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
132 SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
134 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
135 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
139 const Type *SCEVCouldNotCompute::getType() const {
140 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
144 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
149 SCEVHandle SCEVCouldNotCompute::
150 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
151 const SCEVHandle &Conc,
152 ScalarEvolution &SE) const {
156 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
157 OS << "***COULDNOTCOMPUTE***";
160 bool SCEVCouldNotCompute::classof(const SCEV *S) {
161 return S->getSCEVType() == scCouldNotCompute;
165 // SCEVConstants - Only allow the creation of one SCEVConstant for any
166 // particular value. Don't use a SCEVHandle here, or else the object will
168 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
171 SCEVConstant::~SCEVConstant() {
172 SCEVConstants->erase(V);
175 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
176 SCEVConstant *&R = (*SCEVConstants)[V];
177 if (R == 0) R = new SCEVConstant(V);
181 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
182 return getConstant(ConstantInt::get(Val));
185 const Type *SCEVConstant::getType() const { return V->getType(); }
187 void SCEVConstant::print(raw_ostream &OS) const {
188 WriteAsOperand(OS, V, false);
191 SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
192 const SCEVHandle &op, const Type *ty)
193 : SCEV(SCEVTy), Op(op), Ty(ty) {}
195 SCEVCastExpr::~SCEVCastExpr() {}
197 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
198 return Op->dominates(BB, DT);
201 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
202 // particular input. Don't use a SCEVHandle here, or else the object will
204 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
205 SCEVTruncateExpr*> > SCEVTruncates;
207 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
208 : SCEVCastExpr(scTruncate, op, ty) {
209 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
210 (Ty->isInteger() || isa<PointerType>(Ty)) &&
211 "Cannot truncate non-integer value!");
214 SCEVTruncateExpr::~SCEVTruncateExpr() {
215 SCEVTruncates->erase(std::make_pair(Op, Ty));
218 void SCEVTruncateExpr::print(raw_ostream &OS) const {
219 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
222 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
223 // particular input. Don't use a SCEVHandle here, or else the object will never
225 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
226 SCEVZeroExtendExpr*> > SCEVZeroExtends;
228 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
229 : SCEVCastExpr(scZeroExtend, op, ty) {
230 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
231 (Ty->isInteger() || isa<PointerType>(Ty)) &&
232 "Cannot zero extend non-integer value!");
235 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
236 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
239 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
240 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
243 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
244 // particular input. Don't use a SCEVHandle here, or else the object will never
246 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
247 SCEVSignExtendExpr*> > SCEVSignExtends;
249 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
250 : SCEVCastExpr(scSignExtend, op, ty) {
251 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
252 (Ty->isInteger() || isa<PointerType>(Ty)) &&
253 "Cannot sign extend non-integer value!");
256 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
257 SCEVSignExtends->erase(std::make_pair(Op, Ty));
260 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
261 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
264 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
265 // particular input. Don't use a SCEVHandle here, or else the object will never
267 static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >,
268 SCEVCommutativeExpr*> > SCEVCommExprs;
270 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
271 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
272 SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps));
275 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
276 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
277 const char *OpStr = getOperationStr();
278 OS << "(" << *Operands[0];
279 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
280 OS << OpStr << *Operands[i];
284 SCEVHandle SCEVCommutativeExpr::
285 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
286 const SCEVHandle &Conc,
287 ScalarEvolution &SE) const {
288 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
290 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
291 if (H != getOperand(i)) {
292 std::vector<SCEVHandle> NewOps;
293 NewOps.reserve(getNumOperands());
294 for (unsigned j = 0; j != i; ++j)
295 NewOps.push_back(getOperand(j));
297 for (++i; i != e; ++i)
298 NewOps.push_back(getOperand(i)->
299 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
301 if (isa<SCEVAddExpr>(this))
302 return SE.getAddExpr(NewOps);
303 else if (isa<SCEVMulExpr>(this))
304 return SE.getMulExpr(NewOps);
305 else if (isa<SCEVSMaxExpr>(this))
306 return SE.getSMaxExpr(NewOps);
307 else if (isa<SCEVUMaxExpr>(this))
308 return SE.getUMaxExpr(NewOps);
310 assert(0 && "Unknown commutative expr!");
316 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
317 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
318 if (!getOperand(i)->dominates(BB, DT))
325 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
326 // input. Don't use a SCEVHandle here, or else the object will never be
328 static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>,
329 SCEVUDivExpr*> > SCEVUDivs;
331 SCEVUDivExpr::~SCEVUDivExpr() {
332 SCEVUDivs->erase(std::make_pair(LHS, RHS));
335 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
336 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
339 void SCEVUDivExpr::print(raw_ostream &OS) const {
340 OS << "(" << *LHS << " /u " << *RHS << ")";
343 const Type *SCEVUDivExpr::getType() const {
344 return LHS->getType();
347 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
348 // particular input. Don't use a SCEVHandle here, or else the object will never
350 static ManagedStatic<std::map<std::pair<const Loop *,
351 std::vector<const SCEV*> >,
352 SCEVAddRecExpr*> > SCEVAddRecExprs;
354 SCEVAddRecExpr::~SCEVAddRecExpr() {
355 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
356 SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps));
359 SCEVHandle SCEVAddRecExpr::
360 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
361 const SCEVHandle &Conc,
362 ScalarEvolution &SE) const {
363 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
365 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
366 if (H != getOperand(i)) {
367 std::vector<SCEVHandle> NewOps;
368 NewOps.reserve(getNumOperands());
369 for (unsigned j = 0; j != i; ++j)
370 NewOps.push_back(getOperand(j));
372 for (++i; i != e; ++i)
373 NewOps.push_back(getOperand(i)->
374 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
376 return SE.getAddRecExpr(NewOps, L);
383 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
384 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
385 // contain L and if the start is invariant.
386 return !QueryLoop->contains(L->getHeader()) &&
387 getOperand(0)->isLoopInvariant(QueryLoop);
391 void SCEVAddRecExpr::print(raw_ostream &OS) const {
392 OS << "{" << *Operands[0];
393 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
394 OS << ",+," << *Operands[i];
395 OS << "}<" << L->getHeader()->getName() + ">";
398 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
399 // value. Don't use a SCEVHandle here, or else the object will never be
401 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
403 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
405 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
406 // All non-instruction values are loop invariant. All instructions are loop
407 // invariant if they are not contained in the specified loop.
408 if (Instruction *I = dyn_cast<Instruction>(V))
409 return !L->contains(I->getParent());
413 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
414 if (Instruction *I = dyn_cast<Instruction>(getValue()))
415 return DT->dominates(I->getParent(), BB);
419 const Type *SCEVUnknown::getType() const {
423 void SCEVUnknown::print(raw_ostream &OS) const {
424 WriteAsOperand(OS, V, false);
427 //===----------------------------------------------------------------------===//
429 //===----------------------------------------------------------------------===//
432 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
433 /// than the complexity of the RHS. This comparator is used to canonicalize
435 class VISIBILITY_HIDDEN SCEVComplexityCompare {
438 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
440 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
441 // Primarily, sort the SCEVs by their getSCEVType().
442 if (LHS->getSCEVType() != RHS->getSCEVType())
443 return LHS->getSCEVType() < RHS->getSCEVType();
445 // Aside from the getSCEVType() ordering, the particular ordering
446 // isn't very important except that it's beneficial to be consistent,
447 // so that (a + b) and (b + a) don't end up as different expressions.
449 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
450 // not as complete as it could be.
451 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
452 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
454 // Compare getValueID values.
455 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
456 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
458 // Sort arguments by their position.
459 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
460 const Argument *RA = cast<Argument>(RU->getValue());
461 return LA->getArgNo() < RA->getArgNo();
464 // For instructions, compare their loop depth, and their opcode.
465 // This is pretty loose.
466 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
467 Instruction *RV = cast<Instruction>(RU->getValue());
469 // Compare loop depths.
470 if (LI->getLoopDepth(LV->getParent()) !=
471 LI->getLoopDepth(RV->getParent()))
472 return LI->getLoopDepth(LV->getParent()) <
473 LI->getLoopDepth(RV->getParent());
476 if (LV->getOpcode() != RV->getOpcode())
477 return LV->getOpcode() < RV->getOpcode();
479 // Compare the number of operands.
480 if (LV->getNumOperands() != RV->getNumOperands())
481 return LV->getNumOperands() < RV->getNumOperands();
487 // Constant sorting doesn't matter since they'll be folded.
488 if (isa<SCEVConstant>(LHS))
491 // Lexicographically compare n-ary expressions.
492 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
493 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
494 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
495 if (i >= RC->getNumOperands())
497 if (operator()(LC->getOperand(i), RC->getOperand(i)))
499 if (operator()(RC->getOperand(i), LC->getOperand(i)))
502 return LC->getNumOperands() < RC->getNumOperands();
505 // Lexicographically compare udiv expressions.
506 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
507 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
508 if (operator()(LC->getLHS(), RC->getLHS()))
510 if (operator()(RC->getLHS(), LC->getLHS()))
512 if (operator()(LC->getRHS(), RC->getRHS()))
514 if (operator()(RC->getRHS(), LC->getRHS()))
519 // Compare cast expressions by operand.
520 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
521 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
522 return operator()(LC->getOperand(), RC->getOperand());
525 assert(0 && "Unknown SCEV kind!");
531 /// GroupByComplexity - Given a list of SCEV objects, order them by their
532 /// complexity, and group objects of the same complexity together by value.
533 /// When this routine is finished, we know that any duplicates in the vector are
534 /// consecutive and that complexity is monotonically increasing.
536 /// Note that we go take special precautions to ensure that we get determinstic
537 /// results from this routine. In other words, we don't want the results of
538 /// this to depend on where the addresses of various SCEV objects happened to
541 static void GroupByComplexity(std::vector<SCEVHandle> &Ops,
543 if (Ops.size() < 2) return; // Noop
544 if (Ops.size() == 2) {
545 // This is the common case, which also happens to be trivially simple.
547 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
548 std::swap(Ops[0], Ops[1]);
552 // Do the rough sort by complexity.
553 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
555 // Now that we are sorted by complexity, group elements of the same
556 // complexity. Note that this is, at worst, N^2, but the vector is likely to
557 // be extremely short in practice. Note that we take this approach because we
558 // do not want to depend on the addresses of the objects we are grouping.
559 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
560 const SCEV *S = Ops[i];
561 unsigned Complexity = S->getSCEVType();
563 // If there are any objects of the same complexity and same value as this
565 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
566 if (Ops[j] == S) { // Found a duplicate.
567 // Move it to immediately after i'th element.
568 std::swap(Ops[i+1], Ops[j]);
569 ++i; // no need to rescan it.
570 if (i == e-2) return; // Done!
578 //===----------------------------------------------------------------------===//
579 // Simple SCEV method implementations
580 //===----------------------------------------------------------------------===//
582 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
584 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
586 const Type* ResultTy) {
587 // Handle the simplest case efficiently.
589 return SE.getTruncateOrZeroExtend(It, ResultTy);
591 // We are using the following formula for BC(It, K):
593 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
595 // Suppose, W is the bitwidth of the return value. We must be prepared for
596 // overflow. Hence, we must assure that the result of our computation is
597 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
598 // safe in modular arithmetic.
600 // However, this code doesn't use exactly that formula; the formula it uses
601 // is something like the following, where T is the number of factors of 2 in
602 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
605 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
607 // This formula is trivially equivalent to the previous formula. However,
608 // this formula can be implemented much more efficiently. The trick is that
609 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
610 // arithmetic. To do exact division in modular arithmetic, all we have
611 // to do is multiply by the inverse. Therefore, this step can be done at
614 // The next issue is how to safely do the division by 2^T. The way this
615 // is done is by doing the multiplication step at a width of at least W + T
616 // bits. This way, the bottom W+T bits of the product are accurate. Then,
617 // when we perform the division by 2^T (which is equivalent to a right shift
618 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
619 // truncated out after the division by 2^T.
621 // In comparison to just directly using the first formula, this technique
622 // is much more efficient; using the first formula requires W * K bits,
623 // but this formula less than W + K bits. Also, the first formula requires
624 // a division step, whereas this formula only requires multiplies and shifts.
626 // It doesn't matter whether the subtraction step is done in the calculation
627 // width or the input iteration count's width; if the subtraction overflows,
628 // the result must be zero anyway. We prefer here to do it in the width of
629 // the induction variable because it helps a lot for certain cases; CodeGen
630 // isn't smart enough to ignore the overflow, which leads to much less
631 // efficient code if the width of the subtraction is wider than the native
634 // (It's possible to not widen at all by pulling out factors of 2 before
635 // the multiplication; for example, K=2 can be calculated as
636 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
637 // extra arithmetic, so it's not an obvious win, and it gets
638 // much more complicated for K > 3.)
640 // Protection from insane SCEVs; this bound is conservative,
641 // but it probably doesn't matter.
643 return SE.getCouldNotCompute();
645 unsigned W = SE.getTypeSizeInBits(ResultTy);
647 // Calculate K! / 2^T and T; we divide out the factors of two before
648 // multiplying for calculating K! / 2^T to avoid overflow.
649 // Other overflow doesn't matter because we only care about the bottom
650 // W bits of the result.
651 APInt OddFactorial(W, 1);
653 for (unsigned i = 3; i <= K; ++i) {
655 unsigned TwoFactors = Mult.countTrailingZeros();
657 Mult = Mult.lshr(TwoFactors);
658 OddFactorial *= Mult;
661 // We need at least W + T bits for the multiplication step
662 unsigned CalculationBits = W + T;
664 // Calcuate 2^T, at width T+W.
665 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
667 // Calculate the multiplicative inverse of K! / 2^T;
668 // this multiplication factor will perform the exact division by
670 APInt Mod = APInt::getSignedMinValue(W+1);
671 APInt MultiplyFactor = OddFactorial.zext(W+1);
672 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
673 MultiplyFactor = MultiplyFactor.trunc(W);
675 // Calculate the product, at width T+W
676 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
677 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
678 for (unsigned i = 1; i != K; ++i) {
679 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
680 Dividend = SE.getMulExpr(Dividend,
681 SE.getTruncateOrZeroExtend(S, CalculationTy));
685 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
687 // Truncate the result, and divide by K! / 2^T.
689 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
690 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
693 /// evaluateAtIteration - Return the value of this chain of recurrences at
694 /// the specified iteration number. We can evaluate this recurrence by
695 /// multiplying each element in the chain by the binomial coefficient
696 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
698 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
700 /// where BC(It, k) stands for binomial coefficient.
702 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
703 ScalarEvolution &SE) const {
704 SCEVHandle Result = getStart();
705 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
706 // The computation is correct in the face of overflow provided that the
707 // multiplication is performed _after_ the evaluation of the binomial
709 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
710 if (isa<SCEVCouldNotCompute>(Coeff))
713 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
718 //===----------------------------------------------------------------------===//
719 // SCEV Expression folder implementations
720 //===----------------------------------------------------------------------===//
722 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op,
724 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
725 "This is not a truncating conversion!");
726 assert(isSCEVable(Ty) &&
727 "This is not a conversion to a SCEVable type!");
728 Ty = getEffectiveSCEVType(Ty);
730 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
732 ConstantExpr::getTrunc(SC->getValue(), Ty));
734 // trunc(trunc(x)) --> trunc(x)
735 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
736 return getTruncateExpr(ST->getOperand(), Ty);
738 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
739 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
740 return getTruncateOrSignExtend(SS->getOperand(), Ty);
742 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
743 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
744 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
746 // If the input value is a chrec scev made out of constants, truncate
747 // all of the constants.
748 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
749 std::vector<SCEVHandle> Operands;
750 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
751 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
752 return getAddRecExpr(Operands, AddRec->getLoop());
755 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
756 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
760 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
762 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
763 "This is not an extending conversion!");
764 assert(isSCEVable(Ty) &&
765 "This is not a conversion to a SCEVable type!");
766 Ty = getEffectiveSCEVType(Ty);
768 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
769 const Type *IntTy = getEffectiveSCEVType(Ty);
770 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
771 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
772 return getUnknown(C);
775 // zext(zext(x)) --> zext(x)
776 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
777 return getZeroExtendExpr(SZ->getOperand(), Ty);
779 // If the input value is a chrec scev, and we can prove that the value
780 // did not overflow the old, smaller, value, we can zero extend all of the
781 // operands (often constants). This allows analysis of something like
782 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
783 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
784 if (AR->isAffine()) {
785 // Check whether the backedge-taken count is SCEVCouldNotCompute.
786 // Note that this serves two purposes: It filters out loops that are
787 // simply not analyzable, and it covers the case where this code is
788 // being called from within backedge-taken count analysis, such that
789 // attempting to ask for the backedge-taken count would likely result
790 // in infinite recursion. In the later case, the analysis code will
791 // cope with a conservative value, and it will take care to purge
792 // that value once it has finished.
793 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
794 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
795 // Manually compute the final value for AR, checking for
797 SCEVHandle Start = AR->getStart();
798 SCEVHandle Step = AR->getStepRecurrence(*this);
800 // Check whether the backedge-taken count can be losslessly casted to
801 // the addrec's type. The count is always unsigned.
802 SCEVHandle CastedMaxBECount =
803 getTruncateOrZeroExtend(MaxBECount, Start->getType());
805 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) {
807 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
808 // Check whether Start+Step*MaxBECount has no unsigned overflow.
810 getMulExpr(CastedMaxBECount,
811 getTruncateOrZeroExtend(Step, Start->getType()));
812 SCEVHandle Add = getAddExpr(Start, ZMul);
813 if (getZeroExtendExpr(Add, WideTy) ==
814 getAddExpr(getZeroExtendExpr(Start, WideTy),
815 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
816 getZeroExtendExpr(Step, WideTy))))
817 // Return the expression with the addrec on the outside.
818 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
819 getZeroExtendExpr(Step, Ty),
822 // Similar to above, only this time treat the step value as signed.
823 // This covers loops that count down.
825 getMulExpr(CastedMaxBECount,
826 getTruncateOrSignExtend(Step, Start->getType()));
827 Add = getAddExpr(Start, SMul);
828 if (getZeroExtendExpr(Add, WideTy) ==
829 getAddExpr(getZeroExtendExpr(Start, WideTy),
830 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
831 getSignExtendExpr(Step, WideTy))))
832 // Return the expression with the addrec on the outside.
833 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
834 getSignExtendExpr(Step, Ty),
840 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
841 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
845 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
847 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
848 "This is not an extending conversion!");
849 assert(isSCEVable(Ty) &&
850 "This is not a conversion to a SCEVable type!");
851 Ty = getEffectiveSCEVType(Ty);
853 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
854 const Type *IntTy = getEffectiveSCEVType(Ty);
855 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
856 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
857 return getUnknown(C);
860 // sext(sext(x)) --> sext(x)
861 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
862 return getSignExtendExpr(SS->getOperand(), Ty);
864 // If the input value is a chrec scev, and we can prove that the value
865 // did not overflow the old, smaller, value, we can sign extend all of the
866 // operands (often constants). This allows analysis of something like
867 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
868 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
869 if (AR->isAffine()) {
870 // Check whether the backedge-taken count is SCEVCouldNotCompute.
871 // Note that this serves two purposes: It filters out loops that are
872 // simply not analyzable, and it covers the case where this code is
873 // being called from within backedge-taken count analysis, such that
874 // attempting to ask for the backedge-taken count would likely result
875 // in infinite recursion. In the later case, the analysis code will
876 // cope with a conservative value, and it will take care to purge
877 // that value once it has finished.
878 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
879 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
880 // Manually compute the final value for AR, checking for
882 SCEVHandle Start = AR->getStart();
883 SCEVHandle Step = AR->getStepRecurrence(*this);
885 // Check whether the backedge-taken count can be losslessly casted to
886 // the addrec's type. The count is always unsigned.
887 SCEVHandle CastedMaxBECount =
888 getTruncateOrZeroExtend(MaxBECount, Start->getType());
890 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType())) {
892 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
893 // Check whether Start+Step*MaxBECount has no signed overflow.
895 getMulExpr(CastedMaxBECount,
896 getTruncateOrSignExtend(Step, Start->getType()));
897 SCEVHandle Add = getAddExpr(Start, SMul);
898 if (getSignExtendExpr(Add, WideTy) ==
899 getAddExpr(getSignExtendExpr(Start, WideTy),
900 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
901 getSignExtendExpr(Step, WideTy))))
902 // Return the expression with the addrec on the outside.
903 return getAddRecExpr(getSignExtendExpr(Start, Ty),
904 getSignExtendExpr(Step, Ty),
910 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
911 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
915 // get - Get a canonical add expression, or something simpler if possible.
916 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
917 assert(!Ops.empty() && "Cannot get empty add!");
918 if (Ops.size() == 1) return Ops[0];
920 // Sort by complexity, this groups all similar expression types together.
921 GroupByComplexity(Ops, LI);
923 // If there are any constants, fold them together.
925 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
927 assert(Idx < Ops.size());
928 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
929 // We found two constants, fold them together!
930 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
931 RHSC->getValue()->getValue());
932 Ops[0] = getConstant(Fold);
933 Ops.erase(Ops.begin()+1); // Erase the folded element
934 if (Ops.size() == 1) return Ops[0];
935 LHSC = cast<SCEVConstant>(Ops[0]);
938 // If we are left with a constant zero being added, strip it off.
939 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
940 Ops.erase(Ops.begin());
945 if (Ops.size() == 1) return Ops[0];
947 // Okay, check to see if the same value occurs in the operand list twice. If
948 // so, merge them together into an multiply expression. Since we sorted the
949 // list, these values are required to be adjacent.
950 const Type *Ty = Ops[0]->getType();
951 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
952 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
953 // Found a match, merge the two values into a multiply, and add any
954 // remaining values to the result.
955 SCEVHandle Two = getIntegerSCEV(2, Ty);
956 SCEVHandle Mul = getMulExpr(Ops[i], Two);
959 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
961 return getAddExpr(Ops);
964 // Check for truncates. If all the operands are truncated from the same
965 // type, see if factoring out the truncate would permit the result to be
966 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
967 // if the contents of the resulting outer trunc fold to something simple.
968 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
969 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
970 const Type *DstType = Trunc->getType();
971 const Type *SrcType = Trunc->getOperand()->getType();
972 std::vector<SCEVHandle> LargeOps;
974 // Check all the operands to see if they can be represented in the
975 // source type of the truncate.
976 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
977 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
978 if (T->getOperand()->getType() != SrcType) {
982 LargeOps.push_back(T->getOperand());
983 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
984 // This could be either sign or zero extension, but sign extension
985 // is much more likely to be foldable here.
986 LargeOps.push_back(getSignExtendExpr(C, SrcType));
987 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
988 std::vector<SCEVHandle> LargeMulOps;
989 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
990 if (const SCEVTruncateExpr *T =
991 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
992 if (T->getOperand()->getType() != SrcType) {
996 LargeMulOps.push_back(T->getOperand());
997 } else if (const SCEVConstant *C =
998 dyn_cast<SCEVConstant>(M->getOperand(j))) {
999 // This could be either sign or zero extension, but sign extension
1000 // is much more likely to be foldable here.
1001 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1008 LargeOps.push_back(getMulExpr(LargeMulOps));
1015 // Evaluate the expression in the larger type.
1016 SCEVHandle Fold = getAddExpr(LargeOps);
1017 // If it folds to something simple, use it. Otherwise, don't.
1018 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1019 return getTruncateExpr(Fold, DstType);
1023 // Skip past any other cast SCEVs.
1024 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1027 // If there are add operands they would be next.
1028 if (Idx < Ops.size()) {
1029 bool DeletedAdd = false;
1030 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1031 // If we have an add, expand the add operands onto the end of the operands
1033 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1034 Ops.erase(Ops.begin()+Idx);
1038 // If we deleted at least one add, we added operands to the end of the list,
1039 // and they are not necessarily sorted. Recurse to resort and resimplify
1040 // any operands we just aquired.
1042 return getAddExpr(Ops);
1045 // Skip over the add expression until we get to a multiply.
1046 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1049 // If we are adding something to a multiply expression, make sure the
1050 // something is not already an operand of the multiply. If so, merge it into
1052 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1053 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1054 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1055 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1056 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1057 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
1058 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1059 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
1060 if (Mul->getNumOperands() != 2) {
1061 // If the multiply has more than two operands, we must get the
1063 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1064 MulOps.erase(MulOps.begin()+MulOp);
1065 InnerMul = getMulExpr(MulOps);
1067 SCEVHandle One = getIntegerSCEV(1, Ty);
1068 SCEVHandle AddOne = getAddExpr(InnerMul, One);
1069 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1070 if (Ops.size() == 2) return OuterMul;
1072 Ops.erase(Ops.begin()+AddOp);
1073 Ops.erase(Ops.begin()+Idx-1);
1075 Ops.erase(Ops.begin()+Idx);
1076 Ops.erase(Ops.begin()+AddOp-1);
1078 Ops.push_back(OuterMul);
1079 return getAddExpr(Ops);
1082 // Check this multiply against other multiplies being added together.
1083 for (unsigned OtherMulIdx = Idx+1;
1084 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1086 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1087 // If MulOp occurs in OtherMul, we can fold the two multiplies
1089 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1090 OMulOp != e; ++OMulOp)
1091 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1092 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1093 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
1094 if (Mul->getNumOperands() != 2) {
1095 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1096 MulOps.erase(MulOps.begin()+MulOp);
1097 InnerMul1 = getMulExpr(MulOps);
1099 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1100 if (OtherMul->getNumOperands() != 2) {
1101 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
1102 OtherMul->op_end());
1103 MulOps.erase(MulOps.begin()+OMulOp);
1104 InnerMul2 = getMulExpr(MulOps);
1106 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1107 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1108 if (Ops.size() == 2) return OuterMul;
1109 Ops.erase(Ops.begin()+Idx);
1110 Ops.erase(Ops.begin()+OtherMulIdx-1);
1111 Ops.push_back(OuterMul);
1112 return getAddExpr(Ops);
1118 // If there are any add recurrences in the operands list, see if any other
1119 // added values are loop invariant. If so, we can fold them into the
1121 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1124 // Scan over all recurrences, trying to fold loop invariants into them.
1125 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1126 // Scan all of the other operands to this add and add them to the vector if
1127 // they are loop invariant w.r.t. the recurrence.
1128 std::vector<SCEVHandle> LIOps;
1129 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1130 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1131 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1132 LIOps.push_back(Ops[i]);
1133 Ops.erase(Ops.begin()+i);
1137 // If we found some loop invariants, fold them into the recurrence.
1138 if (!LIOps.empty()) {
1139 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1140 LIOps.push_back(AddRec->getStart());
1142 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
1143 AddRecOps[0] = getAddExpr(LIOps);
1145 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1146 // If all of the other operands were loop invariant, we are done.
1147 if (Ops.size() == 1) return NewRec;
1149 // Otherwise, add the folded AddRec by the non-liv parts.
1150 for (unsigned i = 0;; ++i)
1151 if (Ops[i] == AddRec) {
1155 return getAddExpr(Ops);
1158 // Okay, if there weren't any loop invariants to be folded, check to see if
1159 // there are multiple AddRec's with the same loop induction variable being
1160 // added together. If so, we can fold them.
1161 for (unsigned OtherIdx = Idx+1;
1162 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1163 if (OtherIdx != Idx) {
1164 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1165 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1166 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1167 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
1168 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1169 if (i >= NewOps.size()) {
1170 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1171 OtherAddRec->op_end());
1174 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1176 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1178 if (Ops.size() == 2) return NewAddRec;
1180 Ops.erase(Ops.begin()+Idx);
1181 Ops.erase(Ops.begin()+OtherIdx-1);
1182 Ops.push_back(NewAddRec);
1183 return getAddExpr(Ops);
1187 // Otherwise couldn't fold anything into this recurrence. Move onto the
1191 // Okay, it looks like we really DO need an add expr. Check to see if we
1192 // already have one, otherwise create a new one.
1193 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1194 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
1196 if (Result == 0) Result = new SCEVAddExpr(Ops);
1201 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
1202 assert(!Ops.empty() && "Cannot get empty mul!");
1204 // Sort by complexity, this groups all similar expression types together.
1205 GroupByComplexity(Ops, LI);
1207 // If there are any constants, fold them together.
1209 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1211 // C1*(C2+V) -> C1*C2 + C1*V
1212 if (Ops.size() == 2)
1213 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1214 if (Add->getNumOperands() == 2 &&
1215 isa<SCEVConstant>(Add->getOperand(0)))
1216 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1217 getMulExpr(LHSC, Add->getOperand(1)));
1221 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1222 // We found two constants, fold them together!
1223 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1224 RHSC->getValue()->getValue());
1225 Ops[0] = getConstant(Fold);
1226 Ops.erase(Ops.begin()+1); // Erase the folded element
1227 if (Ops.size() == 1) return Ops[0];
1228 LHSC = cast<SCEVConstant>(Ops[0]);
1231 // If we are left with a constant one being multiplied, strip it off.
1232 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1233 Ops.erase(Ops.begin());
1235 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1236 // If we have a multiply of zero, it will always be zero.
1241 // Skip over the add expression until we get to a multiply.
1242 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1245 if (Ops.size() == 1)
1248 // If there are mul operands inline them all into this expression.
1249 if (Idx < Ops.size()) {
1250 bool DeletedMul = false;
1251 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1252 // If we have an mul, expand the mul operands onto the end of the operands
1254 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1255 Ops.erase(Ops.begin()+Idx);
1259 // If we deleted at least one mul, we added operands to the end of the list,
1260 // and they are not necessarily sorted. Recurse to resort and resimplify
1261 // any operands we just aquired.
1263 return getMulExpr(Ops);
1266 // If there are any add recurrences in the operands list, see if any other
1267 // added values are loop invariant. If so, we can fold them into the
1269 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1272 // Scan over all recurrences, trying to fold loop invariants into them.
1273 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1274 // Scan all of the other operands to this mul and add them to the vector if
1275 // they are loop invariant w.r.t. the recurrence.
1276 std::vector<SCEVHandle> LIOps;
1277 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1278 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1279 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1280 LIOps.push_back(Ops[i]);
1281 Ops.erase(Ops.begin()+i);
1285 // If we found some loop invariants, fold them into the recurrence.
1286 if (!LIOps.empty()) {
1287 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1288 std::vector<SCEVHandle> NewOps;
1289 NewOps.reserve(AddRec->getNumOperands());
1290 if (LIOps.size() == 1) {
1291 const SCEV *Scale = LIOps[0];
1292 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1293 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1295 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1296 std::vector<SCEVHandle> MulOps(LIOps);
1297 MulOps.push_back(AddRec->getOperand(i));
1298 NewOps.push_back(getMulExpr(MulOps));
1302 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1304 // If all of the other operands were loop invariant, we are done.
1305 if (Ops.size() == 1) return NewRec;
1307 // Otherwise, multiply the folded AddRec by the non-liv parts.
1308 for (unsigned i = 0;; ++i)
1309 if (Ops[i] == AddRec) {
1313 return getMulExpr(Ops);
1316 // Okay, if there weren't any loop invariants to be folded, check to see if
1317 // there are multiple AddRec's with the same loop induction variable being
1318 // multiplied together. If so, we can fold them.
1319 for (unsigned OtherIdx = Idx+1;
1320 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1321 if (OtherIdx != Idx) {
1322 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1323 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1324 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1325 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1326 SCEVHandle NewStart = getMulExpr(F->getStart(),
1328 SCEVHandle B = F->getStepRecurrence(*this);
1329 SCEVHandle D = G->getStepRecurrence(*this);
1330 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1333 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1335 if (Ops.size() == 2) return NewAddRec;
1337 Ops.erase(Ops.begin()+Idx);
1338 Ops.erase(Ops.begin()+OtherIdx-1);
1339 Ops.push_back(NewAddRec);
1340 return getMulExpr(Ops);
1344 // Otherwise couldn't fold anything into this recurrence. Move onto the
1348 // Okay, it looks like we really DO need an mul expr. Check to see if we
1349 // already have one, otherwise create a new one.
1350 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1351 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1354 Result = new SCEVMulExpr(Ops);
1358 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS,
1359 const SCEVHandle &RHS) {
1360 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1361 if (RHSC->getValue()->equalsInt(1))
1362 return LHS; // X udiv 1 --> x
1364 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1366 // Determine if the division can be folded into the operands of
1368 // TODO: Generalize this to non-constants by using known-bits information.
1369 const Type *Ty = LHS->getType();
1370 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1371 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1372 // For non-power-of-two values, effectively round the value up to the
1373 // nearest power of two.
1374 if (!RHSC->getValue()->getValue().isPowerOf2())
1376 const IntegerType *ExtTy =
1377 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1378 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1379 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1380 if (const SCEVConstant *Step =
1381 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1382 if (!Step->getValue()->getValue()
1383 .urem(RHSC->getValue()->getValue()) &&
1384 getZeroExtendExpr(AR, ExtTy) ==
1385 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1386 getZeroExtendExpr(Step, ExtTy),
1388 std::vector<SCEVHandle> Operands;
1389 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1390 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1391 return getAddRecExpr(Operands, AR->getLoop());
1393 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1394 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1395 std::vector<SCEVHandle> Operands;
1396 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1397 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1398 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1399 // Find an operand that's safely divisible.
1400 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1401 SCEVHandle Op = M->getOperand(i);
1402 SCEVHandle Div = getUDivExpr(Op, RHSC);
1403 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1404 Operands = M->getOperands();
1406 return getMulExpr(Operands);
1410 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1411 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1412 std::vector<SCEVHandle> Operands;
1413 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1414 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1415 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1417 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1418 SCEVHandle Op = getUDivExpr(A->getOperand(i), RHS);
1419 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1421 Operands.push_back(Op);
1423 if (Operands.size() == A->getNumOperands())
1424 return getAddExpr(Operands);
1428 // Fold if both operands are constant.
1429 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1430 Constant *LHSCV = LHSC->getValue();
1431 Constant *RHSCV = RHSC->getValue();
1432 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1436 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1437 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1442 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1443 /// specified loop. Simplify the expression as much as possible.
1444 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1445 const SCEVHandle &Step, const Loop *L) {
1446 std::vector<SCEVHandle> Operands;
1447 Operands.push_back(Start);
1448 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1449 if (StepChrec->getLoop() == L) {
1450 Operands.insert(Operands.end(), StepChrec->op_begin(),
1451 StepChrec->op_end());
1452 return getAddRecExpr(Operands, L);
1455 Operands.push_back(Step);
1456 return getAddRecExpr(Operands, L);
1459 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1460 /// specified loop. Simplify the expression as much as possible.
1461 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1463 if (Operands.size() == 1) return Operands[0];
1465 if (Operands.back()->isZero()) {
1466 Operands.pop_back();
1467 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1470 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1471 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1472 const Loop* NestedLoop = NestedAR->getLoop();
1473 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1474 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1475 NestedAR->op_end());
1476 SCEVHandle NestedARHandle(NestedAR);
1477 Operands[0] = NestedAR->getStart();
1478 NestedOperands[0] = getAddRecExpr(Operands, L);
1479 return getAddRecExpr(NestedOperands, NestedLoop);
1483 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
1484 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)];
1485 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1489 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1490 const SCEVHandle &RHS) {
1491 std::vector<SCEVHandle> Ops;
1494 return getSMaxExpr(Ops);
1497 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1498 assert(!Ops.empty() && "Cannot get empty smax!");
1499 if (Ops.size() == 1) return Ops[0];
1501 // Sort by complexity, this groups all similar expression types together.
1502 GroupByComplexity(Ops, LI);
1504 // If there are any constants, fold them together.
1506 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1508 assert(Idx < Ops.size());
1509 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1510 // We found two constants, fold them together!
1511 ConstantInt *Fold = ConstantInt::get(
1512 APIntOps::smax(LHSC->getValue()->getValue(),
1513 RHSC->getValue()->getValue()));
1514 Ops[0] = getConstant(Fold);
1515 Ops.erase(Ops.begin()+1); // Erase the folded element
1516 if (Ops.size() == 1) return Ops[0];
1517 LHSC = cast<SCEVConstant>(Ops[0]);
1520 // If we are left with a constant -inf, strip it off.
1521 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1522 Ops.erase(Ops.begin());
1527 if (Ops.size() == 1) return Ops[0];
1529 // Find the first SMax
1530 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1533 // Check to see if one of the operands is an SMax. If so, expand its operands
1534 // onto our operand list, and recurse to simplify.
1535 if (Idx < Ops.size()) {
1536 bool DeletedSMax = false;
1537 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1538 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1539 Ops.erase(Ops.begin()+Idx);
1544 return getSMaxExpr(Ops);
1547 // Okay, check to see if the same value occurs in the operand list twice. If
1548 // so, delete one. Since we sorted the list, these values are required to
1550 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1551 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1552 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1556 if (Ops.size() == 1) return Ops[0];
1558 assert(!Ops.empty() && "Reduced smax down to nothing!");
1560 // Okay, it looks like we really DO need an smax expr. Check to see if we
1561 // already have one, otherwise create a new one.
1562 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1563 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1565 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1569 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1570 const SCEVHandle &RHS) {
1571 std::vector<SCEVHandle> Ops;
1574 return getUMaxExpr(Ops);
1577 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1578 assert(!Ops.empty() && "Cannot get empty umax!");
1579 if (Ops.size() == 1) return Ops[0];
1581 // Sort by complexity, this groups all similar expression types together.
1582 GroupByComplexity(Ops, LI);
1584 // If there are any constants, fold them together.
1586 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1588 assert(Idx < Ops.size());
1589 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1590 // We found two constants, fold them together!
1591 ConstantInt *Fold = ConstantInt::get(
1592 APIntOps::umax(LHSC->getValue()->getValue(),
1593 RHSC->getValue()->getValue()));
1594 Ops[0] = getConstant(Fold);
1595 Ops.erase(Ops.begin()+1); // Erase the folded element
1596 if (Ops.size() == 1) return Ops[0];
1597 LHSC = cast<SCEVConstant>(Ops[0]);
1600 // If we are left with a constant zero, strip it off.
1601 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1602 Ops.erase(Ops.begin());
1607 if (Ops.size() == 1) return Ops[0];
1609 // Find the first UMax
1610 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1613 // Check to see if one of the operands is a UMax. If so, expand its operands
1614 // onto our operand list, and recurse to simplify.
1615 if (Idx < Ops.size()) {
1616 bool DeletedUMax = false;
1617 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1618 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1619 Ops.erase(Ops.begin()+Idx);
1624 return getUMaxExpr(Ops);
1627 // Okay, check to see if the same value occurs in the operand list twice. If
1628 // so, delete one. Since we sorted the list, these values are required to
1630 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1631 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1632 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1636 if (Ops.size() == 1) return Ops[0];
1638 assert(!Ops.empty() && "Reduced umax down to nothing!");
1640 // Okay, it looks like we really DO need a umax expr. Check to see if we
1641 // already have one, otherwise create a new one.
1642 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1643 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1645 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1649 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1650 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1651 return getConstant(CI);
1652 if (isa<ConstantPointerNull>(V))
1653 return getIntegerSCEV(0, V->getType());
1654 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1655 if (Result == 0) Result = new SCEVUnknown(V);
1659 //===----------------------------------------------------------------------===//
1660 // Basic SCEV Analysis and PHI Idiom Recognition Code
1663 /// isSCEVable - Test if values of the given type are analyzable within
1664 /// the SCEV framework. This primarily includes integer types, and it
1665 /// can optionally include pointer types if the ScalarEvolution class
1666 /// has access to target-specific information.
1667 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1668 // Integers are always SCEVable.
1669 if (Ty->isInteger())
1672 // Pointers are SCEVable if TargetData information is available
1673 // to provide pointer size information.
1674 if (isa<PointerType>(Ty))
1677 // Otherwise it's not SCEVable.
1681 /// getTypeSizeInBits - Return the size in bits of the specified type,
1682 /// for which isSCEVable must return true.
1683 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1684 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1686 // If we have a TargetData, use it!
1688 return TD->getTypeSizeInBits(Ty);
1690 // Otherwise, we support only integer types.
1691 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1692 return Ty->getPrimitiveSizeInBits();
1695 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1696 /// the given type and which represents how SCEV will treat the given
1697 /// type, for which isSCEVable must return true. For pointer types,
1698 /// this is the pointer-sized integer type.
1699 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1700 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1702 if (Ty->isInteger())
1705 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1706 return TD->getIntPtrType();
1709 SCEVHandle ScalarEvolution::getCouldNotCompute() {
1710 return UnknownValue;
1713 /// hasSCEV - Return true if the SCEV for this value has already been
1715 bool ScalarEvolution::hasSCEV(Value *V) const {
1716 return Scalars.count(V);
1719 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1720 /// expression and create a new one.
1721 SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1722 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1724 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
1725 if (I != Scalars.end()) return I->second;
1726 SCEVHandle S = createSCEV(V);
1727 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
1731 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1732 /// specified signed integer value and return a SCEV for the constant.
1733 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1734 Ty = getEffectiveSCEVType(Ty);
1737 C = Constant::getNullValue(Ty);
1738 else if (Ty->isFloatingPoint())
1739 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1740 APFloat::IEEEdouble, Val));
1742 C = ConstantInt::get(Ty, Val);
1743 return getUnknown(C);
1746 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1748 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1749 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1750 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1752 const Type *Ty = V->getType();
1753 Ty = getEffectiveSCEVType(Ty);
1754 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1757 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1758 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1759 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1760 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1762 const Type *Ty = V->getType();
1763 Ty = getEffectiveSCEVType(Ty);
1764 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1765 return getMinusSCEV(AllOnes, V);
1768 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1770 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1771 const SCEVHandle &RHS) {
1773 return getAddExpr(LHS, getNegativeSCEV(RHS));
1776 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1777 /// input value to the specified type. If the type must be extended, it is zero
1780 ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1782 const Type *SrcTy = V->getType();
1783 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1784 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1785 "Cannot truncate or zero extend with non-integer arguments!");
1786 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1787 return V; // No conversion
1788 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1789 return getTruncateExpr(V, Ty);
1790 return getZeroExtendExpr(V, Ty);
1793 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1794 /// input value to the specified type. If the type must be extended, it is sign
1797 ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1799 const Type *SrcTy = V->getType();
1800 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1801 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1802 "Cannot truncate or zero extend with non-integer arguments!");
1803 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1804 return V; // No conversion
1805 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1806 return getTruncateExpr(V, Ty);
1807 return getSignExtendExpr(V, Ty);
1810 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1811 /// the specified instruction and replaces any references to the symbolic value
1812 /// SymName with the specified value. This is used during PHI resolution.
1813 void ScalarEvolution::
1814 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1815 const SCEVHandle &NewVal) {
1816 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
1817 Scalars.find(SCEVCallbackVH(I, this));
1818 if (SI == Scalars.end()) return;
1821 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
1822 if (NV == SI->second) return; // No change.
1824 SI->second = NV; // Update the scalars map!
1826 // Any instruction values that use this instruction might also need to be
1828 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1830 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1833 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1834 /// a loop header, making it a potential recurrence, or it doesn't.
1836 SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
1837 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1838 if (const Loop *L = LI->getLoopFor(PN->getParent()))
1839 if (L->getHeader() == PN->getParent()) {
1840 // If it lives in the loop header, it has two incoming values, one
1841 // from outside the loop, and one from inside.
1842 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1843 unsigned BackEdge = IncomingEdge^1;
1845 // While we are analyzing this PHI node, handle its value symbolically.
1846 SCEVHandle SymbolicName = getUnknown(PN);
1847 assert(Scalars.find(PN) == Scalars.end() &&
1848 "PHI node already processed?");
1849 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
1851 // Using this symbolic name for the PHI, analyze the value coming around
1853 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1855 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1856 // has a special value for the first iteration of the loop.
1858 // If the value coming around the backedge is an add with the symbolic
1859 // value we just inserted, then we found a simple induction variable!
1860 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1861 // If there is a single occurrence of the symbolic value, replace it
1862 // with a recurrence.
1863 unsigned FoundIndex = Add->getNumOperands();
1864 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1865 if (Add->getOperand(i) == SymbolicName)
1866 if (FoundIndex == e) {
1871 if (FoundIndex != Add->getNumOperands()) {
1872 // Create an add with everything but the specified operand.
1873 std::vector<SCEVHandle> Ops;
1874 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1875 if (i != FoundIndex)
1876 Ops.push_back(Add->getOperand(i));
1877 SCEVHandle Accum = getAddExpr(Ops);
1879 // This is not a valid addrec if the step amount is varying each
1880 // loop iteration, but is not itself an addrec in this loop.
1881 if (Accum->isLoopInvariant(L) ||
1882 (isa<SCEVAddRecExpr>(Accum) &&
1883 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1884 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1885 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
1887 // Okay, for the entire analysis of this edge we assumed the PHI
1888 // to be symbolic. We now need to go back and update all of the
1889 // entries for the scalars that use the PHI (except for the PHI
1890 // itself) to use the new analyzed value instead of the "symbolic"
1892 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1896 } else if (const SCEVAddRecExpr *AddRec =
1897 dyn_cast<SCEVAddRecExpr>(BEValue)) {
1898 // Otherwise, this could be a loop like this:
1899 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1900 // In this case, j = {1,+,1} and BEValue is j.
1901 // Because the other in-value of i (0) fits the evolution of BEValue
1902 // i really is an addrec evolution.
1903 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1904 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1906 // If StartVal = j.start - j.stride, we can use StartVal as the
1907 // initial step of the addrec evolution.
1908 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
1909 AddRec->getOperand(1))) {
1910 SCEVHandle PHISCEV =
1911 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
1913 // Okay, for the entire analysis of this edge we assumed the PHI
1914 // to be symbolic. We now need to go back and update all of the
1915 // entries for the scalars that use the PHI (except for the PHI
1916 // itself) to use the new analyzed value instead of the "symbolic"
1918 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1924 return SymbolicName;
1927 // If it's not a loop phi, we can't handle it yet.
1928 return getUnknown(PN);
1931 /// createNodeForGEP - Expand GEP instructions into add and multiply
1932 /// operations. This allows them to be analyzed by regular SCEV code.
1934 SCEVHandle ScalarEvolution::createNodeForGEP(User *GEP) {
1936 const Type *IntPtrTy = TD->getIntPtrType();
1937 Value *Base = GEP->getOperand(0);
1938 // Don't attempt to analyze GEPs over unsized objects.
1939 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
1940 return getUnknown(GEP);
1941 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
1942 gep_type_iterator GTI = gep_type_begin(GEP);
1943 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
1947 // Compute the (potentially symbolic) offset in bytes for this index.
1948 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
1949 // For a struct, add the member offset.
1950 const StructLayout &SL = *TD->getStructLayout(STy);
1951 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
1952 uint64_t Offset = SL.getElementOffset(FieldNo);
1953 TotalOffset = getAddExpr(TotalOffset,
1954 getIntegerSCEV(Offset, IntPtrTy));
1956 // For an array, add the element offset, explicitly scaled.
1957 SCEVHandle LocalOffset = getSCEV(Index);
1958 if (!isa<PointerType>(LocalOffset->getType()))
1959 // Getelementptr indicies are signed.
1960 LocalOffset = getTruncateOrSignExtend(LocalOffset,
1963 getMulExpr(LocalOffset,
1964 getIntegerSCEV(TD->getTypeAllocSize(*GTI),
1966 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
1969 return getAddExpr(getSCEV(Base), TotalOffset);
1972 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
1973 /// guaranteed to end in (at every loop iteration). It is, at the same time,
1974 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
1975 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
1976 static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
1977 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
1978 return C->getValue()->getValue().countTrailingZeros();
1980 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
1981 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
1982 (uint32_t)SE.getTypeSizeInBits(T->getType()));
1984 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
1985 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1986 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1987 SE.getTypeSizeInBits(E->getType()) : OpRes;
1990 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
1991 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
1992 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
1993 SE.getTypeSizeInBits(E->getType()) : OpRes;
1996 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
1997 // The result is the min of all operands results.
1998 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
1999 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2000 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2004 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2005 // The result is the sum of all operands results.
2006 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2007 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
2008 for (unsigned i = 1, e = M->getNumOperands();
2009 SumOpRes != BitWidth && i != e; ++i)
2010 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
2015 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2016 // The result is the min of all operands results.
2017 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2018 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2019 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2023 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2024 // The result is the min of all operands results.
2025 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2026 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2027 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2031 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2032 // The result is the min of all operands results.
2033 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2034 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2035 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2039 // SCEVUDivExpr, SCEVUnknown
2043 /// createSCEV - We know that there is no SCEV for the specified value.
2044 /// Analyze the expression.
2046 SCEVHandle ScalarEvolution::createSCEV(Value *V) {
2047 if (!isSCEVable(V->getType()))
2048 return getUnknown(V);
2050 unsigned Opcode = Instruction::UserOp1;
2051 if (Instruction *I = dyn_cast<Instruction>(V))
2052 Opcode = I->getOpcode();
2053 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2054 Opcode = CE->getOpcode();
2056 return getUnknown(V);
2058 User *U = cast<User>(V);
2060 case Instruction::Add:
2061 return getAddExpr(getSCEV(U->getOperand(0)),
2062 getSCEV(U->getOperand(1)));
2063 case Instruction::Mul:
2064 return getMulExpr(getSCEV(U->getOperand(0)),
2065 getSCEV(U->getOperand(1)));
2066 case Instruction::UDiv:
2067 return getUDivExpr(getSCEV(U->getOperand(0)),
2068 getSCEV(U->getOperand(1)));
2069 case Instruction::Sub:
2070 return getMinusSCEV(getSCEV(U->getOperand(0)),
2071 getSCEV(U->getOperand(1)));
2072 case Instruction::And:
2073 // For an expression like x&255 that merely masks off the high bits,
2074 // use zext(trunc(x)) as the SCEV expression.
2075 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2076 if (CI->isNullValue())
2077 return getSCEV(U->getOperand(1));
2078 if (CI->isAllOnesValue())
2079 return getSCEV(U->getOperand(0));
2080 const APInt &A = CI->getValue();
2081 unsigned Ones = A.countTrailingOnes();
2082 if (APIntOps::isMask(Ones, A))
2084 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2085 IntegerType::get(Ones)),
2089 case Instruction::Or:
2090 // If the RHS of the Or is a constant, we may have something like:
2091 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2092 // optimizations will transparently handle this case.
2094 // In order for this transformation to be safe, the LHS must be of the
2095 // form X*(2^n) and the Or constant must be less than 2^n.
2096 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2097 SCEVHandle LHS = getSCEV(U->getOperand(0));
2098 const APInt &CIVal = CI->getValue();
2099 if (GetMinTrailingZeros(LHS, *this) >=
2100 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2101 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2104 case Instruction::Xor:
2105 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2106 // If the RHS of the xor is a signbit, then this is just an add.
2107 // Instcombine turns add of signbit into xor as a strength reduction step.
2108 if (CI->getValue().isSignBit())
2109 return getAddExpr(getSCEV(U->getOperand(0)),
2110 getSCEV(U->getOperand(1)));
2112 // If the RHS of xor is -1, then this is a not operation.
2113 else if (CI->isAllOnesValue())
2114 return getNotSCEV(getSCEV(U->getOperand(0)));
2118 case Instruction::Shl:
2119 // Turn shift left of a constant amount into a multiply.
2120 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2121 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2122 Constant *X = ConstantInt::get(
2123 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2124 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2128 case Instruction::LShr:
2129 // Turn logical shift right of a constant into a unsigned divide.
2130 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2131 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2132 Constant *X = ConstantInt::get(
2133 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2134 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2138 case Instruction::AShr:
2139 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2140 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2141 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2142 if (L->getOpcode() == Instruction::Shl &&
2143 L->getOperand(1) == U->getOperand(1)) {
2144 unsigned BitWidth = getTypeSizeInBits(U->getType());
2145 uint64_t Amt = BitWidth - CI->getZExtValue();
2146 if (Amt == BitWidth)
2147 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2149 return getIntegerSCEV(0, U->getType()); // value is undefined
2151 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2152 IntegerType::get(Amt)),
2157 case Instruction::Trunc:
2158 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2160 case Instruction::ZExt:
2161 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2163 case Instruction::SExt:
2164 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2166 case Instruction::BitCast:
2167 // BitCasts are no-op casts so we just eliminate the cast.
2168 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2169 return getSCEV(U->getOperand(0));
2172 case Instruction::IntToPtr:
2173 if (!TD) break; // Without TD we can't analyze pointers.
2174 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2175 TD->getIntPtrType());
2177 case Instruction::PtrToInt:
2178 if (!TD) break; // Without TD we can't analyze pointers.
2179 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2182 case Instruction::GetElementPtr:
2183 if (!TD) break; // Without TD we can't analyze pointers.
2184 return createNodeForGEP(U);
2186 case Instruction::PHI:
2187 return createNodeForPHI(cast<PHINode>(U));
2189 case Instruction::Select:
2190 // This could be a smax or umax that was lowered earlier.
2191 // Try to recover it.
2192 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2193 Value *LHS = ICI->getOperand(0);
2194 Value *RHS = ICI->getOperand(1);
2195 switch (ICI->getPredicate()) {
2196 case ICmpInst::ICMP_SLT:
2197 case ICmpInst::ICMP_SLE:
2198 std::swap(LHS, RHS);
2200 case ICmpInst::ICMP_SGT:
2201 case ICmpInst::ICMP_SGE:
2202 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2203 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2204 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2205 // ~smax(~x, ~y) == smin(x, y).
2206 return getNotSCEV(getSMaxExpr(
2207 getNotSCEV(getSCEV(LHS)),
2208 getNotSCEV(getSCEV(RHS))));
2210 case ICmpInst::ICMP_ULT:
2211 case ICmpInst::ICMP_ULE:
2212 std::swap(LHS, RHS);
2214 case ICmpInst::ICMP_UGT:
2215 case ICmpInst::ICMP_UGE:
2216 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2217 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2218 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2219 // ~umax(~x, ~y) == umin(x, y)
2220 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2221 getNotSCEV(getSCEV(RHS))));
2228 default: // We cannot analyze this expression.
2232 return getUnknown(V);
2237 //===----------------------------------------------------------------------===//
2238 // Iteration Count Computation Code
2241 /// getBackedgeTakenCount - If the specified loop has a predictable
2242 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2243 /// object. The backedge-taken count is the number of times the loop header
2244 /// will be branched to from within the loop. This is one less than the
2245 /// trip count of the loop, since it doesn't count the first iteration,
2246 /// when the header is branched to from outside the loop.
2248 /// Note that it is not valid to call this method on a loop without a
2249 /// loop-invariant backedge-taken count (see
2250 /// hasLoopInvariantBackedgeTakenCount).
2252 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2253 return getBackedgeTakenInfo(L).Exact;
2256 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2257 /// return the least SCEV value that is known never to be less than the
2258 /// actual backedge taken count.
2259 SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2260 return getBackedgeTakenInfo(L).Max;
2263 const ScalarEvolution::BackedgeTakenInfo &
2264 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2265 // Initially insert a CouldNotCompute for this loop. If the insertion
2266 // succeeds, procede to actually compute a backedge-taken count and
2267 // update the value. The temporary CouldNotCompute value tells SCEV
2268 // code elsewhere that it shouldn't attempt to request a new
2269 // backedge-taken count, which could result in infinite recursion.
2270 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2271 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2273 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2274 if (ItCount.Exact != UnknownValue) {
2275 assert(ItCount.Exact->isLoopInvariant(L) &&
2276 ItCount.Max->isLoopInvariant(L) &&
2277 "Computed trip count isn't loop invariant for loop!");
2278 ++NumTripCountsComputed;
2280 // Update the value in the map.
2281 Pair.first->second = ItCount;
2282 } else if (isa<PHINode>(L->getHeader()->begin())) {
2283 // Only count loops that have phi nodes as not being computable.
2284 ++NumTripCountsNotComputed;
2287 // Now that we know more about the trip count for this loop, forget any
2288 // existing SCEV values for PHI nodes in this loop since they are only
2289 // conservative estimates made without the benefit
2290 // of trip count information.
2291 if (ItCount.hasAnyInfo())
2294 return Pair.first->second;
2297 /// forgetLoopBackedgeTakenCount - This method should be called by the
2298 /// client when it has changed a loop in a way that may effect
2299 /// ScalarEvolution's ability to compute a trip count, or if the loop
2301 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2302 BackedgeTakenCounts.erase(L);
2306 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2307 /// PHI nodes in the given loop. This is used when the trip count of
2308 /// the loop may have changed.
2309 void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2310 BasicBlock *Header = L->getHeader();
2312 SmallVector<Instruction *, 16> Worklist;
2313 for (BasicBlock::iterator I = Header->begin();
2314 PHINode *PN = dyn_cast<PHINode>(I); ++I)
2315 Worklist.push_back(PN);
2317 while (!Worklist.empty()) {
2318 Instruction *I = Worklist.pop_back_val();
2319 if (Scalars.erase(I))
2320 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2322 Worklist.push_back(cast<Instruction>(UI));
2326 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2327 /// of the specified loop will execute.
2328 ScalarEvolution::BackedgeTakenInfo
2329 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2330 // If the loop has a non-one exit block count, we can't analyze it.
2331 SmallVector<BasicBlock*, 8> ExitBlocks;
2332 L->getExitBlocks(ExitBlocks);
2333 if (ExitBlocks.size() != 1) return UnknownValue;
2335 // Okay, there is one exit block. Try to find the condition that causes the
2336 // loop to be exited.
2337 BasicBlock *ExitBlock = ExitBlocks[0];
2339 BasicBlock *ExitingBlock = 0;
2340 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
2342 if (L->contains(*PI)) {
2343 if (ExitingBlock == 0)
2346 return UnknownValue; // More than one block exiting!
2348 assert(ExitingBlock && "No exits from loop, something is broken!");
2350 // Okay, we've computed the exiting block. See what condition causes us to
2353 // FIXME: we should be able to handle switch instructions (with a single exit)
2354 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2355 if (ExitBr == 0) return UnknownValue;
2356 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2358 // At this point, we know we have a conditional branch that determines whether
2359 // the loop is exited. However, we don't know if the branch is executed each
2360 // time through the loop. If not, then the execution count of the branch will
2361 // not be equal to the trip count of the loop.
2363 // Currently we check for this by checking to see if the Exit branch goes to
2364 // the loop header. If so, we know it will always execute the same number of
2365 // times as the loop. We also handle the case where the exit block *is* the
2366 // loop header. This is common for un-rotated loops. More extensive analysis
2367 // could be done to handle more cases here.
2368 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2369 ExitBr->getSuccessor(1) != L->getHeader() &&
2370 ExitBr->getParent() != L->getHeader())
2371 return UnknownValue;
2373 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2375 // If it's not an integer or pointer comparison then compute it the hard way.
2377 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2378 ExitBr->getSuccessor(0) == ExitBlock);
2380 // If the condition was exit on true, convert the condition to exit on false
2381 ICmpInst::Predicate Cond;
2382 if (ExitBr->getSuccessor(1) == ExitBlock)
2383 Cond = ExitCond->getPredicate();
2385 Cond = ExitCond->getInversePredicate();
2387 // Handle common loops like: for (X = "string"; *X; ++X)
2388 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2389 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2391 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2392 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2395 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2396 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2398 // Try to evaluate any dependencies out of the loop.
2399 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
2400 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
2401 Tmp = getSCEVAtScope(RHS, L);
2402 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
2404 // At this point, we would like to compute how many iterations of the
2405 // loop the predicate will return true for these inputs.
2406 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2407 // If there is a loop-invariant, force it into the RHS.
2408 std::swap(LHS, RHS);
2409 Cond = ICmpInst::getSwappedPredicate(Cond);
2412 // If we have a comparison of a chrec against a constant, try to use value
2413 // ranges to answer this query.
2414 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2415 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2416 if (AddRec->getLoop() == L) {
2417 // Form the constant range.
2418 ConstantRange CompRange(
2419 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
2421 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2422 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2426 case ICmpInst::ICMP_NE: { // while (X != Y)
2427 // Convert to: while (X-Y != 0)
2428 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2429 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2432 case ICmpInst::ICMP_EQ: {
2433 // Convert to: while (X-Y == 0) // while (X == Y)
2434 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2435 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2438 case ICmpInst::ICMP_SLT: {
2439 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2440 if (BTI.hasAnyInfo()) return BTI;
2443 case ICmpInst::ICMP_SGT: {
2444 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2445 getNotSCEV(RHS), L, true);
2446 if (BTI.hasAnyInfo()) return BTI;
2449 case ICmpInst::ICMP_ULT: {
2450 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2451 if (BTI.hasAnyInfo()) return BTI;
2454 case ICmpInst::ICMP_UGT: {
2455 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2456 getNotSCEV(RHS), L, false);
2457 if (BTI.hasAnyInfo()) return BTI;
2462 errs() << "ComputeBackedgeTakenCount ";
2463 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2464 errs() << "[unsigned] ";
2465 errs() << *LHS << " "
2466 << Instruction::getOpcodeName(Instruction::ICmp)
2467 << " " << *RHS << "\n";
2472 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2473 ExitBr->getSuccessor(0) == ExitBlock);
2476 static ConstantInt *
2477 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2478 ScalarEvolution &SE) {
2479 SCEVHandle InVal = SE.getConstant(C);
2480 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2481 assert(isa<SCEVConstant>(Val) &&
2482 "Evaluation of SCEV at constant didn't fold correctly?");
2483 return cast<SCEVConstant>(Val)->getValue();
2486 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2487 /// and a GEP expression (missing the pointer index) indexing into it, return
2488 /// the addressed element of the initializer or null if the index expression is
2491 GetAddressedElementFromGlobal(GlobalVariable *GV,
2492 const std::vector<ConstantInt*> &Indices) {
2493 Constant *Init = GV->getInitializer();
2494 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2495 uint64_t Idx = Indices[i]->getZExtValue();
2496 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2497 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2498 Init = cast<Constant>(CS->getOperand(Idx));
2499 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2500 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2501 Init = cast<Constant>(CA->getOperand(Idx));
2502 } else if (isa<ConstantAggregateZero>(Init)) {
2503 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2504 assert(Idx < STy->getNumElements() && "Bad struct index!");
2505 Init = Constant::getNullValue(STy->getElementType(Idx));
2506 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2507 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2508 Init = Constant::getNullValue(ATy->getElementType());
2510 assert(0 && "Unknown constant aggregate type!");
2514 return 0; // Unknown initializer type
2520 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2521 /// 'icmp op load X, cst', try to see if we can compute the backedge
2522 /// execution count.
2523 SCEVHandle ScalarEvolution::
2524 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2526 ICmpInst::Predicate predicate) {
2527 if (LI->isVolatile()) return UnknownValue;
2529 // Check to see if the loaded pointer is a getelementptr of a global.
2530 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2531 if (!GEP) return UnknownValue;
2533 // Make sure that it is really a constant global we are gepping, with an
2534 // initializer, and make sure the first IDX is really 0.
2535 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2536 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2537 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2538 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2539 return UnknownValue;
2541 // Okay, we allow one non-constant index into the GEP instruction.
2543 std::vector<ConstantInt*> Indexes;
2544 unsigned VarIdxNum = 0;
2545 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2546 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2547 Indexes.push_back(CI);
2548 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2549 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2550 VarIdx = GEP->getOperand(i);
2552 Indexes.push_back(0);
2555 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2556 // Check to see if X is a loop variant variable value now.
2557 SCEVHandle Idx = getSCEV(VarIdx);
2558 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2559 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2561 // We can only recognize very limited forms of loop index expressions, in
2562 // particular, only affine AddRec's like {C1,+,C2}.
2563 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2564 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2565 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2566 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2567 return UnknownValue;
2569 unsigned MaxSteps = MaxBruteForceIterations;
2570 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2571 ConstantInt *ItCst =
2572 ConstantInt::get(IdxExpr->getType(), IterationNum);
2573 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2575 // Form the GEP offset.
2576 Indexes[VarIdxNum] = Val;
2578 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2579 if (Result == 0) break; // Cannot compute!
2581 // Evaluate the condition for this iteration.
2582 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2583 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2584 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2586 errs() << "\n***\n*** Computed loop count " << *ItCst
2587 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2590 ++NumArrayLenItCounts;
2591 return getConstant(ItCst); // Found terminating iteration!
2594 return UnknownValue;
2598 /// CanConstantFold - Return true if we can constant fold an instruction of the
2599 /// specified type, assuming that all operands were constants.
2600 static bool CanConstantFold(const Instruction *I) {
2601 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2602 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2605 if (const CallInst *CI = dyn_cast<CallInst>(I))
2606 if (const Function *F = CI->getCalledFunction())
2607 return canConstantFoldCallTo(F);
2611 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2612 /// in the loop that V is derived from. We allow arbitrary operations along the
2613 /// way, but the operands of an operation must either be constants or a value
2614 /// derived from a constant PHI. If this expression does not fit with these
2615 /// constraints, return null.
2616 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2617 // If this is not an instruction, or if this is an instruction outside of the
2618 // loop, it can't be derived from a loop PHI.
2619 Instruction *I = dyn_cast<Instruction>(V);
2620 if (I == 0 || !L->contains(I->getParent())) return 0;
2622 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2623 if (L->getHeader() == I->getParent())
2626 // We don't currently keep track of the control flow needed to evaluate
2627 // PHIs, so we cannot handle PHIs inside of loops.
2631 // If we won't be able to constant fold this expression even if the operands
2632 // are constants, return early.
2633 if (!CanConstantFold(I)) return 0;
2635 // Otherwise, we can evaluate this instruction if all of its operands are
2636 // constant or derived from a PHI node themselves.
2638 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2639 if (!(isa<Constant>(I->getOperand(Op)) ||
2640 isa<GlobalValue>(I->getOperand(Op)))) {
2641 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2642 if (P == 0) return 0; // Not evolving from PHI
2646 return 0; // Evolving from multiple different PHIs.
2649 // This is a expression evolving from a constant PHI!
2653 /// EvaluateExpression - Given an expression that passes the
2654 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2655 /// in the loop has the value PHIVal. If we can't fold this expression for some
2656 /// reason, return null.
2657 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2658 if (isa<PHINode>(V)) return PHIVal;
2659 if (Constant *C = dyn_cast<Constant>(V)) return C;
2660 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2661 Instruction *I = cast<Instruction>(V);
2663 std::vector<Constant*> Operands;
2664 Operands.resize(I->getNumOperands());
2666 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2667 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2668 if (Operands[i] == 0) return 0;
2671 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2672 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2673 &Operands[0], Operands.size());
2675 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2676 &Operands[0], Operands.size());
2679 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2680 /// in the header of its containing loop, we know the loop executes a
2681 /// constant number of times, and the PHI node is just a recurrence
2682 /// involving constants, fold it.
2683 Constant *ScalarEvolution::
2684 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2685 std::map<PHINode*, Constant*>::iterator I =
2686 ConstantEvolutionLoopExitValue.find(PN);
2687 if (I != ConstantEvolutionLoopExitValue.end())
2690 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2691 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2693 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2695 // Since the loop is canonicalized, the PHI node must have two entries. One
2696 // entry must be a constant (coming in from outside of the loop), and the
2697 // second must be derived from the same PHI.
2698 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2699 Constant *StartCST =
2700 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2702 return RetVal = 0; // Must be a constant.
2704 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2705 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2707 return RetVal = 0; // Not derived from same PHI.
2709 // Execute the loop symbolically to determine the exit value.
2710 if (BEs.getActiveBits() >= 32)
2711 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2713 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2714 unsigned IterationNum = 0;
2715 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2716 if (IterationNum == NumIterations)
2717 return RetVal = PHIVal; // Got exit value!
2719 // Compute the value of the PHI node for the next iteration.
2720 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2721 if (NextPHI == PHIVal)
2722 return RetVal = NextPHI; // Stopped evolving!
2724 return 0; // Couldn't evaluate!
2729 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2730 /// constant number of times (the condition evolves only from constants),
2731 /// try to evaluate a few iterations of the loop until we get the exit
2732 /// condition gets a value of ExitWhen (true or false). If we cannot
2733 /// evaluate the trip count of the loop, return UnknownValue.
2734 SCEVHandle ScalarEvolution::
2735 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2736 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2737 if (PN == 0) return UnknownValue;
2739 // Since the loop is canonicalized, the PHI node must have two entries. One
2740 // entry must be a constant (coming in from outside of the loop), and the
2741 // second must be derived from the same PHI.
2742 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2743 Constant *StartCST =
2744 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2745 if (StartCST == 0) return UnknownValue; // Must be a constant.
2747 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2748 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2749 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2751 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2752 // the loop symbolically to determine when the condition gets a value of
2754 unsigned IterationNum = 0;
2755 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2756 for (Constant *PHIVal = StartCST;
2757 IterationNum != MaxIterations; ++IterationNum) {
2758 ConstantInt *CondVal =
2759 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2761 // Couldn't symbolically evaluate.
2762 if (!CondVal) return UnknownValue;
2764 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2765 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2766 ++NumBruteForceTripCountsComputed;
2767 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2770 // Compute the value of the PHI node for the next iteration.
2771 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2772 if (NextPHI == 0 || NextPHI == PHIVal)
2773 return UnknownValue; // Couldn't evaluate or not making progress...
2777 // Too many iterations were needed to evaluate.
2778 return UnknownValue;
2781 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
2782 /// at the specified scope in the program. The L value specifies a loop
2783 /// nest to evaluate the expression at, where null is the top-level or a
2784 /// specified loop is immediately inside of the loop.
2786 /// This method can be used to compute the exit value for a variable defined
2787 /// in a loop by querying what the value will hold in the parent loop.
2789 /// If this value is not computable at this scope, a SCEVCouldNotCompute
2790 /// object is returned.
2791 SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
2792 // FIXME: this should be turned into a virtual method on SCEV!
2794 if (isa<SCEVConstant>(V)) return V;
2796 // If this instruction is evolved from a constant-evolving PHI, compute the
2797 // exit value from the loop without using SCEVs.
2798 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2799 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2800 const Loop *LI = (*this->LI)[I->getParent()];
2801 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2802 if (PHINode *PN = dyn_cast<PHINode>(I))
2803 if (PN->getParent() == LI->getHeader()) {
2804 // Okay, there is no closed form solution for the PHI node. Check
2805 // to see if the loop that contains it has a known backedge-taken
2806 // count. If so, we may be able to force computation of the exit
2808 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2809 if (const SCEVConstant *BTCC =
2810 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2811 // Okay, we know how many times the containing loop executes. If
2812 // this is a constant evolving PHI node, get the final value at
2813 // the specified iteration number.
2814 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2815 BTCC->getValue()->getValue(),
2817 if (RV) return getUnknown(RV);
2821 // Okay, this is an expression that we cannot symbolically evaluate
2822 // into a SCEV. Check to see if it's possible to symbolically evaluate
2823 // the arguments into constants, and if so, try to constant propagate the
2824 // result. This is particularly useful for computing loop exit values.
2825 if (CanConstantFold(I)) {
2826 // Check to see if we've folded this instruction at this loop before.
2827 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
2828 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
2829 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
2831 return Pair.first->second ? &*getUnknown(Pair.first->second) : V;
2833 std::vector<Constant*> Operands;
2834 Operands.reserve(I->getNumOperands());
2835 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2836 Value *Op = I->getOperand(i);
2837 if (Constant *C = dyn_cast<Constant>(Op)) {
2838 Operands.push_back(C);
2840 // If any of the operands is non-constant and if they are
2841 // non-integer and non-pointer, don't even try to analyze them
2842 // with scev techniques.
2843 if (!isSCEVable(Op->getType()))
2846 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2847 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
2848 Constant *C = SC->getValue();
2849 if (C->getType() != Op->getType())
2850 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2854 Operands.push_back(C);
2855 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2856 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
2857 if (C->getType() != Op->getType())
2859 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2863 Operands.push_back(C);
2873 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2874 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2875 &Operands[0], Operands.size());
2877 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2878 &Operands[0], Operands.size());
2879 Pair.first->second = C;
2880 return getUnknown(C);
2884 // This is some other type of SCEVUnknown, just return it.
2888 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2889 // Avoid performing the look-up in the common case where the specified
2890 // expression has no loop-variant portions.
2891 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2892 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2893 if (OpAtScope != Comm->getOperand(i)) {
2894 if (OpAtScope == UnknownValue) return UnknownValue;
2895 // Okay, at least one of these operands is loop variant but might be
2896 // foldable. Build a new instance of the folded commutative expression.
2897 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2898 NewOps.push_back(OpAtScope);
2900 for (++i; i != e; ++i) {
2901 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2902 if (OpAtScope == UnknownValue) return UnknownValue;
2903 NewOps.push_back(OpAtScope);
2905 if (isa<SCEVAddExpr>(Comm))
2906 return getAddExpr(NewOps);
2907 if (isa<SCEVMulExpr>(Comm))
2908 return getMulExpr(NewOps);
2909 if (isa<SCEVSMaxExpr>(Comm))
2910 return getSMaxExpr(NewOps);
2911 if (isa<SCEVUMaxExpr>(Comm))
2912 return getUMaxExpr(NewOps);
2913 assert(0 && "Unknown commutative SCEV type!");
2916 // If we got here, all operands are loop invariant.
2920 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
2921 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
2922 if (LHS == UnknownValue) return LHS;
2923 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
2924 if (RHS == UnknownValue) return RHS;
2925 if (LHS == Div->getLHS() && RHS == Div->getRHS())
2926 return Div; // must be loop invariant
2927 return getUDivExpr(LHS, RHS);
2930 // If this is a loop recurrence for a loop that does not contain L, then we
2931 // are dealing with the final value computed by the loop.
2932 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
2933 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
2934 // To evaluate this recurrence, we need to know how many times the AddRec
2935 // loop iterates. Compute this now.
2936 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
2937 if (BackedgeTakenCount == UnknownValue) return UnknownValue;
2939 // Then, evaluate the AddRec.
2940 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
2942 return UnknownValue;
2945 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
2946 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2947 if (Op == UnknownValue) return Op;
2948 if (Op == Cast->getOperand())
2949 return Cast; // must be loop invariant
2950 return getZeroExtendExpr(Op, Cast->getType());
2953 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
2954 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2955 if (Op == UnknownValue) return Op;
2956 if (Op == Cast->getOperand())
2957 return Cast; // must be loop invariant
2958 return getSignExtendExpr(Op, Cast->getType());
2961 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
2962 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
2963 if (Op == UnknownValue) return Op;
2964 if (Op == Cast->getOperand())
2965 return Cast; // must be loop invariant
2966 return getTruncateExpr(Op, Cast->getType());
2969 assert(0 && "Unknown SCEV type!");
2972 /// getSCEVAtScope - This is a convenience function which does
2973 /// getSCEVAtScope(getSCEV(V), L).
2974 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
2975 return getSCEVAtScope(getSCEV(V), L);
2978 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
2979 /// following equation:
2981 /// A * X = B (mod N)
2983 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
2984 /// A and B isn't important.
2986 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
2987 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
2988 ScalarEvolution &SE) {
2989 uint32_t BW = A.getBitWidth();
2990 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
2991 assert(A != 0 && "A must be non-zero.");
2995 // The gcd of A and N may have only one prime factor: 2. The number of
2996 // trailing zeros in A is its multiplicity
2997 uint32_t Mult2 = A.countTrailingZeros();
3000 // 2. Check if B is divisible by D.
3002 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3003 // is not less than multiplicity of this prime factor for D.
3004 if (B.countTrailingZeros() < Mult2)
3005 return SE.getCouldNotCompute();
3007 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3010 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3011 // bit width during computations.
3012 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3013 APInt Mod(BW + 1, 0);
3014 Mod.set(BW - Mult2); // Mod = N / D
3015 APInt I = AD.multiplicativeInverse(Mod);
3017 // 4. Compute the minimum unsigned root of the equation:
3018 // I * (B / D) mod (N / D)
3019 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3021 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3023 return SE.getConstant(Result.trunc(BW));
3026 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3027 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
3028 /// might be the same) or two SCEVCouldNotCompute objects.
3030 static std::pair<SCEVHandle,SCEVHandle>
3031 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
3032 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
3033 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
3034 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
3035 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
3037 // We currently can only solve this if the coefficients are constants.
3038 if (!LC || !MC || !NC) {
3039 const SCEV *CNC = SE.getCouldNotCompute();
3040 return std::make_pair(CNC, CNC);
3043 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
3044 const APInt &L = LC->getValue()->getValue();
3045 const APInt &M = MC->getValue()->getValue();
3046 const APInt &N = NC->getValue()->getValue();
3047 APInt Two(BitWidth, 2);
3048 APInt Four(BitWidth, 4);
3051 using namespace APIntOps;
3053 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
3054 // The B coefficient is M-N/2
3058 // The A coefficient is N/2
3059 APInt A(N.sdiv(Two));
3061 // Compute the B^2-4ac term.
3064 SqrtTerm -= Four * (A * C);
3066 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
3067 // integer value or else APInt::sqrt() will assert.
3068 APInt SqrtVal(SqrtTerm.sqrt());
3070 // Compute the two solutions for the quadratic formula.
3071 // The divisions must be performed as signed divisions.
3073 APInt TwoA( A << 1 );
3074 if (TwoA.isMinValue()) {
3075 const SCEV *CNC = SE.getCouldNotCompute();
3076 return std::make_pair(CNC, CNC);
3079 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
3080 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
3082 return std::make_pair(SE.getConstant(Solution1),
3083 SE.getConstant(Solution2));
3084 } // end APIntOps namespace
3087 /// HowFarToZero - Return the number of times a backedge comparing the specified
3088 /// value to zero will execute. If not computable, return UnknownValue
3089 SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
3090 // If the value is a constant
3091 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3092 // If the value is already zero, the branch will execute zero times.
3093 if (C->getValue()->isZero()) return C;
3094 return UnknownValue; // Otherwise it will loop infinitely.
3097 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
3098 if (!AddRec || AddRec->getLoop() != L)
3099 return UnknownValue;
3101 if (AddRec->isAffine()) {
3102 // If this is an affine expression, the execution count of this branch is
3103 // the minimum unsigned root of the following equation:
3105 // Start + Step*N = 0 (mod 2^BW)
3109 // Step*N = -Start (mod 2^BW)
3111 // where BW is the common bit width of Start and Step.
3113 // Get the initial value for the loop.
3114 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
3115 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
3117 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
3119 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
3120 // For now we handle only constant steps.
3122 // First, handle unitary steps.
3123 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
3124 return getNegativeSCEV(Start); // N = -Start (as unsigned)
3125 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
3126 return Start; // N = Start (as unsigned)
3128 // Then, try to solve the above equation provided that Start is constant.
3129 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
3130 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
3131 -StartC->getValue()->getValue(),
3134 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
3135 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
3136 // the quadratic equation to solve it.
3137 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
3139 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3140 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3143 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
3144 << " sol#2: " << *R2 << "\n";
3146 // Pick the smallest positive root value.
3147 if (ConstantInt *CB =
3148 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3149 R1->getValue(), R2->getValue()))) {
3150 if (CB->getZExtValue() == false)
3151 std::swap(R1, R2); // R1 is the minimum root now.
3153 // We can only use this value if the chrec ends up with an exact zero
3154 // value at this index. When solving for "X*X != 5", for example, we
3155 // should not accept a root of 2.
3156 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
3158 return R1; // We found a quadratic root!
3163 return UnknownValue;
3166 /// HowFarToNonZero - Return the number of times a backedge checking the
3167 /// specified value for nonzero will execute. If not computable, return
3169 SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
3170 // Loops that look like: while (X == 0) are very strange indeed. We don't
3171 // handle them yet except for the trivial case. This could be expanded in the
3172 // future as needed.
3174 // If the value is a constant, check to see if it is known to be non-zero
3175 // already. If so, the backedge will execute zero times.
3176 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3177 if (!C->getValue()->isNullValue())
3178 return getIntegerSCEV(0, C->getType());
3179 return UnknownValue; // Otherwise it will loop infinitely.
3182 // We could implement others, but I really doubt anyone writes loops like
3183 // this, and if they did, they would already be constant folded.
3184 return UnknownValue;
3187 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3188 /// (which may not be an immediate predecessor) which has exactly one
3189 /// successor from which BB is reachable, or null if no such block is
3193 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3194 // If the block has a unique predecessor, then there is no path from the
3195 // predecessor to the block that does not go through the direct edge
3196 // from the predecessor to the block.
3197 if (BasicBlock *Pred = BB->getSinglePredecessor())
3200 // A loop's header is defined to be a block that dominates the loop.
3201 // If the loop has a preheader, it must be a block that has exactly
3202 // one successor that can reach BB. This is slightly more strict
3203 // than necessary, but works if critical edges are split.
3204 if (Loop *L = LI->getLoopFor(BB))
3205 return L->getLoopPreheader();
3210 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
3211 /// a conditional between LHS and RHS. This is used to help avoid max
3212 /// expressions in loop trip counts.
3213 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3214 ICmpInst::Predicate Pred,
3215 const SCEV *LHS, const SCEV *RHS) {
3216 BasicBlock *Preheader = L->getLoopPreheader();
3217 BasicBlock *PreheaderDest = L->getHeader();
3219 // Starting at the preheader, climb up the predecessor chain, as long as
3220 // there are predecessors that can be found that have unique successors
3221 // leading to the original header.
3223 PreheaderDest = Preheader,
3224 Preheader = getPredecessorWithUniqueSuccessorForBB(Preheader)) {
3226 BranchInst *LoopEntryPredicate =
3227 dyn_cast<BranchInst>(Preheader->getTerminator());
3228 if (!LoopEntryPredicate ||
3229 LoopEntryPredicate->isUnconditional())
3232 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3235 // Now that we found a conditional branch that dominates the loop, check to
3236 // see if it is the comparison we are looking for.
3237 Value *PreCondLHS = ICI->getOperand(0);
3238 Value *PreCondRHS = ICI->getOperand(1);
3239 ICmpInst::Predicate Cond;
3240 if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
3241 Cond = ICI->getPredicate();
3243 Cond = ICI->getInversePredicate();
3246 ; // An exact match.
3247 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3248 ; // The actual condition is beyond sufficient.
3250 // Check a few special cases.
3252 case ICmpInst::ICMP_UGT:
3253 if (Pred == ICmpInst::ICMP_ULT) {
3254 std::swap(PreCondLHS, PreCondRHS);
3255 Cond = ICmpInst::ICMP_ULT;
3259 case ICmpInst::ICMP_SGT:
3260 if (Pred == ICmpInst::ICMP_SLT) {
3261 std::swap(PreCondLHS, PreCondRHS);
3262 Cond = ICmpInst::ICMP_SLT;
3266 case ICmpInst::ICMP_NE:
3267 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3268 // so check for this case by checking if the NE is comparing against
3269 // a minimum or maximum constant.
3270 if (!ICmpInst::isTrueWhenEqual(Pred))
3271 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3272 const APInt &A = CI->getValue();
3274 case ICmpInst::ICMP_SLT:
3275 if (A.isMaxSignedValue()) break;
3277 case ICmpInst::ICMP_SGT:
3278 if (A.isMinSignedValue()) break;
3280 case ICmpInst::ICMP_ULT:
3281 if (A.isMaxValue()) break;
3283 case ICmpInst::ICMP_UGT:
3284 if (A.isMinValue()) break;
3289 Cond = ICmpInst::ICMP_NE;
3290 // NE is symmetric but the original comparison may not be. Swap
3291 // the operands if necessary so that they match below.
3292 if (isa<SCEVConstant>(LHS))
3293 std::swap(PreCondLHS, PreCondRHS);
3298 // We weren't able to reconcile the condition.
3302 if (!PreCondLHS->getType()->isInteger()) continue;
3304 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3305 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3306 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3307 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3308 RHS == getNotSCEV(PreCondLHSSCEV)))
3315 /// HowManyLessThans - Return the number of times a backedge containing the
3316 /// specified less-than comparison will execute. If not computable, return
3318 ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3319 HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
3320 const Loop *L, bool isSigned) {
3321 // Only handle: "ADDREC < LoopInvariant".
3322 if (!RHS->isLoopInvariant(L)) return UnknownValue;
3324 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3325 if (!AddRec || AddRec->getLoop() != L)
3326 return UnknownValue;
3328 if (AddRec->isAffine()) {
3329 // FORNOW: We only support unit strides.
3330 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3331 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3332 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3334 // TODO: handle non-constant strides.
3335 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3336 if (!CStep || CStep->isZero())
3337 return UnknownValue;
3338 if (CStep->getValue()->getValue() == 1) {
3339 // With unit stride, the iteration never steps past the limit value.
3340 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3341 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3342 // Test whether a positive iteration iteration can step past the limit
3343 // value and past the maximum value for its type in a single step.
3345 APInt Max = APInt::getSignedMaxValue(BitWidth);
3346 if ((Max - CStep->getValue()->getValue())
3347 .slt(CLimit->getValue()->getValue()))
3348 return UnknownValue;
3350 APInt Max = APInt::getMaxValue(BitWidth);
3351 if ((Max - CStep->getValue()->getValue())
3352 .ult(CLimit->getValue()->getValue()))
3353 return UnknownValue;
3356 // TODO: handle non-constant limit values below.
3357 return UnknownValue;
3359 // TODO: handle negative strides below.
3360 return UnknownValue;
3362 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3363 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3364 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3365 // treat m-n as signed nor unsigned due to overflow possibility.
3367 // First, we get the value of the LHS in the first iteration: n
3368 SCEVHandle Start = AddRec->getOperand(0);
3370 // Determine the minimum constant start value.
3371 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3372 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3373 APInt::getMinValue(BitWidth));
3375 // If we know that the condition is true in order to enter the loop,
3376 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3377 // only know if will execute (max(m,n)-n)/s times. In both cases, the
3378 // division must round up.
3379 SCEVHandle End = RHS;
3380 if (!isLoopGuardedByCond(L,
3381 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3382 getMinusSCEV(Start, Step), RHS))
3383 End = isSigned ? getSMaxExpr(RHS, Start)
3384 : getUMaxExpr(RHS, Start);
3386 // Determine the maximum constant end value.
3387 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3388 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3389 APInt::getMaxValue(BitWidth));
3391 // Finally, we subtract these two values and divide, rounding up, to get
3392 // the number of times the backedge is executed.
3393 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3394 getAddExpr(Step, NegOne)),
3397 // The maximum backedge count is similar, except using the minimum start
3398 // value and the maximum end value.
3399 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3401 getAddExpr(Step, NegOne)),
3404 return BackedgeTakenInfo(BECount, MaxBECount);
3407 return UnknownValue;
3410 /// getNumIterationsInRange - Return the number of iterations of this loop that
3411 /// produce values in the specified constant range. Another way of looking at
3412 /// this is that it returns the first iteration number where the value is not in
3413 /// the condition, thus computing the exit count. If the iteration count can't
3414 /// be computed, an instance of SCEVCouldNotCompute is returned.
3415 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3416 ScalarEvolution &SE) const {
3417 if (Range.isFullSet()) // Infinite loop.
3418 return SE.getCouldNotCompute();
3420 // If the start is a non-zero constant, shift the range to simplify things.
3421 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3422 if (!SC->getValue()->isZero()) {
3423 std::vector<SCEVHandle> Operands(op_begin(), op_end());
3424 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3425 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3426 if (const SCEVAddRecExpr *ShiftedAddRec =
3427 dyn_cast<SCEVAddRecExpr>(Shifted))
3428 return ShiftedAddRec->getNumIterationsInRange(
3429 Range.subtract(SC->getValue()->getValue()), SE);
3430 // This is strange and shouldn't happen.
3431 return SE.getCouldNotCompute();
3434 // The only time we can solve this is when we have all constant indices.
3435 // Otherwise, we cannot determine the overflow conditions.
3436 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3437 if (!isa<SCEVConstant>(getOperand(i)))
3438 return SE.getCouldNotCompute();
3441 // Okay at this point we know that all elements of the chrec are constants and
3442 // that the start element is zero.
3444 // First check to see if the range contains zero. If not, the first
3446 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3447 if (!Range.contains(APInt(BitWidth, 0)))
3448 return SE.getConstant(ConstantInt::get(getType(),0));
3451 // If this is an affine expression then we have this situation:
3452 // Solve {0,+,A} in Range === Ax in Range
3454 // We know that zero is in the range. If A is positive then we know that
3455 // the upper value of the range must be the first possible exit value.
3456 // If A is negative then the lower of the range is the last possible loop
3457 // value. Also note that we already checked for a full range.
3458 APInt One(BitWidth,1);
3459 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3460 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3462 // The exit value should be (End+A)/A.
3463 APInt ExitVal = (End + A).udiv(A);
3464 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3466 // Evaluate at the exit value. If we really did fall out of the valid
3467 // range, then we computed our trip count, otherwise wrap around or other
3468 // things must have happened.
3469 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3470 if (Range.contains(Val->getValue()))
3471 return SE.getCouldNotCompute(); // Something strange happened
3473 // Ensure that the previous value is in the range. This is a sanity check.
3474 assert(Range.contains(
3475 EvaluateConstantChrecAtConstant(this,
3476 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3477 "Linear scev computation is off in a bad way!");
3478 return SE.getConstant(ExitValue);
3479 } else if (isQuadratic()) {
3480 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3481 // quadratic equation to solve it. To do this, we must frame our problem in
3482 // terms of figuring out when zero is crossed, instead of when
3483 // Range.getUpper() is crossed.
3484 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3485 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3486 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3488 // Next, solve the constructed addrec
3489 std::pair<SCEVHandle,SCEVHandle> Roots =
3490 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3491 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3492 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3494 // Pick the smallest positive root value.
3495 if (ConstantInt *CB =
3496 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3497 R1->getValue(), R2->getValue()))) {
3498 if (CB->getZExtValue() == false)
3499 std::swap(R1, R2); // R1 is the minimum root now.
3501 // Make sure the root is not off by one. The returned iteration should
3502 // not be in the range, but the previous one should be. When solving
3503 // for "X*X < 5", for example, we should not return a root of 2.
3504 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3507 if (Range.contains(R1Val->getValue())) {
3508 // The next iteration must be out of the range...
3509 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3511 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3512 if (!Range.contains(R1Val->getValue()))
3513 return SE.getConstant(NextVal);
3514 return SE.getCouldNotCompute(); // Something strange happened
3517 // If R1 was not in the range, then it is a good return value. Make
3518 // sure that R1-1 WAS in the range though, just in case.
3519 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3520 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3521 if (Range.contains(R1Val->getValue()))
3523 return SE.getCouldNotCompute(); // Something strange happened
3528 return SE.getCouldNotCompute();
3533 //===----------------------------------------------------------------------===//
3534 // SCEVCallbackVH Class Implementation
3535 //===----------------------------------------------------------------------===//
3537 void SCEVCallbackVH::deleted() {
3538 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3539 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
3540 SE->ConstantEvolutionLoopExitValue.erase(PN);
3541 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
3542 SE->ValuesAtScopes.erase(I);
3543 SE->Scalars.erase(getValPtr());
3544 // this now dangles!
3547 void SCEVCallbackVH::allUsesReplacedWith(Value *) {
3548 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3550 // Forget all the expressions associated with users of the old value,
3551 // so that future queries will recompute the expressions using the new
3553 SmallVector<User *, 16> Worklist;
3554 Value *Old = getValPtr();
3555 bool DeleteOld = false;
3556 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
3558 Worklist.push_back(*UI);
3559 while (!Worklist.empty()) {
3560 User *U = Worklist.pop_back_val();
3561 // Deleting the Old value will cause this to dangle. Postpone
3562 // that until everything else is done.
3567 if (PHINode *PN = dyn_cast<PHINode>(U))
3568 SE->ConstantEvolutionLoopExitValue.erase(PN);
3569 if (Instruction *I = dyn_cast<Instruction>(U))
3570 SE->ValuesAtScopes.erase(I);
3571 if (SE->Scalars.erase(U))
3572 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
3574 Worklist.push_back(*UI);
3577 if (PHINode *PN = dyn_cast<PHINode>(Old))
3578 SE->ConstantEvolutionLoopExitValue.erase(PN);
3579 if (Instruction *I = dyn_cast<Instruction>(Old))
3580 SE->ValuesAtScopes.erase(I);
3581 SE->Scalars.erase(Old);
3582 // this now dangles!
3587 SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
3588 : CallbackVH(V), SE(se) {}
3590 //===----------------------------------------------------------------------===//
3591 // ScalarEvolution Class Implementation
3592 //===----------------------------------------------------------------------===//
3594 ScalarEvolution::ScalarEvolution()
3595 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) {
3598 bool ScalarEvolution::runOnFunction(Function &F) {
3600 LI = &getAnalysis<LoopInfo>();
3601 TD = getAnalysisIfAvailable<TargetData>();
3605 void ScalarEvolution::releaseMemory() {
3607 BackedgeTakenCounts.clear();
3608 ConstantEvolutionLoopExitValue.clear();
3609 ValuesAtScopes.clear();
3612 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3613 AU.setPreservesAll();
3614 AU.addRequiredTransitive<LoopInfo>();
3617 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3618 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3621 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3623 // Print all inner loops first
3624 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3625 PrintLoopInfo(OS, SE, *I);
3627 OS << "Loop " << L->getHeader()->getName() << ": ";
3629 SmallVector<BasicBlock*, 8> ExitBlocks;
3630 L->getExitBlocks(ExitBlocks);
3631 if (ExitBlocks.size() != 1)
3632 OS << "<multiple exits> ";
3634 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3635 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3637 OS << "Unpredictable backedge-taken count. ";
3643 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3644 // ScalarEvolution's implementaiton of the print method is to print
3645 // out SCEV values of all instructions that are interesting. Doing
3646 // this potentially causes it to create new SCEV objects though,
3647 // which technically conflicts with the const qualifier. This isn't
3648 // observable from outside the class though (the hasSCEV function
3649 // notwithstanding), so casting away the const isn't dangerous.
3650 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3652 OS << "Classifying expressions for: " << F->getName() << "\n";
3653 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3654 if (isSCEVable(I->getType())) {
3657 SCEVHandle SV = SE.getSCEV(&*I);
3661 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3663 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3664 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3665 OS << "<<Unknown>>";
3675 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3676 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3677 PrintLoopInfo(OS, &SE, *I);
3680 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3681 raw_os_ostream OS(o);