1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/Dominators.h"
70 #include "llvm/Analysis/LoopInfo.h"
71 #include "llvm/Assembly/Writer.h"
72 #include "llvm/Target/TargetData.h"
73 #include "llvm/Support/CommandLine.h"
74 #include "llvm/Support/Compiler.h"
75 #include "llvm/Support/ConstantRange.h"
76 #include "llvm/Support/GetElementPtrTypeIterator.h"
77 #include "llvm/Support/InstIterator.h"
78 #include "llvm/Support/ManagedStatic.h"
79 #include "llvm/Support/MathExtras.h"
80 #include "llvm/Support/raw_ostream.h"
81 #include "llvm/ADT/Statistic.h"
82 #include "llvm/ADT/STLExtras.h"
86 STATISTIC(NumArrayLenItCounts,
87 "Number of trip counts computed with array length");
88 STATISTIC(NumTripCountsComputed,
89 "Number of loops with predictable loop counts");
90 STATISTIC(NumTripCountsNotComputed,
91 "Number of loops without predictable loop counts");
92 STATISTIC(NumBruteForceTripCountsComputed,
93 "Number of loops with trip counts computed by force");
95 static cl::opt<unsigned>
96 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
97 cl::desc("Maximum number of iterations SCEV will "
98 "symbolically execute a constant derived loop"),
101 static RegisterPass<ScalarEvolution>
102 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
103 char ScalarEvolution::ID = 0;
105 //===----------------------------------------------------------------------===//
106 // SCEV class definitions
107 //===----------------------------------------------------------------------===//
109 //===----------------------------------------------------------------------===//
110 // Implementation of the SCEV class.
113 void SCEV::dump() const {
118 void SCEV::print(std::ostream &o) const {
119 raw_os_ostream OS(o);
123 bool SCEV::isZero() const {
124 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
125 return SC->getValue()->isZero();
129 bool SCEV::isOne() const {
130 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
131 return SC->getValue()->isOne();
135 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
136 SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
138 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
139 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
143 const Type *SCEVCouldNotCompute::getType() const {
144 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
148 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
149 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
153 SCEVHandle SCEVCouldNotCompute::
154 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
155 const SCEVHandle &Conc,
156 ScalarEvolution &SE) const {
160 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
161 OS << "***COULDNOTCOMPUTE***";
164 bool SCEVCouldNotCompute::classof(const SCEV *S) {
165 return S->getSCEVType() == scCouldNotCompute;
169 // SCEVConstants - Only allow the creation of one SCEVConstant for any
170 // particular value. Don't use a SCEVHandle here, or else the object will
172 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
175 SCEVConstant::~SCEVConstant() {
176 SCEVConstants->erase(V);
179 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
180 SCEVConstant *&R = (*SCEVConstants)[V];
181 if (R == 0) R = new SCEVConstant(V);
185 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
186 return getConstant(ConstantInt::get(Val));
189 const Type *SCEVConstant::getType() const { return V->getType(); }
191 void SCEVConstant::print(raw_ostream &OS) const {
192 WriteAsOperand(OS, V, false);
195 SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
196 const SCEVHandle &op, const Type *ty)
197 : SCEV(SCEVTy), Op(op), Ty(ty) {}
199 SCEVCastExpr::~SCEVCastExpr() {}
201 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
202 return Op->dominates(BB, DT);
205 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
206 // particular input. Don't use a SCEVHandle here, or else the object will
208 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
209 SCEVTruncateExpr*> > SCEVTruncates;
211 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
212 : SCEVCastExpr(scTruncate, op, ty) {
213 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
214 (Ty->isInteger() || isa<PointerType>(Ty)) &&
215 "Cannot truncate non-integer value!");
218 SCEVTruncateExpr::~SCEVTruncateExpr() {
219 SCEVTruncates->erase(std::make_pair(Op, Ty));
222 void SCEVTruncateExpr::print(raw_ostream &OS) const {
223 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
226 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
227 // particular input. Don't use a SCEVHandle here, or else the object will never
229 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
230 SCEVZeroExtendExpr*> > SCEVZeroExtends;
232 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
233 : SCEVCastExpr(scZeroExtend, op, ty) {
234 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
235 (Ty->isInteger() || isa<PointerType>(Ty)) &&
236 "Cannot zero extend non-integer value!");
239 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
240 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
243 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
244 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
247 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
248 // particular input. Don't use a SCEVHandle here, or else the object will never
250 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
251 SCEVSignExtendExpr*> > SCEVSignExtends;
253 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
254 : SCEVCastExpr(scSignExtend, op, ty) {
255 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
256 (Ty->isInteger() || isa<PointerType>(Ty)) &&
257 "Cannot sign extend non-integer value!");
260 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
261 SCEVSignExtends->erase(std::make_pair(Op, Ty));
264 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
265 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
268 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
269 // particular input. Don't use a SCEVHandle here, or else the object will never
271 static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >,
272 SCEVCommutativeExpr*> > SCEVCommExprs;
274 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
275 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
276 SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps));
279 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
280 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
281 const char *OpStr = getOperationStr();
282 OS << "(" << *Operands[0];
283 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
284 OS << OpStr << *Operands[i];
288 SCEVHandle SCEVCommutativeExpr::
289 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
290 const SCEVHandle &Conc,
291 ScalarEvolution &SE) const {
292 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
294 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
295 if (H != getOperand(i)) {
296 SmallVector<SCEVHandle, 8> NewOps;
297 NewOps.reserve(getNumOperands());
298 for (unsigned j = 0; j != i; ++j)
299 NewOps.push_back(getOperand(j));
301 for (++i; i != e; ++i)
302 NewOps.push_back(getOperand(i)->
303 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
305 if (isa<SCEVAddExpr>(this))
306 return SE.getAddExpr(NewOps);
307 else if (isa<SCEVMulExpr>(this))
308 return SE.getMulExpr(NewOps);
309 else if (isa<SCEVSMaxExpr>(this))
310 return SE.getSMaxExpr(NewOps);
311 else if (isa<SCEVUMaxExpr>(this))
312 return SE.getUMaxExpr(NewOps);
314 assert(0 && "Unknown commutative expr!");
320 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
321 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
322 if (!getOperand(i)->dominates(BB, DT))
329 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
330 // input. Don't use a SCEVHandle here, or else the object will never be
332 static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>,
333 SCEVUDivExpr*> > SCEVUDivs;
335 SCEVUDivExpr::~SCEVUDivExpr() {
336 SCEVUDivs->erase(std::make_pair(LHS, RHS));
339 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
340 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
343 void SCEVUDivExpr::print(raw_ostream &OS) const {
344 OS << "(" << *LHS << " /u " << *RHS << ")";
347 const Type *SCEVUDivExpr::getType() const {
348 // In most cases the types of LHS and RHS will be the same, but in some
349 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
350 // depend on the type for correctness, but handling types carefully can
351 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
352 // a pointer type than the RHS, so use the RHS' type here.
353 return RHS->getType();
356 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
357 // particular input. Don't use a SCEVHandle here, or else the object will never
359 static ManagedStatic<std::map<std::pair<const Loop *,
360 std::vector<const SCEV*> >,
361 SCEVAddRecExpr*> > SCEVAddRecExprs;
363 SCEVAddRecExpr::~SCEVAddRecExpr() {
364 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
365 SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps));
368 SCEVHandle SCEVAddRecExpr::
369 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
370 const SCEVHandle &Conc,
371 ScalarEvolution &SE) const {
372 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
374 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
375 if (H != getOperand(i)) {
376 SmallVector<SCEVHandle, 8> NewOps;
377 NewOps.reserve(getNumOperands());
378 for (unsigned j = 0; j != i; ++j)
379 NewOps.push_back(getOperand(j));
381 for (++i; i != e; ++i)
382 NewOps.push_back(getOperand(i)->
383 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
385 return SE.getAddRecExpr(NewOps, L);
392 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
393 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
394 // contain L and if the start is invariant.
395 // Add recurrences are never invariant in the function-body (null loop).
397 !QueryLoop->contains(L->getHeader()) &&
398 getOperand(0)->isLoopInvariant(QueryLoop);
402 void SCEVAddRecExpr::print(raw_ostream &OS) const {
403 OS << "{" << *Operands[0];
404 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
405 OS << ",+," << *Operands[i];
406 OS << "}<" << L->getHeader()->getName() + ">";
409 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
410 // value. Don't use a SCEVHandle here, or else the object will never be
412 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
414 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
416 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
417 // All non-instruction values are loop invariant. All instructions are loop
418 // invariant if they are not contained in the specified loop.
419 // Instructions are never considered invariant in the function body
420 // (null loop) because they are defined within the "loop".
421 if (Instruction *I = dyn_cast<Instruction>(V))
422 return L && !L->contains(I->getParent());
426 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
427 if (Instruction *I = dyn_cast<Instruction>(getValue()))
428 return DT->dominates(I->getParent(), BB);
432 const Type *SCEVUnknown::getType() const {
436 void SCEVUnknown::print(raw_ostream &OS) const {
437 WriteAsOperand(OS, V, false);
440 //===----------------------------------------------------------------------===//
442 //===----------------------------------------------------------------------===//
445 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
446 /// than the complexity of the RHS. This comparator is used to canonicalize
448 class VISIBILITY_HIDDEN SCEVComplexityCompare {
451 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
453 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
454 // Primarily, sort the SCEVs by their getSCEVType().
455 if (LHS->getSCEVType() != RHS->getSCEVType())
456 return LHS->getSCEVType() < RHS->getSCEVType();
458 // Aside from the getSCEVType() ordering, the particular ordering
459 // isn't very important except that it's beneficial to be consistent,
460 // so that (a + b) and (b + a) don't end up as different expressions.
462 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
463 // not as complete as it could be.
464 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
465 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
467 // Order pointer values after integer values. This helps SCEVExpander
469 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
471 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
474 // Compare getValueID values.
475 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
476 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
478 // Sort arguments by their position.
479 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
480 const Argument *RA = cast<Argument>(RU->getValue());
481 return LA->getArgNo() < RA->getArgNo();
484 // For instructions, compare their loop depth, and their opcode.
485 // This is pretty loose.
486 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
487 Instruction *RV = cast<Instruction>(RU->getValue());
489 // Compare loop depths.
490 if (LI->getLoopDepth(LV->getParent()) !=
491 LI->getLoopDepth(RV->getParent()))
492 return LI->getLoopDepth(LV->getParent()) <
493 LI->getLoopDepth(RV->getParent());
496 if (LV->getOpcode() != RV->getOpcode())
497 return LV->getOpcode() < RV->getOpcode();
499 // Compare the number of operands.
500 if (LV->getNumOperands() != RV->getNumOperands())
501 return LV->getNumOperands() < RV->getNumOperands();
507 // Constant sorting doesn't matter since they'll be folded.
508 if (isa<SCEVConstant>(LHS))
511 // Lexicographically compare n-ary expressions.
512 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
513 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
514 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
515 if (i >= RC->getNumOperands())
517 if (operator()(LC->getOperand(i), RC->getOperand(i)))
519 if (operator()(RC->getOperand(i), LC->getOperand(i)))
522 return LC->getNumOperands() < RC->getNumOperands();
525 // Lexicographically compare udiv expressions.
526 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
527 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
528 if (operator()(LC->getLHS(), RC->getLHS()))
530 if (operator()(RC->getLHS(), LC->getLHS()))
532 if (operator()(LC->getRHS(), RC->getRHS()))
534 if (operator()(RC->getRHS(), LC->getRHS()))
539 // Compare cast expressions by operand.
540 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
541 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
542 return operator()(LC->getOperand(), RC->getOperand());
545 assert(0 && "Unknown SCEV kind!");
551 /// GroupByComplexity - Given a list of SCEV objects, order them by their
552 /// complexity, and group objects of the same complexity together by value.
553 /// When this routine is finished, we know that any duplicates in the vector are
554 /// consecutive and that complexity is monotonically increasing.
556 /// Note that we go take special precautions to ensure that we get determinstic
557 /// results from this routine. In other words, we don't want the results of
558 /// this to depend on where the addresses of various SCEV objects happened to
561 static void GroupByComplexity(SmallVectorImpl<SCEVHandle> &Ops,
563 if (Ops.size() < 2) return; // Noop
564 if (Ops.size() == 2) {
565 // This is the common case, which also happens to be trivially simple.
567 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
568 std::swap(Ops[0], Ops[1]);
572 // Do the rough sort by complexity.
573 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
575 // Now that we are sorted by complexity, group elements of the same
576 // complexity. Note that this is, at worst, N^2, but the vector is likely to
577 // be extremely short in practice. Note that we take this approach because we
578 // do not want to depend on the addresses of the objects we are grouping.
579 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
580 const SCEV *S = Ops[i];
581 unsigned Complexity = S->getSCEVType();
583 // If there are any objects of the same complexity and same value as this
585 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
586 if (Ops[j] == S) { // Found a duplicate.
587 // Move it to immediately after i'th element.
588 std::swap(Ops[i+1], Ops[j]);
589 ++i; // no need to rescan it.
590 if (i == e-2) return; // Done!
598 //===----------------------------------------------------------------------===//
599 // Simple SCEV method implementations
600 //===----------------------------------------------------------------------===//
602 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
604 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
606 const Type* ResultTy) {
607 // Handle the simplest case efficiently.
609 return SE.getTruncateOrZeroExtend(It, ResultTy);
611 // We are using the following formula for BC(It, K):
613 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
615 // Suppose, W is the bitwidth of the return value. We must be prepared for
616 // overflow. Hence, we must assure that the result of our computation is
617 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
618 // safe in modular arithmetic.
620 // However, this code doesn't use exactly that formula; the formula it uses
621 // is something like the following, where T is the number of factors of 2 in
622 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
625 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
627 // This formula is trivially equivalent to the previous formula. However,
628 // this formula can be implemented much more efficiently. The trick is that
629 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
630 // arithmetic. To do exact division in modular arithmetic, all we have
631 // to do is multiply by the inverse. Therefore, this step can be done at
634 // The next issue is how to safely do the division by 2^T. The way this
635 // is done is by doing the multiplication step at a width of at least W + T
636 // bits. This way, the bottom W+T bits of the product are accurate. Then,
637 // when we perform the division by 2^T (which is equivalent to a right shift
638 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
639 // truncated out after the division by 2^T.
641 // In comparison to just directly using the first formula, this technique
642 // is much more efficient; using the first formula requires W * K bits,
643 // but this formula less than W + K bits. Also, the first formula requires
644 // a division step, whereas this formula only requires multiplies and shifts.
646 // It doesn't matter whether the subtraction step is done in the calculation
647 // width or the input iteration count's width; if the subtraction overflows,
648 // the result must be zero anyway. We prefer here to do it in the width of
649 // the induction variable because it helps a lot for certain cases; CodeGen
650 // isn't smart enough to ignore the overflow, which leads to much less
651 // efficient code if the width of the subtraction is wider than the native
654 // (It's possible to not widen at all by pulling out factors of 2 before
655 // the multiplication; for example, K=2 can be calculated as
656 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
657 // extra arithmetic, so it's not an obvious win, and it gets
658 // much more complicated for K > 3.)
660 // Protection from insane SCEVs; this bound is conservative,
661 // but it probably doesn't matter.
663 return SE.getCouldNotCompute();
665 unsigned W = SE.getTypeSizeInBits(ResultTy);
667 // Calculate K! / 2^T and T; we divide out the factors of two before
668 // multiplying for calculating K! / 2^T to avoid overflow.
669 // Other overflow doesn't matter because we only care about the bottom
670 // W bits of the result.
671 APInt OddFactorial(W, 1);
673 for (unsigned i = 3; i <= K; ++i) {
675 unsigned TwoFactors = Mult.countTrailingZeros();
677 Mult = Mult.lshr(TwoFactors);
678 OddFactorial *= Mult;
681 // We need at least W + T bits for the multiplication step
682 unsigned CalculationBits = W + T;
684 // Calcuate 2^T, at width T+W.
685 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
687 // Calculate the multiplicative inverse of K! / 2^T;
688 // this multiplication factor will perform the exact division by
690 APInt Mod = APInt::getSignedMinValue(W+1);
691 APInt MultiplyFactor = OddFactorial.zext(W+1);
692 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
693 MultiplyFactor = MultiplyFactor.trunc(W);
695 // Calculate the product, at width T+W
696 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
697 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
698 for (unsigned i = 1; i != K; ++i) {
699 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
700 Dividend = SE.getMulExpr(Dividend,
701 SE.getTruncateOrZeroExtend(S, CalculationTy));
705 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
707 // Truncate the result, and divide by K! / 2^T.
709 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
710 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
713 /// evaluateAtIteration - Return the value of this chain of recurrences at
714 /// the specified iteration number. We can evaluate this recurrence by
715 /// multiplying each element in the chain by the binomial coefficient
716 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
718 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
720 /// where BC(It, k) stands for binomial coefficient.
722 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
723 ScalarEvolution &SE) const {
724 SCEVHandle Result = getStart();
725 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
726 // The computation is correct in the face of overflow provided that the
727 // multiplication is performed _after_ the evaluation of the binomial
729 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
730 if (isa<SCEVCouldNotCompute>(Coeff))
733 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
738 //===----------------------------------------------------------------------===//
739 // SCEV Expression folder implementations
740 //===----------------------------------------------------------------------===//
742 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op,
744 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
745 "This is not a truncating conversion!");
746 assert(isSCEVable(Ty) &&
747 "This is not a conversion to a SCEVable type!");
748 Ty = getEffectiveSCEVType(Ty);
750 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
752 ConstantExpr::getTrunc(SC->getValue(), Ty));
754 // trunc(trunc(x)) --> trunc(x)
755 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
756 return getTruncateExpr(ST->getOperand(), Ty);
758 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
759 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
760 return getTruncateOrSignExtend(SS->getOperand(), Ty);
762 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
763 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
764 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
766 // If the input value is a chrec scev made out of constants, truncate
767 // all of the constants.
768 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
769 SmallVector<SCEVHandle, 4> Operands;
770 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
771 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
772 return getAddRecExpr(Operands, AddRec->getLoop());
775 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
776 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
780 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
782 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
783 "This is not an extending conversion!");
784 assert(isSCEVable(Ty) &&
785 "This is not a conversion to a SCEVable type!");
786 Ty = getEffectiveSCEVType(Ty);
788 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
789 const Type *IntTy = getEffectiveSCEVType(Ty);
790 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
791 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
792 return getUnknown(C);
795 // zext(zext(x)) --> zext(x)
796 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
797 return getZeroExtendExpr(SZ->getOperand(), Ty);
799 // If the input value is a chrec scev, and we can prove that the value
800 // did not overflow the old, smaller, value, we can zero extend all of the
801 // operands (often constants). This allows analysis of something like
802 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
803 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
804 if (AR->isAffine()) {
805 // Check whether the backedge-taken count is SCEVCouldNotCompute.
806 // Note that this serves two purposes: It filters out loops that are
807 // simply not analyzable, and it covers the case where this code is
808 // being called from within backedge-taken count analysis, such that
809 // attempting to ask for the backedge-taken count would likely result
810 // in infinite recursion. In the later case, the analysis code will
811 // cope with a conservative value, and it will take care to purge
812 // that value once it has finished.
813 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
814 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
815 // Manually compute the final value for AR, checking for
817 SCEVHandle Start = AR->getStart();
818 SCEVHandle Step = AR->getStepRecurrence(*this);
820 // Check whether the backedge-taken count can be losslessly casted to
821 // the addrec's type. The count is always unsigned.
822 SCEVHandle CastedMaxBECount =
823 getTruncateOrZeroExtend(MaxBECount, Start->getType());
824 SCEVHandle RecastedMaxBECount =
825 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
826 if (MaxBECount == RecastedMaxBECount) {
828 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
829 // Check whether Start+Step*MaxBECount has no unsigned overflow.
831 getMulExpr(CastedMaxBECount,
832 getTruncateOrZeroExtend(Step, Start->getType()));
833 SCEVHandle Add = getAddExpr(Start, ZMul);
834 SCEVHandle OperandExtendedAdd =
835 getAddExpr(getZeroExtendExpr(Start, WideTy),
836 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
837 getZeroExtendExpr(Step, WideTy)));
838 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
839 // Return the expression with the addrec on the outside.
840 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
841 getZeroExtendExpr(Step, Ty),
844 // Similar to above, only this time treat the step value as signed.
845 // This covers loops that count down.
847 getMulExpr(CastedMaxBECount,
848 getTruncateOrSignExtend(Step, Start->getType()));
849 Add = getAddExpr(Start, SMul);
851 getAddExpr(getZeroExtendExpr(Start, WideTy),
852 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
853 getSignExtendExpr(Step, WideTy)));
854 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
855 // Return the expression with the addrec on the outside.
856 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
857 getSignExtendExpr(Step, Ty),
863 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
864 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
868 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
870 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
871 "This is not an extending conversion!");
872 assert(isSCEVable(Ty) &&
873 "This is not a conversion to a SCEVable type!");
874 Ty = getEffectiveSCEVType(Ty);
876 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
877 const Type *IntTy = getEffectiveSCEVType(Ty);
878 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
879 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
880 return getUnknown(C);
883 // sext(sext(x)) --> sext(x)
884 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
885 return getSignExtendExpr(SS->getOperand(), Ty);
887 // If the input value is a chrec scev, and we can prove that the value
888 // did not overflow the old, smaller, value, we can sign extend all of the
889 // operands (often constants). This allows analysis of something like
890 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
891 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
892 if (AR->isAffine()) {
893 // Check whether the backedge-taken count is SCEVCouldNotCompute.
894 // Note that this serves two purposes: It filters out loops that are
895 // simply not analyzable, and it covers the case where this code is
896 // being called from within backedge-taken count analysis, such that
897 // attempting to ask for the backedge-taken count would likely result
898 // in infinite recursion. In the later case, the analysis code will
899 // cope with a conservative value, and it will take care to purge
900 // that value once it has finished.
901 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
902 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
903 // Manually compute the final value for AR, checking for
905 SCEVHandle Start = AR->getStart();
906 SCEVHandle Step = AR->getStepRecurrence(*this);
908 // Check whether the backedge-taken count can be losslessly casted to
909 // the addrec's type. The count is always unsigned.
910 SCEVHandle CastedMaxBECount =
911 getTruncateOrZeroExtend(MaxBECount, Start->getType());
912 SCEVHandle RecastedMaxBECount =
913 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
914 if (MaxBECount == RecastedMaxBECount) {
916 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
917 // Check whether Start+Step*MaxBECount has no signed overflow.
919 getMulExpr(CastedMaxBECount,
920 getTruncateOrSignExtend(Step, Start->getType()));
921 SCEVHandle Add = getAddExpr(Start, SMul);
922 SCEVHandle OperandExtendedAdd =
923 getAddExpr(getSignExtendExpr(Start, WideTy),
924 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
925 getSignExtendExpr(Step, WideTy)));
926 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
927 // Return the expression with the addrec on the outside.
928 return getAddRecExpr(getSignExtendExpr(Start, Ty),
929 getSignExtendExpr(Step, Ty),
935 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
936 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
940 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
941 /// unspecified bits out to the given type.
943 SCEVHandle ScalarEvolution::getAnyExtendExpr(const SCEVHandle &Op,
945 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
946 "This is not an extending conversion!");
947 assert(isSCEVable(Ty) &&
948 "This is not a conversion to a SCEVable type!");
949 Ty = getEffectiveSCEVType(Ty);
951 // Sign-extend negative constants.
952 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
953 if (SC->getValue()->getValue().isNegative())
954 return getSignExtendExpr(Op, Ty);
956 // Peel off a truncate cast.
957 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
958 SCEVHandle NewOp = T->getOperand();
959 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
960 return getAnyExtendExpr(NewOp, Ty);
961 return getTruncateOrNoop(NewOp, Ty);
964 // Next try a zext cast. If the cast is folded, use it.
965 SCEVHandle ZExt = getZeroExtendExpr(Op, Ty);
966 if (!isa<SCEVZeroExtendExpr>(ZExt))
969 // Next try a sext cast. If the cast is folded, use it.
970 SCEVHandle SExt = getSignExtendExpr(Op, Ty);
971 if (!isa<SCEVSignExtendExpr>(SExt))
974 // If the expression is obviously signed, use the sext cast value.
975 if (isa<SCEVSMaxExpr>(Op))
978 // Absent any other information, use the zext cast value.
982 /// getAddExpr - Get a canonical add expression, or something simpler if
984 SCEVHandle ScalarEvolution::getAddExpr(SmallVectorImpl<SCEVHandle> &Ops) {
985 assert(!Ops.empty() && "Cannot get empty add!");
986 if (Ops.size() == 1) return Ops[0];
988 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
989 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
990 getEffectiveSCEVType(Ops[0]->getType()) &&
991 "SCEVAddExpr operand types don't match!");
994 // Sort by complexity, this groups all similar expression types together.
995 GroupByComplexity(Ops, LI);
997 // If there are any constants, fold them together.
999 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1001 assert(Idx < Ops.size());
1002 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1003 // We found two constants, fold them together!
1004 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1005 RHSC->getValue()->getValue());
1006 Ops.erase(Ops.begin()+1); // Erase the folded element
1007 if (Ops.size() == 1) return Ops[0];
1008 LHSC = cast<SCEVConstant>(Ops[0]);
1011 // If we are left with a constant zero being added, strip it off.
1012 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1013 Ops.erase(Ops.begin());
1018 if (Ops.size() == 1) return Ops[0];
1020 // Okay, check to see if the same value occurs in the operand list twice. If
1021 // so, merge them together into an multiply expression. Since we sorted the
1022 // list, these values are required to be adjacent.
1023 const Type *Ty = Ops[0]->getType();
1024 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1025 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1026 // Found a match, merge the two values into a multiply, and add any
1027 // remaining values to the result.
1028 SCEVHandle Two = getIntegerSCEV(2, Ty);
1029 SCEVHandle Mul = getMulExpr(Ops[i], Two);
1030 if (Ops.size() == 2)
1032 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1034 return getAddExpr(Ops);
1037 // Check for truncates. If all the operands are truncated from the same
1038 // type, see if factoring out the truncate would permit the result to be
1039 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1040 // if the contents of the resulting outer trunc fold to something simple.
1041 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1042 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1043 const Type *DstType = Trunc->getType();
1044 const Type *SrcType = Trunc->getOperand()->getType();
1045 SmallVector<SCEVHandle, 8> LargeOps;
1047 // Check all the operands to see if they can be represented in the
1048 // source type of the truncate.
1049 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1050 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1051 if (T->getOperand()->getType() != SrcType) {
1055 LargeOps.push_back(T->getOperand());
1056 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1057 // This could be either sign or zero extension, but sign extension
1058 // is much more likely to be foldable here.
1059 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1060 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1061 SmallVector<SCEVHandle, 8> LargeMulOps;
1062 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1063 if (const SCEVTruncateExpr *T =
1064 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1065 if (T->getOperand()->getType() != SrcType) {
1069 LargeMulOps.push_back(T->getOperand());
1070 } else if (const SCEVConstant *C =
1071 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1072 // This could be either sign or zero extension, but sign extension
1073 // is much more likely to be foldable here.
1074 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1081 LargeOps.push_back(getMulExpr(LargeMulOps));
1088 // Evaluate the expression in the larger type.
1089 SCEVHandle Fold = getAddExpr(LargeOps);
1090 // If it folds to something simple, use it. Otherwise, don't.
1091 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1092 return getTruncateExpr(Fold, DstType);
1096 // Skip past any other cast SCEVs.
1097 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1100 // If there are add operands they would be next.
1101 if (Idx < Ops.size()) {
1102 bool DeletedAdd = false;
1103 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1104 // If we have an add, expand the add operands onto the end of the operands
1106 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1107 Ops.erase(Ops.begin()+Idx);
1111 // If we deleted at least one add, we added operands to the end of the list,
1112 // and they are not necessarily sorted. Recurse to resort and resimplify
1113 // any operands we just aquired.
1115 return getAddExpr(Ops);
1118 // Skip over the add expression until we get to a multiply.
1119 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1122 // If we are adding something to a multiply expression, make sure the
1123 // something is not already an operand of the multiply. If so, merge it into
1125 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1126 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1127 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1128 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1129 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1130 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1131 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1132 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
1133 if (Mul->getNumOperands() != 2) {
1134 // If the multiply has more than two operands, we must get the
1136 SmallVector<SCEVHandle, 4> MulOps(Mul->op_begin(), Mul->op_end());
1137 MulOps.erase(MulOps.begin()+MulOp);
1138 InnerMul = getMulExpr(MulOps);
1140 SCEVHandle One = getIntegerSCEV(1, Ty);
1141 SCEVHandle AddOne = getAddExpr(InnerMul, One);
1142 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1143 if (Ops.size() == 2) return OuterMul;
1145 Ops.erase(Ops.begin()+AddOp);
1146 Ops.erase(Ops.begin()+Idx-1);
1148 Ops.erase(Ops.begin()+Idx);
1149 Ops.erase(Ops.begin()+AddOp-1);
1151 Ops.push_back(OuterMul);
1152 return getAddExpr(Ops);
1155 // Check this multiply against other multiplies being added together.
1156 for (unsigned OtherMulIdx = Idx+1;
1157 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1159 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1160 // If MulOp occurs in OtherMul, we can fold the two multiplies
1162 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1163 OMulOp != e; ++OMulOp)
1164 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1165 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1166 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
1167 if (Mul->getNumOperands() != 2) {
1168 SmallVector<SCEVHandle, 4> MulOps(Mul->op_begin(), Mul->op_end());
1169 MulOps.erase(MulOps.begin()+MulOp);
1170 InnerMul1 = getMulExpr(MulOps);
1172 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1173 if (OtherMul->getNumOperands() != 2) {
1174 SmallVector<SCEVHandle, 4> MulOps(OtherMul->op_begin(),
1175 OtherMul->op_end());
1176 MulOps.erase(MulOps.begin()+OMulOp);
1177 InnerMul2 = getMulExpr(MulOps);
1179 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1180 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1181 if (Ops.size() == 2) return OuterMul;
1182 Ops.erase(Ops.begin()+Idx);
1183 Ops.erase(Ops.begin()+OtherMulIdx-1);
1184 Ops.push_back(OuterMul);
1185 return getAddExpr(Ops);
1191 // If there are any add recurrences in the operands list, see if any other
1192 // added values are loop invariant. If so, we can fold them into the
1194 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1197 // Scan over all recurrences, trying to fold loop invariants into them.
1198 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1199 // Scan all of the other operands to this add and add them to the vector if
1200 // they are loop invariant w.r.t. the recurrence.
1201 SmallVector<SCEVHandle, 8> LIOps;
1202 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1203 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1204 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1205 LIOps.push_back(Ops[i]);
1206 Ops.erase(Ops.begin()+i);
1210 // If we found some loop invariants, fold them into the recurrence.
1211 if (!LIOps.empty()) {
1212 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1213 LIOps.push_back(AddRec->getStart());
1215 SmallVector<SCEVHandle, 4> AddRecOps(AddRec->op_begin(),
1217 AddRecOps[0] = getAddExpr(LIOps);
1219 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1220 // If all of the other operands were loop invariant, we are done.
1221 if (Ops.size() == 1) return NewRec;
1223 // Otherwise, add the folded AddRec by the non-liv parts.
1224 for (unsigned i = 0;; ++i)
1225 if (Ops[i] == AddRec) {
1229 return getAddExpr(Ops);
1232 // Okay, if there weren't any loop invariants to be folded, check to see if
1233 // there are multiple AddRec's with the same loop induction variable being
1234 // added together. If so, we can fold them.
1235 for (unsigned OtherIdx = Idx+1;
1236 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1237 if (OtherIdx != Idx) {
1238 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1239 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1240 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1241 SmallVector<SCEVHandle, 4> NewOps(AddRec->op_begin(), AddRec->op_end());
1242 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1243 if (i >= NewOps.size()) {
1244 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1245 OtherAddRec->op_end());
1248 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1250 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1252 if (Ops.size() == 2) return NewAddRec;
1254 Ops.erase(Ops.begin()+Idx);
1255 Ops.erase(Ops.begin()+OtherIdx-1);
1256 Ops.push_back(NewAddRec);
1257 return getAddExpr(Ops);
1261 // Otherwise couldn't fold anything into this recurrence. Move onto the
1265 // Okay, it looks like we really DO need an add expr. Check to see if we
1266 // already have one, otherwise create a new one.
1267 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1268 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
1270 if (Result == 0) Result = new SCEVAddExpr(Ops);
1275 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1277 SCEVHandle ScalarEvolution::getMulExpr(SmallVectorImpl<SCEVHandle> &Ops) {
1278 assert(!Ops.empty() && "Cannot get empty mul!");
1280 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1281 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1282 getEffectiveSCEVType(Ops[0]->getType()) &&
1283 "SCEVMulExpr operand types don't match!");
1286 // Sort by complexity, this groups all similar expression types together.
1287 GroupByComplexity(Ops, LI);
1289 // If there are any constants, fold them together.
1291 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1293 // C1*(C2+V) -> C1*C2 + C1*V
1294 if (Ops.size() == 2)
1295 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1296 if (Add->getNumOperands() == 2 &&
1297 isa<SCEVConstant>(Add->getOperand(0)))
1298 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1299 getMulExpr(LHSC, Add->getOperand(1)));
1303 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1304 // We found two constants, fold them together!
1305 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1306 RHSC->getValue()->getValue());
1307 Ops[0] = getConstant(Fold);
1308 Ops.erase(Ops.begin()+1); // Erase the folded element
1309 if (Ops.size() == 1) return Ops[0];
1310 LHSC = cast<SCEVConstant>(Ops[0]);
1313 // If we are left with a constant one being multiplied, strip it off.
1314 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1315 Ops.erase(Ops.begin());
1317 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1318 // If we have a multiply of zero, it will always be zero.
1323 // Skip over the add expression until we get to a multiply.
1324 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1327 if (Ops.size() == 1)
1330 // If there are mul operands inline them all into this expression.
1331 if (Idx < Ops.size()) {
1332 bool DeletedMul = false;
1333 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1334 // If we have an mul, expand the mul operands onto the end of the operands
1336 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1337 Ops.erase(Ops.begin()+Idx);
1341 // If we deleted at least one mul, we added operands to the end of the list,
1342 // and they are not necessarily sorted. Recurse to resort and resimplify
1343 // any operands we just aquired.
1345 return getMulExpr(Ops);
1348 // If there are any add recurrences in the operands list, see if any other
1349 // added values are loop invariant. If so, we can fold them into the
1351 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1354 // Scan over all recurrences, trying to fold loop invariants into them.
1355 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1356 // Scan all of the other operands to this mul and add them to the vector if
1357 // they are loop invariant w.r.t. the recurrence.
1358 SmallVector<SCEVHandle, 8> LIOps;
1359 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1360 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1361 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1362 LIOps.push_back(Ops[i]);
1363 Ops.erase(Ops.begin()+i);
1367 // If we found some loop invariants, fold them into the recurrence.
1368 if (!LIOps.empty()) {
1369 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1370 SmallVector<SCEVHandle, 4> NewOps;
1371 NewOps.reserve(AddRec->getNumOperands());
1372 if (LIOps.size() == 1) {
1373 const SCEV *Scale = LIOps[0];
1374 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1375 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1377 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1378 SmallVector<SCEVHandle, 4> MulOps(LIOps.begin(), LIOps.end());
1379 MulOps.push_back(AddRec->getOperand(i));
1380 NewOps.push_back(getMulExpr(MulOps));
1384 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1386 // If all of the other operands were loop invariant, we are done.
1387 if (Ops.size() == 1) return NewRec;
1389 // Otherwise, multiply the folded AddRec by the non-liv parts.
1390 for (unsigned i = 0;; ++i)
1391 if (Ops[i] == AddRec) {
1395 return getMulExpr(Ops);
1398 // Okay, if there weren't any loop invariants to be folded, check to see if
1399 // there are multiple AddRec's with the same loop induction variable being
1400 // multiplied together. If so, we can fold them.
1401 for (unsigned OtherIdx = Idx+1;
1402 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1403 if (OtherIdx != Idx) {
1404 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1405 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1406 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1407 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1408 SCEVHandle NewStart = getMulExpr(F->getStart(),
1410 SCEVHandle B = F->getStepRecurrence(*this);
1411 SCEVHandle D = G->getStepRecurrence(*this);
1412 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1415 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1417 if (Ops.size() == 2) return NewAddRec;
1419 Ops.erase(Ops.begin()+Idx);
1420 Ops.erase(Ops.begin()+OtherIdx-1);
1421 Ops.push_back(NewAddRec);
1422 return getMulExpr(Ops);
1426 // Otherwise couldn't fold anything into this recurrence. Move onto the
1430 // Okay, it looks like we really DO need an mul expr. Check to see if we
1431 // already have one, otherwise create a new one.
1432 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1433 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1436 Result = new SCEVMulExpr(Ops);
1440 /// getUDivExpr - Get a canonical multiply expression, or something simpler if
1442 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS,
1443 const SCEVHandle &RHS) {
1444 assert(getEffectiveSCEVType(LHS->getType()) ==
1445 getEffectiveSCEVType(RHS->getType()) &&
1446 "SCEVUDivExpr operand types don't match!");
1448 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1449 if (RHSC->getValue()->equalsInt(1))
1450 return LHS; // X udiv 1 --> x
1452 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1454 // Determine if the division can be folded into the operands of
1456 // TODO: Generalize this to non-constants by using known-bits information.
1457 const Type *Ty = LHS->getType();
1458 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1459 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1460 // For non-power-of-two values, effectively round the value up to the
1461 // nearest power of two.
1462 if (!RHSC->getValue()->getValue().isPowerOf2())
1464 const IntegerType *ExtTy =
1465 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1466 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1467 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1468 if (const SCEVConstant *Step =
1469 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1470 if (!Step->getValue()->getValue()
1471 .urem(RHSC->getValue()->getValue()) &&
1472 getZeroExtendExpr(AR, ExtTy) ==
1473 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1474 getZeroExtendExpr(Step, ExtTy),
1476 SmallVector<SCEVHandle, 4> Operands;
1477 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1478 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1479 return getAddRecExpr(Operands, AR->getLoop());
1481 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1482 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1483 SmallVector<SCEVHandle, 4> Operands;
1484 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1485 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1486 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1487 // Find an operand that's safely divisible.
1488 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1489 SCEVHandle Op = M->getOperand(i);
1490 SCEVHandle Div = getUDivExpr(Op, RHSC);
1491 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1492 const SmallVectorImpl<SCEVHandle> &MOperands = M->getOperands();
1493 Operands = SmallVector<SCEVHandle, 4>(MOperands.begin(),
1496 return getMulExpr(Operands);
1500 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1501 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1502 SmallVector<SCEVHandle, 4> Operands;
1503 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1504 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1505 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1507 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1508 SCEVHandle Op = getUDivExpr(A->getOperand(i), RHS);
1509 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1511 Operands.push_back(Op);
1513 if (Operands.size() == A->getNumOperands())
1514 return getAddExpr(Operands);
1518 // Fold if both operands are constant.
1519 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1520 Constant *LHSCV = LHSC->getValue();
1521 Constant *RHSCV = RHSC->getValue();
1522 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1526 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1527 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1532 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1533 /// Simplify the expression as much as possible.
1534 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1535 const SCEVHandle &Step, const Loop *L) {
1536 SmallVector<SCEVHandle, 4> Operands;
1537 Operands.push_back(Start);
1538 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1539 if (StepChrec->getLoop() == L) {
1540 Operands.insert(Operands.end(), StepChrec->op_begin(),
1541 StepChrec->op_end());
1542 return getAddRecExpr(Operands, L);
1545 Operands.push_back(Step);
1546 return getAddRecExpr(Operands, L);
1549 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1550 /// Simplify the expression as much as possible.
1551 SCEVHandle ScalarEvolution::getAddRecExpr(SmallVectorImpl<SCEVHandle> &Operands,
1553 if (Operands.size() == 1) return Operands[0];
1555 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1556 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1557 getEffectiveSCEVType(Operands[0]->getType()) &&
1558 "SCEVAddRecExpr operand types don't match!");
1561 if (Operands.back()->isZero()) {
1562 Operands.pop_back();
1563 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1566 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1567 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1568 const Loop* NestedLoop = NestedAR->getLoop();
1569 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1570 SmallVector<SCEVHandle, 4> NestedOperands(NestedAR->op_begin(),
1571 NestedAR->op_end());
1572 SCEVHandle NestedARHandle(NestedAR);
1573 Operands[0] = NestedAR->getStart();
1574 NestedOperands[0] = getAddRecExpr(Operands, L);
1575 return getAddRecExpr(NestedOperands, NestedLoop);
1579 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
1580 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)];
1581 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1585 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1586 const SCEVHandle &RHS) {
1587 SmallVector<SCEVHandle, 2> Ops;
1590 return getSMaxExpr(Ops);
1594 ScalarEvolution::getSMaxExpr(SmallVectorImpl<SCEVHandle> &Ops) {
1595 assert(!Ops.empty() && "Cannot get empty smax!");
1596 if (Ops.size() == 1) return Ops[0];
1598 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1599 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1600 getEffectiveSCEVType(Ops[0]->getType()) &&
1601 "SCEVSMaxExpr operand types don't match!");
1604 // Sort by complexity, this groups all similar expression types together.
1605 GroupByComplexity(Ops, LI);
1607 // If there are any constants, fold them together.
1609 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1611 assert(Idx < Ops.size());
1612 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1613 // We found two constants, fold them together!
1614 ConstantInt *Fold = ConstantInt::get(
1615 APIntOps::smax(LHSC->getValue()->getValue(),
1616 RHSC->getValue()->getValue()));
1617 Ops[0] = getConstant(Fold);
1618 Ops.erase(Ops.begin()+1); // Erase the folded element
1619 if (Ops.size() == 1) return Ops[0];
1620 LHSC = cast<SCEVConstant>(Ops[0]);
1623 // If we are left with a constant -inf, strip it off.
1624 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1625 Ops.erase(Ops.begin());
1630 if (Ops.size() == 1) return Ops[0];
1632 // Find the first SMax
1633 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1636 // Check to see if one of the operands is an SMax. If so, expand its operands
1637 // onto our operand list, and recurse to simplify.
1638 if (Idx < Ops.size()) {
1639 bool DeletedSMax = false;
1640 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1641 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1642 Ops.erase(Ops.begin()+Idx);
1647 return getSMaxExpr(Ops);
1650 // Okay, check to see if the same value occurs in the operand list twice. If
1651 // so, delete one. Since we sorted the list, these values are required to
1653 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1654 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1655 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1659 if (Ops.size() == 1) return Ops[0];
1661 assert(!Ops.empty() && "Reduced smax down to nothing!");
1663 // Okay, it looks like we really DO need an smax expr. Check to see if we
1664 // already have one, otherwise create a new one.
1665 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1666 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1668 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1672 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1673 const SCEVHandle &RHS) {
1674 SmallVector<SCEVHandle, 2> Ops;
1677 return getUMaxExpr(Ops);
1681 ScalarEvolution::getUMaxExpr(SmallVectorImpl<SCEVHandle> &Ops) {
1682 assert(!Ops.empty() && "Cannot get empty umax!");
1683 if (Ops.size() == 1) return Ops[0];
1685 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1686 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1687 getEffectiveSCEVType(Ops[0]->getType()) &&
1688 "SCEVUMaxExpr operand types don't match!");
1691 // Sort by complexity, this groups all similar expression types together.
1692 GroupByComplexity(Ops, LI);
1694 // If there are any constants, fold them together.
1696 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1698 assert(Idx < Ops.size());
1699 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1700 // We found two constants, fold them together!
1701 ConstantInt *Fold = ConstantInt::get(
1702 APIntOps::umax(LHSC->getValue()->getValue(),
1703 RHSC->getValue()->getValue()));
1704 Ops[0] = getConstant(Fold);
1705 Ops.erase(Ops.begin()+1); // Erase the folded element
1706 if (Ops.size() == 1) return Ops[0];
1707 LHSC = cast<SCEVConstant>(Ops[0]);
1710 // If we are left with a constant zero, strip it off.
1711 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1712 Ops.erase(Ops.begin());
1717 if (Ops.size() == 1) return Ops[0];
1719 // Find the first UMax
1720 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1723 // Check to see if one of the operands is a UMax. If so, expand its operands
1724 // onto our operand list, and recurse to simplify.
1725 if (Idx < Ops.size()) {
1726 bool DeletedUMax = false;
1727 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1728 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1729 Ops.erase(Ops.begin()+Idx);
1734 return getUMaxExpr(Ops);
1737 // Okay, check to see if the same value occurs in the operand list twice. If
1738 // so, delete one. Since we sorted the list, these values are required to
1740 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1741 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1742 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1746 if (Ops.size() == 1) return Ops[0];
1748 assert(!Ops.empty() && "Reduced umax down to nothing!");
1750 // Okay, it looks like we really DO need a umax expr. Check to see if we
1751 // already have one, otherwise create a new one.
1752 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1753 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1755 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1759 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1760 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1761 return getConstant(CI);
1762 if (isa<ConstantPointerNull>(V))
1763 return getIntegerSCEV(0, V->getType());
1764 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1765 if (Result == 0) Result = new SCEVUnknown(V);
1769 //===----------------------------------------------------------------------===//
1770 // Basic SCEV Analysis and PHI Idiom Recognition Code
1773 /// isSCEVable - Test if values of the given type are analyzable within
1774 /// the SCEV framework. This primarily includes integer types, and it
1775 /// can optionally include pointer types if the ScalarEvolution class
1776 /// has access to target-specific information.
1777 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1778 // Integers are always SCEVable.
1779 if (Ty->isInteger())
1782 // Pointers are SCEVable if TargetData information is available
1783 // to provide pointer size information.
1784 if (isa<PointerType>(Ty))
1787 // Otherwise it's not SCEVable.
1791 /// getTypeSizeInBits - Return the size in bits of the specified type,
1792 /// for which isSCEVable must return true.
1793 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1794 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1796 // If we have a TargetData, use it!
1798 return TD->getTypeSizeInBits(Ty);
1800 // Otherwise, we support only integer types.
1801 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1802 return Ty->getPrimitiveSizeInBits();
1805 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1806 /// the given type and which represents how SCEV will treat the given
1807 /// type, for which isSCEVable must return true. For pointer types,
1808 /// this is the pointer-sized integer type.
1809 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1810 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1812 if (Ty->isInteger())
1815 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1816 return TD->getIntPtrType();
1819 SCEVHandle ScalarEvolution::getCouldNotCompute() {
1820 return CouldNotCompute;
1823 /// hasSCEV - Return true if the SCEV for this value has already been
1825 bool ScalarEvolution::hasSCEV(Value *V) const {
1826 return Scalars.count(V);
1829 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1830 /// expression and create a new one.
1831 SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1832 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1834 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
1835 if (I != Scalars.end()) return I->second;
1836 SCEVHandle S = createSCEV(V);
1837 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
1841 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1842 /// specified signed integer value and return a SCEV for the constant.
1843 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1844 Ty = getEffectiveSCEVType(Ty);
1847 C = Constant::getNullValue(Ty);
1848 else if (Ty->isFloatingPoint())
1849 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1850 APFloat::IEEEdouble, Val));
1852 C = ConstantInt::get(Ty, Val);
1853 return getUnknown(C);
1856 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1858 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1859 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1860 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1862 const Type *Ty = V->getType();
1863 Ty = getEffectiveSCEVType(Ty);
1864 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1867 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1868 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1869 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1870 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1872 const Type *Ty = V->getType();
1873 Ty = getEffectiveSCEVType(Ty);
1874 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1875 return getMinusSCEV(AllOnes, V);
1878 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1880 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1881 const SCEVHandle &RHS) {
1883 return getAddExpr(LHS, getNegativeSCEV(RHS));
1886 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1887 /// input value to the specified type. If the type must be extended, it is zero
1890 ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1892 const Type *SrcTy = V->getType();
1893 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1894 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1895 "Cannot truncate or zero extend with non-integer arguments!");
1896 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1897 return V; // No conversion
1898 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1899 return getTruncateExpr(V, Ty);
1900 return getZeroExtendExpr(V, Ty);
1903 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1904 /// input value to the specified type. If the type must be extended, it is sign
1907 ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1909 const Type *SrcTy = V->getType();
1910 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1911 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1912 "Cannot truncate or zero extend with non-integer arguments!");
1913 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1914 return V; // No conversion
1915 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1916 return getTruncateExpr(V, Ty);
1917 return getSignExtendExpr(V, Ty);
1920 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
1921 /// input value to the specified type. If the type must be extended, it is zero
1922 /// extended. The conversion must not be narrowing.
1924 ScalarEvolution::getNoopOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
1925 const Type *SrcTy = V->getType();
1926 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1927 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1928 "Cannot noop or zero extend with non-integer arguments!");
1929 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1930 "getNoopOrZeroExtend cannot truncate!");
1931 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1932 return V; // No conversion
1933 return getZeroExtendExpr(V, Ty);
1936 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
1937 /// input value to the specified type. If the type must be extended, it is sign
1938 /// extended. The conversion must not be narrowing.
1940 ScalarEvolution::getNoopOrSignExtend(const SCEVHandle &V, const Type *Ty) {
1941 const Type *SrcTy = V->getType();
1942 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1943 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1944 "Cannot noop or sign extend with non-integer arguments!");
1945 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1946 "getNoopOrSignExtend cannot truncate!");
1947 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1948 return V; // No conversion
1949 return getSignExtendExpr(V, Ty);
1952 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
1953 /// the input value to the specified type. If the type must be extended,
1954 /// it is extended with unspecified bits. The conversion must not be
1957 ScalarEvolution::getNoopOrAnyExtend(const SCEVHandle &V, const Type *Ty) {
1958 const Type *SrcTy = V->getType();
1959 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1960 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1961 "Cannot noop or any extend with non-integer arguments!");
1962 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1963 "getNoopOrAnyExtend cannot truncate!");
1964 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1965 return V; // No conversion
1966 return getAnyExtendExpr(V, Ty);
1969 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
1970 /// input value to the specified type. The conversion must not be widening.
1972 ScalarEvolution::getTruncateOrNoop(const SCEVHandle &V, const Type *Ty) {
1973 const Type *SrcTy = V->getType();
1974 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1975 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1976 "Cannot truncate or noop with non-integer arguments!");
1977 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
1978 "getTruncateOrNoop cannot extend!");
1979 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1980 return V; // No conversion
1981 return getTruncateExpr(V, Ty);
1984 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1985 /// the specified instruction and replaces any references to the symbolic value
1986 /// SymName with the specified value. This is used during PHI resolution.
1987 void ScalarEvolution::
1988 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1989 const SCEVHandle &NewVal) {
1990 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
1991 Scalars.find(SCEVCallbackVH(I, this));
1992 if (SI == Scalars.end()) return;
1995 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
1996 if (NV == SI->second) return; // No change.
1998 SI->second = NV; // Update the scalars map!
2000 // Any instruction values that use this instruction might also need to be
2002 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
2004 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
2007 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2008 /// a loop header, making it a potential recurrence, or it doesn't.
2010 SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
2011 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2012 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2013 if (L->getHeader() == PN->getParent()) {
2014 // If it lives in the loop header, it has two incoming values, one
2015 // from outside the loop, and one from inside.
2016 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2017 unsigned BackEdge = IncomingEdge^1;
2019 // While we are analyzing this PHI node, handle its value symbolically.
2020 SCEVHandle SymbolicName = getUnknown(PN);
2021 assert(Scalars.find(PN) == Scalars.end() &&
2022 "PHI node already processed?");
2023 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2025 // Using this symbolic name for the PHI, analyze the value coming around
2027 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
2029 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2030 // has a special value for the first iteration of the loop.
2032 // If the value coming around the backedge is an add with the symbolic
2033 // value we just inserted, then we found a simple induction variable!
2034 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2035 // If there is a single occurrence of the symbolic value, replace it
2036 // with a recurrence.
2037 unsigned FoundIndex = Add->getNumOperands();
2038 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2039 if (Add->getOperand(i) == SymbolicName)
2040 if (FoundIndex == e) {
2045 if (FoundIndex != Add->getNumOperands()) {
2046 // Create an add with everything but the specified operand.
2047 SmallVector<SCEVHandle, 8> Ops;
2048 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2049 if (i != FoundIndex)
2050 Ops.push_back(Add->getOperand(i));
2051 SCEVHandle Accum = getAddExpr(Ops);
2053 // This is not a valid addrec if the step amount is varying each
2054 // loop iteration, but is not itself an addrec in this loop.
2055 if (Accum->isLoopInvariant(L) ||
2056 (isa<SCEVAddRecExpr>(Accum) &&
2057 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2058 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2059 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
2061 // Okay, for the entire analysis of this edge we assumed the PHI
2062 // to be symbolic. We now need to go back and update all of the
2063 // entries for the scalars that use the PHI (except for the PHI
2064 // itself) to use the new analyzed value instead of the "symbolic"
2066 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2070 } else if (const SCEVAddRecExpr *AddRec =
2071 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2072 // Otherwise, this could be a loop like this:
2073 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2074 // In this case, j = {1,+,1} and BEValue is j.
2075 // Because the other in-value of i (0) fits the evolution of BEValue
2076 // i really is an addrec evolution.
2077 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2078 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2080 // If StartVal = j.start - j.stride, we can use StartVal as the
2081 // initial step of the addrec evolution.
2082 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2083 AddRec->getOperand(1))) {
2084 SCEVHandle PHISCEV =
2085 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2087 // Okay, for the entire analysis of this edge we assumed the PHI
2088 // to be symbolic. We now need to go back and update all of the
2089 // entries for the scalars that use the PHI (except for the PHI
2090 // itself) to use the new analyzed value instead of the "symbolic"
2092 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2098 return SymbolicName;
2101 // If it's not a loop phi, we can't handle it yet.
2102 return getUnknown(PN);
2105 /// createNodeForGEP - Expand GEP instructions into add and multiply
2106 /// operations. This allows them to be analyzed by regular SCEV code.
2108 SCEVHandle ScalarEvolution::createNodeForGEP(User *GEP) {
2110 const Type *IntPtrTy = TD->getIntPtrType();
2111 Value *Base = GEP->getOperand(0);
2112 // Don't attempt to analyze GEPs over unsized objects.
2113 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2114 return getUnknown(GEP);
2115 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
2116 gep_type_iterator GTI = gep_type_begin(GEP);
2117 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2121 // Compute the (potentially symbolic) offset in bytes for this index.
2122 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2123 // For a struct, add the member offset.
2124 const StructLayout &SL = *TD->getStructLayout(STy);
2125 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2126 uint64_t Offset = SL.getElementOffset(FieldNo);
2127 TotalOffset = getAddExpr(TotalOffset,
2128 getIntegerSCEV(Offset, IntPtrTy));
2130 // For an array, add the element offset, explicitly scaled.
2131 SCEVHandle LocalOffset = getSCEV(Index);
2132 if (!isa<PointerType>(LocalOffset->getType()))
2133 // Getelementptr indicies are signed.
2134 LocalOffset = getTruncateOrSignExtend(LocalOffset,
2137 getMulExpr(LocalOffset,
2138 getIntegerSCEV(TD->getTypeAllocSize(*GTI),
2140 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2143 return getAddExpr(getSCEV(Base), TotalOffset);
2146 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2147 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2148 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2149 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2150 static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
2151 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2152 return C->getValue()->getValue().countTrailingZeros();
2154 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2155 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
2156 (uint32_t)SE.getTypeSizeInBits(T->getType()));
2158 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2159 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2160 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2161 SE.getTypeSizeInBits(E->getType()) : OpRes;
2164 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2165 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2166 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2167 SE.getTypeSizeInBits(E->getType()) : OpRes;
2170 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2171 // The result is the min of all operands results.
2172 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2173 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2174 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2178 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2179 // The result is the sum of all operands results.
2180 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2181 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
2182 for (unsigned i = 1, e = M->getNumOperands();
2183 SumOpRes != BitWidth && i != e; ++i)
2184 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
2189 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2190 // The result is the min of all operands results.
2191 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2192 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2193 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2197 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2198 // The result is the min of all operands results.
2199 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2200 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2201 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2205 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2206 // The result is the min of all operands results.
2207 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2208 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2209 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2213 // SCEVUDivExpr, SCEVUnknown
2217 /// createSCEV - We know that there is no SCEV for the specified value.
2218 /// Analyze the expression.
2220 SCEVHandle ScalarEvolution::createSCEV(Value *V) {
2221 if (!isSCEVable(V->getType()))
2222 return getUnknown(V);
2224 unsigned Opcode = Instruction::UserOp1;
2225 if (Instruction *I = dyn_cast<Instruction>(V))
2226 Opcode = I->getOpcode();
2227 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2228 Opcode = CE->getOpcode();
2230 return getUnknown(V);
2232 User *U = cast<User>(V);
2234 case Instruction::Add:
2235 return getAddExpr(getSCEV(U->getOperand(0)),
2236 getSCEV(U->getOperand(1)));
2237 case Instruction::Mul:
2238 return getMulExpr(getSCEV(U->getOperand(0)),
2239 getSCEV(U->getOperand(1)));
2240 case Instruction::UDiv:
2241 return getUDivExpr(getSCEV(U->getOperand(0)),
2242 getSCEV(U->getOperand(1)));
2243 case Instruction::Sub:
2244 return getMinusSCEV(getSCEV(U->getOperand(0)),
2245 getSCEV(U->getOperand(1)));
2246 case Instruction::And:
2247 // For an expression like x&255 that merely masks off the high bits,
2248 // use zext(trunc(x)) as the SCEV expression.
2249 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2250 if (CI->isNullValue())
2251 return getSCEV(U->getOperand(1));
2252 if (CI->isAllOnesValue())
2253 return getSCEV(U->getOperand(0));
2254 const APInt &A = CI->getValue();
2255 unsigned Ones = A.countTrailingOnes();
2256 if (APIntOps::isMask(Ones, A))
2258 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2259 IntegerType::get(Ones)),
2263 case Instruction::Or:
2264 // If the RHS of the Or is a constant, we may have something like:
2265 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2266 // optimizations will transparently handle this case.
2268 // In order for this transformation to be safe, the LHS must be of the
2269 // form X*(2^n) and the Or constant must be less than 2^n.
2270 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2271 SCEVHandle LHS = getSCEV(U->getOperand(0));
2272 const APInt &CIVal = CI->getValue();
2273 if (GetMinTrailingZeros(LHS, *this) >=
2274 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2275 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2278 case Instruction::Xor:
2279 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2280 // If the RHS of the xor is a signbit, then this is just an add.
2281 // Instcombine turns add of signbit into xor as a strength reduction step.
2282 if (CI->getValue().isSignBit())
2283 return getAddExpr(getSCEV(U->getOperand(0)),
2284 getSCEV(U->getOperand(1)));
2286 // If the RHS of xor is -1, then this is a not operation.
2287 if (CI->isAllOnesValue())
2288 return getNotSCEV(getSCEV(U->getOperand(0)));
2290 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2291 // This is a variant of the check for xor with -1, and it handles
2292 // the case where instcombine has trimmed non-demanded bits out
2293 // of an xor with -1.
2294 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2295 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2296 if (BO->getOpcode() == Instruction::And &&
2297 LCI->getValue() == CI->getValue())
2298 if (const SCEVZeroExtendExpr *Z =
2299 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0))))
2300 return getZeroExtendExpr(getNotSCEV(Z->getOperand()),
2305 case Instruction::Shl:
2306 // Turn shift left of a constant amount into a multiply.
2307 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2308 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2309 Constant *X = ConstantInt::get(
2310 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2311 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2315 case Instruction::LShr:
2316 // Turn logical shift right of a constant into a unsigned divide.
2317 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2318 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2319 Constant *X = ConstantInt::get(
2320 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2321 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2325 case Instruction::AShr:
2326 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2327 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2328 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2329 if (L->getOpcode() == Instruction::Shl &&
2330 L->getOperand(1) == U->getOperand(1)) {
2331 unsigned BitWidth = getTypeSizeInBits(U->getType());
2332 uint64_t Amt = BitWidth - CI->getZExtValue();
2333 if (Amt == BitWidth)
2334 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2336 return getIntegerSCEV(0, U->getType()); // value is undefined
2338 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2339 IntegerType::get(Amt)),
2344 case Instruction::Trunc:
2345 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2347 case Instruction::ZExt:
2348 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2350 case Instruction::SExt:
2351 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2353 case Instruction::BitCast:
2354 // BitCasts are no-op casts so we just eliminate the cast.
2355 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2356 return getSCEV(U->getOperand(0));
2359 case Instruction::IntToPtr:
2360 if (!TD) break; // Without TD we can't analyze pointers.
2361 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2362 TD->getIntPtrType());
2364 case Instruction::PtrToInt:
2365 if (!TD) break; // Without TD we can't analyze pointers.
2366 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2369 case Instruction::GetElementPtr:
2370 if (!TD) break; // Without TD we can't analyze pointers.
2371 return createNodeForGEP(U);
2373 case Instruction::PHI:
2374 return createNodeForPHI(cast<PHINode>(U));
2376 case Instruction::Select:
2377 // This could be a smax or umax that was lowered earlier.
2378 // Try to recover it.
2379 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2380 Value *LHS = ICI->getOperand(0);
2381 Value *RHS = ICI->getOperand(1);
2382 switch (ICI->getPredicate()) {
2383 case ICmpInst::ICMP_SLT:
2384 case ICmpInst::ICMP_SLE:
2385 std::swap(LHS, RHS);
2387 case ICmpInst::ICMP_SGT:
2388 case ICmpInst::ICMP_SGE:
2389 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2390 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2391 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2392 // ~smax(~x, ~y) == smin(x, y).
2393 return getNotSCEV(getSMaxExpr(
2394 getNotSCEV(getSCEV(LHS)),
2395 getNotSCEV(getSCEV(RHS))));
2397 case ICmpInst::ICMP_ULT:
2398 case ICmpInst::ICMP_ULE:
2399 std::swap(LHS, RHS);
2401 case ICmpInst::ICMP_UGT:
2402 case ICmpInst::ICMP_UGE:
2403 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2404 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2405 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2406 // ~umax(~x, ~y) == umin(x, y)
2407 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2408 getNotSCEV(getSCEV(RHS))));
2415 default: // We cannot analyze this expression.
2419 return getUnknown(V);
2424 //===----------------------------------------------------------------------===//
2425 // Iteration Count Computation Code
2428 /// getBackedgeTakenCount - If the specified loop has a predictable
2429 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2430 /// object. The backedge-taken count is the number of times the loop header
2431 /// will be branched to from within the loop. This is one less than the
2432 /// trip count of the loop, since it doesn't count the first iteration,
2433 /// when the header is branched to from outside the loop.
2435 /// Note that it is not valid to call this method on a loop without a
2436 /// loop-invariant backedge-taken count (see
2437 /// hasLoopInvariantBackedgeTakenCount).
2439 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2440 return getBackedgeTakenInfo(L).Exact;
2443 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2444 /// return the least SCEV value that is known never to be less than the
2445 /// actual backedge taken count.
2446 SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2447 return getBackedgeTakenInfo(L).Max;
2450 const ScalarEvolution::BackedgeTakenInfo &
2451 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2452 // Initially insert a CouldNotCompute for this loop. If the insertion
2453 // succeeds, procede to actually compute a backedge-taken count and
2454 // update the value. The temporary CouldNotCompute value tells SCEV
2455 // code elsewhere that it shouldn't attempt to request a new
2456 // backedge-taken count, which could result in infinite recursion.
2457 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2458 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2460 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2461 if (ItCount.Exact != CouldNotCompute) {
2462 assert(ItCount.Exact->isLoopInvariant(L) &&
2463 ItCount.Max->isLoopInvariant(L) &&
2464 "Computed trip count isn't loop invariant for loop!");
2465 ++NumTripCountsComputed;
2467 // Update the value in the map.
2468 Pair.first->second = ItCount;
2469 } else if (isa<PHINode>(L->getHeader()->begin())) {
2470 // Only count loops that have phi nodes as not being computable.
2471 ++NumTripCountsNotComputed;
2474 // Now that we know more about the trip count for this loop, forget any
2475 // existing SCEV values for PHI nodes in this loop since they are only
2476 // conservative estimates made without the benefit
2477 // of trip count information.
2478 if (ItCount.hasAnyInfo())
2481 return Pair.first->second;
2484 /// forgetLoopBackedgeTakenCount - This method should be called by the
2485 /// client when it has changed a loop in a way that may effect
2486 /// ScalarEvolution's ability to compute a trip count, or if the loop
2488 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2489 BackedgeTakenCounts.erase(L);
2493 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2494 /// PHI nodes in the given loop. This is used when the trip count of
2495 /// the loop may have changed.
2496 void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2497 BasicBlock *Header = L->getHeader();
2499 // Push all Loop-header PHIs onto the Worklist stack, except those
2500 // that are presently represented via a SCEVUnknown. SCEVUnknown for
2501 // a PHI either means that it has an unrecognized structure, or it's
2502 // a PHI that's in the progress of being computed by createNodeForPHI.
2503 // In the former case, additional loop trip count information isn't
2504 // going to change anything. In the later case, createNodeForPHI will
2505 // perform the necessary updates on its own when it gets to that point.
2506 SmallVector<Instruction *, 16> Worklist;
2507 for (BasicBlock::iterator I = Header->begin();
2508 PHINode *PN = dyn_cast<PHINode>(I); ++I) {
2509 std::map<SCEVCallbackVH, SCEVHandle>::iterator It = Scalars.find((Value*)I);
2510 if (It != Scalars.end() && !isa<SCEVUnknown>(It->second))
2511 Worklist.push_back(PN);
2514 while (!Worklist.empty()) {
2515 Instruction *I = Worklist.pop_back_val();
2516 if (Scalars.erase(I))
2517 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2519 Worklist.push_back(cast<Instruction>(UI));
2523 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2524 /// of the specified loop will execute.
2525 ScalarEvolution::BackedgeTakenInfo
2526 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2527 // If the loop has a non-one exit block count, we can't analyze it.
2528 BasicBlock *ExitBlock = L->getExitBlock();
2530 return CouldNotCompute;
2532 // Okay, there is one exit block. Try to find the condition that causes the
2533 // loop to be exited.
2534 BasicBlock *ExitingBlock = L->getExitingBlock();
2536 return CouldNotCompute; // More than one block exiting!
2538 // Okay, we've computed the exiting block. See what condition causes us to
2541 // FIXME: we should be able to handle switch instructions (with a single exit)
2542 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2543 if (ExitBr == 0) return CouldNotCompute;
2544 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2546 // At this point, we know we have a conditional branch that determines whether
2547 // the loop is exited. However, we don't know if the branch is executed each
2548 // time through the loop. If not, then the execution count of the branch will
2549 // not be equal to the trip count of the loop.
2551 // Currently we check for this by checking to see if the Exit branch goes to
2552 // the loop header. If so, we know it will always execute the same number of
2553 // times as the loop. We also handle the case where the exit block *is* the
2554 // loop header. This is common for un-rotated loops. More extensive analysis
2555 // could be done to handle more cases here.
2556 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2557 ExitBr->getSuccessor(1) != L->getHeader() &&
2558 ExitBr->getParent() != L->getHeader())
2559 return CouldNotCompute;
2561 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2563 // If it's not an integer or pointer comparison then compute it the hard way.
2565 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2566 ExitBr->getSuccessor(0) == ExitBlock);
2568 // If the condition was exit on true, convert the condition to exit on false
2569 ICmpInst::Predicate Cond;
2570 if (ExitBr->getSuccessor(1) == ExitBlock)
2571 Cond = ExitCond->getPredicate();
2573 Cond = ExitCond->getInversePredicate();
2575 // Handle common loops like: for (X = "string"; *X; ++X)
2576 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2577 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2579 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2580 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2583 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2584 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2586 // Try to evaluate any dependencies out of the loop.
2587 LHS = getSCEVAtScope(LHS, L);
2588 RHS = getSCEVAtScope(RHS, L);
2590 // At this point, we would like to compute how many iterations of the
2591 // loop the predicate will return true for these inputs.
2592 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2593 // If there is a loop-invariant, force it into the RHS.
2594 std::swap(LHS, RHS);
2595 Cond = ICmpInst::getSwappedPredicate(Cond);
2598 // If we have a comparison of a chrec against a constant, try to use value
2599 // ranges to answer this query.
2600 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2601 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2602 if (AddRec->getLoop() == L) {
2603 // Form the constant range.
2604 ConstantRange CompRange(
2605 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
2607 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2608 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2612 case ICmpInst::ICMP_NE: { // while (X != Y)
2613 // Convert to: while (X-Y != 0)
2614 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2615 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2618 case ICmpInst::ICMP_EQ: {
2619 // Convert to: while (X-Y == 0) // while (X == Y)
2620 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2621 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2624 case ICmpInst::ICMP_SLT: {
2625 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2626 if (BTI.hasAnyInfo()) return BTI;
2629 case ICmpInst::ICMP_SGT: {
2630 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2631 getNotSCEV(RHS), L, true);
2632 if (BTI.hasAnyInfo()) return BTI;
2635 case ICmpInst::ICMP_ULT: {
2636 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2637 if (BTI.hasAnyInfo()) return BTI;
2640 case ICmpInst::ICMP_UGT: {
2641 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2642 getNotSCEV(RHS), L, false);
2643 if (BTI.hasAnyInfo()) return BTI;
2648 errs() << "ComputeBackedgeTakenCount ";
2649 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2650 errs() << "[unsigned] ";
2651 errs() << *LHS << " "
2652 << Instruction::getOpcodeName(Instruction::ICmp)
2653 << " " << *RHS << "\n";
2658 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2659 ExitBr->getSuccessor(0) == ExitBlock);
2662 static ConstantInt *
2663 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2664 ScalarEvolution &SE) {
2665 SCEVHandle InVal = SE.getConstant(C);
2666 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2667 assert(isa<SCEVConstant>(Val) &&
2668 "Evaluation of SCEV at constant didn't fold correctly?");
2669 return cast<SCEVConstant>(Val)->getValue();
2672 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2673 /// and a GEP expression (missing the pointer index) indexing into it, return
2674 /// the addressed element of the initializer or null if the index expression is
2677 GetAddressedElementFromGlobal(GlobalVariable *GV,
2678 const std::vector<ConstantInt*> &Indices) {
2679 Constant *Init = GV->getInitializer();
2680 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2681 uint64_t Idx = Indices[i]->getZExtValue();
2682 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2683 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2684 Init = cast<Constant>(CS->getOperand(Idx));
2685 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2686 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2687 Init = cast<Constant>(CA->getOperand(Idx));
2688 } else if (isa<ConstantAggregateZero>(Init)) {
2689 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2690 assert(Idx < STy->getNumElements() && "Bad struct index!");
2691 Init = Constant::getNullValue(STy->getElementType(Idx));
2692 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2693 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2694 Init = Constant::getNullValue(ATy->getElementType());
2696 assert(0 && "Unknown constant aggregate type!");
2700 return 0; // Unknown initializer type
2706 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2707 /// 'icmp op load X, cst', try to see if we can compute the backedge
2708 /// execution count.
2709 SCEVHandle ScalarEvolution::
2710 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2712 ICmpInst::Predicate predicate) {
2713 if (LI->isVolatile()) return CouldNotCompute;
2715 // Check to see if the loaded pointer is a getelementptr of a global.
2716 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2717 if (!GEP) return CouldNotCompute;
2719 // Make sure that it is really a constant global we are gepping, with an
2720 // initializer, and make sure the first IDX is really 0.
2721 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2722 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2723 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2724 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2725 return CouldNotCompute;
2727 // Okay, we allow one non-constant index into the GEP instruction.
2729 std::vector<ConstantInt*> Indexes;
2730 unsigned VarIdxNum = 0;
2731 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2732 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2733 Indexes.push_back(CI);
2734 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2735 if (VarIdx) return CouldNotCompute; // Multiple non-constant idx's.
2736 VarIdx = GEP->getOperand(i);
2738 Indexes.push_back(0);
2741 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2742 // Check to see if X is a loop variant variable value now.
2743 SCEVHandle Idx = getSCEV(VarIdx);
2744 Idx = getSCEVAtScope(Idx, L);
2746 // We can only recognize very limited forms of loop index expressions, in
2747 // particular, only affine AddRec's like {C1,+,C2}.
2748 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2749 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2750 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2751 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2752 return CouldNotCompute;
2754 unsigned MaxSteps = MaxBruteForceIterations;
2755 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2756 ConstantInt *ItCst =
2757 ConstantInt::get(IdxExpr->getType(), IterationNum);
2758 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2760 // Form the GEP offset.
2761 Indexes[VarIdxNum] = Val;
2763 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2764 if (Result == 0) break; // Cannot compute!
2766 // Evaluate the condition for this iteration.
2767 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2768 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2769 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2771 errs() << "\n***\n*** Computed loop count " << *ItCst
2772 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2775 ++NumArrayLenItCounts;
2776 return getConstant(ItCst); // Found terminating iteration!
2779 return CouldNotCompute;
2783 /// CanConstantFold - Return true if we can constant fold an instruction of the
2784 /// specified type, assuming that all operands were constants.
2785 static bool CanConstantFold(const Instruction *I) {
2786 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2787 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2790 if (const CallInst *CI = dyn_cast<CallInst>(I))
2791 if (const Function *F = CI->getCalledFunction())
2792 return canConstantFoldCallTo(F);
2796 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2797 /// in the loop that V is derived from. We allow arbitrary operations along the
2798 /// way, but the operands of an operation must either be constants or a value
2799 /// derived from a constant PHI. If this expression does not fit with these
2800 /// constraints, return null.
2801 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2802 // If this is not an instruction, or if this is an instruction outside of the
2803 // loop, it can't be derived from a loop PHI.
2804 Instruction *I = dyn_cast<Instruction>(V);
2805 if (I == 0 || !L->contains(I->getParent())) return 0;
2807 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2808 if (L->getHeader() == I->getParent())
2811 // We don't currently keep track of the control flow needed to evaluate
2812 // PHIs, so we cannot handle PHIs inside of loops.
2816 // If we won't be able to constant fold this expression even if the operands
2817 // are constants, return early.
2818 if (!CanConstantFold(I)) return 0;
2820 // Otherwise, we can evaluate this instruction if all of its operands are
2821 // constant or derived from a PHI node themselves.
2823 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2824 if (!(isa<Constant>(I->getOperand(Op)) ||
2825 isa<GlobalValue>(I->getOperand(Op)))) {
2826 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2827 if (P == 0) return 0; // Not evolving from PHI
2831 return 0; // Evolving from multiple different PHIs.
2834 // This is a expression evolving from a constant PHI!
2838 /// EvaluateExpression - Given an expression that passes the
2839 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2840 /// in the loop has the value PHIVal. If we can't fold this expression for some
2841 /// reason, return null.
2842 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2843 if (isa<PHINode>(V)) return PHIVal;
2844 if (Constant *C = dyn_cast<Constant>(V)) return C;
2845 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2846 Instruction *I = cast<Instruction>(V);
2848 std::vector<Constant*> Operands;
2849 Operands.resize(I->getNumOperands());
2851 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2852 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2853 if (Operands[i] == 0) return 0;
2856 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2857 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2858 &Operands[0], Operands.size());
2860 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2861 &Operands[0], Operands.size());
2864 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2865 /// in the header of its containing loop, we know the loop executes a
2866 /// constant number of times, and the PHI node is just a recurrence
2867 /// involving constants, fold it.
2868 Constant *ScalarEvolution::
2869 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2870 std::map<PHINode*, Constant*>::iterator I =
2871 ConstantEvolutionLoopExitValue.find(PN);
2872 if (I != ConstantEvolutionLoopExitValue.end())
2875 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2876 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2878 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2880 // Since the loop is canonicalized, the PHI node must have two entries. One
2881 // entry must be a constant (coming in from outside of the loop), and the
2882 // second must be derived from the same PHI.
2883 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2884 Constant *StartCST =
2885 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2887 return RetVal = 0; // Must be a constant.
2889 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2890 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2892 return RetVal = 0; // Not derived from same PHI.
2894 // Execute the loop symbolically to determine the exit value.
2895 if (BEs.getActiveBits() >= 32)
2896 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2898 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2899 unsigned IterationNum = 0;
2900 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2901 if (IterationNum == NumIterations)
2902 return RetVal = PHIVal; // Got exit value!
2904 // Compute the value of the PHI node for the next iteration.
2905 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2906 if (NextPHI == PHIVal)
2907 return RetVal = NextPHI; // Stopped evolving!
2909 return 0; // Couldn't evaluate!
2914 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2915 /// constant number of times (the condition evolves only from constants),
2916 /// try to evaluate a few iterations of the loop until we get the exit
2917 /// condition gets a value of ExitWhen (true or false). If we cannot
2918 /// evaluate the trip count of the loop, return CouldNotCompute.
2919 SCEVHandle ScalarEvolution::
2920 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2921 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2922 if (PN == 0) return CouldNotCompute;
2924 // Since the loop is canonicalized, the PHI node must have two entries. One
2925 // entry must be a constant (coming in from outside of the loop), and the
2926 // second must be derived from the same PHI.
2927 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2928 Constant *StartCST =
2929 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2930 if (StartCST == 0) return CouldNotCompute; // Must be a constant.
2932 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2933 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2934 if (PN2 != PN) return CouldNotCompute; // Not derived from same PHI.
2936 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2937 // the loop symbolically to determine when the condition gets a value of
2939 unsigned IterationNum = 0;
2940 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2941 for (Constant *PHIVal = StartCST;
2942 IterationNum != MaxIterations; ++IterationNum) {
2943 ConstantInt *CondVal =
2944 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2946 // Couldn't symbolically evaluate.
2947 if (!CondVal) return CouldNotCompute;
2949 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2950 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2951 ++NumBruteForceTripCountsComputed;
2952 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2955 // Compute the value of the PHI node for the next iteration.
2956 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2957 if (NextPHI == 0 || NextPHI == PHIVal)
2958 return CouldNotCompute; // Couldn't evaluate or not making progress...
2962 // Too many iterations were needed to evaluate.
2963 return CouldNotCompute;
2966 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
2967 /// at the specified scope in the program. The L value specifies a loop
2968 /// nest to evaluate the expression at, where null is the top-level or a
2969 /// specified loop is immediately inside of the loop.
2971 /// This method can be used to compute the exit value for a variable defined
2972 /// in a loop by querying what the value will hold in the parent loop.
2974 /// In the case that a relevant loop exit value cannot be computed, the
2975 /// original value V is returned.
2976 SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
2977 // FIXME: this should be turned into a virtual method on SCEV!
2979 if (isa<SCEVConstant>(V)) return V;
2981 // If this instruction is evolved from a constant-evolving PHI, compute the
2982 // exit value from the loop without using SCEVs.
2983 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2984 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2985 const Loop *LI = (*this->LI)[I->getParent()];
2986 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2987 if (PHINode *PN = dyn_cast<PHINode>(I))
2988 if (PN->getParent() == LI->getHeader()) {
2989 // Okay, there is no closed form solution for the PHI node. Check
2990 // to see if the loop that contains it has a known backedge-taken
2991 // count. If so, we may be able to force computation of the exit
2993 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2994 if (const SCEVConstant *BTCC =
2995 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2996 // Okay, we know how many times the containing loop executes. If
2997 // this is a constant evolving PHI node, get the final value at
2998 // the specified iteration number.
2999 Constant *RV = getConstantEvolutionLoopExitValue(PN,
3000 BTCC->getValue()->getValue(),
3002 if (RV) return getUnknown(RV);
3006 // Okay, this is an expression that we cannot symbolically evaluate
3007 // into a SCEV. Check to see if it's possible to symbolically evaluate
3008 // the arguments into constants, and if so, try to constant propagate the
3009 // result. This is particularly useful for computing loop exit values.
3010 if (CanConstantFold(I)) {
3011 // Check to see if we've folded this instruction at this loop before.
3012 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
3013 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
3014 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
3016 return Pair.first->second ? &*getUnknown(Pair.first->second) : V;
3018 std::vector<Constant*> Operands;
3019 Operands.reserve(I->getNumOperands());
3020 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3021 Value *Op = I->getOperand(i);
3022 if (Constant *C = dyn_cast<Constant>(Op)) {
3023 Operands.push_back(C);
3025 // If any of the operands is non-constant and if they are
3026 // non-integer and non-pointer, don't even try to analyze them
3027 // with scev techniques.
3028 if (!isSCEVable(Op->getType()))
3031 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
3032 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
3033 Constant *C = SC->getValue();
3034 if (C->getType() != Op->getType())
3035 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3039 Operands.push_back(C);
3040 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
3041 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
3042 if (C->getType() != Op->getType())
3044 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3048 Operands.push_back(C);
3058 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3059 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
3060 &Operands[0], Operands.size());
3062 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3063 &Operands[0], Operands.size());
3064 Pair.first->second = C;
3065 return getUnknown(C);
3069 // This is some other type of SCEVUnknown, just return it.
3073 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3074 // Avoid performing the look-up in the common case where the specified
3075 // expression has no loop-variant portions.
3076 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3077 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3078 if (OpAtScope != Comm->getOperand(i)) {
3079 // Okay, at least one of these operands is loop variant but might be
3080 // foldable. Build a new instance of the folded commutative expression.
3081 SmallVector<SCEVHandle, 8> NewOps(Comm->op_begin(), Comm->op_begin()+i);
3082 NewOps.push_back(OpAtScope);
3084 for (++i; i != e; ++i) {
3085 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3086 NewOps.push_back(OpAtScope);
3088 if (isa<SCEVAddExpr>(Comm))
3089 return getAddExpr(NewOps);
3090 if (isa<SCEVMulExpr>(Comm))
3091 return getMulExpr(NewOps);
3092 if (isa<SCEVSMaxExpr>(Comm))
3093 return getSMaxExpr(NewOps);
3094 if (isa<SCEVUMaxExpr>(Comm))
3095 return getUMaxExpr(NewOps);
3096 assert(0 && "Unknown commutative SCEV type!");
3099 // If we got here, all operands are loop invariant.
3103 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3104 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
3105 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
3106 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3107 return Div; // must be loop invariant
3108 return getUDivExpr(LHS, RHS);
3111 // If this is a loop recurrence for a loop that does not contain L, then we
3112 // are dealing with the final value computed by the loop.
3113 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3114 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3115 // To evaluate this recurrence, we need to know how many times the AddRec
3116 // loop iterates. Compute this now.
3117 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3118 if (BackedgeTakenCount == CouldNotCompute) return AddRec;
3120 // Then, evaluate the AddRec.
3121 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3126 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3127 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3128 if (Op == Cast->getOperand())
3129 return Cast; // must be loop invariant
3130 return getZeroExtendExpr(Op, Cast->getType());
3133 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3134 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3135 if (Op == Cast->getOperand())
3136 return Cast; // must be loop invariant
3137 return getSignExtendExpr(Op, Cast->getType());
3140 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3141 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3142 if (Op == Cast->getOperand())
3143 return Cast; // must be loop invariant
3144 return getTruncateExpr(Op, Cast->getType());
3147 assert(0 && "Unknown SCEV type!");
3151 /// getSCEVAtScope - This is a convenience function which does
3152 /// getSCEVAtScope(getSCEV(V), L).
3153 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3154 return getSCEVAtScope(getSCEV(V), L);
3157 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3158 /// following equation:
3160 /// A * X = B (mod N)
3162 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3163 /// A and B isn't important.
3165 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3166 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3167 ScalarEvolution &SE) {
3168 uint32_t BW = A.getBitWidth();
3169 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3170 assert(A != 0 && "A must be non-zero.");
3174 // The gcd of A and N may have only one prime factor: 2. The number of
3175 // trailing zeros in A is its multiplicity
3176 uint32_t Mult2 = A.countTrailingZeros();
3179 // 2. Check if B is divisible by D.
3181 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3182 // is not less than multiplicity of this prime factor for D.
3183 if (B.countTrailingZeros() < Mult2)
3184 return SE.getCouldNotCompute();
3186 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3189 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3190 // bit width during computations.
3191 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3192 APInt Mod(BW + 1, 0);
3193 Mod.set(BW - Mult2); // Mod = N / D
3194 APInt I = AD.multiplicativeInverse(Mod);
3196 // 4. Compute the minimum unsigned root of the equation:
3197 // I * (B / D) mod (N / D)
3198 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3200 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3202 return SE.getConstant(Result.trunc(BW));
3205 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3206 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
3207 /// might be the same) or two SCEVCouldNotCompute objects.
3209 static std::pair<SCEVHandle,SCEVHandle>
3210 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
3211 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
3212 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
3213 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
3214 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
3216 // We currently can only solve this if the coefficients are constants.
3217 if (!LC || !MC || !NC) {
3218 const SCEV *CNC = SE.getCouldNotCompute();
3219 return std::make_pair(CNC, CNC);
3222 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
3223 const APInt &L = LC->getValue()->getValue();
3224 const APInt &M = MC->getValue()->getValue();
3225 const APInt &N = NC->getValue()->getValue();
3226 APInt Two(BitWidth, 2);
3227 APInt Four(BitWidth, 4);
3230 using namespace APIntOps;
3232 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
3233 // The B coefficient is M-N/2
3237 // The A coefficient is N/2
3238 APInt A(N.sdiv(Two));
3240 // Compute the B^2-4ac term.
3243 SqrtTerm -= Four * (A * C);
3245 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
3246 // integer value or else APInt::sqrt() will assert.
3247 APInt SqrtVal(SqrtTerm.sqrt());
3249 // Compute the two solutions for the quadratic formula.
3250 // The divisions must be performed as signed divisions.
3252 APInt TwoA( A << 1 );
3253 if (TwoA.isMinValue()) {
3254 const SCEV *CNC = SE.getCouldNotCompute();
3255 return std::make_pair(CNC, CNC);
3258 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
3259 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
3261 return std::make_pair(SE.getConstant(Solution1),
3262 SE.getConstant(Solution2));
3263 } // end APIntOps namespace
3266 /// HowFarToZero - Return the number of times a backedge comparing the specified
3267 /// value to zero will execute. If not computable, return CouldNotCompute.
3268 SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
3269 // If the value is a constant
3270 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3271 // If the value is already zero, the branch will execute zero times.
3272 if (C->getValue()->isZero()) return C;
3273 return CouldNotCompute; // Otherwise it will loop infinitely.
3276 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
3277 if (!AddRec || AddRec->getLoop() != L)
3278 return CouldNotCompute;
3280 if (AddRec->isAffine()) {
3281 // If this is an affine expression, the execution count of this branch is
3282 // the minimum unsigned root of the following equation:
3284 // Start + Step*N = 0 (mod 2^BW)
3288 // Step*N = -Start (mod 2^BW)
3290 // where BW is the common bit width of Start and Step.
3292 // Get the initial value for the loop.
3293 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
3294 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
3296 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
3297 // For now we handle only constant steps.
3299 // First, handle unitary steps.
3300 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
3301 return getNegativeSCEV(Start); // N = -Start (as unsigned)
3302 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
3303 return Start; // N = Start (as unsigned)
3305 // Then, try to solve the above equation provided that Start is constant.
3306 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
3307 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
3308 -StartC->getValue()->getValue(),
3311 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
3312 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
3313 // the quadratic equation to solve it.
3314 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
3316 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3317 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3320 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
3321 << " sol#2: " << *R2 << "\n";
3323 // Pick the smallest positive root value.
3324 if (ConstantInt *CB =
3325 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3326 R1->getValue(), R2->getValue()))) {
3327 if (CB->getZExtValue() == false)
3328 std::swap(R1, R2); // R1 is the minimum root now.
3330 // We can only use this value if the chrec ends up with an exact zero
3331 // value at this index. When solving for "X*X != 5", for example, we
3332 // should not accept a root of 2.
3333 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
3335 return R1; // We found a quadratic root!
3340 return CouldNotCompute;
3343 /// HowFarToNonZero - Return the number of times a backedge checking the
3344 /// specified value for nonzero will execute. If not computable, return
3346 SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
3347 // Loops that look like: while (X == 0) are very strange indeed. We don't
3348 // handle them yet except for the trivial case. This could be expanded in the
3349 // future as needed.
3351 // If the value is a constant, check to see if it is known to be non-zero
3352 // already. If so, the backedge will execute zero times.
3353 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3354 if (!C->getValue()->isNullValue())
3355 return getIntegerSCEV(0, C->getType());
3356 return CouldNotCompute; // Otherwise it will loop infinitely.
3359 // We could implement others, but I really doubt anyone writes loops like
3360 // this, and if they did, they would already be constant folded.
3361 return CouldNotCompute;
3364 /// getLoopPredecessor - If the given loop's header has exactly one unique
3365 /// predecessor outside the loop, return it. Otherwise return null.
3367 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
3368 BasicBlock *Header = L->getHeader();
3369 BasicBlock *Pred = 0;
3370 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
3372 if (!L->contains(*PI)) {
3373 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
3379 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3380 /// (which may not be an immediate predecessor) which has exactly one
3381 /// successor from which BB is reachable, or null if no such block is
3385 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3386 // If the block has a unique predecessor, then there is no path from the
3387 // predecessor to the block that does not go through the direct edge
3388 // from the predecessor to the block.
3389 if (BasicBlock *Pred = BB->getSinglePredecessor())
3392 // A loop's header is defined to be a block that dominates the loop.
3393 // If the header has a unique predecessor outside the loop, it must be
3394 // a block that has exactly one successor that can reach the loop.
3395 if (Loop *L = LI->getLoopFor(BB))
3396 return getLoopPredecessor(L);
3401 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
3402 /// a conditional between LHS and RHS. This is used to help avoid max
3403 /// expressions in loop trip counts.
3404 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3405 ICmpInst::Predicate Pred,
3406 const SCEV *LHS, const SCEV *RHS) {
3407 // Interpret a null as meaning no loop, where there is obviously no guard
3408 // (interprocedural conditions notwithstanding).
3409 if (!L) return false;
3411 BasicBlock *Predecessor = getLoopPredecessor(L);
3412 BasicBlock *PredecessorDest = L->getHeader();
3414 // Starting at the loop predecessor, climb up the predecessor chain, as long
3415 // as there are predecessors that can be found that have unique successors
3416 // leading to the original header.
3418 PredecessorDest = Predecessor,
3419 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
3421 BranchInst *LoopEntryPredicate =
3422 dyn_cast<BranchInst>(Predecessor->getTerminator());
3423 if (!LoopEntryPredicate ||
3424 LoopEntryPredicate->isUnconditional())
3427 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3430 // Now that we found a conditional branch that dominates the loop, check to
3431 // see if it is the comparison we are looking for.
3432 Value *PreCondLHS = ICI->getOperand(0);
3433 Value *PreCondRHS = ICI->getOperand(1);
3434 ICmpInst::Predicate Cond;
3435 if (LoopEntryPredicate->getSuccessor(0) == PredecessorDest)
3436 Cond = ICI->getPredicate();
3438 Cond = ICI->getInversePredicate();
3441 ; // An exact match.
3442 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3443 ; // The actual condition is beyond sufficient.
3445 // Check a few special cases.
3447 case ICmpInst::ICMP_UGT:
3448 if (Pred == ICmpInst::ICMP_ULT) {
3449 std::swap(PreCondLHS, PreCondRHS);
3450 Cond = ICmpInst::ICMP_ULT;
3454 case ICmpInst::ICMP_SGT:
3455 if (Pred == ICmpInst::ICMP_SLT) {
3456 std::swap(PreCondLHS, PreCondRHS);
3457 Cond = ICmpInst::ICMP_SLT;
3461 case ICmpInst::ICMP_NE:
3462 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3463 // so check for this case by checking if the NE is comparing against
3464 // a minimum or maximum constant.
3465 if (!ICmpInst::isTrueWhenEqual(Pred))
3466 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3467 const APInt &A = CI->getValue();
3469 case ICmpInst::ICMP_SLT:
3470 if (A.isMaxSignedValue()) break;
3472 case ICmpInst::ICMP_SGT:
3473 if (A.isMinSignedValue()) break;
3475 case ICmpInst::ICMP_ULT:
3476 if (A.isMaxValue()) break;
3478 case ICmpInst::ICMP_UGT:
3479 if (A.isMinValue()) break;
3484 Cond = ICmpInst::ICMP_NE;
3485 // NE is symmetric but the original comparison may not be. Swap
3486 // the operands if necessary so that they match below.
3487 if (isa<SCEVConstant>(LHS))
3488 std::swap(PreCondLHS, PreCondRHS);
3493 // We weren't able to reconcile the condition.
3497 if (!PreCondLHS->getType()->isInteger()) continue;
3499 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3500 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3501 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3502 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3503 RHS == getNotSCEV(PreCondLHSSCEV)))
3510 /// HowManyLessThans - Return the number of times a backedge containing the
3511 /// specified less-than comparison will execute. If not computable, return
3512 /// CouldNotCompute.
3513 ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3514 HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
3515 const Loop *L, bool isSigned) {
3516 // Only handle: "ADDREC < LoopInvariant".
3517 if (!RHS->isLoopInvariant(L)) return CouldNotCompute;
3519 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3520 if (!AddRec || AddRec->getLoop() != L)
3521 return CouldNotCompute;
3523 if (AddRec->isAffine()) {
3524 // FORNOW: We only support unit strides.
3525 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3526 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3527 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3529 // TODO: handle non-constant strides.
3530 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3531 if (!CStep || CStep->isZero())
3532 return CouldNotCompute;
3533 if (CStep->isOne()) {
3534 // With unit stride, the iteration never steps past the limit value.
3535 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3536 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3537 // Test whether a positive iteration iteration can step past the limit
3538 // value and past the maximum value for its type in a single step.
3540 APInt Max = APInt::getSignedMaxValue(BitWidth);
3541 if ((Max - CStep->getValue()->getValue())
3542 .slt(CLimit->getValue()->getValue()))
3543 return CouldNotCompute;
3545 APInt Max = APInt::getMaxValue(BitWidth);
3546 if ((Max - CStep->getValue()->getValue())
3547 .ult(CLimit->getValue()->getValue()))
3548 return CouldNotCompute;
3551 // TODO: handle non-constant limit values below.
3552 return CouldNotCompute;
3554 // TODO: handle negative strides below.
3555 return CouldNotCompute;
3557 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3558 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3559 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3560 // treat m-n as signed nor unsigned due to overflow possibility.
3562 // First, we get the value of the LHS in the first iteration: n
3563 SCEVHandle Start = AddRec->getOperand(0);
3565 // Determine the minimum constant start value.
3566 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3567 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3568 APInt::getMinValue(BitWidth));
3570 // If we know that the condition is true in order to enter the loop,
3571 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3572 // only know that it will execute (max(m,n)-n)/s times. In both cases,
3573 // the division must round up.
3574 SCEVHandle End = RHS;
3575 if (!isLoopGuardedByCond(L,
3576 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3577 getMinusSCEV(Start, Step), RHS))
3578 End = isSigned ? getSMaxExpr(RHS, Start)
3579 : getUMaxExpr(RHS, Start);
3581 // Determine the maximum constant end value.
3582 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3583 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3584 APInt::getMaxValue(BitWidth));
3586 // Finally, we subtract these two values and divide, rounding up, to get
3587 // the number of times the backedge is executed.
3588 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3589 getAddExpr(Step, NegOne)),
3592 // The maximum backedge count is similar, except using the minimum start
3593 // value and the maximum end value.
3594 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3596 getAddExpr(Step, NegOne)),
3599 return BackedgeTakenInfo(BECount, MaxBECount);
3602 return CouldNotCompute;
3605 /// getNumIterationsInRange - Return the number of iterations of this loop that
3606 /// produce values in the specified constant range. Another way of looking at
3607 /// this is that it returns the first iteration number where the value is not in
3608 /// the condition, thus computing the exit count. If the iteration count can't
3609 /// be computed, an instance of SCEVCouldNotCompute is returned.
3610 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3611 ScalarEvolution &SE) const {
3612 if (Range.isFullSet()) // Infinite loop.
3613 return SE.getCouldNotCompute();
3615 // If the start is a non-zero constant, shift the range to simplify things.
3616 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3617 if (!SC->getValue()->isZero()) {
3618 SmallVector<SCEVHandle, 4> Operands(op_begin(), op_end());
3619 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3620 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3621 if (const SCEVAddRecExpr *ShiftedAddRec =
3622 dyn_cast<SCEVAddRecExpr>(Shifted))
3623 return ShiftedAddRec->getNumIterationsInRange(
3624 Range.subtract(SC->getValue()->getValue()), SE);
3625 // This is strange and shouldn't happen.
3626 return SE.getCouldNotCompute();
3629 // The only time we can solve this is when we have all constant indices.
3630 // Otherwise, we cannot determine the overflow conditions.
3631 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3632 if (!isa<SCEVConstant>(getOperand(i)))
3633 return SE.getCouldNotCompute();
3636 // Okay at this point we know that all elements of the chrec are constants and
3637 // that the start element is zero.
3639 // First check to see if the range contains zero. If not, the first
3641 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3642 if (!Range.contains(APInt(BitWidth, 0)))
3643 return SE.getConstant(ConstantInt::get(getType(),0));
3646 // If this is an affine expression then we have this situation:
3647 // Solve {0,+,A} in Range === Ax in Range
3649 // We know that zero is in the range. If A is positive then we know that
3650 // the upper value of the range must be the first possible exit value.
3651 // If A is negative then the lower of the range is the last possible loop
3652 // value. Also note that we already checked for a full range.
3653 APInt One(BitWidth,1);
3654 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3655 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3657 // The exit value should be (End+A)/A.
3658 APInt ExitVal = (End + A).udiv(A);
3659 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3661 // Evaluate at the exit value. If we really did fall out of the valid
3662 // range, then we computed our trip count, otherwise wrap around or other
3663 // things must have happened.
3664 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3665 if (Range.contains(Val->getValue()))
3666 return SE.getCouldNotCompute(); // Something strange happened
3668 // Ensure that the previous value is in the range. This is a sanity check.
3669 assert(Range.contains(
3670 EvaluateConstantChrecAtConstant(this,
3671 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3672 "Linear scev computation is off in a bad way!");
3673 return SE.getConstant(ExitValue);
3674 } else if (isQuadratic()) {
3675 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3676 // quadratic equation to solve it. To do this, we must frame our problem in
3677 // terms of figuring out when zero is crossed, instead of when
3678 // Range.getUpper() is crossed.
3679 SmallVector<SCEVHandle, 4> NewOps(op_begin(), op_end());
3680 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3681 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3683 // Next, solve the constructed addrec
3684 std::pair<SCEVHandle,SCEVHandle> Roots =
3685 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3686 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3687 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3689 // Pick the smallest positive root value.
3690 if (ConstantInt *CB =
3691 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3692 R1->getValue(), R2->getValue()))) {
3693 if (CB->getZExtValue() == false)
3694 std::swap(R1, R2); // R1 is the minimum root now.
3696 // Make sure the root is not off by one. The returned iteration should
3697 // not be in the range, but the previous one should be. When solving
3698 // for "X*X < 5", for example, we should not return a root of 2.
3699 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3702 if (Range.contains(R1Val->getValue())) {
3703 // The next iteration must be out of the range...
3704 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3706 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3707 if (!Range.contains(R1Val->getValue()))
3708 return SE.getConstant(NextVal);
3709 return SE.getCouldNotCompute(); // Something strange happened
3712 // If R1 was not in the range, then it is a good return value. Make
3713 // sure that R1-1 WAS in the range though, just in case.
3714 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3715 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3716 if (Range.contains(R1Val->getValue()))
3718 return SE.getCouldNotCompute(); // Something strange happened
3723 return SE.getCouldNotCompute();
3728 //===----------------------------------------------------------------------===//
3729 // SCEVCallbackVH Class Implementation
3730 //===----------------------------------------------------------------------===//
3732 void ScalarEvolution::SCEVCallbackVH::deleted() {
3733 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3734 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
3735 SE->ConstantEvolutionLoopExitValue.erase(PN);
3736 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
3737 SE->ValuesAtScopes.erase(I);
3738 SE->Scalars.erase(getValPtr());
3739 // this now dangles!
3742 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
3743 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3745 // Forget all the expressions associated with users of the old value,
3746 // so that future queries will recompute the expressions using the new
3748 SmallVector<User *, 16> Worklist;
3749 Value *Old = getValPtr();
3750 bool DeleteOld = false;
3751 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
3753 Worklist.push_back(*UI);
3754 while (!Worklist.empty()) {
3755 User *U = Worklist.pop_back_val();
3756 // Deleting the Old value will cause this to dangle. Postpone
3757 // that until everything else is done.
3762 if (PHINode *PN = dyn_cast<PHINode>(U))
3763 SE->ConstantEvolutionLoopExitValue.erase(PN);
3764 if (Instruction *I = dyn_cast<Instruction>(U))
3765 SE->ValuesAtScopes.erase(I);
3766 if (SE->Scalars.erase(U))
3767 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
3769 Worklist.push_back(*UI);
3772 if (PHINode *PN = dyn_cast<PHINode>(Old))
3773 SE->ConstantEvolutionLoopExitValue.erase(PN);
3774 if (Instruction *I = dyn_cast<Instruction>(Old))
3775 SE->ValuesAtScopes.erase(I);
3776 SE->Scalars.erase(Old);
3777 // this now dangles!
3782 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
3783 : CallbackVH(V), SE(se) {}
3785 //===----------------------------------------------------------------------===//
3786 // ScalarEvolution Class Implementation
3787 //===----------------------------------------------------------------------===//
3789 ScalarEvolution::ScalarEvolution()
3790 : FunctionPass(&ID), CouldNotCompute(new SCEVCouldNotCompute()) {
3793 bool ScalarEvolution::runOnFunction(Function &F) {
3795 LI = &getAnalysis<LoopInfo>();
3796 TD = getAnalysisIfAvailable<TargetData>();
3800 void ScalarEvolution::releaseMemory() {
3802 BackedgeTakenCounts.clear();
3803 ConstantEvolutionLoopExitValue.clear();
3804 ValuesAtScopes.clear();
3807 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3808 AU.setPreservesAll();
3809 AU.addRequiredTransitive<LoopInfo>();
3812 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3813 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3816 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3818 // Print all inner loops first
3819 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3820 PrintLoopInfo(OS, SE, *I);
3822 OS << "Loop " << L->getHeader()->getName() << ": ";
3824 SmallVector<BasicBlock*, 8> ExitBlocks;
3825 L->getExitBlocks(ExitBlocks);
3826 if (ExitBlocks.size() != 1)
3827 OS << "<multiple exits> ";
3829 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3830 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3832 OS << "Unpredictable backedge-taken count. ";
3838 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3839 // ScalarEvolution's implementaiton of the print method is to print
3840 // out SCEV values of all instructions that are interesting. Doing
3841 // this potentially causes it to create new SCEV objects though,
3842 // which technically conflicts with the const qualifier. This isn't
3843 // observable from outside the class though (the hasSCEV function
3844 // notwithstanding), so casting away the const isn't dangerous.
3845 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3847 OS << "Classifying expressions for: " << F->getName() << "\n";
3848 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3849 if (isSCEVable(I->getType())) {
3852 SCEVHandle SV = SE.getSCEV(&*I);
3856 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3858 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3859 if (!ExitValue->isLoopInvariant(L)) {
3860 OS << "<<Unknown>>";
3869 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3870 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3871 PrintLoopInfo(OS, &SE, *I);
3874 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3875 raw_os_ostream OS(o);