1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/Dominators.h"
70 #include "llvm/Analysis/LoopInfo.h"
71 #include "llvm/Assembly/Writer.h"
72 #include "llvm/Target/TargetData.h"
73 #include "llvm/Support/CommandLine.h"
74 #include "llvm/Support/Compiler.h"
75 #include "llvm/Support/ConstantRange.h"
76 #include "llvm/Support/GetElementPtrTypeIterator.h"
77 #include "llvm/Support/InstIterator.h"
78 #include "llvm/Support/ManagedStatic.h"
79 #include "llvm/Support/MathExtras.h"
80 #include "llvm/Support/raw_ostream.h"
81 #include "llvm/ADT/Statistic.h"
82 #include "llvm/ADT/STLExtras.h"
87 STATISTIC(NumArrayLenItCounts,
88 "Number of trip counts computed with array length");
89 STATISTIC(NumTripCountsComputed,
90 "Number of loops with predictable loop counts");
91 STATISTIC(NumTripCountsNotComputed,
92 "Number of loops without predictable loop counts");
93 STATISTIC(NumBruteForceTripCountsComputed,
94 "Number of loops with trip counts computed by force");
96 static cl::opt<unsigned>
97 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
98 cl::desc("Maximum number of iterations SCEV will "
99 "symbolically execute a constant derived loop"),
102 static RegisterPass<ScalarEvolution>
103 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
104 char ScalarEvolution::ID = 0;
106 //===----------------------------------------------------------------------===//
107 // SCEV class definitions
108 //===----------------------------------------------------------------------===//
110 //===----------------------------------------------------------------------===//
111 // Implementation of the SCEV class.
114 void SCEV::dump() const {
119 void SCEV::print(std::ostream &o) const {
120 raw_os_ostream OS(o);
124 bool SCEV::isZero() const {
125 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
126 return SC->getValue()->isZero();
130 bool SCEV::isOne() const {
131 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
132 return SC->getValue()->isOne();
136 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
137 SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
139 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
140 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
144 const Type *SCEVCouldNotCompute::getType() const {
145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
149 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
150 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
154 SCEVHandle SCEVCouldNotCompute::
155 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
156 const SCEVHandle &Conc,
157 ScalarEvolution &SE) const {
161 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
162 OS << "***COULDNOTCOMPUTE***";
165 bool SCEVCouldNotCompute::classof(const SCEV *S) {
166 return S->getSCEVType() == scCouldNotCompute;
170 // SCEVConstants - Only allow the creation of one SCEVConstant for any
171 // particular value. Don't use a SCEVHandle here, or else the object will
173 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
176 SCEVConstant::~SCEVConstant() {
177 SCEVConstants->erase(V);
180 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
181 SCEVConstant *&R = (*SCEVConstants)[V];
182 if (R == 0) R = new SCEVConstant(V);
186 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
187 return getConstant(ConstantInt::get(Val));
190 const Type *SCEVConstant::getType() const { return V->getType(); }
192 void SCEVConstant::print(raw_ostream &OS) const {
193 WriteAsOperand(OS, V, false);
196 SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
197 const SCEVHandle &op, const Type *ty)
198 : SCEV(SCEVTy), Op(op), Ty(ty) {}
200 SCEVCastExpr::~SCEVCastExpr() {}
202 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
203 return Op->dominates(BB, DT);
206 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
207 // particular input. Don't use a SCEVHandle here, or else the object will
209 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
210 SCEVTruncateExpr*> > SCEVTruncates;
212 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
213 : SCEVCastExpr(scTruncate, op, ty) {
214 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
215 (Ty->isInteger() || isa<PointerType>(Ty)) &&
216 "Cannot truncate non-integer value!");
219 SCEVTruncateExpr::~SCEVTruncateExpr() {
220 SCEVTruncates->erase(std::make_pair(Op, Ty));
223 void SCEVTruncateExpr::print(raw_ostream &OS) const {
224 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
227 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
228 // particular input. Don't use a SCEVHandle here, or else the object will never
230 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
231 SCEVZeroExtendExpr*> > SCEVZeroExtends;
233 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
234 : SCEVCastExpr(scZeroExtend, op, ty) {
235 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
236 (Ty->isInteger() || isa<PointerType>(Ty)) &&
237 "Cannot zero extend non-integer value!");
240 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
241 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
244 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
245 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
248 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
249 // particular input. Don't use a SCEVHandle here, or else the object will never
251 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
252 SCEVSignExtendExpr*> > SCEVSignExtends;
254 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
255 : SCEVCastExpr(scSignExtend, op, ty) {
256 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
257 (Ty->isInteger() || isa<PointerType>(Ty)) &&
258 "Cannot sign extend non-integer value!");
261 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
262 SCEVSignExtends->erase(std::make_pair(Op, Ty));
265 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
266 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
269 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
270 // particular input. Don't use a SCEVHandle here, or else the object will never
272 static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >,
273 SCEVCommutativeExpr*> > SCEVCommExprs;
275 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
276 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
277 SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps));
280 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
281 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
282 const char *OpStr = getOperationStr();
283 OS << "(" << *Operands[0];
284 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
285 OS << OpStr << *Operands[i];
289 SCEVHandle SCEVCommutativeExpr::
290 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
291 const SCEVHandle &Conc,
292 ScalarEvolution &SE) const {
293 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
295 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
296 if (H != getOperand(i)) {
297 std::vector<SCEVHandle> NewOps;
298 NewOps.reserve(getNumOperands());
299 for (unsigned j = 0; j != i; ++j)
300 NewOps.push_back(getOperand(j));
302 for (++i; i != e; ++i)
303 NewOps.push_back(getOperand(i)->
304 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
306 if (isa<SCEVAddExpr>(this))
307 return SE.getAddExpr(NewOps);
308 else if (isa<SCEVMulExpr>(this))
309 return SE.getMulExpr(NewOps);
310 else if (isa<SCEVSMaxExpr>(this))
311 return SE.getSMaxExpr(NewOps);
312 else if (isa<SCEVUMaxExpr>(this))
313 return SE.getUMaxExpr(NewOps);
315 assert(0 && "Unknown commutative expr!");
321 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
322 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
323 if (!getOperand(i)->dominates(BB, DT))
330 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
331 // input. Don't use a SCEVHandle here, or else the object will never be
333 static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>,
334 SCEVUDivExpr*> > SCEVUDivs;
336 SCEVUDivExpr::~SCEVUDivExpr() {
337 SCEVUDivs->erase(std::make_pair(LHS, RHS));
340 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
341 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
344 void SCEVUDivExpr::print(raw_ostream &OS) const {
345 OS << "(" << *LHS << " /u " << *RHS << ")";
348 const Type *SCEVUDivExpr::getType() const {
349 return LHS->getType();
352 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
353 // particular input. Don't use a SCEVHandle here, or else the object will never
355 static ManagedStatic<std::map<std::pair<const Loop *,
356 std::vector<const SCEV*> >,
357 SCEVAddRecExpr*> > SCEVAddRecExprs;
359 SCEVAddRecExpr::~SCEVAddRecExpr() {
360 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
361 SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps));
364 SCEVHandle SCEVAddRecExpr::
365 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
366 const SCEVHandle &Conc,
367 ScalarEvolution &SE) const {
368 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
370 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
371 if (H != getOperand(i)) {
372 std::vector<SCEVHandle> NewOps;
373 NewOps.reserve(getNumOperands());
374 for (unsigned j = 0; j != i; ++j)
375 NewOps.push_back(getOperand(j));
377 for (++i; i != e; ++i)
378 NewOps.push_back(getOperand(i)->
379 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
381 return SE.getAddRecExpr(NewOps, L);
388 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
389 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
390 // contain L and if the start is invariant.
391 return !QueryLoop->contains(L->getHeader()) &&
392 getOperand(0)->isLoopInvariant(QueryLoop);
396 void SCEVAddRecExpr::print(raw_ostream &OS) const {
397 OS << "{" << *Operands[0];
398 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
399 OS << ",+," << *Operands[i];
400 OS << "}<" << L->getHeader()->getName() + ">";
403 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
404 // value. Don't use a SCEVHandle here, or else the object will never be
406 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
408 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
410 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
411 // All non-instruction values are loop invariant. All instructions are loop
412 // invariant if they are not contained in the specified loop.
413 if (Instruction *I = dyn_cast<Instruction>(V))
414 return !L->contains(I->getParent());
418 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
419 if (Instruction *I = dyn_cast<Instruction>(getValue()))
420 return DT->dominates(I->getParent(), BB);
424 const Type *SCEVUnknown::getType() const {
428 void SCEVUnknown::print(raw_ostream &OS) const {
429 WriteAsOperand(OS, V, false);
432 //===----------------------------------------------------------------------===//
434 //===----------------------------------------------------------------------===//
437 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
438 /// than the complexity of the RHS. This comparator is used to canonicalize
440 class VISIBILITY_HIDDEN SCEVComplexityCompare {
443 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
445 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
446 // Primarily, sort the SCEVs by their getSCEVType().
447 if (LHS->getSCEVType() != RHS->getSCEVType())
448 return LHS->getSCEVType() < RHS->getSCEVType();
450 // Aside from the getSCEVType() ordering, the particular ordering
451 // isn't very important except that it's beneficial to be consistent,
452 // so that (a + b) and (b + a) don't end up as different expressions.
454 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
455 // not as complete as it could be.
456 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
457 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
459 // Compare getValueID values.
460 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
461 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
463 // Sort arguments by their position.
464 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
465 const Argument *RA = cast<Argument>(RU->getValue());
466 return LA->getArgNo() < RA->getArgNo();
469 // For instructions, compare their loop depth, and their opcode.
470 // This is pretty loose.
471 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
472 Instruction *RV = cast<Instruction>(RU->getValue());
474 // Compare loop depths.
475 if (LI->getLoopDepth(LV->getParent()) !=
476 LI->getLoopDepth(RV->getParent()))
477 return LI->getLoopDepth(LV->getParent()) <
478 LI->getLoopDepth(RV->getParent());
481 if (LV->getOpcode() != RV->getOpcode())
482 return LV->getOpcode() < RV->getOpcode();
484 // Compare the number of operands.
485 if (LV->getNumOperands() != RV->getNumOperands())
486 return LV->getNumOperands() < RV->getNumOperands();
492 // Constant sorting doesn't matter since they'll be folded.
493 if (isa<SCEVConstant>(LHS))
496 // Lexicographically compare n-ary expressions.
497 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
498 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
499 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
500 if (i >= RC->getNumOperands())
502 if (operator()(LC->getOperand(i), RC->getOperand(i)))
504 if (operator()(RC->getOperand(i), LC->getOperand(i)))
507 return LC->getNumOperands() < RC->getNumOperands();
510 // Lexicographically compare udiv expressions.
511 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
512 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
513 if (operator()(LC->getLHS(), RC->getLHS()))
515 if (operator()(RC->getLHS(), LC->getLHS()))
517 if (operator()(LC->getRHS(), RC->getRHS()))
519 if (operator()(RC->getRHS(), LC->getRHS()))
524 // Compare cast expressions by operand.
525 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
526 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
527 return operator()(LC->getOperand(), RC->getOperand());
530 assert(0 && "Unknown SCEV kind!");
536 /// GroupByComplexity - Given a list of SCEV objects, order them by their
537 /// complexity, and group objects of the same complexity together by value.
538 /// When this routine is finished, we know that any duplicates in the vector are
539 /// consecutive and that complexity is monotonically increasing.
541 /// Note that we go take special precautions to ensure that we get determinstic
542 /// results from this routine. In other words, we don't want the results of
543 /// this to depend on where the addresses of various SCEV objects happened to
546 static void GroupByComplexity(std::vector<SCEVHandle> &Ops,
548 if (Ops.size() < 2) return; // Noop
549 if (Ops.size() == 2) {
550 // This is the common case, which also happens to be trivially simple.
552 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
553 std::swap(Ops[0], Ops[1]);
557 // Do the rough sort by complexity.
558 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
560 // Now that we are sorted by complexity, group elements of the same
561 // complexity. Note that this is, at worst, N^2, but the vector is likely to
562 // be extremely short in practice. Note that we take this approach because we
563 // do not want to depend on the addresses of the objects we are grouping.
564 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
565 const SCEV *S = Ops[i];
566 unsigned Complexity = S->getSCEVType();
568 // If there are any objects of the same complexity and same value as this
570 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
571 if (Ops[j] == S) { // Found a duplicate.
572 // Move it to immediately after i'th element.
573 std::swap(Ops[i+1], Ops[j]);
574 ++i; // no need to rescan it.
575 if (i == e-2) return; // Done!
583 //===----------------------------------------------------------------------===//
584 // Simple SCEV method implementations
585 //===----------------------------------------------------------------------===//
587 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
589 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
591 const Type* ResultTy) {
592 // Handle the simplest case efficiently.
594 return SE.getTruncateOrZeroExtend(It, ResultTy);
596 // We are using the following formula for BC(It, K):
598 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
600 // Suppose, W is the bitwidth of the return value. We must be prepared for
601 // overflow. Hence, we must assure that the result of our computation is
602 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
603 // safe in modular arithmetic.
605 // However, this code doesn't use exactly that formula; the formula it uses
606 // is something like the following, where T is the number of factors of 2 in
607 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
610 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
612 // This formula is trivially equivalent to the previous formula. However,
613 // this formula can be implemented much more efficiently. The trick is that
614 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
615 // arithmetic. To do exact division in modular arithmetic, all we have
616 // to do is multiply by the inverse. Therefore, this step can be done at
619 // The next issue is how to safely do the division by 2^T. The way this
620 // is done is by doing the multiplication step at a width of at least W + T
621 // bits. This way, the bottom W+T bits of the product are accurate. Then,
622 // when we perform the division by 2^T (which is equivalent to a right shift
623 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
624 // truncated out after the division by 2^T.
626 // In comparison to just directly using the first formula, this technique
627 // is much more efficient; using the first formula requires W * K bits,
628 // but this formula less than W + K bits. Also, the first formula requires
629 // a division step, whereas this formula only requires multiplies and shifts.
631 // It doesn't matter whether the subtraction step is done in the calculation
632 // width or the input iteration count's width; if the subtraction overflows,
633 // the result must be zero anyway. We prefer here to do it in the width of
634 // the induction variable because it helps a lot for certain cases; CodeGen
635 // isn't smart enough to ignore the overflow, which leads to much less
636 // efficient code if the width of the subtraction is wider than the native
639 // (It's possible to not widen at all by pulling out factors of 2 before
640 // the multiplication; for example, K=2 can be calculated as
641 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
642 // extra arithmetic, so it's not an obvious win, and it gets
643 // much more complicated for K > 3.)
645 // Protection from insane SCEVs; this bound is conservative,
646 // but it probably doesn't matter.
648 return SE.getCouldNotCompute();
650 unsigned W = SE.getTypeSizeInBits(ResultTy);
652 // Calculate K! / 2^T and T; we divide out the factors of two before
653 // multiplying for calculating K! / 2^T to avoid overflow.
654 // Other overflow doesn't matter because we only care about the bottom
655 // W bits of the result.
656 APInt OddFactorial(W, 1);
658 for (unsigned i = 3; i <= K; ++i) {
660 unsigned TwoFactors = Mult.countTrailingZeros();
662 Mult = Mult.lshr(TwoFactors);
663 OddFactorial *= Mult;
666 // We need at least W + T bits for the multiplication step
667 unsigned CalculationBits = W + T;
669 // Calcuate 2^T, at width T+W.
670 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
672 // Calculate the multiplicative inverse of K! / 2^T;
673 // this multiplication factor will perform the exact division by
675 APInt Mod = APInt::getSignedMinValue(W+1);
676 APInt MultiplyFactor = OddFactorial.zext(W+1);
677 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
678 MultiplyFactor = MultiplyFactor.trunc(W);
680 // Calculate the product, at width T+W
681 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
682 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
683 for (unsigned i = 1; i != K; ++i) {
684 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
685 Dividend = SE.getMulExpr(Dividend,
686 SE.getTruncateOrZeroExtend(S, CalculationTy));
690 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
692 // Truncate the result, and divide by K! / 2^T.
694 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
695 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
698 /// evaluateAtIteration - Return the value of this chain of recurrences at
699 /// the specified iteration number. We can evaluate this recurrence by
700 /// multiplying each element in the chain by the binomial coefficient
701 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
703 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
705 /// where BC(It, k) stands for binomial coefficient.
707 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
708 ScalarEvolution &SE) const {
709 SCEVHandle Result = getStart();
710 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
711 // The computation is correct in the face of overflow provided that the
712 // multiplication is performed _after_ the evaluation of the binomial
714 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
715 if (isa<SCEVCouldNotCompute>(Coeff))
718 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
723 //===----------------------------------------------------------------------===//
724 // SCEV Expression folder implementations
725 //===----------------------------------------------------------------------===//
727 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op,
729 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
730 "This is not a truncating conversion!");
731 assert(isSCEVable(Ty) &&
732 "This is not a conversion to a SCEVable type!");
733 Ty = getEffectiveSCEVType(Ty);
735 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
737 ConstantExpr::getTrunc(SC->getValue(), Ty));
739 // trunc(trunc(x)) --> trunc(x)
740 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
741 return getTruncateExpr(ST->getOperand(), Ty);
743 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
744 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
745 return getTruncateOrSignExtend(SS->getOperand(), Ty);
747 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
748 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
749 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
751 // If the input value is a chrec scev made out of constants, truncate
752 // all of the constants.
753 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
754 std::vector<SCEVHandle> Operands;
755 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
756 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
757 return getAddRecExpr(Operands, AddRec->getLoop());
760 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
761 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
765 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
767 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
768 "This is not an extending conversion!");
769 assert(isSCEVable(Ty) &&
770 "This is not a conversion to a SCEVable type!");
771 Ty = getEffectiveSCEVType(Ty);
773 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
774 const Type *IntTy = getEffectiveSCEVType(Ty);
775 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
776 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
777 return getUnknown(C);
780 // zext(zext(x)) --> zext(x)
781 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
782 return getZeroExtendExpr(SZ->getOperand(), Ty);
784 // If the input value is a chrec scev, and we can prove that the value
785 // did not overflow the old, smaller, value, we can zero extend all of the
786 // operands (often constants). This allows analysis of something like
787 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
788 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
789 if (AR->isAffine()) {
790 // Check whether the backedge-taken count is SCEVCouldNotCompute.
791 // Note that this serves two purposes: It filters out loops that are
792 // simply not analyzable, and it covers the case where this code is
793 // being called from within backedge-taken count analysis, such that
794 // attempting to ask for the backedge-taken count would likely result
795 // in infinite recursion. In the later case, the analysis code will
796 // cope with a conservative value, and it will take care to purge
797 // that value once it has finished.
798 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
799 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
800 // Manually compute the final value for AR, checking for
802 SCEVHandle Start = AR->getStart();
803 SCEVHandle Step = AR->getStepRecurrence(*this);
805 // Check whether the backedge-taken count can be losslessly casted to
806 // the addrec's type. The count is always unsigned.
807 SCEVHandle CastedMaxBECount =
808 getTruncateOrZeroExtend(MaxBECount, Start->getType());
809 SCEVHandle RecastedMaxBECount =
810 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
811 if (MaxBECount == RecastedMaxBECount) {
813 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
814 // Check whether Start+Step*MaxBECount has no unsigned overflow.
816 getMulExpr(CastedMaxBECount,
817 getTruncateOrZeroExtend(Step, Start->getType()));
818 SCEVHandle Add = getAddExpr(Start, ZMul);
819 SCEVHandle OperandExtendedAdd =
820 getAddExpr(getZeroExtendExpr(Start, WideTy),
821 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
822 getZeroExtendExpr(Step, WideTy)));
823 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
824 // Return the expression with the addrec on the outside.
825 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
826 getZeroExtendExpr(Step, Ty),
829 // Similar to above, only this time treat the step value as signed.
830 // This covers loops that count down.
832 getMulExpr(CastedMaxBECount,
833 getTruncateOrSignExtend(Step, Start->getType()));
834 Add = getAddExpr(Start, SMul);
836 getAddExpr(getZeroExtendExpr(Start, WideTy),
837 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
838 getSignExtendExpr(Step, WideTy)));
839 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
840 // Return the expression with the addrec on the outside.
841 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
842 getSignExtendExpr(Step, Ty),
848 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
849 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
853 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
855 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
856 "This is not an extending conversion!");
857 assert(isSCEVable(Ty) &&
858 "This is not a conversion to a SCEVable type!");
859 Ty = getEffectiveSCEVType(Ty);
861 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
862 const Type *IntTy = getEffectiveSCEVType(Ty);
863 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
864 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
865 return getUnknown(C);
868 // sext(sext(x)) --> sext(x)
869 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
870 return getSignExtendExpr(SS->getOperand(), Ty);
872 // If the input value is a chrec scev, and we can prove that the value
873 // did not overflow the old, smaller, value, we can sign extend all of the
874 // operands (often constants). This allows analysis of something like
875 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
876 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
877 if (AR->isAffine()) {
878 // Check whether the backedge-taken count is SCEVCouldNotCompute.
879 // Note that this serves two purposes: It filters out loops that are
880 // simply not analyzable, and it covers the case where this code is
881 // being called from within backedge-taken count analysis, such that
882 // attempting to ask for the backedge-taken count would likely result
883 // in infinite recursion. In the later case, the analysis code will
884 // cope with a conservative value, and it will take care to purge
885 // that value once it has finished.
886 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
887 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
888 // Manually compute the final value for AR, checking for
890 SCEVHandle Start = AR->getStart();
891 SCEVHandle Step = AR->getStepRecurrence(*this);
893 // Check whether the backedge-taken count can be losslessly casted to
894 // the addrec's type. The count is always unsigned.
895 SCEVHandle CastedMaxBECount =
896 getTruncateOrZeroExtend(MaxBECount, Start->getType());
897 SCEVHandle RecastedMaxBECount =
898 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
899 if (MaxBECount == RecastedMaxBECount) {
901 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
902 // Check whether Start+Step*MaxBECount has no signed overflow.
904 getMulExpr(CastedMaxBECount,
905 getTruncateOrSignExtend(Step, Start->getType()));
906 SCEVHandle Add = getAddExpr(Start, SMul);
907 SCEVHandle OperandExtendedAdd =
908 getAddExpr(getSignExtendExpr(Start, WideTy),
909 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
910 getSignExtendExpr(Step, WideTy)));
911 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
912 // Return the expression with the addrec on the outside.
913 return getAddRecExpr(getSignExtendExpr(Start, Ty),
914 getSignExtendExpr(Step, Ty),
920 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
921 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
925 // get - Get a canonical add expression, or something simpler if possible.
926 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
927 assert(!Ops.empty() && "Cannot get empty add!");
928 if (Ops.size() == 1) return Ops[0];
930 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
931 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
932 getEffectiveSCEVType(Ops[0]->getType()) &&
933 "SCEVAddExpr operand types don't match!");
936 // Sort by complexity, this groups all similar expression types together.
937 GroupByComplexity(Ops, LI);
939 // If there are any constants, fold them together.
941 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
943 assert(Idx < Ops.size());
944 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
945 // We found two constants, fold them together!
946 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
947 RHSC->getValue()->getValue());
948 Ops[0] = getConstant(Fold);
949 Ops.erase(Ops.begin()+1); // Erase the folded element
950 if (Ops.size() == 1) return Ops[0];
951 LHSC = cast<SCEVConstant>(Ops[0]);
954 // If we are left with a constant zero being added, strip it off.
955 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
956 Ops.erase(Ops.begin());
961 if (Ops.size() == 1) return Ops[0];
963 // Okay, check to see if the same value occurs in the operand list twice. If
964 // so, merge them together into an multiply expression. Since we sorted the
965 // list, these values are required to be adjacent.
966 const Type *Ty = Ops[0]->getType();
967 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
968 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
969 // Found a match, merge the two values into a multiply, and add any
970 // remaining values to the result.
971 SCEVHandle Two = getIntegerSCEV(2, Ty);
972 SCEVHandle Mul = getMulExpr(Ops[i], Two);
975 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
977 return getAddExpr(Ops);
980 // Check for truncates. If all the operands are truncated from the same
981 // type, see if factoring out the truncate would permit the result to be
982 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
983 // if the contents of the resulting outer trunc fold to something simple.
984 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
985 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
986 const Type *DstType = Trunc->getType();
987 const Type *SrcType = Trunc->getOperand()->getType();
988 std::vector<SCEVHandle> LargeOps;
990 // Check all the operands to see if they can be represented in the
991 // source type of the truncate.
992 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
993 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
994 if (T->getOperand()->getType() != SrcType) {
998 LargeOps.push_back(T->getOperand());
999 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1000 // This could be either sign or zero extension, but sign extension
1001 // is much more likely to be foldable here.
1002 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1003 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1004 std::vector<SCEVHandle> LargeMulOps;
1005 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1006 if (const SCEVTruncateExpr *T =
1007 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1008 if (T->getOperand()->getType() != SrcType) {
1012 LargeMulOps.push_back(T->getOperand());
1013 } else if (const SCEVConstant *C =
1014 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1015 // This could be either sign or zero extension, but sign extension
1016 // is much more likely to be foldable here.
1017 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1024 LargeOps.push_back(getMulExpr(LargeMulOps));
1031 // Evaluate the expression in the larger type.
1032 SCEVHandle Fold = getAddExpr(LargeOps);
1033 // If it folds to something simple, use it. Otherwise, don't.
1034 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1035 return getTruncateExpr(Fold, DstType);
1039 // Skip past any other cast SCEVs.
1040 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1043 // If there are add operands they would be next.
1044 if (Idx < Ops.size()) {
1045 bool DeletedAdd = false;
1046 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1047 // If we have an add, expand the add operands onto the end of the operands
1049 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1050 Ops.erase(Ops.begin()+Idx);
1054 // If we deleted at least one add, we added operands to the end of the list,
1055 // and they are not necessarily sorted. Recurse to resort and resimplify
1056 // any operands we just aquired.
1058 return getAddExpr(Ops);
1061 // Skip over the add expression until we get to a multiply.
1062 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1065 // If we are adding something to a multiply expression, make sure the
1066 // something is not already an operand of the multiply. If so, merge it into
1068 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1069 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1070 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1071 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1072 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1073 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
1074 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1075 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
1076 if (Mul->getNumOperands() != 2) {
1077 // If the multiply has more than two operands, we must get the
1079 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1080 MulOps.erase(MulOps.begin()+MulOp);
1081 InnerMul = getMulExpr(MulOps);
1083 SCEVHandle One = getIntegerSCEV(1, Ty);
1084 SCEVHandle AddOne = getAddExpr(InnerMul, One);
1085 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1086 if (Ops.size() == 2) return OuterMul;
1088 Ops.erase(Ops.begin()+AddOp);
1089 Ops.erase(Ops.begin()+Idx-1);
1091 Ops.erase(Ops.begin()+Idx);
1092 Ops.erase(Ops.begin()+AddOp-1);
1094 Ops.push_back(OuterMul);
1095 return getAddExpr(Ops);
1098 // Check this multiply against other multiplies being added together.
1099 for (unsigned OtherMulIdx = Idx+1;
1100 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1102 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1103 // If MulOp occurs in OtherMul, we can fold the two multiplies
1105 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1106 OMulOp != e; ++OMulOp)
1107 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1108 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1109 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
1110 if (Mul->getNumOperands() != 2) {
1111 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1112 MulOps.erase(MulOps.begin()+MulOp);
1113 InnerMul1 = getMulExpr(MulOps);
1115 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1116 if (OtherMul->getNumOperands() != 2) {
1117 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
1118 OtherMul->op_end());
1119 MulOps.erase(MulOps.begin()+OMulOp);
1120 InnerMul2 = getMulExpr(MulOps);
1122 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1123 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1124 if (Ops.size() == 2) return OuterMul;
1125 Ops.erase(Ops.begin()+Idx);
1126 Ops.erase(Ops.begin()+OtherMulIdx-1);
1127 Ops.push_back(OuterMul);
1128 return getAddExpr(Ops);
1134 // If there are any add recurrences in the operands list, see if any other
1135 // added values are loop invariant. If so, we can fold them into the
1137 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1140 // Scan over all recurrences, trying to fold loop invariants into them.
1141 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1142 // Scan all of the other operands to this add and add them to the vector if
1143 // they are loop invariant w.r.t. the recurrence.
1144 std::vector<SCEVHandle> LIOps;
1145 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1146 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1147 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1148 LIOps.push_back(Ops[i]);
1149 Ops.erase(Ops.begin()+i);
1153 // If we found some loop invariants, fold them into the recurrence.
1154 if (!LIOps.empty()) {
1155 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1156 LIOps.push_back(AddRec->getStart());
1158 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
1159 AddRecOps[0] = getAddExpr(LIOps);
1161 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1162 // If all of the other operands were loop invariant, we are done.
1163 if (Ops.size() == 1) return NewRec;
1165 // Otherwise, add the folded AddRec by the non-liv parts.
1166 for (unsigned i = 0;; ++i)
1167 if (Ops[i] == AddRec) {
1171 return getAddExpr(Ops);
1174 // Okay, if there weren't any loop invariants to be folded, check to see if
1175 // there are multiple AddRec's with the same loop induction variable being
1176 // added together. If so, we can fold them.
1177 for (unsigned OtherIdx = Idx+1;
1178 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1179 if (OtherIdx != Idx) {
1180 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1181 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1182 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1183 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
1184 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1185 if (i >= NewOps.size()) {
1186 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1187 OtherAddRec->op_end());
1190 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1192 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1194 if (Ops.size() == 2) return NewAddRec;
1196 Ops.erase(Ops.begin()+Idx);
1197 Ops.erase(Ops.begin()+OtherIdx-1);
1198 Ops.push_back(NewAddRec);
1199 return getAddExpr(Ops);
1203 // Otherwise couldn't fold anything into this recurrence. Move onto the
1207 // Okay, it looks like we really DO need an add expr. Check to see if we
1208 // already have one, otherwise create a new one.
1209 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1210 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
1212 if (Result == 0) Result = new SCEVAddExpr(Ops);
1217 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
1218 assert(!Ops.empty() && "Cannot get empty mul!");
1220 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1221 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1222 getEffectiveSCEVType(Ops[0]->getType()) &&
1223 "SCEVMulExpr operand types don't match!");
1226 // Sort by complexity, this groups all similar expression types together.
1227 GroupByComplexity(Ops, LI);
1229 // If there are any constants, fold them together.
1231 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1233 // C1*(C2+V) -> C1*C2 + C1*V
1234 if (Ops.size() == 2)
1235 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1236 if (Add->getNumOperands() == 2 &&
1237 isa<SCEVConstant>(Add->getOperand(0)))
1238 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1239 getMulExpr(LHSC, Add->getOperand(1)));
1243 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1244 // We found two constants, fold them together!
1245 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1246 RHSC->getValue()->getValue());
1247 Ops[0] = getConstant(Fold);
1248 Ops.erase(Ops.begin()+1); // Erase the folded element
1249 if (Ops.size() == 1) return Ops[0];
1250 LHSC = cast<SCEVConstant>(Ops[0]);
1253 // If we are left with a constant one being multiplied, strip it off.
1254 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1255 Ops.erase(Ops.begin());
1257 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1258 // If we have a multiply of zero, it will always be zero.
1263 // Skip over the add expression until we get to a multiply.
1264 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1267 if (Ops.size() == 1)
1270 // If there are mul operands inline them all into this expression.
1271 if (Idx < Ops.size()) {
1272 bool DeletedMul = false;
1273 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1274 // If we have an mul, expand the mul operands onto the end of the operands
1276 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1277 Ops.erase(Ops.begin()+Idx);
1281 // If we deleted at least one mul, we added operands to the end of the list,
1282 // and they are not necessarily sorted. Recurse to resort and resimplify
1283 // any operands we just aquired.
1285 return getMulExpr(Ops);
1288 // If there are any add recurrences in the operands list, see if any other
1289 // added values are loop invariant. If so, we can fold them into the
1291 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1294 // Scan over all recurrences, trying to fold loop invariants into them.
1295 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1296 // Scan all of the other operands to this mul and add them to the vector if
1297 // they are loop invariant w.r.t. the recurrence.
1298 std::vector<SCEVHandle> LIOps;
1299 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1300 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1301 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1302 LIOps.push_back(Ops[i]);
1303 Ops.erase(Ops.begin()+i);
1307 // If we found some loop invariants, fold them into the recurrence.
1308 if (!LIOps.empty()) {
1309 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1310 std::vector<SCEVHandle> NewOps;
1311 NewOps.reserve(AddRec->getNumOperands());
1312 if (LIOps.size() == 1) {
1313 const SCEV *Scale = LIOps[0];
1314 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1315 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1317 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1318 std::vector<SCEVHandle> MulOps(LIOps);
1319 MulOps.push_back(AddRec->getOperand(i));
1320 NewOps.push_back(getMulExpr(MulOps));
1324 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1326 // If all of the other operands were loop invariant, we are done.
1327 if (Ops.size() == 1) return NewRec;
1329 // Otherwise, multiply the folded AddRec by the non-liv parts.
1330 for (unsigned i = 0;; ++i)
1331 if (Ops[i] == AddRec) {
1335 return getMulExpr(Ops);
1338 // Okay, if there weren't any loop invariants to be folded, check to see if
1339 // there are multiple AddRec's with the same loop induction variable being
1340 // multiplied together. If so, we can fold them.
1341 for (unsigned OtherIdx = Idx+1;
1342 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1343 if (OtherIdx != Idx) {
1344 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1345 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1346 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1347 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1348 SCEVHandle NewStart = getMulExpr(F->getStart(),
1350 SCEVHandle B = F->getStepRecurrence(*this);
1351 SCEVHandle D = G->getStepRecurrence(*this);
1352 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1355 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1357 if (Ops.size() == 2) return NewAddRec;
1359 Ops.erase(Ops.begin()+Idx);
1360 Ops.erase(Ops.begin()+OtherIdx-1);
1361 Ops.push_back(NewAddRec);
1362 return getMulExpr(Ops);
1366 // Otherwise couldn't fold anything into this recurrence. Move onto the
1370 // Okay, it looks like we really DO need an mul expr. Check to see if we
1371 // already have one, otherwise create a new one.
1372 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1373 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1376 Result = new SCEVMulExpr(Ops);
1380 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS,
1381 const SCEVHandle &RHS) {
1382 assert(getEffectiveSCEVType(LHS->getType()) ==
1383 getEffectiveSCEVType(RHS->getType()) &&
1384 "SCEVUDivExpr operand types don't match!");
1386 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1387 if (RHSC->getValue()->equalsInt(1))
1388 return LHS; // X udiv 1 --> x
1390 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1392 // Determine if the division can be folded into the operands of
1394 // TODO: Generalize this to non-constants by using known-bits information.
1395 const Type *Ty = LHS->getType();
1396 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1397 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1398 // For non-power-of-two values, effectively round the value up to the
1399 // nearest power of two.
1400 if (!RHSC->getValue()->getValue().isPowerOf2())
1402 const IntegerType *ExtTy =
1403 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1404 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1405 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1406 if (const SCEVConstant *Step =
1407 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1408 if (!Step->getValue()->getValue()
1409 .urem(RHSC->getValue()->getValue()) &&
1410 getZeroExtendExpr(AR, ExtTy) ==
1411 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1412 getZeroExtendExpr(Step, ExtTy),
1414 std::vector<SCEVHandle> Operands;
1415 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1416 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1417 return getAddRecExpr(Operands, AR->getLoop());
1419 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1420 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1421 std::vector<SCEVHandle> Operands;
1422 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1423 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1424 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1425 // Find an operand that's safely divisible.
1426 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1427 SCEVHandle Op = M->getOperand(i);
1428 SCEVHandle Div = getUDivExpr(Op, RHSC);
1429 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1430 Operands = M->getOperands();
1432 return getMulExpr(Operands);
1436 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1437 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1438 std::vector<SCEVHandle> Operands;
1439 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1440 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1441 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1443 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1444 SCEVHandle Op = getUDivExpr(A->getOperand(i), RHS);
1445 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1447 Operands.push_back(Op);
1449 if (Operands.size() == A->getNumOperands())
1450 return getAddExpr(Operands);
1454 // Fold if both operands are constant.
1455 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1456 Constant *LHSCV = LHSC->getValue();
1457 Constant *RHSCV = RHSC->getValue();
1458 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1462 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1463 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1468 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1469 /// specified loop. Simplify the expression as much as possible.
1470 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1471 const SCEVHandle &Step, const Loop *L) {
1472 std::vector<SCEVHandle> Operands;
1473 Operands.push_back(Start);
1474 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1475 if (StepChrec->getLoop() == L) {
1476 Operands.insert(Operands.end(), StepChrec->op_begin(),
1477 StepChrec->op_end());
1478 return getAddRecExpr(Operands, L);
1481 Operands.push_back(Step);
1482 return getAddRecExpr(Operands, L);
1485 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1486 /// specified loop. Simplify the expression as much as possible.
1487 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1489 if (Operands.size() == 1) return Operands[0];
1491 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1492 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1493 getEffectiveSCEVType(Operands[0]->getType()) &&
1494 "SCEVAddRecExpr operand types don't match!");
1497 if (Operands.back()->isZero()) {
1498 Operands.pop_back();
1499 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1502 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1503 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1504 const Loop* NestedLoop = NestedAR->getLoop();
1505 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1506 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1507 NestedAR->op_end());
1508 SCEVHandle NestedARHandle(NestedAR);
1509 Operands[0] = NestedAR->getStart();
1510 NestedOperands[0] = getAddRecExpr(Operands, L);
1511 return getAddRecExpr(NestedOperands, NestedLoop);
1515 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
1516 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)];
1517 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1521 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1522 const SCEVHandle &RHS) {
1523 std::vector<SCEVHandle> Ops;
1526 return getSMaxExpr(Ops);
1529 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1530 assert(!Ops.empty() && "Cannot get empty smax!");
1531 if (Ops.size() == 1) return Ops[0];
1533 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1534 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1535 getEffectiveSCEVType(Ops[0]->getType()) &&
1536 "SCEVSMaxExpr operand types don't match!");
1539 // Sort by complexity, this groups all similar expression types together.
1540 GroupByComplexity(Ops, LI);
1542 // If there are any constants, fold them together.
1544 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1546 assert(Idx < Ops.size());
1547 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1548 // We found two constants, fold them together!
1549 ConstantInt *Fold = ConstantInt::get(
1550 APIntOps::smax(LHSC->getValue()->getValue(),
1551 RHSC->getValue()->getValue()));
1552 Ops[0] = getConstant(Fold);
1553 Ops.erase(Ops.begin()+1); // Erase the folded element
1554 if (Ops.size() == 1) return Ops[0];
1555 LHSC = cast<SCEVConstant>(Ops[0]);
1558 // If we are left with a constant -inf, strip it off.
1559 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1560 Ops.erase(Ops.begin());
1565 if (Ops.size() == 1) return Ops[0];
1567 // Find the first SMax
1568 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1571 // Check to see if one of the operands is an SMax. If so, expand its operands
1572 // onto our operand list, and recurse to simplify.
1573 if (Idx < Ops.size()) {
1574 bool DeletedSMax = false;
1575 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1576 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1577 Ops.erase(Ops.begin()+Idx);
1582 return getSMaxExpr(Ops);
1585 // Okay, check to see if the same value occurs in the operand list twice. If
1586 // so, delete one. Since we sorted the list, these values are required to
1588 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1589 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1590 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1594 if (Ops.size() == 1) return Ops[0];
1596 assert(!Ops.empty() && "Reduced smax down to nothing!");
1598 // Okay, it looks like we really DO need an smax expr. Check to see if we
1599 // already have one, otherwise create a new one.
1600 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1601 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1603 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1607 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1608 const SCEVHandle &RHS) {
1609 std::vector<SCEVHandle> Ops;
1612 return getUMaxExpr(Ops);
1615 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1616 assert(!Ops.empty() && "Cannot get empty umax!");
1617 if (Ops.size() == 1) return Ops[0];
1619 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1620 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1621 getEffectiveSCEVType(Ops[0]->getType()) &&
1622 "SCEVUMaxExpr operand types don't match!");
1625 // Sort by complexity, this groups all similar expression types together.
1626 GroupByComplexity(Ops, LI);
1628 // If there are any constants, fold them together.
1630 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1632 assert(Idx < Ops.size());
1633 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1634 // We found two constants, fold them together!
1635 ConstantInt *Fold = ConstantInt::get(
1636 APIntOps::umax(LHSC->getValue()->getValue(),
1637 RHSC->getValue()->getValue()));
1638 Ops[0] = getConstant(Fold);
1639 Ops.erase(Ops.begin()+1); // Erase the folded element
1640 if (Ops.size() == 1) return Ops[0];
1641 LHSC = cast<SCEVConstant>(Ops[0]);
1644 // If we are left with a constant zero, strip it off.
1645 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1646 Ops.erase(Ops.begin());
1651 if (Ops.size() == 1) return Ops[0];
1653 // Find the first UMax
1654 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1657 // Check to see if one of the operands is a UMax. If so, expand its operands
1658 // onto our operand list, and recurse to simplify.
1659 if (Idx < Ops.size()) {
1660 bool DeletedUMax = false;
1661 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1662 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1663 Ops.erase(Ops.begin()+Idx);
1668 return getUMaxExpr(Ops);
1671 // Okay, check to see if the same value occurs in the operand list twice. If
1672 // so, delete one. Since we sorted the list, these values are required to
1674 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1675 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1676 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1680 if (Ops.size() == 1) return Ops[0];
1682 assert(!Ops.empty() && "Reduced umax down to nothing!");
1684 // Okay, it looks like we really DO need a umax expr. Check to see if we
1685 // already have one, otherwise create a new one.
1686 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1687 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1689 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1693 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1694 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1695 return getConstant(CI);
1696 if (isa<ConstantPointerNull>(V))
1697 return getIntegerSCEV(0, V->getType());
1698 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1699 if (Result == 0) Result = new SCEVUnknown(V);
1703 //===----------------------------------------------------------------------===//
1704 // Basic SCEV Analysis and PHI Idiom Recognition Code
1707 /// isSCEVable - Test if values of the given type are analyzable within
1708 /// the SCEV framework. This primarily includes integer types, and it
1709 /// can optionally include pointer types if the ScalarEvolution class
1710 /// has access to target-specific information.
1711 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1712 // Integers are always SCEVable.
1713 if (Ty->isInteger())
1716 // Pointers are SCEVable if TargetData information is available
1717 // to provide pointer size information.
1718 if (isa<PointerType>(Ty))
1721 // Otherwise it's not SCEVable.
1725 /// getTypeSizeInBits - Return the size in bits of the specified type,
1726 /// for which isSCEVable must return true.
1727 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1728 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1730 // If we have a TargetData, use it!
1732 return TD->getTypeSizeInBits(Ty);
1734 // Otherwise, we support only integer types.
1735 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1736 return Ty->getPrimitiveSizeInBits();
1739 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1740 /// the given type and which represents how SCEV will treat the given
1741 /// type, for which isSCEVable must return true. For pointer types,
1742 /// this is the pointer-sized integer type.
1743 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1744 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1746 if (Ty->isInteger())
1749 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1750 return TD->getIntPtrType();
1753 SCEVHandle ScalarEvolution::getCouldNotCompute() {
1754 return UnknownValue;
1757 /// hasSCEV - Return true if the SCEV for this value has already been
1759 bool ScalarEvolution::hasSCEV(Value *V) const {
1760 return Scalars.count(V);
1763 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1764 /// expression and create a new one.
1765 SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1766 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1768 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
1769 if (I != Scalars.end()) return I->second;
1770 SCEVHandle S = createSCEV(V);
1771 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
1775 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1776 /// specified signed integer value and return a SCEV for the constant.
1777 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1778 Ty = getEffectiveSCEVType(Ty);
1781 C = Constant::getNullValue(Ty);
1782 else if (Ty->isFloatingPoint())
1783 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1784 APFloat::IEEEdouble, Val));
1786 C = ConstantInt::get(Ty, Val);
1787 return getUnknown(C);
1790 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1792 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1793 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1794 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1796 const Type *Ty = V->getType();
1797 Ty = getEffectiveSCEVType(Ty);
1798 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1801 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1802 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1803 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1804 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1806 const Type *Ty = V->getType();
1807 Ty = getEffectiveSCEVType(Ty);
1808 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1809 return getMinusSCEV(AllOnes, V);
1812 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1814 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1815 const SCEVHandle &RHS) {
1817 return getAddExpr(LHS, getNegativeSCEV(RHS));
1820 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1821 /// input value to the specified type. If the type must be extended, it is zero
1824 ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1826 const Type *SrcTy = V->getType();
1827 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1828 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1829 "Cannot truncate or zero extend with non-integer arguments!");
1830 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1831 return V; // No conversion
1832 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1833 return getTruncateExpr(V, Ty);
1834 return getZeroExtendExpr(V, Ty);
1837 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1838 /// input value to the specified type. If the type must be extended, it is sign
1841 ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1843 const Type *SrcTy = V->getType();
1844 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1845 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1846 "Cannot truncate or zero extend with non-integer arguments!");
1847 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1848 return V; // No conversion
1849 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1850 return getTruncateExpr(V, Ty);
1851 return getSignExtendExpr(V, Ty);
1854 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
1855 /// input value to the specified type. If the type must be extended, it is zero
1856 /// extended. The conversion must not be narrowing.
1858 ScalarEvolution::getNoopOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
1859 const Type *SrcTy = V->getType();
1860 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1861 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1862 "Cannot noop or zero extend with non-integer arguments!");
1863 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1864 "getNoopOrZeroExtend cannot truncate!");
1865 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1866 return V; // No conversion
1867 return getZeroExtendExpr(V, Ty);
1870 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
1871 /// input value to the specified type. If the type must be extended, it is sign
1872 /// extended. The conversion must not be narrowing.
1874 ScalarEvolution::getNoopOrSignExtend(const SCEVHandle &V, const Type *Ty) {
1875 const Type *SrcTy = V->getType();
1876 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1877 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1878 "Cannot noop or sign extend with non-integer arguments!");
1879 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1880 "getNoopOrSignExtend cannot truncate!");
1881 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1882 return V; // No conversion
1883 return getSignExtendExpr(V, Ty);
1886 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
1887 /// input value to the specified type. The conversion must not be widening.
1889 ScalarEvolution::getTruncateOrNoop(const SCEVHandle &V, const Type *Ty) {
1890 const Type *SrcTy = V->getType();
1891 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1892 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1893 "Cannot truncate or noop with non-integer arguments!");
1894 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
1895 "getTruncateOrNoop cannot extend!");
1896 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1897 return V; // No conversion
1898 return getTruncateExpr(V, Ty);
1901 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1902 /// the specified instruction and replaces any references to the symbolic value
1903 /// SymName with the specified value. This is used during PHI resolution.
1904 void ScalarEvolution::
1905 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1906 const SCEVHandle &NewVal) {
1907 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
1908 Scalars.find(SCEVCallbackVH(I, this));
1909 if (SI == Scalars.end()) return;
1912 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
1913 if (NV == SI->second) return; // No change.
1915 SI->second = NV; // Update the scalars map!
1917 // Any instruction values that use this instruction might also need to be
1919 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1921 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1924 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1925 /// a loop header, making it a potential recurrence, or it doesn't.
1927 SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
1928 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1929 if (const Loop *L = LI->getLoopFor(PN->getParent()))
1930 if (L->getHeader() == PN->getParent()) {
1931 // If it lives in the loop header, it has two incoming values, one
1932 // from outside the loop, and one from inside.
1933 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1934 unsigned BackEdge = IncomingEdge^1;
1936 // While we are analyzing this PHI node, handle its value symbolically.
1937 SCEVHandle SymbolicName = getUnknown(PN);
1938 assert(Scalars.find(PN) == Scalars.end() &&
1939 "PHI node already processed?");
1940 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
1942 // Using this symbolic name for the PHI, analyze the value coming around
1944 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1946 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1947 // has a special value for the first iteration of the loop.
1949 // If the value coming around the backedge is an add with the symbolic
1950 // value we just inserted, then we found a simple induction variable!
1951 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1952 // If there is a single occurrence of the symbolic value, replace it
1953 // with a recurrence.
1954 unsigned FoundIndex = Add->getNumOperands();
1955 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1956 if (Add->getOperand(i) == SymbolicName)
1957 if (FoundIndex == e) {
1962 if (FoundIndex != Add->getNumOperands()) {
1963 // Create an add with everything but the specified operand.
1964 std::vector<SCEVHandle> Ops;
1965 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1966 if (i != FoundIndex)
1967 Ops.push_back(Add->getOperand(i));
1968 SCEVHandle Accum = getAddExpr(Ops);
1970 // This is not a valid addrec if the step amount is varying each
1971 // loop iteration, but is not itself an addrec in this loop.
1972 if (Accum->isLoopInvariant(L) ||
1973 (isa<SCEVAddRecExpr>(Accum) &&
1974 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1975 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1976 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
1978 // Okay, for the entire analysis of this edge we assumed the PHI
1979 // to be symbolic. We now need to go back and update all of the
1980 // entries for the scalars that use the PHI (except for the PHI
1981 // itself) to use the new analyzed value instead of the "symbolic"
1983 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1987 } else if (const SCEVAddRecExpr *AddRec =
1988 dyn_cast<SCEVAddRecExpr>(BEValue)) {
1989 // Otherwise, this could be a loop like this:
1990 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
1991 // In this case, j = {1,+,1} and BEValue is j.
1992 // Because the other in-value of i (0) fits the evolution of BEValue
1993 // i really is an addrec evolution.
1994 if (AddRec->getLoop() == L && AddRec->isAffine()) {
1995 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1997 // If StartVal = j.start - j.stride, we can use StartVal as the
1998 // initial step of the addrec evolution.
1999 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2000 AddRec->getOperand(1))) {
2001 SCEVHandle PHISCEV =
2002 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2004 // Okay, for the entire analysis of this edge we assumed the PHI
2005 // to be symbolic. We now need to go back and update all of the
2006 // entries for the scalars that use the PHI (except for the PHI
2007 // itself) to use the new analyzed value instead of the "symbolic"
2009 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2015 return SymbolicName;
2018 // If it's not a loop phi, we can't handle it yet.
2019 return getUnknown(PN);
2022 /// createNodeForGEP - Expand GEP instructions into add and multiply
2023 /// operations. This allows them to be analyzed by regular SCEV code.
2025 SCEVHandle ScalarEvolution::createNodeForGEP(User *GEP) {
2027 const Type *IntPtrTy = TD->getIntPtrType();
2028 Value *Base = GEP->getOperand(0);
2029 // Don't attempt to analyze GEPs over unsized objects.
2030 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2031 return getUnknown(GEP);
2032 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
2033 gep_type_iterator GTI = gep_type_begin(GEP);
2034 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2038 // Compute the (potentially symbolic) offset in bytes for this index.
2039 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2040 // For a struct, add the member offset.
2041 const StructLayout &SL = *TD->getStructLayout(STy);
2042 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2043 uint64_t Offset = SL.getElementOffset(FieldNo);
2044 TotalOffset = getAddExpr(TotalOffset,
2045 getIntegerSCEV(Offset, IntPtrTy));
2047 // For an array, add the element offset, explicitly scaled.
2048 SCEVHandle LocalOffset = getSCEV(Index);
2049 if (!isa<PointerType>(LocalOffset->getType()))
2050 // Getelementptr indicies are signed.
2051 LocalOffset = getTruncateOrSignExtend(LocalOffset,
2054 getMulExpr(LocalOffset,
2055 getIntegerSCEV(TD->getTypeAllocSize(*GTI),
2057 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2060 return getAddExpr(getSCEV(Base), TotalOffset);
2063 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2064 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2065 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2066 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2067 static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
2068 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2069 return C->getValue()->getValue().countTrailingZeros();
2071 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2072 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
2073 (uint32_t)SE.getTypeSizeInBits(T->getType()));
2075 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2076 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2077 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2078 SE.getTypeSizeInBits(E->getType()) : OpRes;
2081 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2082 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2083 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2084 SE.getTypeSizeInBits(E->getType()) : OpRes;
2087 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2088 // The result is the min of all operands results.
2089 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2090 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2091 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2095 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2096 // The result is the sum of all operands results.
2097 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2098 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
2099 for (unsigned i = 1, e = M->getNumOperands();
2100 SumOpRes != BitWidth && i != e; ++i)
2101 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
2106 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2107 // The result is the min of all operands results.
2108 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2109 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2110 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2114 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2115 // The result is the min of all operands results.
2116 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2117 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2118 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2122 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2123 // The result is the min of all operands results.
2124 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2125 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2126 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2130 // SCEVUDivExpr, SCEVUnknown
2134 /// createSCEV - We know that there is no SCEV for the specified value.
2135 /// Analyze the expression.
2137 SCEVHandle ScalarEvolution::createSCEV(Value *V) {
2138 if (!isSCEVable(V->getType()))
2139 return getUnknown(V);
2141 unsigned Opcode = Instruction::UserOp1;
2142 if (Instruction *I = dyn_cast<Instruction>(V))
2143 Opcode = I->getOpcode();
2144 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2145 Opcode = CE->getOpcode();
2147 return getUnknown(V);
2149 User *U = cast<User>(V);
2151 case Instruction::Add:
2152 return getAddExpr(getSCEV(U->getOperand(0)),
2153 getSCEV(U->getOperand(1)));
2154 case Instruction::Mul:
2155 return getMulExpr(getSCEV(U->getOperand(0)),
2156 getSCEV(U->getOperand(1)));
2157 case Instruction::UDiv:
2158 return getUDivExpr(getSCEV(U->getOperand(0)),
2159 getSCEV(U->getOperand(1)));
2160 case Instruction::Sub:
2161 return getMinusSCEV(getSCEV(U->getOperand(0)),
2162 getSCEV(U->getOperand(1)));
2163 case Instruction::And:
2164 // For an expression like x&255 that merely masks off the high bits,
2165 // use zext(trunc(x)) as the SCEV expression.
2166 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2167 if (CI->isNullValue())
2168 return getSCEV(U->getOperand(1));
2169 if (CI->isAllOnesValue())
2170 return getSCEV(U->getOperand(0));
2171 const APInt &A = CI->getValue();
2172 unsigned Ones = A.countTrailingOnes();
2173 if (APIntOps::isMask(Ones, A))
2175 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2176 IntegerType::get(Ones)),
2180 case Instruction::Or:
2181 // If the RHS of the Or is a constant, we may have something like:
2182 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2183 // optimizations will transparently handle this case.
2185 // In order for this transformation to be safe, the LHS must be of the
2186 // form X*(2^n) and the Or constant must be less than 2^n.
2187 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2188 SCEVHandle LHS = getSCEV(U->getOperand(0));
2189 const APInt &CIVal = CI->getValue();
2190 if (GetMinTrailingZeros(LHS, *this) >=
2191 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2192 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2195 case Instruction::Xor:
2196 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2197 // If the RHS of the xor is a signbit, then this is just an add.
2198 // Instcombine turns add of signbit into xor as a strength reduction step.
2199 if (CI->getValue().isSignBit())
2200 return getAddExpr(getSCEV(U->getOperand(0)),
2201 getSCEV(U->getOperand(1)));
2203 // If the RHS of xor is -1, then this is a not operation.
2204 else if (CI->isAllOnesValue())
2205 return getNotSCEV(getSCEV(U->getOperand(0)));
2209 case Instruction::Shl:
2210 // Turn shift left of a constant amount into a multiply.
2211 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2212 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2213 Constant *X = ConstantInt::get(
2214 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2215 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2219 case Instruction::LShr:
2220 // Turn logical shift right of a constant into a unsigned divide.
2221 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2222 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2223 Constant *X = ConstantInt::get(
2224 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2225 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2229 case Instruction::AShr:
2230 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2231 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2232 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2233 if (L->getOpcode() == Instruction::Shl &&
2234 L->getOperand(1) == U->getOperand(1)) {
2235 unsigned BitWidth = getTypeSizeInBits(U->getType());
2236 uint64_t Amt = BitWidth - CI->getZExtValue();
2237 if (Amt == BitWidth)
2238 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2240 return getIntegerSCEV(0, U->getType()); // value is undefined
2242 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2243 IntegerType::get(Amt)),
2248 case Instruction::Trunc:
2249 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2251 case Instruction::ZExt:
2252 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2254 case Instruction::SExt:
2255 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2257 case Instruction::BitCast:
2258 // BitCasts are no-op casts so we just eliminate the cast.
2259 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2260 return getSCEV(U->getOperand(0));
2263 case Instruction::IntToPtr:
2264 if (!TD) break; // Without TD we can't analyze pointers.
2265 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2266 TD->getIntPtrType());
2268 case Instruction::PtrToInt:
2269 if (!TD) break; // Without TD we can't analyze pointers.
2270 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2273 case Instruction::GetElementPtr:
2274 if (!TD) break; // Without TD we can't analyze pointers.
2275 return createNodeForGEP(U);
2277 case Instruction::PHI:
2278 return createNodeForPHI(cast<PHINode>(U));
2280 case Instruction::Select:
2281 // This could be a smax or umax that was lowered earlier.
2282 // Try to recover it.
2283 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2284 Value *LHS = ICI->getOperand(0);
2285 Value *RHS = ICI->getOperand(1);
2286 switch (ICI->getPredicate()) {
2287 case ICmpInst::ICMP_SLT:
2288 case ICmpInst::ICMP_SLE:
2289 std::swap(LHS, RHS);
2291 case ICmpInst::ICMP_SGT:
2292 case ICmpInst::ICMP_SGE:
2293 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2294 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2295 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2296 // ~smax(~x, ~y) == smin(x, y).
2297 return getNotSCEV(getSMaxExpr(
2298 getNotSCEV(getSCEV(LHS)),
2299 getNotSCEV(getSCEV(RHS))));
2301 case ICmpInst::ICMP_ULT:
2302 case ICmpInst::ICMP_ULE:
2303 std::swap(LHS, RHS);
2305 case ICmpInst::ICMP_UGT:
2306 case ICmpInst::ICMP_UGE:
2307 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2308 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2309 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2310 // ~umax(~x, ~y) == umin(x, y)
2311 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2312 getNotSCEV(getSCEV(RHS))));
2319 default: // We cannot analyze this expression.
2323 return getUnknown(V);
2328 //===----------------------------------------------------------------------===//
2329 // Iteration Count Computation Code
2332 /// getBackedgeTakenCount - If the specified loop has a predictable
2333 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2334 /// object. The backedge-taken count is the number of times the loop header
2335 /// will be branched to from within the loop. This is one less than the
2336 /// trip count of the loop, since it doesn't count the first iteration,
2337 /// when the header is branched to from outside the loop.
2339 /// Note that it is not valid to call this method on a loop without a
2340 /// loop-invariant backedge-taken count (see
2341 /// hasLoopInvariantBackedgeTakenCount).
2343 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2344 return getBackedgeTakenInfo(L).Exact;
2347 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2348 /// return the least SCEV value that is known never to be less than the
2349 /// actual backedge taken count.
2350 SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2351 return getBackedgeTakenInfo(L).Max;
2354 const ScalarEvolution::BackedgeTakenInfo &
2355 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2356 // Initially insert a CouldNotCompute for this loop. If the insertion
2357 // succeeds, procede to actually compute a backedge-taken count and
2358 // update the value. The temporary CouldNotCompute value tells SCEV
2359 // code elsewhere that it shouldn't attempt to request a new
2360 // backedge-taken count, which could result in infinite recursion.
2361 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2362 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2364 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2365 if (ItCount.Exact != UnknownValue) {
2366 assert(ItCount.Exact->isLoopInvariant(L) &&
2367 ItCount.Max->isLoopInvariant(L) &&
2368 "Computed trip count isn't loop invariant for loop!");
2369 ++NumTripCountsComputed;
2371 // Update the value in the map.
2372 Pair.first->second = ItCount;
2373 } else if (isa<PHINode>(L->getHeader()->begin())) {
2374 // Only count loops that have phi nodes as not being computable.
2375 ++NumTripCountsNotComputed;
2378 // Now that we know more about the trip count for this loop, forget any
2379 // existing SCEV values for PHI nodes in this loop since they are only
2380 // conservative estimates made without the benefit
2381 // of trip count information.
2382 if (ItCount.hasAnyInfo())
2385 return Pair.first->second;
2388 /// forgetLoopBackedgeTakenCount - This method should be called by the
2389 /// client when it has changed a loop in a way that may effect
2390 /// ScalarEvolution's ability to compute a trip count, or if the loop
2392 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2393 BackedgeTakenCounts.erase(L);
2397 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2398 /// PHI nodes in the given loop. This is used when the trip count of
2399 /// the loop may have changed.
2400 void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2401 BasicBlock *Header = L->getHeader();
2403 // Push all Loop-header PHIs onto the Worklist stack, except those
2404 // that are presently represented via a SCEVUnknown. SCEVUnknown for
2405 // a PHI either means that it has an unrecognized structure, or it's
2406 // a PHI that's in the progress of being computed by createNodeForPHI.
2407 // In the former case, additional loop trip count information isn't
2408 // going to change anything. In the later case, createNodeForPHI will
2409 // perform the necessary updates on its own when it gets to that point.
2410 SmallVector<Instruction *, 16> Worklist;
2411 for (BasicBlock::iterator I = Header->begin();
2412 PHINode *PN = dyn_cast<PHINode>(I); ++I) {
2413 std::map<SCEVCallbackVH, SCEVHandle>::iterator It = Scalars.find((Value*)I);
2414 if (It != Scalars.end() && !isa<SCEVUnknown>(It->second))
2415 Worklist.push_back(PN);
2418 while (!Worklist.empty()) {
2419 Instruction *I = Worklist.pop_back_val();
2420 if (Scalars.erase(I))
2421 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2423 Worklist.push_back(cast<Instruction>(UI));
2427 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2428 /// of the specified loop will execute.
2429 ScalarEvolution::BackedgeTakenInfo
2430 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2431 // If the loop has a non-one exit block count, we can't analyze it.
2432 SmallVector<BasicBlock*, 8> ExitBlocks;
2433 L->getExitBlocks(ExitBlocks);
2434 if (ExitBlocks.size() != 1) return UnknownValue;
2436 // Okay, there is one exit block. Try to find the condition that causes the
2437 // loop to be exited.
2438 BasicBlock *ExitBlock = ExitBlocks[0];
2440 BasicBlock *ExitingBlock = 0;
2441 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
2443 if (L->contains(*PI)) {
2444 if (ExitingBlock == 0)
2447 return UnknownValue; // More than one block exiting!
2449 assert(ExitingBlock && "No exits from loop, something is broken!");
2451 // Okay, we've computed the exiting block. See what condition causes us to
2454 // FIXME: we should be able to handle switch instructions (with a single exit)
2455 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2456 if (ExitBr == 0) return UnknownValue;
2457 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2459 // At this point, we know we have a conditional branch that determines whether
2460 // the loop is exited. However, we don't know if the branch is executed each
2461 // time through the loop. If not, then the execution count of the branch will
2462 // not be equal to the trip count of the loop.
2464 // Currently we check for this by checking to see if the Exit branch goes to
2465 // the loop header. If so, we know it will always execute the same number of
2466 // times as the loop. We also handle the case where the exit block *is* the
2467 // loop header. This is common for un-rotated loops. More extensive analysis
2468 // could be done to handle more cases here.
2469 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2470 ExitBr->getSuccessor(1) != L->getHeader() &&
2471 ExitBr->getParent() != L->getHeader())
2472 return UnknownValue;
2474 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2476 // If it's not an integer or pointer comparison then compute it the hard way.
2478 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2479 ExitBr->getSuccessor(0) == ExitBlock);
2481 // If the condition was exit on true, convert the condition to exit on false
2482 ICmpInst::Predicate Cond;
2483 if (ExitBr->getSuccessor(1) == ExitBlock)
2484 Cond = ExitCond->getPredicate();
2486 Cond = ExitCond->getInversePredicate();
2488 // Handle common loops like: for (X = "string"; *X; ++X)
2489 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2490 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2492 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2493 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2496 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2497 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2499 // Try to evaluate any dependencies out of the loop.
2500 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
2501 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
2502 Tmp = getSCEVAtScope(RHS, L);
2503 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
2505 // At this point, we would like to compute how many iterations of the
2506 // loop the predicate will return true for these inputs.
2507 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2508 // If there is a loop-invariant, force it into the RHS.
2509 std::swap(LHS, RHS);
2510 Cond = ICmpInst::getSwappedPredicate(Cond);
2513 // If we have a comparison of a chrec against a constant, try to use value
2514 // ranges to answer this query.
2515 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2516 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2517 if (AddRec->getLoop() == L) {
2518 // Form the constant range.
2519 ConstantRange CompRange(
2520 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
2522 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2523 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2527 case ICmpInst::ICMP_NE: { // while (X != Y)
2528 // Convert to: while (X-Y != 0)
2529 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2530 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2533 case ICmpInst::ICMP_EQ: {
2534 // Convert to: while (X-Y == 0) // while (X == Y)
2535 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2536 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2539 case ICmpInst::ICMP_SLT: {
2540 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2541 if (BTI.hasAnyInfo()) return BTI;
2544 case ICmpInst::ICMP_SGT: {
2545 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2546 getNotSCEV(RHS), L, true);
2547 if (BTI.hasAnyInfo()) return BTI;
2550 case ICmpInst::ICMP_ULT: {
2551 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2552 if (BTI.hasAnyInfo()) return BTI;
2555 case ICmpInst::ICMP_UGT: {
2556 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2557 getNotSCEV(RHS), L, false);
2558 if (BTI.hasAnyInfo()) return BTI;
2563 errs() << "ComputeBackedgeTakenCount ";
2564 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2565 errs() << "[unsigned] ";
2566 errs() << *LHS << " "
2567 << Instruction::getOpcodeName(Instruction::ICmp)
2568 << " " << *RHS << "\n";
2573 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2574 ExitBr->getSuccessor(0) == ExitBlock);
2577 static ConstantInt *
2578 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2579 ScalarEvolution &SE) {
2580 SCEVHandle InVal = SE.getConstant(C);
2581 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2582 assert(isa<SCEVConstant>(Val) &&
2583 "Evaluation of SCEV at constant didn't fold correctly?");
2584 return cast<SCEVConstant>(Val)->getValue();
2587 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2588 /// and a GEP expression (missing the pointer index) indexing into it, return
2589 /// the addressed element of the initializer or null if the index expression is
2592 GetAddressedElementFromGlobal(GlobalVariable *GV,
2593 const std::vector<ConstantInt*> &Indices) {
2594 Constant *Init = GV->getInitializer();
2595 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2596 uint64_t Idx = Indices[i]->getZExtValue();
2597 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2598 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2599 Init = cast<Constant>(CS->getOperand(Idx));
2600 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2601 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2602 Init = cast<Constant>(CA->getOperand(Idx));
2603 } else if (isa<ConstantAggregateZero>(Init)) {
2604 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2605 assert(Idx < STy->getNumElements() && "Bad struct index!");
2606 Init = Constant::getNullValue(STy->getElementType(Idx));
2607 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2608 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2609 Init = Constant::getNullValue(ATy->getElementType());
2611 assert(0 && "Unknown constant aggregate type!");
2615 return 0; // Unknown initializer type
2621 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2622 /// 'icmp op load X, cst', try to see if we can compute the backedge
2623 /// execution count.
2624 SCEVHandle ScalarEvolution::
2625 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2627 ICmpInst::Predicate predicate) {
2628 if (LI->isVolatile()) return UnknownValue;
2630 // Check to see if the loaded pointer is a getelementptr of a global.
2631 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2632 if (!GEP) return UnknownValue;
2634 // Make sure that it is really a constant global we are gepping, with an
2635 // initializer, and make sure the first IDX is really 0.
2636 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2637 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2638 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2639 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2640 return UnknownValue;
2642 // Okay, we allow one non-constant index into the GEP instruction.
2644 std::vector<ConstantInt*> Indexes;
2645 unsigned VarIdxNum = 0;
2646 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2647 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2648 Indexes.push_back(CI);
2649 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2650 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2651 VarIdx = GEP->getOperand(i);
2653 Indexes.push_back(0);
2656 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2657 // Check to see if X is a loop variant variable value now.
2658 SCEVHandle Idx = getSCEV(VarIdx);
2659 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2660 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2662 // We can only recognize very limited forms of loop index expressions, in
2663 // particular, only affine AddRec's like {C1,+,C2}.
2664 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2665 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2666 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2667 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2668 return UnknownValue;
2670 unsigned MaxSteps = MaxBruteForceIterations;
2671 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2672 ConstantInt *ItCst =
2673 ConstantInt::get(IdxExpr->getType(), IterationNum);
2674 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2676 // Form the GEP offset.
2677 Indexes[VarIdxNum] = Val;
2679 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2680 if (Result == 0) break; // Cannot compute!
2682 // Evaluate the condition for this iteration.
2683 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2684 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2685 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2687 errs() << "\n***\n*** Computed loop count " << *ItCst
2688 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2691 ++NumArrayLenItCounts;
2692 return getConstant(ItCst); // Found terminating iteration!
2695 return UnknownValue;
2699 /// CanConstantFold - Return true if we can constant fold an instruction of the
2700 /// specified type, assuming that all operands were constants.
2701 static bool CanConstantFold(const Instruction *I) {
2702 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2703 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2706 if (const CallInst *CI = dyn_cast<CallInst>(I))
2707 if (const Function *F = CI->getCalledFunction())
2708 return canConstantFoldCallTo(F);
2712 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2713 /// in the loop that V is derived from. We allow arbitrary operations along the
2714 /// way, but the operands of an operation must either be constants or a value
2715 /// derived from a constant PHI. If this expression does not fit with these
2716 /// constraints, return null.
2717 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2718 // If this is not an instruction, or if this is an instruction outside of the
2719 // loop, it can't be derived from a loop PHI.
2720 Instruction *I = dyn_cast<Instruction>(V);
2721 if (I == 0 || !L->contains(I->getParent())) return 0;
2723 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2724 if (L->getHeader() == I->getParent())
2727 // We don't currently keep track of the control flow needed to evaluate
2728 // PHIs, so we cannot handle PHIs inside of loops.
2732 // If we won't be able to constant fold this expression even if the operands
2733 // are constants, return early.
2734 if (!CanConstantFold(I)) return 0;
2736 // Otherwise, we can evaluate this instruction if all of its operands are
2737 // constant or derived from a PHI node themselves.
2739 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2740 if (!(isa<Constant>(I->getOperand(Op)) ||
2741 isa<GlobalValue>(I->getOperand(Op)))) {
2742 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2743 if (P == 0) return 0; // Not evolving from PHI
2747 return 0; // Evolving from multiple different PHIs.
2750 // This is a expression evolving from a constant PHI!
2754 /// EvaluateExpression - Given an expression that passes the
2755 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2756 /// in the loop has the value PHIVal. If we can't fold this expression for some
2757 /// reason, return null.
2758 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2759 if (isa<PHINode>(V)) return PHIVal;
2760 if (Constant *C = dyn_cast<Constant>(V)) return C;
2761 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2762 Instruction *I = cast<Instruction>(V);
2764 std::vector<Constant*> Operands;
2765 Operands.resize(I->getNumOperands());
2767 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2768 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2769 if (Operands[i] == 0) return 0;
2772 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2773 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2774 &Operands[0], Operands.size());
2776 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2777 &Operands[0], Operands.size());
2780 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2781 /// in the header of its containing loop, we know the loop executes a
2782 /// constant number of times, and the PHI node is just a recurrence
2783 /// involving constants, fold it.
2784 Constant *ScalarEvolution::
2785 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2786 std::map<PHINode*, Constant*>::iterator I =
2787 ConstantEvolutionLoopExitValue.find(PN);
2788 if (I != ConstantEvolutionLoopExitValue.end())
2791 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2792 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2794 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2796 // Since the loop is canonicalized, the PHI node must have two entries. One
2797 // entry must be a constant (coming in from outside of the loop), and the
2798 // second must be derived from the same PHI.
2799 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2800 Constant *StartCST =
2801 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2803 return RetVal = 0; // Must be a constant.
2805 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2806 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2808 return RetVal = 0; // Not derived from same PHI.
2810 // Execute the loop symbolically to determine the exit value.
2811 if (BEs.getActiveBits() >= 32)
2812 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2814 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2815 unsigned IterationNum = 0;
2816 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2817 if (IterationNum == NumIterations)
2818 return RetVal = PHIVal; // Got exit value!
2820 // Compute the value of the PHI node for the next iteration.
2821 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2822 if (NextPHI == PHIVal)
2823 return RetVal = NextPHI; // Stopped evolving!
2825 return 0; // Couldn't evaluate!
2830 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2831 /// constant number of times (the condition evolves only from constants),
2832 /// try to evaluate a few iterations of the loop until we get the exit
2833 /// condition gets a value of ExitWhen (true or false). If we cannot
2834 /// evaluate the trip count of the loop, return UnknownValue.
2835 SCEVHandle ScalarEvolution::
2836 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2837 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2838 if (PN == 0) return UnknownValue;
2840 // Since the loop is canonicalized, the PHI node must have two entries. One
2841 // entry must be a constant (coming in from outside of the loop), and the
2842 // second must be derived from the same PHI.
2843 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2844 Constant *StartCST =
2845 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2846 if (StartCST == 0) return UnknownValue; // Must be a constant.
2848 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2849 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2850 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2852 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2853 // the loop symbolically to determine when the condition gets a value of
2855 unsigned IterationNum = 0;
2856 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2857 for (Constant *PHIVal = StartCST;
2858 IterationNum != MaxIterations; ++IterationNum) {
2859 ConstantInt *CondVal =
2860 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2862 // Couldn't symbolically evaluate.
2863 if (!CondVal) return UnknownValue;
2865 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2866 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2867 ++NumBruteForceTripCountsComputed;
2868 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2871 // Compute the value of the PHI node for the next iteration.
2872 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2873 if (NextPHI == 0 || NextPHI == PHIVal)
2874 return UnknownValue; // Couldn't evaluate or not making progress...
2878 // Too many iterations were needed to evaluate.
2879 return UnknownValue;
2882 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
2883 /// at the specified scope in the program. The L value specifies a loop
2884 /// nest to evaluate the expression at, where null is the top-level or a
2885 /// specified loop is immediately inside of the loop.
2887 /// This method can be used to compute the exit value for a variable defined
2888 /// in a loop by querying what the value will hold in the parent loop.
2890 /// If this value is not computable at this scope, a SCEVCouldNotCompute
2891 /// object is returned.
2892 SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
2893 // FIXME: this should be turned into a virtual method on SCEV!
2895 if (isa<SCEVConstant>(V)) return V;
2897 // If this instruction is evolved from a constant-evolving PHI, compute the
2898 // exit value from the loop without using SCEVs.
2899 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2900 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2901 const Loop *LI = (*this->LI)[I->getParent()];
2902 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2903 if (PHINode *PN = dyn_cast<PHINode>(I))
2904 if (PN->getParent() == LI->getHeader()) {
2905 // Okay, there is no closed form solution for the PHI node. Check
2906 // to see if the loop that contains it has a known backedge-taken
2907 // count. If so, we may be able to force computation of the exit
2909 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2910 if (const SCEVConstant *BTCC =
2911 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2912 // Okay, we know how many times the containing loop executes. If
2913 // this is a constant evolving PHI node, get the final value at
2914 // the specified iteration number.
2915 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2916 BTCC->getValue()->getValue(),
2918 if (RV) return getUnknown(RV);
2922 // Okay, this is an expression that we cannot symbolically evaluate
2923 // into a SCEV. Check to see if it's possible to symbolically evaluate
2924 // the arguments into constants, and if so, try to constant propagate the
2925 // result. This is particularly useful for computing loop exit values.
2926 if (CanConstantFold(I)) {
2927 // Check to see if we've folded this instruction at this loop before.
2928 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
2929 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
2930 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
2932 return Pair.first->second ? &*getUnknown(Pair.first->second) : V;
2934 std::vector<Constant*> Operands;
2935 Operands.reserve(I->getNumOperands());
2936 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2937 Value *Op = I->getOperand(i);
2938 if (Constant *C = dyn_cast<Constant>(Op)) {
2939 Operands.push_back(C);
2941 // If any of the operands is non-constant and if they are
2942 // non-integer and non-pointer, don't even try to analyze them
2943 // with scev techniques.
2944 if (!isSCEVable(Op->getType()))
2947 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2948 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
2949 Constant *C = SC->getValue();
2950 if (C->getType() != Op->getType())
2951 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2955 Operands.push_back(C);
2956 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2957 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
2958 if (C->getType() != Op->getType())
2960 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2964 Operands.push_back(C);
2974 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2975 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
2976 &Operands[0], Operands.size());
2978 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2979 &Operands[0], Operands.size());
2980 Pair.first->second = C;
2981 return getUnknown(C);
2985 // This is some other type of SCEVUnknown, just return it.
2989 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
2990 // Avoid performing the look-up in the common case where the specified
2991 // expression has no loop-variant portions.
2992 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
2993 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
2994 if (OpAtScope != Comm->getOperand(i)) {
2995 if (OpAtScope == UnknownValue) return UnknownValue;
2996 // Okay, at least one of these operands is loop variant but might be
2997 // foldable. Build a new instance of the folded commutative expression.
2998 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
2999 NewOps.push_back(OpAtScope);
3001 for (++i; i != e; ++i) {
3002 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3003 if (OpAtScope == UnknownValue) return UnknownValue;
3004 NewOps.push_back(OpAtScope);
3006 if (isa<SCEVAddExpr>(Comm))
3007 return getAddExpr(NewOps);
3008 if (isa<SCEVMulExpr>(Comm))
3009 return getMulExpr(NewOps);
3010 if (isa<SCEVSMaxExpr>(Comm))
3011 return getSMaxExpr(NewOps);
3012 if (isa<SCEVUMaxExpr>(Comm))
3013 return getUMaxExpr(NewOps);
3014 assert(0 && "Unknown commutative SCEV type!");
3017 // If we got here, all operands are loop invariant.
3021 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3022 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
3023 if (LHS == UnknownValue) return LHS;
3024 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
3025 if (RHS == UnknownValue) return RHS;
3026 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3027 return Div; // must be loop invariant
3028 return getUDivExpr(LHS, RHS);
3031 // If this is a loop recurrence for a loop that does not contain L, then we
3032 // are dealing with the final value computed by the loop.
3033 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3034 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3035 // To evaluate this recurrence, we need to know how many times the AddRec
3036 // loop iterates. Compute this now.
3037 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3038 if (BackedgeTakenCount == UnknownValue) return UnknownValue;
3040 // Then, evaluate the AddRec.
3041 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3043 return UnknownValue;
3046 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3047 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3048 if (Op == UnknownValue) return Op;
3049 if (Op == Cast->getOperand())
3050 return Cast; // must be loop invariant
3051 return getZeroExtendExpr(Op, Cast->getType());
3054 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3055 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3056 if (Op == UnknownValue) return Op;
3057 if (Op == Cast->getOperand())
3058 return Cast; // must be loop invariant
3059 return getSignExtendExpr(Op, Cast->getType());
3062 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3063 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3064 if (Op == UnknownValue) return Op;
3065 if (Op == Cast->getOperand())
3066 return Cast; // must be loop invariant
3067 return getTruncateExpr(Op, Cast->getType());
3070 assert(0 && "Unknown SCEV type!");
3073 /// getSCEVAtScope - This is a convenience function which does
3074 /// getSCEVAtScope(getSCEV(V), L).
3075 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3076 return getSCEVAtScope(getSCEV(V), L);
3079 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3080 /// following equation:
3082 /// A * X = B (mod N)
3084 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3085 /// A and B isn't important.
3087 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3088 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3089 ScalarEvolution &SE) {
3090 uint32_t BW = A.getBitWidth();
3091 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3092 assert(A != 0 && "A must be non-zero.");
3096 // The gcd of A and N may have only one prime factor: 2. The number of
3097 // trailing zeros in A is its multiplicity
3098 uint32_t Mult2 = A.countTrailingZeros();
3101 // 2. Check if B is divisible by D.
3103 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3104 // is not less than multiplicity of this prime factor for D.
3105 if (B.countTrailingZeros() < Mult2)
3106 return SE.getCouldNotCompute();
3108 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3111 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3112 // bit width during computations.
3113 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3114 APInt Mod(BW + 1, 0);
3115 Mod.set(BW - Mult2); // Mod = N / D
3116 APInt I = AD.multiplicativeInverse(Mod);
3118 // 4. Compute the minimum unsigned root of the equation:
3119 // I * (B / D) mod (N / D)
3120 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3122 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3124 return SE.getConstant(Result.trunc(BW));
3127 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3128 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
3129 /// might be the same) or two SCEVCouldNotCompute objects.
3131 static std::pair<SCEVHandle,SCEVHandle>
3132 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
3133 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
3134 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
3135 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
3136 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
3138 // We currently can only solve this if the coefficients are constants.
3139 if (!LC || !MC || !NC) {
3140 const SCEV *CNC = SE.getCouldNotCompute();
3141 return std::make_pair(CNC, CNC);
3144 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
3145 const APInt &L = LC->getValue()->getValue();
3146 const APInt &M = MC->getValue()->getValue();
3147 const APInt &N = NC->getValue()->getValue();
3148 APInt Two(BitWidth, 2);
3149 APInt Four(BitWidth, 4);
3152 using namespace APIntOps;
3154 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
3155 // The B coefficient is M-N/2
3159 // The A coefficient is N/2
3160 APInt A(N.sdiv(Two));
3162 // Compute the B^2-4ac term.
3165 SqrtTerm -= Four * (A * C);
3167 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
3168 // integer value or else APInt::sqrt() will assert.
3169 APInt SqrtVal(SqrtTerm.sqrt());
3171 // Compute the two solutions for the quadratic formula.
3172 // The divisions must be performed as signed divisions.
3174 APInt TwoA( A << 1 );
3175 if (TwoA.isMinValue()) {
3176 const SCEV *CNC = SE.getCouldNotCompute();
3177 return std::make_pair(CNC, CNC);
3180 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
3181 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
3183 return std::make_pair(SE.getConstant(Solution1),
3184 SE.getConstant(Solution2));
3185 } // end APIntOps namespace
3188 /// HowFarToZero - Return the number of times a backedge comparing the specified
3189 /// value to zero will execute. If not computable, return UnknownValue
3190 SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
3191 // If the value is a constant
3192 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3193 // If the value is already zero, the branch will execute zero times.
3194 if (C->getValue()->isZero()) return C;
3195 return UnknownValue; // Otherwise it will loop infinitely.
3198 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
3199 if (!AddRec || AddRec->getLoop() != L)
3200 return UnknownValue;
3202 if (AddRec->isAffine()) {
3203 // If this is an affine expression, the execution count of this branch is
3204 // the minimum unsigned root of the following equation:
3206 // Start + Step*N = 0 (mod 2^BW)
3210 // Step*N = -Start (mod 2^BW)
3212 // where BW is the common bit width of Start and Step.
3214 // Get the initial value for the loop.
3215 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
3216 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
3218 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
3220 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
3221 // For now we handle only constant steps.
3223 // First, handle unitary steps.
3224 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
3225 return getNegativeSCEV(Start); // N = -Start (as unsigned)
3226 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
3227 return Start; // N = Start (as unsigned)
3229 // Then, try to solve the above equation provided that Start is constant.
3230 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
3231 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
3232 -StartC->getValue()->getValue(),
3235 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
3236 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
3237 // the quadratic equation to solve it.
3238 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
3240 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3241 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3244 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
3245 << " sol#2: " << *R2 << "\n";
3247 // Pick the smallest positive root value.
3248 if (ConstantInt *CB =
3249 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3250 R1->getValue(), R2->getValue()))) {
3251 if (CB->getZExtValue() == false)
3252 std::swap(R1, R2); // R1 is the minimum root now.
3254 // We can only use this value if the chrec ends up with an exact zero
3255 // value at this index. When solving for "X*X != 5", for example, we
3256 // should not accept a root of 2.
3257 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
3259 return R1; // We found a quadratic root!
3264 return UnknownValue;
3267 /// HowFarToNonZero - Return the number of times a backedge checking the
3268 /// specified value for nonzero will execute. If not computable, return
3270 SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
3271 // Loops that look like: while (X == 0) are very strange indeed. We don't
3272 // handle them yet except for the trivial case. This could be expanded in the
3273 // future as needed.
3275 // If the value is a constant, check to see if it is known to be non-zero
3276 // already. If so, the backedge will execute zero times.
3277 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3278 if (!C->getValue()->isNullValue())
3279 return getIntegerSCEV(0, C->getType());
3280 return UnknownValue; // Otherwise it will loop infinitely.
3283 // We could implement others, but I really doubt anyone writes loops like
3284 // this, and if they did, they would already be constant folded.
3285 return UnknownValue;
3288 /// getLoopPredecessor - If the given loop's header has exactly one unique
3289 /// predecessor outside the loop, return it. Otherwise return null.
3291 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
3292 BasicBlock *Header = L->getHeader();
3293 BasicBlock *Pred = 0;
3294 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
3296 if (!L->contains(*PI)) {
3297 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
3303 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3304 /// (which may not be an immediate predecessor) which has exactly one
3305 /// successor from which BB is reachable, or null if no such block is
3309 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3310 // If the block has a unique predecessor, then there is no path from the
3311 // predecessor to the block that does not go through the direct edge
3312 // from the predecessor to the block.
3313 if (BasicBlock *Pred = BB->getSinglePredecessor())
3316 // A loop's header is defined to be a block that dominates the loop.
3317 // If the header has a unique predecessor outside the loop, it must be
3318 // a block that has exactly one successor that can reach the loop.
3319 if (Loop *L = LI->getLoopFor(BB))
3320 return getLoopPredecessor(L);
3325 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
3326 /// a conditional between LHS and RHS. This is used to help avoid max
3327 /// expressions in loop trip counts.
3328 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3329 ICmpInst::Predicate Pred,
3330 const SCEV *LHS, const SCEV *RHS) {
3331 BasicBlock *Predecessor = getLoopPredecessor(L);
3332 BasicBlock *PredecessorDest = L->getHeader();
3334 // Starting at the loop predecessor, climb up the predecessor chain, as long
3335 // as there are predecessors that can be found that have unique successors
3336 // leading to the original header.
3338 PredecessorDest = Predecessor,
3339 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
3341 BranchInst *LoopEntryPredicate =
3342 dyn_cast<BranchInst>(Predecessor->getTerminator());
3343 if (!LoopEntryPredicate ||
3344 LoopEntryPredicate->isUnconditional())
3347 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3350 // Now that we found a conditional branch that dominates the loop, check to
3351 // see if it is the comparison we are looking for.
3352 Value *PreCondLHS = ICI->getOperand(0);
3353 Value *PreCondRHS = ICI->getOperand(1);
3354 ICmpInst::Predicate Cond;
3355 if (LoopEntryPredicate->getSuccessor(0) == PredecessorDest)
3356 Cond = ICI->getPredicate();
3358 Cond = ICI->getInversePredicate();
3361 ; // An exact match.
3362 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3363 ; // The actual condition is beyond sufficient.
3365 // Check a few special cases.
3367 case ICmpInst::ICMP_UGT:
3368 if (Pred == ICmpInst::ICMP_ULT) {
3369 std::swap(PreCondLHS, PreCondRHS);
3370 Cond = ICmpInst::ICMP_ULT;
3374 case ICmpInst::ICMP_SGT:
3375 if (Pred == ICmpInst::ICMP_SLT) {
3376 std::swap(PreCondLHS, PreCondRHS);
3377 Cond = ICmpInst::ICMP_SLT;
3381 case ICmpInst::ICMP_NE:
3382 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3383 // so check for this case by checking if the NE is comparing against
3384 // a minimum or maximum constant.
3385 if (!ICmpInst::isTrueWhenEqual(Pred))
3386 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3387 const APInt &A = CI->getValue();
3389 case ICmpInst::ICMP_SLT:
3390 if (A.isMaxSignedValue()) break;
3392 case ICmpInst::ICMP_SGT:
3393 if (A.isMinSignedValue()) break;
3395 case ICmpInst::ICMP_ULT:
3396 if (A.isMaxValue()) break;
3398 case ICmpInst::ICMP_UGT:
3399 if (A.isMinValue()) break;
3404 Cond = ICmpInst::ICMP_NE;
3405 // NE is symmetric but the original comparison may not be. Swap
3406 // the operands if necessary so that they match below.
3407 if (isa<SCEVConstant>(LHS))
3408 std::swap(PreCondLHS, PreCondRHS);
3413 // We weren't able to reconcile the condition.
3417 if (!PreCondLHS->getType()->isInteger()) continue;
3419 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3420 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3421 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3422 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3423 RHS == getNotSCEV(PreCondLHSSCEV)))
3430 /// HowManyLessThans - Return the number of times a backedge containing the
3431 /// specified less-than comparison will execute. If not computable, return
3433 ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3434 HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
3435 const Loop *L, bool isSigned) {
3436 // Only handle: "ADDREC < LoopInvariant".
3437 if (!RHS->isLoopInvariant(L)) return UnknownValue;
3439 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3440 if (!AddRec || AddRec->getLoop() != L)
3441 return UnknownValue;
3443 if (AddRec->isAffine()) {
3444 // FORNOW: We only support unit strides.
3445 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3446 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3447 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3449 // TODO: handle non-constant strides.
3450 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3451 if (!CStep || CStep->isZero())
3452 return UnknownValue;
3453 if (CStep->isOne()) {
3454 // With unit stride, the iteration never steps past the limit value.
3455 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3456 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3457 // Test whether a positive iteration iteration can step past the limit
3458 // value and past the maximum value for its type in a single step.
3460 APInt Max = APInt::getSignedMaxValue(BitWidth);
3461 if ((Max - CStep->getValue()->getValue())
3462 .slt(CLimit->getValue()->getValue()))
3463 return UnknownValue;
3465 APInt Max = APInt::getMaxValue(BitWidth);
3466 if ((Max - CStep->getValue()->getValue())
3467 .ult(CLimit->getValue()->getValue()))
3468 return UnknownValue;
3471 // TODO: handle non-constant limit values below.
3472 return UnknownValue;
3474 // TODO: handle negative strides below.
3475 return UnknownValue;
3477 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3478 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3479 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3480 // treat m-n as signed nor unsigned due to overflow possibility.
3482 // First, we get the value of the LHS in the first iteration: n
3483 SCEVHandle Start = AddRec->getOperand(0);
3485 // Determine the minimum constant start value.
3486 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3487 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3488 APInt::getMinValue(BitWidth));
3490 // If we know that the condition is true in order to enter the loop,
3491 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3492 // only know if will execute (max(m,n)-n)/s times. In both cases, the
3493 // division must round up.
3494 SCEVHandle End = RHS;
3495 if (!isLoopGuardedByCond(L,
3496 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3497 getMinusSCEV(Start, Step), RHS))
3498 End = isSigned ? getSMaxExpr(RHS, Start)
3499 : getUMaxExpr(RHS, Start);
3501 // Determine the maximum constant end value.
3502 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3503 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3504 APInt::getMaxValue(BitWidth));
3506 // Finally, we subtract these two values and divide, rounding up, to get
3507 // the number of times the backedge is executed.
3508 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3509 getAddExpr(Step, NegOne)),
3512 // The maximum backedge count is similar, except using the minimum start
3513 // value and the maximum end value.
3514 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3516 getAddExpr(Step, NegOne)),
3519 return BackedgeTakenInfo(BECount, MaxBECount);
3522 return UnknownValue;
3525 /// getNumIterationsInRange - Return the number of iterations of this loop that
3526 /// produce values in the specified constant range. Another way of looking at
3527 /// this is that it returns the first iteration number where the value is not in
3528 /// the condition, thus computing the exit count. If the iteration count can't
3529 /// be computed, an instance of SCEVCouldNotCompute is returned.
3530 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3531 ScalarEvolution &SE) const {
3532 if (Range.isFullSet()) // Infinite loop.
3533 return SE.getCouldNotCompute();
3535 // If the start is a non-zero constant, shift the range to simplify things.
3536 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3537 if (!SC->getValue()->isZero()) {
3538 std::vector<SCEVHandle> Operands(op_begin(), op_end());
3539 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3540 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3541 if (const SCEVAddRecExpr *ShiftedAddRec =
3542 dyn_cast<SCEVAddRecExpr>(Shifted))
3543 return ShiftedAddRec->getNumIterationsInRange(
3544 Range.subtract(SC->getValue()->getValue()), SE);
3545 // This is strange and shouldn't happen.
3546 return SE.getCouldNotCompute();
3549 // The only time we can solve this is when we have all constant indices.
3550 // Otherwise, we cannot determine the overflow conditions.
3551 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3552 if (!isa<SCEVConstant>(getOperand(i)))
3553 return SE.getCouldNotCompute();
3556 // Okay at this point we know that all elements of the chrec are constants and
3557 // that the start element is zero.
3559 // First check to see if the range contains zero. If not, the first
3561 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3562 if (!Range.contains(APInt(BitWidth, 0)))
3563 return SE.getConstant(ConstantInt::get(getType(),0));
3566 // If this is an affine expression then we have this situation:
3567 // Solve {0,+,A} in Range === Ax in Range
3569 // We know that zero is in the range. If A is positive then we know that
3570 // the upper value of the range must be the first possible exit value.
3571 // If A is negative then the lower of the range is the last possible loop
3572 // value. Also note that we already checked for a full range.
3573 APInt One(BitWidth,1);
3574 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3575 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3577 // The exit value should be (End+A)/A.
3578 APInt ExitVal = (End + A).udiv(A);
3579 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3581 // Evaluate at the exit value. If we really did fall out of the valid
3582 // range, then we computed our trip count, otherwise wrap around or other
3583 // things must have happened.
3584 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3585 if (Range.contains(Val->getValue()))
3586 return SE.getCouldNotCompute(); // Something strange happened
3588 // Ensure that the previous value is in the range. This is a sanity check.
3589 assert(Range.contains(
3590 EvaluateConstantChrecAtConstant(this,
3591 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3592 "Linear scev computation is off in a bad way!");
3593 return SE.getConstant(ExitValue);
3594 } else if (isQuadratic()) {
3595 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3596 // quadratic equation to solve it. To do this, we must frame our problem in
3597 // terms of figuring out when zero is crossed, instead of when
3598 // Range.getUpper() is crossed.
3599 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3600 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3601 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3603 // Next, solve the constructed addrec
3604 std::pair<SCEVHandle,SCEVHandle> Roots =
3605 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3606 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3607 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3609 // Pick the smallest positive root value.
3610 if (ConstantInt *CB =
3611 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3612 R1->getValue(), R2->getValue()))) {
3613 if (CB->getZExtValue() == false)
3614 std::swap(R1, R2); // R1 is the minimum root now.
3616 // Make sure the root is not off by one. The returned iteration should
3617 // not be in the range, but the previous one should be. When solving
3618 // for "X*X < 5", for example, we should not return a root of 2.
3619 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3622 if (Range.contains(R1Val->getValue())) {
3623 // The next iteration must be out of the range...
3624 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3626 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3627 if (!Range.contains(R1Val->getValue()))
3628 return SE.getConstant(NextVal);
3629 return SE.getCouldNotCompute(); // Something strange happened
3632 // If R1 was not in the range, then it is a good return value. Make
3633 // sure that R1-1 WAS in the range though, just in case.
3634 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3635 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3636 if (Range.contains(R1Val->getValue()))
3638 return SE.getCouldNotCompute(); // Something strange happened
3643 return SE.getCouldNotCompute();
3648 //===----------------------------------------------------------------------===//
3649 // SCEVCallbackVH Class Implementation
3650 //===----------------------------------------------------------------------===//
3652 void SCEVCallbackVH::deleted() {
3653 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3654 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
3655 SE->ConstantEvolutionLoopExitValue.erase(PN);
3656 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
3657 SE->ValuesAtScopes.erase(I);
3658 SE->Scalars.erase(getValPtr());
3659 // this now dangles!
3662 void SCEVCallbackVH::allUsesReplacedWith(Value *) {
3663 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3665 // Forget all the expressions associated with users of the old value,
3666 // so that future queries will recompute the expressions using the new
3668 SmallVector<User *, 16> Worklist;
3669 Value *Old = getValPtr();
3670 bool DeleteOld = false;
3671 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
3673 Worklist.push_back(*UI);
3674 while (!Worklist.empty()) {
3675 User *U = Worklist.pop_back_val();
3676 // Deleting the Old value will cause this to dangle. Postpone
3677 // that until everything else is done.
3682 if (PHINode *PN = dyn_cast<PHINode>(U))
3683 SE->ConstantEvolutionLoopExitValue.erase(PN);
3684 if (Instruction *I = dyn_cast<Instruction>(U))
3685 SE->ValuesAtScopes.erase(I);
3686 if (SE->Scalars.erase(U))
3687 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
3689 Worklist.push_back(*UI);
3692 if (PHINode *PN = dyn_cast<PHINode>(Old))
3693 SE->ConstantEvolutionLoopExitValue.erase(PN);
3694 if (Instruction *I = dyn_cast<Instruction>(Old))
3695 SE->ValuesAtScopes.erase(I);
3696 SE->Scalars.erase(Old);
3697 // this now dangles!
3702 SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
3703 : CallbackVH(V), SE(se) {}
3705 //===----------------------------------------------------------------------===//
3706 // ScalarEvolution Class Implementation
3707 //===----------------------------------------------------------------------===//
3709 ScalarEvolution::ScalarEvolution()
3710 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) {
3713 bool ScalarEvolution::runOnFunction(Function &F) {
3715 LI = &getAnalysis<LoopInfo>();
3716 TD = getAnalysisIfAvailable<TargetData>();
3720 void ScalarEvolution::releaseMemory() {
3722 BackedgeTakenCounts.clear();
3723 ConstantEvolutionLoopExitValue.clear();
3724 ValuesAtScopes.clear();
3727 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3728 AU.setPreservesAll();
3729 AU.addRequiredTransitive<LoopInfo>();
3732 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3733 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3736 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3738 // Print all inner loops first
3739 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3740 PrintLoopInfo(OS, SE, *I);
3742 OS << "Loop " << L->getHeader()->getName() << ": ";
3744 SmallVector<BasicBlock*, 8> ExitBlocks;
3745 L->getExitBlocks(ExitBlocks);
3746 if (ExitBlocks.size() != 1)
3747 OS << "<multiple exits> ";
3749 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3750 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3752 OS << "Unpredictable backedge-taken count. ";
3758 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3759 // ScalarEvolution's implementaiton of the print method is to print
3760 // out SCEV values of all instructions that are interesting. Doing
3761 // this potentially causes it to create new SCEV objects though,
3762 // which technically conflicts with the const qualifier. This isn't
3763 // observable from outside the class though (the hasSCEV function
3764 // notwithstanding), so casting away the const isn't dangerous.
3765 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3767 OS << "Classifying expressions for: " << F->getName() << "\n";
3768 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3769 if (isSCEVable(I->getType())) {
3772 SCEVHandle SV = SE.getSCEV(&*I);
3776 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3778 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3779 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3780 OS << "<<Unknown>>";
3790 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3791 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3792 PrintLoopInfo(OS, &SE, *I);
3795 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3796 raw_os_ostream OS(o);