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 const SCEV*
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/Analysis/ValueTracking.h"
72 #include "llvm/Assembly/Writer.h"
73 #include "llvm/Target/TargetData.h"
74 #include "llvm/Support/CommandLine.h"
75 #include "llvm/Support/Compiler.h"
76 #include "llvm/Support/ConstantRange.h"
77 #include "llvm/Support/GetElementPtrTypeIterator.h"
78 #include "llvm/Support/InstIterator.h"
79 #include "llvm/Support/ManagedStatic.h"
80 #include "llvm/Support/MathExtras.h"
81 #include "llvm/Support/raw_ostream.h"
82 #include "llvm/ADT/Statistic.h"
83 #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(const ScalarEvolution* p) :
137 SCEV(scCouldNotCompute, p) {}
138 SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
140 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
141 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
145 const Type *SCEVCouldNotCompute::getType() const {
146 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
150 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
151 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
155 const SCEV* SCEVCouldNotCompute::
156 replaceSymbolicValuesWithConcrete(const SCEV* Sym,
158 ScalarEvolution &SE) const {
162 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
163 OS << "***COULDNOTCOMPUTE***";
166 bool SCEVCouldNotCompute::classof(const SCEV *S) {
167 return S->getSCEVType() == scCouldNotCompute;
171 // SCEVConstants - Only allow the creation of one SCEVConstant for any
172 // particular value. Don't use a const SCEV* here, or else the object will
175 const SCEV* ScalarEvolution::getConstant(ConstantInt *V) {
176 SCEVConstant *&R = SCEVConstants[V];
177 if (R == 0) R = new SCEVConstant(V, this);
181 const SCEV* ScalarEvolution::getConstant(const APInt& Val) {
182 return getConstant(ConstantInt::get(Val));
186 ScalarEvolution::getConstant(const Type *Ty, uint64_t V, bool isSigned) {
187 return getConstant(ConstantInt::get(cast<IntegerType>(Ty), V, isSigned));
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 SCEV* op, const Type *ty,
198 const ScalarEvolution* p)
199 : SCEV(SCEVTy, p), Op(op), Ty(ty) {}
201 SCEVCastExpr::~SCEVCastExpr() {}
203 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
204 return Op->dominates(BB, DT);
207 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
208 // particular input. Don't use a const SCEV* here, or else the object will
211 SCEVTruncateExpr::SCEVTruncateExpr(const SCEV* op, const Type *ty,
212 const ScalarEvolution* p)
213 : SCEVCastExpr(scTruncate, op, ty, p) {
214 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
215 (Ty->isInteger() || isa<PointerType>(Ty)) &&
216 "Cannot truncate non-integer value!");
220 void SCEVTruncateExpr::print(raw_ostream &OS) const {
221 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
224 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
225 // particular input. Don't use a const SCEV* here, or else the object will never
228 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEV* op, const Type *ty,
229 const ScalarEvolution* p)
230 : SCEVCastExpr(scZeroExtend, op, ty, p) {
231 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
232 (Ty->isInteger() || isa<PointerType>(Ty)) &&
233 "Cannot zero extend non-integer value!");
236 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
237 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
240 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
241 // particular input. Don't use a const SCEV* here, or else the object will never
244 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEV* op, const Type *ty,
245 const ScalarEvolution* p)
246 : SCEVCastExpr(scSignExtend, op, ty, p) {
247 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
248 (Ty->isInteger() || isa<PointerType>(Ty)) &&
249 "Cannot sign extend non-integer value!");
252 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
253 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
256 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
257 // particular input. Don't use a const SCEV* here, or else the object will never
260 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
261 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
262 const char *OpStr = getOperationStr();
263 OS << "(" << *Operands[0];
264 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
265 OS << OpStr << *Operands[i];
269 const SCEV* SCEVCommutativeExpr::
270 replaceSymbolicValuesWithConcrete(const SCEV* Sym,
272 ScalarEvolution &SE) const {
273 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
275 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
276 if (H != getOperand(i)) {
277 SmallVector<const SCEV*, 8> NewOps;
278 NewOps.reserve(getNumOperands());
279 for (unsigned j = 0; j != i; ++j)
280 NewOps.push_back(getOperand(j));
282 for (++i; i != e; ++i)
283 NewOps.push_back(getOperand(i)->
284 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
286 if (isa<SCEVAddExpr>(this))
287 return SE.getAddExpr(NewOps);
288 else if (isa<SCEVMulExpr>(this))
289 return SE.getMulExpr(NewOps);
290 else if (isa<SCEVSMaxExpr>(this))
291 return SE.getSMaxExpr(NewOps);
292 else if (isa<SCEVUMaxExpr>(this))
293 return SE.getUMaxExpr(NewOps);
295 assert(0 && "Unknown commutative expr!");
301 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
302 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
303 if (!getOperand(i)->dominates(BB, DT))
310 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
311 // input. Don't use a const SCEV* here, or else the object will never be
314 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
315 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
318 void SCEVUDivExpr::print(raw_ostream &OS) const {
319 OS << "(" << *LHS << " /u " << *RHS << ")";
322 const Type *SCEVUDivExpr::getType() const {
323 // In most cases the types of LHS and RHS will be the same, but in some
324 // crazy cases one or the other may be a pointer. ScalarEvolution doesn't
325 // depend on the type for correctness, but handling types carefully can
326 // avoid extra casts in the SCEVExpander. The LHS is more likely to be
327 // a pointer type than the RHS, so use the RHS' type here.
328 return RHS->getType();
331 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
332 // particular input. Don't use a const SCEV* here, or else the object will never
335 const SCEV* SCEVAddRecExpr::
336 replaceSymbolicValuesWithConcrete(const SCEV* Sym,
338 ScalarEvolution &SE) const {
339 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
341 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
342 if (H != getOperand(i)) {
343 SmallVector<const SCEV*, 8> NewOps;
344 NewOps.reserve(getNumOperands());
345 for (unsigned j = 0; j != i; ++j)
346 NewOps.push_back(getOperand(j));
348 for (++i; i != e; ++i)
349 NewOps.push_back(getOperand(i)->
350 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
352 return SE.getAddRecExpr(NewOps, L);
359 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
360 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
361 // contain L and if the start is invariant.
362 // Add recurrences are never invariant in the function-body (null loop).
364 !QueryLoop->contains(L->getHeader()) &&
365 getOperand(0)->isLoopInvariant(QueryLoop);
369 void SCEVAddRecExpr::print(raw_ostream &OS) const {
370 OS << "{" << *Operands[0];
371 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
372 OS << ",+," << *Operands[i];
373 OS << "}<" << L->getHeader()->getName() + ">";
376 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
377 // value. Don't use a const SCEV* here, or else the object will never be
380 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
381 // All non-instruction values are loop invariant. All instructions are loop
382 // invariant if they are not contained in the specified loop.
383 // Instructions are never considered invariant in the function body
384 // (null loop) because they are defined within the "loop".
385 if (Instruction *I = dyn_cast<Instruction>(V))
386 return L && !L->contains(I->getParent());
390 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
391 if (Instruction *I = dyn_cast<Instruction>(getValue()))
392 return DT->dominates(I->getParent(), BB);
396 const Type *SCEVUnknown::getType() const {
400 void SCEVUnknown::print(raw_ostream &OS) const {
401 WriteAsOperand(OS, V, false);
404 //===----------------------------------------------------------------------===//
406 //===----------------------------------------------------------------------===//
409 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
410 /// than the complexity of the RHS. This comparator is used to canonicalize
412 class VISIBILITY_HIDDEN SCEVComplexityCompare {
415 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
417 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
418 // Primarily, sort the SCEVs by their getSCEVType().
419 if (LHS->getSCEVType() != RHS->getSCEVType())
420 return LHS->getSCEVType() < RHS->getSCEVType();
422 // Aside from the getSCEVType() ordering, the particular ordering
423 // isn't very important except that it's beneficial to be consistent,
424 // so that (a + b) and (b + a) don't end up as different expressions.
426 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
427 // not as complete as it could be.
428 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
429 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
431 // Order pointer values after integer values. This helps SCEVExpander
433 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
435 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
438 // Compare getValueID values.
439 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
440 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
442 // Sort arguments by their position.
443 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
444 const Argument *RA = cast<Argument>(RU->getValue());
445 return LA->getArgNo() < RA->getArgNo();
448 // For instructions, compare their loop depth, and their opcode.
449 // This is pretty loose.
450 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
451 Instruction *RV = cast<Instruction>(RU->getValue());
453 // Compare loop depths.
454 if (LI->getLoopDepth(LV->getParent()) !=
455 LI->getLoopDepth(RV->getParent()))
456 return LI->getLoopDepth(LV->getParent()) <
457 LI->getLoopDepth(RV->getParent());
460 if (LV->getOpcode() != RV->getOpcode())
461 return LV->getOpcode() < RV->getOpcode();
463 // Compare the number of operands.
464 if (LV->getNumOperands() != RV->getNumOperands())
465 return LV->getNumOperands() < RV->getNumOperands();
471 // Compare constant values.
472 if (const SCEVConstant *LC = dyn_cast<SCEVConstant>(LHS)) {
473 const SCEVConstant *RC = cast<SCEVConstant>(RHS);
474 return LC->getValue()->getValue().ult(RC->getValue()->getValue());
477 // Compare addrec loop depths.
478 if (const SCEVAddRecExpr *LA = dyn_cast<SCEVAddRecExpr>(LHS)) {
479 const SCEVAddRecExpr *RA = cast<SCEVAddRecExpr>(RHS);
480 if (LA->getLoop()->getLoopDepth() != RA->getLoop()->getLoopDepth())
481 return LA->getLoop()->getLoopDepth() < RA->getLoop()->getLoopDepth();
484 // Lexicographically compare n-ary expressions.
485 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
486 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
487 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
488 if (i >= RC->getNumOperands())
490 if (operator()(LC->getOperand(i), RC->getOperand(i)))
492 if (operator()(RC->getOperand(i), LC->getOperand(i)))
495 return LC->getNumOperands() < RC->getNumOperands();
498 // Lexicographically compare udiv expressions.
499 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
500 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
501 if (operator()(LC->getLHS(), RC->getLHS()))
503 if (operator()(RC->getLHS(), LC->getLHS()))
505 if (operator()(LC->getRHS(), RC->getRHS()))
507 if (operator()(RC->getRHS(), LC->getRHS()))
512 // Compare cast expressions by operand.
513 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
514 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
515 return operator()(LC->getOperand(), RC->getOperand());
518 assert(0 && "Unknown SCEV kind!");
524 /// GroupByComplexity - Given a list of SCEV objects, order them by their
525 /// complexity, and group objects of the same complexity together by value.
526 /// When this routine is finished, we know that any duplicates in the vector are
527 /// consecutive and that complexity is monotonically increasing.
529 /// Note that we go take special precautions to ensure that we get determinstic
530 /// results from this routine. In other words, we don't want the results of
531 /// this to depend on where the addresses of various SCEV objects happened to
534 static void GroupByComplexity(SmallVectorImpl<const SCEV*> &Ops,
536 if (Ops.size() < 2) return; // Noop
537 if (Ops.size() == 2) {
538 // This is the common case, which also happens to be trivially simple.
540 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
541 std::swap(Ops[0], Ops[1]);
545 // Do the rough sort by complexity.
546 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
548 // Now that we are sorted by complexity, group elements of the same
549 // complexity. Note that this is, at worst, N^2, but the vector is likely to
550 // be extremely short in practice. Note that we take this approach because we
551 // do not want to depend on the addresses of the objects we are grouping.
552 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
553 const SCEV *S = Ops[i];
554 unsigned Complexity = S->getSCEVType();
556 // If there are any objects of the same complexity and same value as this
558 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
559 if (Ops[j] == S) { // Found a duplicate.
560 // Move it to immediately after i'th element.
561 std::swap(Ops[i+1], Ops[j]);
562 ++i; // no need to rescan it.
563 if (i == e-2) return; // Done!
571 //===----------------------------------------------------------------------===//
572 // Simple SCEV method implementations
573 //===----------------------------------------------------------------------===//
575 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
577 static const SCEV* BinomialCoefficient(const SCEV* It, unsigned K,
579 const Type* ResultTy) {
580 // Handle the simplest case efficiently.
582 return SE.getTruncateOrZeroExtend(It, ResultTy);
584 // We are using the following formula for BC(It, K):
586 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
588 // Suppose, W is the bitwidth of the return value. We must be prepared for
589 // overflow. Hence, we must assure that the result of our computation is
590 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
591 // safe in modular arithmetic.
593 // However, this code doesn't use exactly that formula; the formula it uses
594 // is something like the following, where T is the number of factors of 2 in
595 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
598 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
600 // This formula is trivially equivalent to the previous formula. However,
601 // this formula can be implemented much more efficiently. The trick is that
602 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
603 // arithmetic. To do exact division in modular arithmetic, all we have
604 // to do is multiply by the inverse. Therefore, this step can be done at
607 // The next issue is how to safely do the division by 2^T. The way this
608 // is done is by doing the multiplication step at a width of at least W + T
609 // bits. This way, the bottom W+T bits of the product are accurate. Then,
610 // when we perform the division by 2^T (which is equivalent to a right shift
611 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
612 // truncated out after the division by 2^T.
614 // In comparison to just directly using the first formula, this technique
615 // is much more efficient; using the first formula requires W * K bits,
616 // but this formula less than W + K bits. Also, the first formula requires
617 // a division step, whereas this formula only requires multiplies and shifts.
619 // It doesn't matter whether the subtraction step is done in the calculation
620 // width or the input iteration count's width; if the subtraction overflows,
621 // the result must be zero anyway. We prefer here to do it in the width of
622 // the induction variable because it helps a lot for certain cases; CodeGen
623 // isn't smart enough to ignore the overflow, which leads to much less
624 // efficient code if the width of the subtraction is wider than the native
627 // (It's possible to not widen at all by pulling out factors of 2 before
628 // the multiplication; for example, K=2 can be calculated as
629 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
630 // extra arithmetic, so it's not an obvious win, and it gets
631 // much more complicated for K > 3.)
633 // Protection from insane SCEVs; this bound is conservative,
634 // but it probably doesn't matter.
636 return SE.getCouldNotCompute();
638 unsigned W = SE.getTypeSizeInBits(ResultTy);
640 // Calculate K! / 2^T and T; we divide out the factors of two before
641 // multiplying for calculating K! / 2^T to avoid overflow.
642 // Other overflow doesn't matter because we only care about the bottom
643 // W bits of the result.
644 APInt OddFactorial(W, 1);
646 for (unsigned i = 3; i <= K; ++i) {
648 unsigned TwoFactors = Mult.countTrailingZeros();
650 Mult = Mult.lshr(TwoFactors);
651 OddFactorial *= Mult;
654 // We need at least W + T bits for the multiplication step
655 unsigned CalculationBits = W + T;
657 // Calcuate 2^T, at width T+W.
658 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
660 // Calculate the multiplicative inverse of K! / 2^T;
661 // this multiplication factor will perform the exact division by
663 APInt Mod = APInt::getSignedMinValue(W+1);
664 APInt MultiplyFactor = OddFactorial.zext(W+1);
665 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
666 MultiplyFactor = MultiplyFactor.trunc(W);
668 // Calculate the product, at width T+W
669 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
670 const SCEV* Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
671 for (unsigned i = 1; i != K; ++i) {
672 const SCEV* S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
673 Dividend = SE.getMulExpr(Dividend,
674 SE.getTruncateOrZeroExtend(S, CalculationTy));
678 const SCEV* DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
680 // Truncate the result, and divide by K! / 2^T.
682 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
683 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
686 /// evaluateAtIteration - Return the value of this chain of recurrences at
687 /// the specified iteration number. We can evaluate this recurrence by
688 /// multiplying each element in the chain by the binomial coefficient
689 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
691 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
693 /// where BC(It, k) stands for binomial coefficient.
695 const SCEV* SCEVAddRecExpr::evaluateAtIteration(const SCEV* It,
696 ScalarEvolution &SE) const {
697 const SCEV* Result = getStart();
698 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
699 // The computation is correct in the face of overflow provided that the
700 // multiplication is performed _after_ the evaluation of the binomial
702 const SCEV* Coeff = BinomialCoefficient(It, i, SE, getType());
703 if (isa<SCEVCouldNotCompute>(Coeff))
706 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
711 //===----------------------------------------------------------------------===//
712 // SCEV Expression folder implementations
713 //===----------------------------------------------------------------------===//
715 const SCEV* ScalarEvolution::getTruncateExpr(const SCEV* Op,
717 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
718 "This is not a truncating conversion!");
719 assert(isSCEVable(Ty) &&
720 "This is not a conversion to a SCEVable type!");
721 Ty = getEffectiveSCEVType(Ty);
723 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
725 ConstantExpr::getTrunc(SC->getValue(), Ty));
727 // trunc(trunc(x)) --> trunc(x)
728 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
729 return getTruncateExpr(ST->getOperand(), Ty);
731 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
732 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
733 return getTruncateOrSignExtend(SS->getOperand(), Ty);
735 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
736 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
737 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
739 // If the input value is a chrec scev, truncate the chrec's operands.
740 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
741 SmallVector<const SCEV*, 4> Operands;
742 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
743 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
744 return getAddRecExpr(Operands, AddRec->getLoop());
747 SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)];
748 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty, this);
752 const SCEV* ScalarEvolution::getZeroExtendExpr(const SCEV* Op,
754 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
755 "This is not an extending conversion!");
756 assert(isSCEVable(Ty) &&
757 "This is not a conversion to a SCEVable type!");
758 Ty = getEffectiveSCEVType(Ty);
760 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
761 const Type *IntTy = getEffectiveSCEVType(Ty);
762 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
763 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
764 return getUnknown(C);
767 // zext(zext(x)) --> zext(x)
768 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
769 return getZeroExtendExpr(SZ->getOperand(), Ty);
771 // If the input value is a chrec scev, and we can prove that the value
772 // did not overflow the old, smaller, value, we can zero extend all of the
773 // operands (often constants). This allows analysis of something like
774 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
775 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
776 if (AR->isAffine()) {
777 // Check whether the backedge-taken count is SCEVCouldNotCompute.
778 // Note that this serves two purposes: It filters out loops that are
779 // simply not analyzable, and it covers the case where this code is
780 // being called from within backedge-taken count analysis, such that
781 // attempting to ask for the backedge-taken count would likely result
782 // in infinite recursion. In the later case, the analysis code will
783 // cope with a conservative value, and it will take care to purge
784 // that value once it has finished.
785 const SCEV* MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
786 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
787 // Manually compute the final value for AR, checking for
789 const SCEV* Start = AR->getStart();
790 const SCEV* Step = AR->getStepRecurrence(*this);
792 // Check whether the backedge-taken count can be losslessly casted to
793 // the addrec's type. The count is always unsigned.
794 const SCEV* CastedMaxBECount =
795 getTruncateOrZeroExtend(MaxBECount, Start->getType());
796 const SCEV* RecastedMaxBECount =
797 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
798 if (MaxBECount == RecastedMaxBECount) {
800 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
801 // Check whether Start+Step*MaxBECount has no unsigned overflow.
803 getMulExpr(CastedMaxBECount,
804 getTruncateOrZeroExtend(Step, Start->getType()));
805 const SCEV* Add = getAddExpr(Start, ZMul);
806 const SCEV* OperandExtendedAdd =
807 getAddExpr(getZeroExtendExpr(Start, WideTy),
808 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
809 getZeroExtendExpr(Step, WideTy)));
810 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
811 // Return the expression with the addrec on the outside.
812 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
813 getZeroExtendExpr(Step, Ty),
816 // Similar to above, only this time treat the step value as signed.
817 // This covers loops that count down.
819 getMulExpr(CastedMaxBECount,
820 getTruncateOrSignExtend(Step, Start->getType()));
821 Add = getAddExpr(Start, SMul);
823 getAddExpr(getZeroExtendExpr(Start, WideTy),
824 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
825 getSignExtendExpr(Step, WideTy)));
826 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
827 // Return the expression with the addrec on the outside.
828 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
829 getSignExtendExpr(Step, Ty),
835 SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)];
836 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty, this);
840 const SCEV* ScalarEvolution::getSignExtendExpr(const SCEV* Op,
842 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
843 "This is not an extending conversion!");
844 assert(isSCEVable(Ty) &&
845 "This is not a conversion to a SCEVable type!");
846 Ty = getEffectiveSCEVType(Ty);
848 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
849 const Type *IntTy = getEffectiveSCEVType(Ty);
850 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
851 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
852 return getUnknown(C);
855 // sext(sext(x)) --> sext(x)
856 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
857 return getSignExtendExpr(SS->getOperand(), Ty);
859 // If the input value is a chrec scev, and we can prove that the value
860 // did not overflow the old, smaller, value, we can sign extend all of the
861 // operands (often constants). This allows analysis of something like
862 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
863 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
864 if (AR->isAffine()) {
865 // Check whether the backedge-taken count is SCEVCouldNotCompute.
866 // Note that this serves two purposes: It filters out loops that are
867 // simply not analyzable, and it covers the case where this code is
868 // being called from within backedge-taken count analysis, such that
869 // attempting to ask for the backedge-taken count would likely result
870 // in infinite recursion. In the later case, the analysis code will
871 // cope with a conservative value, and it will take care to purge
872 // that value once it has finished.
873 const SCEV* MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
874 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
875 // Manually compute the final value for AR, checking for
877 const SCEV* Start = AR->getStart();
878 const SCEV* Step = AR->getStepRecurrence(*this);
880 // Check whether the backedge-taken count can be losslessly casted to
881 // the addrec's type. The count is always unsigned.
882 const SCEV* CastedMaxBECount =
883 getTruncateOrZeroExtend(MaxBECount, Start->getType());
884 const SCEV* RecastedMaxBECount =
885 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
886 if (MaxBECount == RecastedMaxBECount) {
888 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
889 // Check whether Start+Step*MaxBECount has no signed overflow.
891 getMulExpr(CastedMaxBECount,
892 getTruncateOrSignExtend(Step, Start->getType()));
893 const SCEV* Add = getAddExpr(Start, SMul);
894 const SCEV* OperandExtendedAdd =
895 getAddExpr(getSignExtendExpr(Start, WideTy),
896 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
897 getSignExtendExpr(Step, WideTy)));
898 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
899 // Return the expression with the addrec on the outside.
900 return getAddRecExpr(getSignExtendExpr(Start, Ty),
901 getSignExtendExpr(Step, Ty),
907 SCEVSignExtendExpr *&Result = SCEVSignExtends[std::make_pair(Op, Ty)];
908 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty, this);
912 /// getAnyExtendExpr - Return a SCEV for the given operand extended with
913 /// unspecified bits out to the given type.
915 const SCEV* ScalarEvolution::getAnyExtendExpr(const SCEV* Op,
917 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
918 "This is not an extending conversion!");
919 assert(isSCEVable(Ty) &&
920 "This is not a conversion to a SCEVable type!");
921 Ty = getEffectiveSCEVType(Ty);
923 // Sign-extend negative constants.
924 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
925 if (SC->getValue()->getValue().isNegative())
926 return getSignExtendExpr(Op, Ty);
928 // Peel off a truncate cast.
929 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Op)) {
930 const SCEV* NewOp = T->getOperand();
931 if (getTypeSizeInBits(NewOp->getType()) < getTypeSizeInBits(Ty))
932 return getAnyExtendExpr(NewOp, Ty);
933 return getTruncateOrNoop(NewOp, Ty);
936 // Next try a zext cast. If the cast is folded, use it.
937 const SCEV* ZExt = getZeroExtendExpr(Op, Ty);
938 if (!isa<SCEVZeroExtendExpr>(ZExt))
941 // Next try a sext cast. If the cast is folded, use it.
942 const SCEV* SExt = getSignExtendExpr(Op, Ty);
943 if (!isa<SCEVSignExtendExpr>(SExt))
946 // If the expression is obviously signed, use the sext cast value.
947 if (isa<SCEVSMaxExpr>(Op))
950 // Absent any other information, use the zext cast value.
954 /// CollectAddOperandsWithScales - Process the given Ops list, which is
955 /// a list of operands to be added under the given scale, update the given
956 /// map. This is a helper function for getAddRecExpr. As an example of
957 /// what it does, given a sequence of operands that would form an add
958 /// expression like this:
960 /// m + n + 13 + (A * (o + p + (B * q + m + 29))) + r + (-1 * r)
962 /// where A and B are constants, update the map with these values:
964 /// (m, 1+A*B), (n, 1), (o, A), (p, A), (q, A*B), (r, 0)
966 /// and add 13 + A*B*29 to AccumulatedConstant.
967 /// This will allow getAddRecExpr to produce this:
969 /// 13+A*B*29 + n + (m * (1+A*B)) + ((o + p) * A) + (q * A*B)
971 /// This form often exposes folding opportunities that are hidden in
972 /// the original operand list.
974 /// Return true iff it appears that any interesting folding opportunities
975 /// may be exposed. This helps getAddRecExpr short-circuit extra work in
976 /// the common case where no interesting opportunities are present, and
977 /// is also used as a check to avoid infinite recursion.
980 CollectAddOperandsWithScales(DenseMap<const SCEV*, APInt> &M,
981 SmallVector<const SCEV*, 8> &NewOps,
982 APInt &AccumulatedConstant,
983 const SmallVectorImpl<const SCEV*> &Ops,
985 ScalarEvolution &SE) {
986 bool Interesting = false;
988 // Iterate over the add operands.
989 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
990 const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[i]);
991 if (Mul && isa<SCEVConstant>(Mul->getOperand(0))) {
993 Scale * cast<SCEVConstant>(Mul->getOperand(0))->getValue()->getValue();
994 if (Mul->getNumOperands() == 2 && isa<SCEVAddExpr>(Mul->getOperand(1))) {
995 // A multiplication of a constant with another add; recurse.
997 CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
998 cast<SCEVAddExpr>(Mul->getOperand(1))
1002 // A multiplication of a constant with some other value. Update
1004 SmallVector<const SCEV*, 4> MulOps(Mul->op_begin()+1, Mul->op_end());
1005 const SCEV* Key = SE.getMulExpr(MulOps);
1006 std::pair<DenseMap<const SCEV*, APInt>::iterator, bool> Pair =
1007 M.insert(std::make_pair(Key, APInt()));
1009 Pair.first->second = NewScale;
1010 NewOps.push_back(Pair.first->first);
1012 Pair.first->second += NewScale;
1013 // The map already had an entry for this value, which may indicate
1014 // a folding opportunity.
1018 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1019 // Pull a buried constant out to the outside.
1020 if (Scale != 1 || AccumulatedConstant != 0 || C->isZero())
1022 AccumulatedConstant += Scale * C->getValue()->getValue();
1024 // An ordinary operand. Update the map.
1025 std::pair<DenseMap<const SCEV*, APInt>::iterator, bool> Pair =
1026 M.insert(std::make_pair(Ops[i], APInt()));
1028 Pair.first->second = Scale;
1029 NewOps.push_back(Pair.first->first);
1031 Pair.first->second += Scale;
1032 // The map already had an entry for this value, which may indicate
1033 // a folding opportunity.
1043 struct APIntCompare {
1044 bool operator()(const APInt &LHS, const APInt &RHS) const {
1045 return LHS.ult(RHS);
1050 /// getAddExpr - Get a canonical add expression, or something simpler if
1052 const SCEV* ScalarEvolution::getAddExpr(SmallVectorImpl<const SCEV*> &Ops) {
1053 assert(!Ops.empty() && "Cannot get empty add!");
1054 if (Ops.size() == 1) return Ops[0];
1056 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1057 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1058 getEffectiveSCEVType(Ops[0]->getType()) &&
1059 "SCEVAddExpr operand types don't match!");
1062 // Sort by complexity, this groups all similar expression types together.
1063 GroupByComplexity(Ops, LI);
1065 // If there are any constants, fold them together.
1067 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1069 assert(Idx < Ops.size());
1070 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1071 // We found two constants, fold them together!
1072 Ops[0] = getConstant(LHSC->getValue()->getValue() +
1073 RHSC->getValue()->getValue());
1074 if (Ops.size() == 2) return Ops[0];
1075 Ops.erase(Ops.begin()+1); // Erase the folded element
1076 LHSC = cast<SCEVConstant>(Ops[0]);
1079 // If we are left with a constant zero being added, strip it off.
1080 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1081 Ops.erase(Ops.begin());
1086 if (Ops.size() == 1) return Ops[0];
1088 // Okay, check to see if the same value occurs in the operand list twice. If
1089 // so, merge them together into an multiply expression. Since we sorted the
1090 // list, these values are required to be adjacent.
1091 const Type *Ty = Ops[0]->getType();
1092 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1093 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
1094 // Found a match, merge the two values into a multiply, and add any
1095 // remaining values to the result.
1096 const SCEV* Two = getIntegerSCEV(2, Ty);
1097 const SCEV* Mul = getMulExpr(Ops[i], Two);
1098 if (Ops.size() == 2)
1100 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
1102 return getAddExpr(Ops);
1105 // Check for truncates. If all the operands are truncated from the same
1106 // type, see if factoring out the truncate would permit the result to be
1107 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
1108 // if the contents of the resulting outer trunc fold to something simple.
1109 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
1110 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
1111 const Type *DstType = Trunc->getType();
1112 const Type *SrcType = Trunc->getOperand()->getType();
1113 SmallVector<const SCEV*, 8> LargeOps;
1115 // Check all the operands to see if they can be represented in the
1116 // source type of the truncate.
1117 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1118 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1119 if (T->getOperand()->getType() != SrcType) {
1123 LargeOps.push_back(T->getOperand());
1124 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1125 // This could be either sign or zero extension, but sign extension
1126 // is much more likely to be foldable here.
1127 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1128 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1129 SmallVector<const SCEV*, 8> LargeMulOps;
1130 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1131 if (const SCEVTruncateExpr *T =
1132 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1133 if (T->getOperand()->getType() != SrcType) {
1137 LargeMulOps.push_back(T->getOperand());
1138 } else if (const SCEVConstant *C =
1139 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1140 // This could be either sign or zero extension, but sign extension
1141 // is much more likely to be foldable here.
1142 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1149 LargeOps.push_back(getMulExpr(LargeMulOps));
1156 // Evaluate the expression in the larger type.
1157 const SCEV* Fold = getAddExpr(LargeOps);
1158 // If it folds to something simple, use it. Otherwise, don't.
1159 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1160 return getTruncateExpr(Fold, DstType);
1164 // Skip past any other cast SCEVs.
1165 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1168 // If there are add operands they would be next.
1169 if (Idx < Ops.size()) {
1170 bool DeletedAdd = false;
1171 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1172 // If we have an add, expand the add operands onto the end of the operands
1174 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1175 Ops.erase(Ops.begin()+Idx);
1179 // If we deleted at least one add, we added operands to the end of the list,
1180 // and they are not necessarily sorted. Recurse to resort and resimplify
1181 // any operands we just aquired.
1183 return getAddExpr(Ops);
1186 // Skip over the add expression until we get to a multiply.
1187 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1190 // Check to see if there are any folding opportunities present with
1191 // operands multiplied by constant values.
1192 if (Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx])) {
1193 uint64_t BitWidth = getTypeSizeInBits(Ty);
1194 DenseMap<const SCEV*, APInt> M;
1195 SmallVector<const SCEV*, 8> NewOps;
1196 APInt AccumulatedConstant(BitWidth, 0);
1197 if (CollectAddOperandsWithScales(M, NewOps, AccumulatedConstant,
1198 Ops, APInt(BitWidth, 1), *this)) {
1199 // Some interesting folding opportunity is present, so its worthwhile to
1200 // re-generate the operands list. Group the operands by constant scale,
1201 // to avoid multiplying by the same constant scale multiple times.
1202 std::map<APInt, SmallVector<const SCEV*, 4>, APIntCompare> MulOpLists;
1203 for (SmallVector<const SCEV*, 8>::iterator I = NewOps.begin(),
1204 E = NewOps.end(); I != E; ++I)
1205 MulOpLists[M.find(*I)->second].push_back(*I);
1206 // Re-generate the operands list.
1208 if (AccumulatedConstant != 0)
1209 Ops.push_back(getConstant(AccumulatedConstant));
1210 for (std::map<APInt, SmallVector<const SCEV*, 4>, APIntCompare>::iterator I =
1211 MulOpLists.begin(), E = MulOpLists.end(); I != E; ++I)
1213 Ops.push_back(getMulExpr(getConstant(I->first), getAddExpr(I->second)));
1215 return getIntegerSCEV(0, Ty);
1216 if (Ops.size() == 1)
1218 return getAddExpr(Ops);
1222 // If we are adding something to a multiply expression, make sure the
1223 // something is not already an operand of the multiply. If so, merge it into
1225 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1226 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1227 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1228 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1229 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1230 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(Ops[AddOp])) {
1231 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1232 const SCEV* InnerMul = Mul->getOperand(MulOp == 0);
1233 if (Mul->getNumOperands() != 2) {
1234 // If the multiply has more than two operands, we must get the
1236 SmallVector<const SCEV*, 4> MulOps(Mul->op_begin(), Mul->op_end());
1237 MulOps.erase(MulOps.begin()+MulOp);
1238 InnerMul = getMulExpr(MulOps);
1240 const SCEV* One = getIntegerSCEV(1, Ty);
1241 const SCEV* AddOne = getAddExpr(InnerMul, One);
1242 const SCEV* OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1243 if (Ops.size() == 2) return OuterMul;
1245 Ops.erase(Ops.begin()+AddOp);
1246 Ops.erase(Ops.begin()+Idx-1);
1248 Ops.erase(Ops.begin()+Idx);
1249 Ops.erase(Ops.begin()+AddOp-1);
1251 Ops.push_back(OuterMul);
1252 return getAddExpr(Ops);
1255 // Check this multiply against other multiplies being added together.
1256 for (unsigned OtherMulIdx = Idx+1;
1257 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1259 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1260 // If MulOp occurs in OtherMul, we can fold the two multiplies
1262 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1263 OMulOp != e; ++OMulOp)
1264 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1265 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1266 const SCEV* InnerMul1 = Mul->getOperand(MulOp == 0);
1267 if (Mul->getNumOperands() != 2) {
1268 SmallVector<const SCEV*, 4> MulOps(Mul->op_begin(), Mul->op_end());
1269 MulOps.erase(MulOps.begin()+MulOp);
1270 InnerMul1 = getMulExpr(MulOps);
1272 const SCEV* InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1273 if (OtherMul->getNumOperands() != 2) {
1274 SmallVector<const SCEV*, 4> MulOps(OtherMul->op_begin(),
1275 OtherMul->op_end());
1276 MulOps.erase(MulOps.begin()+OMulOp);
1277 InnerMul2 = getMulExpr(MulOps);
1279 const SCEV* InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1280 const SCEV* OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1281 if (Ops.size() == 2) return OuterMul;
1282 Ops.erase(Ops.begin()+Idx);
1283 Ops.erase(Ops.begin()+OtherMulIdx-1);
1284 Ops.push_back(OuterMul);
1285 return getAddExpr(Ops);
1291 // If there are any add recurrences in the operands list, see if any other
1292 // added values are loop invariant. If so, we can fold them into the
1294 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1297 // Scan over all recurrences, trying to fold loop invariants into them.
1298 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1299 // Scan all of the other operands to this add and add them to the vector if
1300 // they are loop invariant w.r.t. the recurrence.
1301 SmallVector<const SCEV*, 8> LIOps;
1302 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1303 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1304 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1305 LIOps.push_back(Ops[i]);
1306 Ops.erase(Ops.begin()+i);
1310 // If we found some loop invariants, fold them into the recurrence.
1311 if (!LIOps.empty()) {
1312 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1313 LIOps.push_back(AddRec->getStart());
1315 SmallVector<const SCEV*, 4> AddRecOps(AddRec->op_begin(),
1317 AddRecOps[0] = getAddExpr(LIOps);
1319 const SCEV* NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1320 // If all of the other operands were loop invariant, we are done.
1321 if (Ops.size() == 1) return NewRec;
1323 // Otherwise, add the folded AddRec by the non-liv parts.
1324 for (unsigned i = 0;; ++i)
1325 if (Ops[i] == AddRec) {
1329 return getAddExpr(Ops);
1332 // Okay, if there weren't any loop invariants to be folded, check to see if
1333 // there are multiple AddRec's with the same loop induction variable being
1334 // added together. If so, we can fold them.
1335 for (unsigned OtherIdx = Idx+1;
1336 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1337 if (OtherIdx != Idx) {
1338 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1339 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1340 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1341 SmallVector<const SCEV*, 4> NewOps(AddRec->op_begin(), AddRec->op_end());
1342 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1343 if (i >= NewOps.size()) {
1344 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1345 OtherAddRec->op_end());
1348 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1350 const SCEV* NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1352 if (Ops.size() == 2) return NewAddRec;
1354 Ops.erase(Ops.begin()+Idx);
1355 Ops.erase(Ops.begin()+OtherIdx-1);
1356 Ops.push_back(NewAddRec);
1357 return getAddExpr(Ops);
1361 // Otherwise couldn't fold anything into this recurrence. Move onto the
1365 // Okay, it looks like we really DO need an add expr. Check to see if we
1366 // already have one, otherwise create a new one.
1367 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1368 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr,
1370 if (Result == 0) Result = new SCEVAddExpr(Ops, this);
1375 /// getMulExpr - Get a canonical multiply expression, or something simpler if
1377 const SCEV* ScalarEvolution::getMulExpr(SmallVectorImpl<const SCEV*> &Ops) {
1378 assert(!Ops.empty() && "Cannot get empty mul!");
1380 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1381 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1382 getEffectiveSCEVType(Ops[0]->getType()) &&
1383 "SCEVMulExpr operand types don't match!");
1386 // Sort by complexity, this groups all similar expression types together.
1387 GroupByComplexity(Ops, LI);
1389 // If there are any constants, fold them together.
1391 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1393 // C1*(C2+V) -> C1*C2 + C1*V
1394 if (Ops.size() == 2)
1395 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1396 if (Add->getNumOperands() == 2 &&
1397 isa<SCEVConstant>(Add->getOperand(0)))
1398 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1399 getMulExpr(LHSC, Add->getOperand(1)));
1403 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1404 // We found two constants, fold them together!
1405 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1406 RHSC->getValue()->getValue());
1407 Ops[0] = getConstant(Fold);
1408 Ops.erase(Ops.begin()+1); // Erase the folded element
1409 if (Ops.size() == 1) return Ops[0];
1410 LHSC = cast<SCEVConstant>(Ops[0]);
1413 // If we are left with a constant one being multiplied, strip it off.
1414 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1415 Ops.erase(Ops.begin());
1417 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1418 // If we have a multiply of zero, it will always be zero.
1423 // Skip over the add expression until we get to a multiply.
1424 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1427 if (Ops.size() == 1)
1430 // If there are mul operands inline them all into this expression.
1431 if (Idx < Ops.size()) {
1432 bool DeletedMul = false;
1433 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1434 // If we have an mul, expand the mul operands onto the end of the operands
1436 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1437 Ops.erase(Ops.begin()+Idx);
1441 // If we deleted at least one mul, we added operands to the end of the list,
1442 // and they are not necessarily sorted. Recurse to resort and resimplify
1443 // any operands we just aquired.
1445 return getMulExpr(Ops);
1448 // If there are any add recurrences in the operands list, see if any other
1449 // added values are loop invariant. If so, we can fold them into the
1451 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1454 // Scan over all recurrences, trying to fold loop invariants into them.
1455 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1456 // Scan all of the other operands to this mul and add them to the vector if
1457 // they are loop invariant w.r.t. the recurrence.
1458 SmallVector<const SCEV*, 8> LIOps;
1459 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1460 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1461 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1462 LIOps.push_back(Ops[i]);
1463 Ops.erase(Ops.begin()+i);
1467 // If we found some loop invariants, fold them into the recurrence.
1468 if (!LIOps.empty()) {
1469 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1470 SmallVector<const SCEV*, 4> NewOps;
1471 NewOps.reserve(AddRec->getNumOperands());
1472 if (LIOps.size() == 1) {
1473 const SCEV *Scale = LIOps[0];
1474 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1475 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1477 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1478 SmallVector<const SCEV*, 4> MulOps(LIOps.begin(), LIOps.end());
1479 MulOps.push_back(AddRec->getOperand(i));
1480 NewOps.push_back(getMulExpr(MulOps));
1484 const SCEV* NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1486 // If all of the other operands were loop invariant, we are done.
1487 if (Ops.size() == 1) return NewRec;
1489 // Otherwise, multiply the folded AddRec by the non-liv parts.
1490 for (unsigned i = 0;; ++i)
1491 if (Ops[i] == AddRec) {
1495 return getMulExpr(Ops);
1498 // Okay, if there weren't any loop invariants to be folded, check to see if
1499 // there are multiple AddRec's with the same loop induction variable being
1500 // multiplied together. If so, we can fold them.
1501 for (unsigned OtherIdx = Idx+1;
1502 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1503 if (OtherIdx != Idx) {
1504 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1505 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1506 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1507 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1508 const SCEV* NewStart = getMulExpr(F->getStart(),
1510 const SCEV* B = F->getStepRecurrence(*this);
1511 const SCEV* D = G->getStepRecurrence(*this);
1512 const SCEV* NewStep = getAddExpr(getMulExpr(F, D),
1515 const SCEV* NewAddRec = getAddRecExpr(NewStart, NewStep,
1517 if (Ops.size() == 2) return NewAddRec;
1519 Ops.erase(Ops.begin()+Idx);
1520 Ops.erase(Ops.begin()+OtherIdx-1);
1521 Ops.push_back(NewAddRec);
1522 return getMulExpr(Ops);
1526 // Otherwise couldn't fold anything into this recurrence. Move onto the
1530 // Okay, it looks like we really DO need an mul expr. Check to see if we
1531 // already have one, otherwise create a new one.
1532 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1533 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr,
1536 Result = new SCEVMulExpr(Ops, this);
1540 /// getUDivExpr - Get a canonical multiply expression, or something simpler if
1542 const SCEV* ScalarEvolution::getUDivExpr(const SCEV* LHS,
1544 assert(getEffectiveSCEVType(LHS->getType()) ==
1545 getEffectiveSCEVType(RHS->getType()) &&
1546 "SCEVUDivExpr operand types don't match!");
1548 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1549 if (RHSC->getValue()->equalsInt(1))
1550 return LHS; // X udiv 1 --> x
1552 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1554 // Determine if the division can be folded into the operands of
1556 // TODO: Generalize this to non-constants by using known-bits information.
1557 const Type *Ty = LHS->getType();
1558 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1559 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1560 // For non-power-of-two values, effectively round the value up to the
1561 // nearest power of two.
1562 if (!RHSC->getValue()->getValue().isPowerOf2())
1564 const IntegerType *ExtTy =
1565 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1566 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1567 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1568 if (const SCEVConstant *Step =
1569 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1570 if (!Step->getValue()->getValue()
1571 .urem(RHSC->getValue()->getValue()) &&
1572 getZeroExtendExpr(AR, ExtTy) ==
1573 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1574 getZeroExtendExpr(Step, ExtTy),
1576 SmallVector<const SCEV*, 4> Operands;
1577 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1578 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1579 return getAddRecExpr(Operands, AR->getLoop());
1581 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1582 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1583 SmallVector<const SCEV*, 4> Operands;
1584 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1585 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1586 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1587 // Find an operand that's safely divisible.
1588 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1589 const SCEV* Op = M->getOperand(i);
1590 const SCEV* Div = getUDivExpr(Op, RHSC);
1591 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1592 const SmallVectorImpl<const SCEV*> &MOperands = M->getOperands();
1593 Operands = SmallVector<const SCEV*, 4>(MOperands.begin(),
1596 return getMulExpr(Operands);
1600 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1601 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1602 SmallVector<const SCEV*, 4> Operands;
1603 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1604 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1605 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1607 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1608 const SCEV* Op = getUDivExpr(A->getOperand(i), RHS);
1609 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1611 Operands.push_back(Op);
1613 if (Operands.size() == A->getNumOperands())
1614 return getAddExpr(Operands);
1618 // Fold if both operands are constant.
1619 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1620 Constant *LHSCV = LHSC->getValue();
1621 Constant *RHSCV = RHSC->getValue();
1622 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1626 SCEVUDivExpr *&Result = SCEVUDivs[std::make_pair(LHS, RHS)];
1627 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS, this);
1632 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1633 /// Simplify the expression as much as possible.
1634 const SCEV* ScalarEvolution::getAddRecExpr(const SCEV* Start,
1635 const SCEV* Step, const Loop *L) {
1636 SmallVector<const SCEV*, 4> Operands;
1637 Operands.push_back(Start);
1638 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1639 if (StepChrec->getLoop() == L) {
1640 Operands.insert(Operands.end(), StepChrec->op_begin(),
1641 StepChrec->op_end());
1642 return getAddRecExpr(Operands, L);
1645 Operands.push_back(Step);
1646 return getAddRecExpr(Operands, L);
1649 /// getAddRecExpr - Get an add recurrence expression for the specified loop.
1650 /// Simplify the expression as much as possible.
1651 const SCEV* ScalarEvolution::getAddRecExpr(SmallVectorImpl<const SCEV*> &Operands,
1653 if (Operands.size() == 1) return Operands[0];
1655 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1656 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1657 getEffectiveSCEVType(Operands[0]->getType()) &&
1658 "SCEVAddRecExpr operand types don't match!");
1661 if (Operands.back()->isZero()) {
1662 Operands.pop_back();
1663 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1666 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1667 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1668 const Loop* NestedLoop = NestedAR->getLoop();
1669 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1670 SmallVector<const SCEV*, 4> NestedOperands(NestedAR->op_begin(),
1671 NestedAR->op_end());
1672 Operands[0] = NestedAR->getStart();
1673 NestedOperands[0] = getAddRecExpr(Operands, L);
1674 return getAddRecExpr(NestedOperands, NestedLoop);
1678 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
1679 SCEVAddRecExpr *&Result = SCEVAddRecExprs[std::make_pair(L, SCEVOps)];
1680 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L, this);
1684 const SCEV* ScalarEvolution::getSMaxExpr(const SCEV* LHS,
1686 SmallVector<const SCEV*, 2> Ops;
1689 return getSMaxExpr(Ops);
1693 ScalarEvolution::getSMaxExpr(SmallVectorImpl<const SCEV*> &Ops) {
1694 assert(!Ops.empty() && "Cannot get empty smax!");
1695 if (Ops.size() == 1) return Ops[0];
1697 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1698 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1699 getEffectiveSCEVType(Ops[0]->getType()) &&
1700 "SCEVSMaxExpr operand types don't match!");
1703 // Sort by complexity, this groups all similar expression types together.
1704 GroupByComplexity(Ops, LI);
1706 // If there are any constants, fold them together.
1708 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1710 assert(Idx < Ops.size());
1711 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1712 // We found two constants, fold them together!
1713 ConstantInt *Fold = ConstantInt::get(
1714 APIntOps::smax(LHSC->getValue()->getValue(),
1715 RHSC->getValue()->getValue()));
1716 Ops[0] = getConstant(Fold);
1717 Ops.erase(Ops.begin()+1); // Erase the folded element
1718 if (Ops.size() == 1) return Ops[0];
1719 LHSC = cast<SCEVConstant>(Ops[0]);
1722 // If we are left with a constant -inf, strip it off.
1723 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1724 Ops.erase(Ops.begin());
1729 if (Ops.size() == 1) return Ops[0];
1731 // Find the first SMax
1732 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1735 // Check to see if one of the operands is an SMax. If so, expand its operands
1736 // onto our operand list, and recurse to simplify.
1737 if (Idx < Ops.size()) {
1738 bool DeletedSMax = false;
1739 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1740 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1741 Ops.erase(Ops.begin()+Idx);
1746 return getSMaxExpr(Ops);
1749 // Okay, check to see if the same value occurs in the operand list twice. If
1750 // so, delete one. Since we sorted the list, these values are required to
1752 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1753 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1754 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1758 if (Ops.size() == 1) return Ops[0];
1760 assert(!Ops.empty() && "Reduced smax down to nothing!");
1762 // Okay, it looks like we really DO need an smax expr. Check to see if we
1763 // already have one, otherwise create a new one.
1764 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1765 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scSMaxExpr,
1767 if (Result == 0) Result = new SCEVSMaxExpr(Ops, this);
1771 const SCEV* ScalarEvolution::getUMaxExpr(const SCEV* LHS,
1773 SmallVector<const SCEV*, 2> Ops;
1776 return getUMaxExpr(Ops);
1780 ScalarEvolution::getUMaxExpr(SmallVectorImpl<const SCEV*> &Ops) {
1781 assert(!Ops.empty() && "Cannot get empty umax!");
1782 if (Ops.size() == 1) return Ops[0];
1784 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1785 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1786 getEffectiveSCEVType(Ops[0]->getType()) &&
1787 "SCEVUMaxExpr operand types don't match!");
1790 // Sort by complexity, this groups all similar expression types together.
1791 GroupByComplexity(Ops, LI);
1793 // If there are any constants, fold them together.
1795 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1797 assert(Idx < Ops.size());
1798 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1799 // We found two constants, fold them together!
1800 ConstantInt *Fold = ConstantInt::get(
1801 APIntOps::umax(LHSC->getValue()->getValue(),
1802 RHSC->getValue()->getValue()));
1803 Ops[0] = getConstant(Fold);
1804 Ops.erase(Ops.begin()+1); // Erase the folded element
1805 if (Ops.size() == 1) return Ops[0];
1806 LHSC = cast<SCEVConstant>(Ops[0]);
1809 // If we are left with a constant zero, strip it off.
1810 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1811 Ops.erase(Ops.begin());
1816 if (Ops.size() == 1) return Ops[0];
1818 // Find the first UMax
1819 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1822 // Check to see if one of the operands is a UMax. If so, expand its operands
1823 // onto our operand list, and recurse to simplify.
1824 if (Idx < Ops.size()) {
1825 bool DeletedUMax = false;
1826 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1827 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1828 Ops.erase(Ops.begin()+Idx);
1833 return getUMaxExpr(Ops);
1836 // Okay, check to see if the same value occurs in the operand list twice. If
1837 // so, delete one. Since we sorted the list, these values are required to
1839 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1840 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1841 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1845 if (Ops.size() == 1) return Ops[0];
1847 assert(!Ops.empty() && "Reduced umax down to nothing!");
1849 // Okay, it looks like we really DO need a umax expr. Check to see if we
1850 // already have one, otherwise create a new one.
1851 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1852 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scUMaxExpr,
1854 if (Result == 0) Result = new SCEVUMaxExpr(Ops, this);
1858 const SCEV* ScalarEvolution::getSMinExpr(const SCEV* LHS,
1860 // ~smax(~x, ~y) == smin(x, y).
1861 return getNotSCEV(getSMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
1864 const SCEV* ScalarEvolution::getUMinExpr(const SCEV* LHS,
1866 // ~umax(~x, ~y) == umin(x, y)
1867 return getNotSCEV(getUMaxExpr(getNotSCEV(LHS), getNotSCEV(RHS)));
1870 const SCEV* ScalarEvolution::getUnknown(Value *V) {
1871 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1872 return getConstant(CI);
1873 if (isa<ConstantPointerNull>(V))
1874 return getIntegerSCEV(0, V->getType());
1875 SCEVUnknown *&Result = SCEVUnknowns[V];
1876 if (Result == 0) Result = new SCEVUnknown(V, this);
1880 //===----------------------------------------------------------------------===//
1881 // Basic SCEV Analysis and PHI Idiom Recognition Code
1884 /// isSCEVable - Test if values of the given type are analyzable within
1885 /// the SCEV framework. This primarily includes integer types, and it
1886 /// can optionally include pointer types if the ScalarEvolution class
1887 /// has access to target-specific information.
1888 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1889 // Integers are always SCEVable.
1890 if (Ty->isInteger())
1893 // Pointers are SCEVable if TargetData information is available
1894 // to provide pointer size information.
1895 if (isa<PointerType>(Ty))
1898 // Otherwise it's not SCEVable.
1902 /// getTypeSizeInBits - Return the size in bits of the specified type,
1903 /// for which isSCEVable must return true.
1904 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1905 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1907 // If we have a TargetData, use it!
1909 return TD->getTypeSizeInBits(Ty);
1911 // Otherwise, we support only integer types.
1912 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1913 return Ty->getPrimitiveSizeInBits();
1916 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1917 /// the given type and which represents how SCEV will treat the given
1918 /// type, for which isSCEVable must return true. For pointer types,
1919 /// this is the pointer-sized integer type.
1920 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1921 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1923 if (Ty->isInteger())
1926 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1927 return TD->getIntPtrType();
1930 const SCEV* ScalarEvolution::getCouldNotCompute() {
1931 return CouldNotCompute;
1934 /// hasSCEV - Return true if the SCEV for this value has already been
1936 bool ScalarEvolution::hasSCEV(Value *V) const {
1937 return Scalars.count(V);
1940 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1941 /// expression and create a new one.
1942 const SCEV* ScalarEvolution::getSCEV(Value *V) {
1943 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1945 std::map<SCEVCallbackVH, const SCEV*>::iterator I = Scalars.find(V);
1946 if (I != Scalars.end()) return I->second;
1947 const SCEV* S = createSCEV(V);
1948 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
1952 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1953 /// specified signed integer value and return a SCEV for the constant.
1954 const SCEV* ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1955 Ty = getEffectiveSCEVType(Ty);
1958 C = Constant::getNullValue(Ty);
1959 else if (Ty->isFloatingPoint())
1960 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1961 APFloat::IEEEdouble, Val));
1963 C = ConstantInt::get(Ty, Val);
1964 return getUnknown(C);
1967 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1969 const SCEV* ScalarEvolution::getNegativeSCEV(const SCEV* V) {
1970 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1971 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1973 const Type *Ty = V->getType();
1974 Ty = getEffectiveSCEVType(Ty);
1975 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1978 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1979 const SCEV* ScalarEvolution::getNotSCEV(const SCEV* V) {
1980 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1981 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1983 const Type *Ty = V->getType();
1984 Ty = getEffectiveSCEVType(Ty);
1985 const SCEV* AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1986 return getMinusSCEV(AllOnes, V);
1989 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1991 const SCEV* ScalarEvolution::getMinusSCEV(const SCEV* LHS,
1994 return getAddExpr(LHS, getNegativeSCEV(RHS));
1997 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1998 /// input value to the specified type. If the type must be extended, it is zero
2001 ScalarEvolution::getTruncateOrZeroExtend(const SCEV* V,
2003 const Type *SrcTy = V->getType();
2004 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2005 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2006 "Cannot truncate or zero extend with non-integer arguments!");
2007 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2008 return V; // No conversion
2009 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2010 return getTruncateExpr(V, Ty);
2011 return getZeroExtendExpr(V, Ty);
2014 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
2015 /// input value to the specified type. If the type must be extended, it is sign
2018 ScalarEvolution::getTruncateOrSignExtend(const SCEV* V,
2020 const Type *SrcTy = V->getType();
2021 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2022 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2023 "Cannot truncate or zero extend with non-integer arguments!");
2024 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2025 return V; // No conversion
2026 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
2027 return getTruncateExpr(V, Ty);
2028 return getSignExtendExpr(V, Ty);
2031 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
2032 /// input value to the specified type. If the type must be extended, it is zero
2033 /// extended. The conversion must not be narrowing.
2035 ScalarEvolution::getNoopOrZeroExtend(const SCEV* V, const Type *Ty) {
2036 const Type *SrcTy = V->getType();
2037 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2038 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2039 "Cannot noop or zero extend with non-integer arguments!");
2040 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2041 "getNoopOrZeroExtend cannot truncate!");
2042 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2043 return V; // No conversion
2044 return getZeroExtendExpr(V, Ty);
2047 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
2048 /// input value to the specified type. If the type must be extended, it is sign
2049 /// extended. The conversion must not be narrowing.
2051 ScalarEvolution::getNoopOrSignExtend(const SCEV* V, const Type *Ty) {
2052 const Type *SrcTy = V->getType();
2053 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2054 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2055 "Cannot noop or sign extend with non-integer arguments!");
2056 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2057 "getNoopOrSignExtend cannot truncate!");
2058 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2059 return V; // No conversion
2060 return getSignExtendExpr(V, Ty);
2063 /// getNoopOrAnyExtend - Return a SCEV corresponding to a conversion of
2064 /// the input value to the specified type. If the type must be extended,
2065 /// it is extended with unspecified bits. The conversion must not be
2068 ScalarEvolution::getNoopOrAnyExtend(const SCEV* V, const Type *Ty) {
2069 const Type *SrcTy = V->getType();
2070 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2071 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2072 "Cannot noop or any extend with non-integer arguments!");
2073 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
2074 "getNoopOrAnyExtend cannot truncate!");
2075 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2076 return V; // No conversion
2077 return getAnyExtendExpr(V, Ty);
2080 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
2081 /// input value to the specified type. The conversion must not be widening.
2083 ScalarEvolution::getTruncateOrNoop(const SCEV* V, const Type *Ty) {
2084 const Type *SrcTy = V->getType();
2085 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
2086 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
2087 "Cannot truncate or noop with non-integer arguments!");
2088 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
2089 "getTruncateOrNoop cannot extend!");
2090 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
2091 return V; // No conversion
2092 return getTruncateExpr(V, Ty);
2095 /// getUMaxFromMismatchedTypes - Promote the operands to the wider of
2096 /// the types using zero-extension, and then perform a umax operation
2098 const SCEV* ScalarEvolution::getUMaxFromMismatchedTypes(const SCEV* LHS,
2100 const SCEV* PromotedLHS = LHS;
2101 const SCEV* PromotedRHS = RHS;
2103 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2104 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2106 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2108 return getUMaxExpr(PromotedLHS, PromotedRHS);
2111 /// getUMinFromMismatchedTypes - Promote the operands to the wider of
2112 /// the types using zero-extension, and then perform a umin operation
2114 const SCEV* ScalarEvolution::getUMinFromMismatchedTypes(const SCEV* LHS,
2116 const SCEV* PromotedLHS = LHS;
2117 const SCEV* PromotedRHS = RHS;
2119 if (getTypeSizeInBits(LHS->getType()) > getTypeSizeInBits(RHS->getType()))
2120 PromotedRHS = getZeroExtendExpr(RHS, LHS->getType());
2122 PromotedLHS = getNoopOrZeroExtend(LHS, RHS->getType());
2124 return getUMinExpr(PromotedLHS, PromotedRHS);
2127 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
2128 /// the specified instruction and replaces any references to the symbolic value
2129 /// SymName with the specified value. This is used during PHI resolution.
2130 void ScalarEvolution::
2131 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEV* SymName,
2132 const SCEV* NewVal) {
2133 std::map<SCEVCallbackVH, const SCEV*>::iterator SI =
2134 Scalars.find(SCEVCallbackVH(I, this));
2135 if (SI == Scalars.end()) return;
2138 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
2139 if (NV == SI->second) return; // No change.
2141 SI->second = NV; // Update the scalars map!
2143 // Any instruction values that use this instruction might also need to be
2145 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
2147 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
2150 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
2151 /// a loop header, making it a potential recurrence, or it doesn't.
2153 const SCEV* ScalarEvolution::createNodeForPHI(PHINode *PN) {
2154 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
2155 if (const Loop *L = LI->getLoopFor(PN->getParent()))
2156 if (L->getHeader() == PN->getParent()) {
2157 // If it lives in the loop header, it has two incoming values, one
2158 // from outside the loop, and one from inside.
2159 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
2160 unsigned BackEdge = IncomingEdge^1;
2162 // While we are analyzing this PHI node, handle its value symbolically.
2163 const SCEV* SymbolicName = getUnknown(PN);
2164 assert(Scalars.find(PN) == Scalars.end() &&
2165 "PHI node already processed?");
2166 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
2168 // Using this symbolic name for the PHI, analyze the value coming around
2170 const SCEV* BEValue = getSCEV(PN->getIncomingValue(BackEdge));
2172 // NOTE: If BEValue is loop invariant, we know that the PHI node just
2173 // has a special value for the first iteration of the loop.
2175 // If the value coming around the backedge is an add with the symbolic
2176 // value we just inserted, then we found a simple induction variable!
2177 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
2178 // If there is a single occurrence of the symbolic value, replace it
2179 // with a recurrence.
2180 unsigned FoundIndex = Add->getNumOperands();
2181 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2182 if (Add->getOperand(i) == SymbolicName)
2183 if (FoundIndex == e) {
2188 if (FoundIndex != Add->getNumOperands()) {
2189 // Create an add with everything but the specified operand.
2190 SmallVector<const SCEV*, 8> Ops;
2191 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
2192 if (i != FoundIndex)
2193 Ops.push_back(Add->getOperand(i));
2194 const SCEV* Accum = getAddExpr(Ops);
2196 // This is not a valid addrec if the step amount is varying each
2197 // loop iteration, but is not itself an addrec in this loop.
2198 if (Accum->isLoopInvariant(L) ||
2199 (isa<SCEVAddRecExpr>(Accum) &&
2200 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
2201 const SCEV* StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2202 const SCEV* PHISCEV = getAddRecExpr(StartVal, Accum, L);
2204 // Okay, for the entire analysis of this edge we assumed the PHI
2205 // to be symbolic. We now need to go back and update all of the
2206 // entries for the scalars that use the PHI (except for the PHI
2207 // itself) to use the new analyzed value instead of the "symbolic"
2209 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2213 } else if (const SCEVAddRecExpr *AddRec =
2214 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2215 // Otherwise, this could be a loop like this:
2216 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2217 // In this case, j = {1,+,1} and BEValue is j.
2218 // Because the other in-value of i (0) fits the evolution of BEValue
2219 // i really is an addrec evolution.
2220 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2221 const SCEV* StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2223 // If StartVal = j.start - j.stride, we can use StartVal as the
2224 // initial step of the addrec evolution.
2225 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2226 AddRec->getOperand(1))) {
2227 const SCEV* PHISCEV =
2228 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2230 // Okay, for the entire analysis of this edge we assumed the PHI
2231 // to be symbolic. We now need to go back and update all of the
2232 // entries for the scalars that use the PHI (except for the PHI
2233 // itself) to use the new analyzed value instead of the "symbolic"
2235 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2241 return SymbolicName;
2244 // If it's not a loop phi, we can't handle it yet.
2245 return getUnknown(PN);
2248 /// createNodeForGEP - Expand GEP instructions into add and multiply
2249 /// operations. This allows them to be analyzed by regular SCEV code.
2251 const SCEV* ScalarEvolution::createNodeForGEP(User *GEP) {
2253 const Type *IntPtrTy = TD->getIntPtrType();
2254 Value *Base = GEP->getOperand(0);
2255 // Don't attempt to analyze GEPs over unsized objects.
2256 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2257 return getUnknown(GEP);
2258 const SCEV* TotalOffset = getIntegerSCEV(0, IntPtrTy);
2259 gep_type_iterator GTI = gep_type_begin(GEP);
2260 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2264 // Compute the (potentially symbolic) offset in bytes for this index.
2265 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2266 // For a struct, add the member offset.
2267 const StructLayout &SL = *TD->getStructLayout(STy);
2268 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2269 uint64_t Offset = SL.getElementOffset(FieldNo);
2270 TotalOffset = getAddExpr(TotalOffset,
2271 getIntegerSCEV(Offset, IntPtrTy));
2273 // For an array, add the element offset, explicitly scaled.
2274 const SCEV* LocalOffset = getSCEV(Index);
2275 if (!isa<PointerType>(LocalOffset->getType()))
2276 // Getelementptr indicies are signed.
2277 LocalOffset = getTruncateOrSignExtend(LocalOffset,
2280 getMulExpr(LocalOffset,
2281 getIntegerSCEV(TD->getTypeAllocSize(*GTI),
2283 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2286 return getAddExpr(getSCEV(Base), TotalOffset);
2289 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2290 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2291 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2292 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2294 ScalarEvolution::GetMinTrailingZeros(const SCEV* S) {
2295 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2296 return C->getValue()->getValue().countTrailingZeros();
2298 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2299 return std::min(GetMinTrailingZeros(T->getOperand()),
2300 (uint32_t)getTypeSizeInBits(T->getType()));
2302 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2303 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2304 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2305 getTypeSizeInBits(E->getType()) : OpRes;
2308 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2309 uint32_t OpRes = GetMinTrailingZeros(E->getOperand());
2310 return OpRes == getTypeSizeInBits(E->getOperand()->getType()) ?
2311 getTypeSizeInBits(E->getType()) : OpRes;
2314 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2315 // The result is the min of all operands results.
2316 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2317 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2318 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2322 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2323 // The result is the sum of all operands results.
2324 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0));
2325 uint32_t BitWidth = getTypeSizeInBits(M->getType());
2326 for (unsigned i = 1, e = M->getNumOperands();
2327 SumOpRes != BitWidth && i != e; ++i)
2328 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i)),
2333 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2334 // The result is the min of all operands results.
2335 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0));
2336 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2337 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i)));
2341 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2342 // The result is the min of all operands results.
2343 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2344 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2345 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2349 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2350 // The result is the min of all operands results.
2351 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0));
2352 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2353 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i)));
2357 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2358 // For a SCEVUnknown, ask ValueTracking.
2359 unsigned BitWidth = getTypeSizeInBits(U->getType());
2360 APInt Mask = APInt::getAllOnesValue(BitWidth);
2361 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2362 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones);
2363 return Zeros.countTrailingOnes();
2371 ScalarEvolution::GetMinLeadingZeros(const SCEV* S) {
2372 // TODO: Handle other SCEV expression types here.
2374 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2375 return C->getValue()->getValue().countLeadingZeros();
2377 if (const SCEVZeroExtendExpr *C = dyn_cast<SCEVZeroExtendExpr>(S)) {
2378 // A zero-extension cast adds zero bits.
2379 return GetMinLeadingZeros(C->getOperand()) +
2380 (getTypeSizeInBits(C->getType()) -
2381 getTypeSizeInBits(C->getOperand()->getType()));
2384 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2385 // For a SCEVUnknown, ask ValueTracking.
2386 unsigned BitWidth = getTypeSizeInBits(U->getType());
2387 APInt Mask = APInt::getAllOnesValue(BitWidth);
2388 APInt Zeros(BitWidth, 0), Ones(BitWidth, 0);
2389 ComputeMaskedBits(U->getValue(), Mask, Zeros, Ones, TD);
2390 return Zeros.countLeadingOnes();
2397 ScalarEvolution::GetMinSignBits(const SCEV* S) {
2398 // TODO: Handle other SCEV expression types here.
2400 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
2401 const APInt &A = C->getValue()->getValue();
2402 return A.isNegative() ? A.countLeadingOnes() :
2403 A.countLeadingZeros();
2406 if (const SCEVSignExtendExpr *C = dyn_cast<SCEVSignExtendExpr>(S)) {
2407 // A sign-extension cast adds sign bits.
2408 return GetMinSignBits(C->getOperand()) +
2409 (getTypeSizeInBits(C->getType()) -
2410 getTypeSizeInBits(C->getOperand()->getType()));
2413 if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
2414 // For a SCEVUnknown, ask ValueTracking.
2415 return ComputeNumSignBits(U->getValue(), TD);
2421 /// createSCEV - We know that there is no SCEV for the specified value.
2422 /// Analyze the expression.
2424 const SCEV* ScalarEvolution::createSCEV(Value *V) {
2425 if (!isSCEVable(V->getType()))
2426 return getUnknown(V);
2428 unsigned Opcode = Instruction::UserOp1;
2429 if (Instruction *I = dyn_cast<Instruction>(V))
2430 Opcode = I->getOpcode();
2431 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2432 Opcode = CE->getOpcode();
2434 return getUnknown(V);
2436 User *U = cast<User>(V);
2438 case Instruction::Add:
2439 return getAddExpr(getSCEV(U->getOperand(0)),
2440 getSCEV(U->getOperand(1)));
2441 case Instruction::Mul:
2442 return getMulExpr(getSCEV(U->getOperand(0)),
2443 getSCEV(U->getOperand(1)));
2444 case Instruction::UDiv:
2445 return getUDivExpr(getSCEV(U->getOperand(0)),
2446 getSCEV(U->getOperand(1)));
2447 case Instruction::Sub:
2448 return getMinusSCEV(getSCEV(U->getOperand(0)),
2449 getSCEV(U->getOperand(1)));
2450 case Instruction::And:
2451 // For an expression like x&255 that merely masks off the high bits,
2452 // use zext(trunc(x)) as the SCEV expression.
2453 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2454 if (CI->isNullValue())
2455 return getSCEV(U->getOperand(1));
2456 if (CI->isAllOnesValue())
2457 return getSCEV(U->getOperand(0));
2458 const APInt &A = CI->getValue();
2460 // Instcombine's ShrinkDemandedConstant may strip bits out of
2461 // constants, obscuring what would otherwise be a low-bits mask.
2462 // Use ComputeMaskedBits to compute what ShrinkDemandedConstant
2463 // knew about to reconstruct a low-bits mask value.
2464 unsigned LZ = A.countLeadingZeros();
2465 unsigned BitWidth = A.getBitWidth();
2466 APInt AllOnes = APInt::getAllOnesValue(BitWidth);
2467 APInt KnownZero(BitWidth, 0), KnownOne(BitWidth, 0);
2468 ComputeMaskedBits(U->getOperand(0), AllOnes, KnownZero, KnownOne, TD);
2470 APInt EffectiveMask = APInt::getLowBitsSet(BitWidth, BitWidth - LZ);
2472 if (LZ != 0 && !((~A & ~KnownZero) & EffectiveMask))
2474 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2475 IntegerType::get(BitWidth - LZ)),
2480 case Instruction::Or:
2481 // If the RHS of the Or is a constant, we may have something like:
2482 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2483 // optimizations will transparently handle this case.
2485 // In order for this transformation to be safe, the LHS must be of the
2486 // form X*(2^n) and the Or constant must be less than 2^n.
2487 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2488 const SCEV* LHS = getSCEV(U->getOperand(0));
2489 const APInt &CIVal = CI->getValue();
2490 if (GetMinTrailingZeros(LHS) >=
2491 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2492 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2495 case Instruction::Xor:
2496 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2497 // If the RHS of the xor is a signbit, then this is just an add.
2498 // Instcombine turns add of signbit into xor as a strength reduction step.
2499 if (CI->getValue().isSignBit())
2500 return getAddExpr(getSCEV(U->getOperand(0)),
2501 getSCEV(U->getOperand(1)));
2503 // If the RHS of xor is -1, then this is a not operation.
2504 if (CI->isAllOnesValue())
2505 return getNotSCEV(getSCEV(U->getOperand(0)));
2507 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2508 // This is a variant of the check for xor with -1, and it handles
2509 // the case where instcombine has trimmed non-demanded bits out
2510 // of an xor with -1.
2511 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2512 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2513 if (BO->getOpcode() == Instruction::And &&
2514 LCI->getValue() == CI->getValue())
2515 if (const SCEVZeroExtendExpr *Z =
2516 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0)))) {
2517 const Type *UTy = U->getType();
2518 const SCEV* Z0 = Z->getOperand();
2519 const Type *Z0Ty = Z0->getType();
2520 unsigned Z0TySize = getTypeSizeInBits(Z0Ty);
2522 // If C is a low-bits mask, the zero extend is zerving to
2523 // mask off the high bits. Complement the operand and
2524 // re-apply the zext.
2525 if (APIntOps::isMask(Z0TySize, CI->getValue()))
2526 return getZeroExtendExpr(getNotSCEV(Z0), UTy);
2528 // If C is a single bit, it may be in the sign-bit position
2529 // before the zero-extend. In this case, represent the xor
2530 // using an add, which is equivalent, and re-apply the zext.
2531 APInt Trunc = APInt(CI->getValue()).trunc(Z0TySize);
2532 if (APInt(Trunc).zext(getTypeSizeInBits(UTy)) == CI->getValue() &&
2534 return getZeroExtendExpr(getAddExpr(Z0, getConstant(Trunc)),
2540 case Instruction::Shl:
2541 // Turn shift left of a constant amount into a multiply.
2542 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2543 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2544 Constant *X = ConstantInt::get(
2545 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2546 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2550 case Instruction::LShr:
2551 // Turn logical shift right of a constant into a unsigned divide.
2552 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2553 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2554 Constant *X = ConstantInt::get(
2555 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2556 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2560 case Instruction::AShr:
2561 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2562 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2563 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2564 if (L->getOpcode() == Instruction::Shl &&
2565 L->getOperand(1) == U->getOperand(1)) {
2566 unsigned BitWidth = getTypeSizeInBits(U->getType());
2567 uint64_t Amt = BitWidth - CI->getZExtValue();
2568 if (Amt == BitWidth)
2569 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2571 return getIntegerSCEV(0, U->getType()); // value is undefined
2573 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2574 IntegerType::get(Amt)),
2579 case Instruction::Trunc:
2580 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2582 case Instruction::ZExt:
2583 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2585 case Instruction::SExt:
2586 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2588 case Instruction::BitCast:
2589 // BitCasts are no-op casts so we just eliminate the cast.
2590 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2591 return getSCEV(U->getOperand(0));
2594 case Instruction::IntToPtr:
2595 if (!TD) break; // Without TD we can't analyze pointers.
2596 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2597 TD->getIntPtrType());
2599 case Instruction::PtrToInt:
2600 if (!TD) break; // Without TD we can't analyze pointers.
2601 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2604 case Instruction::GetElementPtr:
2605 if (!TD) break; // Without TD we can't analyze pointers.
2606 return createNodeForGEP(U);
2608 case Instruction::PHI:
2609 return createNodeForPHI(cast<PHINode>(U));
2611 case Instruction::Select:
2612 // This could be a smax or umax that was lowered earlier.
2613 // Try to recover it.
2614 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2615 Value *LHS = ICI->getOperand(0);
2616 Value *RHS = ICI->getOperand(1);
2617 switch (ICI->getPredicate()) {
2618 case ICmpInst::ICMP_SLT:
2619 case ICmpInst::ICMP_SLE:
2620 std::swap(LHS, RHS);
2622 case ICmpInst::ICMP_SGT:
2623 case ICmpInst::ICMP_SGE:
2624 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2625 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2626 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2627 return getSMinExpr(getSCEV(LHS), getSCEV(RHS));
2629 case ICmpInst::ICMP_ULT:
2630 case ICmpInst::ICMP_ULE:
2631 std::swap(LHS, RHS);
2633 case ICmpInst::ICMP_UGT:
2634 case ICmpInst::ICMP_UGE:
2635 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2636 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2637 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2638 return getUMinExpr(getSCEV(LHS), getSCEV(RHS));
2640 case ICmpInst::ICMP_NE:
2641 // n != 0 ? n : 1 -> umax(n, 1)
2642 if (LHS == U->getOperand(1) &&
2643 isa<ConstantInt>(U->getOperand(2)) &&
2644 cast<ConstantInt>(U->getOperand(2))->isOne() &&
2645 isa<ConstantInt>(RHS) &&
2646 cast<ConstantInt>(RHS)->isZero())
2647 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(2)));
2649 case ICmpInst::ICMP_EQ:
2650 // n == 0 ? 1 : n -> umax(n, 1)
2651 if (LHS == U->getOperand(2) &&
2652 isa<ConstantInt>(U->getOperand(1)) &&
2653 cast<ConstantInt>(U->getOperand(1))->isOne() &&
2654 isa<ConstantInt>(RHS) &&
2655 cast<ConstantInt>(RHS)->isZero())
2656 return getUMaxExpr(getSCEV(LHS), getSCEV(U->getOperand(1)));
2663 default: // We cannot analyze this expression.
2667 return getUnknown(V);
2672 //===----------------------------------------------------------------------===//
2673 // Iteration Count Computation Code
2676 /// getBackedgeTakenCount - If the specified loop has a predictable
2677 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2678 /// object. The backedge-taken count is the number of times the loop header
2679 /// will be branched to from within the loop. This is one less than the
2680 /// trip count of the loop, since it doesn't count the first iteration,
2681 /// when the header is branched to from outside the loop.
2683 /// Note that it is not valid to call this method on a loop without a
2684 /// loop-invariant backedge-taken count (see
2685 /// hasLoopInvariantBackedgeTakenCount).
2687 const SCEV* ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2688 return getBackedgeTakenInfo(L).Exact;
2691 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2692 /// return the least SCEV value that is known never to be less than the
2693 /// actual backedge taken count.
2694 const SCEV* ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2695 return getBackedgeTakenInfo(L).Max;
2698 const ScalarEvolution::BackedgeTakenInfo &
2699 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2700 // Initially insert a CouldNotCompute for this loop. If the insertion
2701 // succeeds, procede to actually compute a backedge-taken count and
2702 // update the value. The temporary CouldNotCompute value tells SCEV
2703 // code elsewhere that it shouldn't attempt to request a new
2704 // backedge-taken count, which could result in infinite recursion.
2705 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2706 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2708 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2709 if (ItCount.Exact != CouldNotCompute) {
2710 assert(ItCount.Exact->isLoopInvariant(L) &&
2711 ItCount.Max->isLoopInvariant(L) &&
2712 "Computed trip count isn't loop invariant for loop!");
2713 ++NumTripCountsComputed;
2715 // Update the value in the map.
2716 Pair.first->second = ItCount;
2718 if (ItCount.Max != CouldNotCompute)
2719 // Update the value in the map.
2720 Pair.first->second = ItCount;
2721 if (isa<PHINode>(L->getHeader()->begin()))
2722 // Only count loops that have phi nodes as not being computable.
2723 ++NumTripCountsNotComputed;
2726 // Now that we know more about the trip count for this loop, forget any
2727 // existing SCEV values for PHI nodes in this loop since they are only
2728 // conservative estimates made without the benefit
2729 // of trip count information.
2730 if (ItCount.hasAnyInfo())
2733 return Pair.first->second;
2736 /// forgetLoopBackedgeTakenCount - This method should be called by the
2737 /// client when it has changed a loop in a way that may effect
2738 /// ScalarEvolution's ability to compute a trip count, or if the loop
2740 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2741 BackedgeTakenCounts.erase(L);
2745 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2746 /// PHI nodes in the given loop. This is used when the trip count of
2747 /// the loop may have changed.
2748 void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2749 BasicBlock *Header = L->getHeader();
2751 // Push all Loop-header PHIs onto the Worklist stack, except those
2752 // that are presently represented via a SCEVUnknown. SCEVUnknown for
2753 // a PHI either means that it has an unrecognized structure, or it's
2754 // a PHI that's in the progress of being computed by createNodeForPHI.
2755 // In the former case, additional loop trip count information isn't
2756 // going to change anything. In the later case, createNodeForPHI will
2757 // perform the necessary updates on its own when it gets to that point.
2758 SmallVector<Instruction *, 16> Worklist;
2759 for (BasicBlock::iterator I = Header->begin();
2760 PHINode *PN = dyn_cast<PHINode>(I); ++I) {
2761 std::map<SCEVCallbackVH, const SCEV*>::iterator It = Scalars.find((Value*)I);
2762 if (It != Scalars.end() && !isa<SCEVUnknown>(It->second))
2763 Worklist.push_back(PN);
2766 while (!Worklist.empty()) {
2767 Instruction *I = Worklist.pop_back_val();
2768 if (Scalars.erase(I))
2769 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2771 Worklist.push_back(cast<Instruction>(UI));
2775 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2776 /// of the specified loop will execute.
2777 ScalarEvolution::BackedgeTakenInfo
2778 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2779 SmallVector<BasicBlock*, 8> ExitingBlocks;
2780 L->getExitingBlocks(ExitingBlocks);
2782 // Examine all exits and pick the most conservative values.
2783 const SCEV* BECount = CouldNotCompute;
2784 const SCEV* MaxBECount = CouldNotCompute;
2785 bool CouldNotComputeBECount = false;
2786 bool CouldNotComputeMaxBECount = false;
2787 for (unsigned i = 0, e = ExitingBlocks.size(); i != e; ++i) {
2788 BackedgeTakenInfo NewBTI =
2789 ComputeBackedgeTakenCountFromExit(L, ExitingBlocks[i]);
2791 if (NewBTI.Exact == CouldNotCompute) {
2792 // We couldn't compute an exact value for this exit, so
2793 // we won't be able to compute an exact value for the loop.
2794 CouldNotComputeBECount = true;
2795 BECount = CouldNotCompute;
2796 } else if (!CouldNotComputeBECount) {
2797 if (BECount == CouldNotCompute)
2798 BECount = NewBTI.Exact;
2800 // TODO: More analysis could be done here. For example, a
2801 // loop with a short-circuiting && operator has an exact count
2802 // of the min of both sides.
2803 CouldNotComputeBECount = true;
2804 BECount = CouldNotCompute;
2807 if (NewBTI.Max == CouldNotCompute) {
2808 // We couldn't compute an maximum value for this exit, so
2809 // we won't be able to compute an maximum value for the loop.
2810 CouldNotComputeMaxBECount = true;
2811 MaxBECount = CouldNotCompute;
2812 } else if (!CouldNotComputeMaxBECount) {
2813 if (MaxBECount == CouldNotCompute)
2814 MaxBECount = NewBTI.Max;
2816 MaxBECount = getUMaxFromMismatchedTypes(MaxBECount, NewBTI.Max);
2820 return BackedgeTakenInfo(BECount, MaxBECount);
2823 /// ComputeBackedgeTakenCountFromExit - Compute the number of times the backedge
2824 /// of the specified loop will execute if it exits via the specified block.
2825 ScalarEvolution::BackedgeTakenInfo
2826 ScalarEvolution::ComputeBackedgeTakenCountFromExit(const Loop *L,
2827 BasicBlock *ExitingBlock) {
2829 // Okay, we've chosen an exiting block. See what condition causes us to
2830 // exit at this block.
2832 // FIXME: we should be able to handle switch instructions (with a single exit)
2833 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2834 if (ExitBr == 0) return CouldNotCompute;
2835 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2837 // At this point, we know we have a conditional branch that determines whether
2838 // the loop is exited. However, we don't know if the branch is executed each
2839 // time through the loop. If not, then the execution count of the branch will
2840 // not be equal to the trip count of the loop.
2842 // Currently we check for this by checking to see if the Exit branch goes to
2843 // the loop header. If so, we know it will always execute the same number of
2844 // times as the loop. We also handle the case where the exit block *is* the
2845 // loop header. This is common for un-rotated loops.
2847 // If both of those tests fail, walk up the unique predecessor chain to the
2848 // header, stopping if there is an edge that doesn't exit the loop. If the
2849 // header is reached, the execution count of the branch will be equal to the
2850 // trip count of the loop.
2852 // More extensive analysis could be done to handle more cases here.
2854 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2855 ExitBr->getSuccessor(1) != L->getHeader() &&
2856 ExitBr->getParent() != L->getHeader()) {
2857 // The simple checks failed, try climbing the unique predecessor chain
2858 // up to the header.
2860 for (BasicBlock *BB = ExitBr->getParent(); BB; ) {
2861 BasicBlock *Pred = BB->getUniquePredecessor();
2863 return CouldNotCompute;
2864 TerminatorInst *PredTerm = Pred->getTerminator();
2865 for (unsigned i = 0, e = PredTerm->getNumSuccessors(); i != e; ++i) {
2866 BasicBlock *PredSucc = PredTerm->getSuccessor(i);
2869 // If the predecessor has a successor that isn't BB and isn't
2870 // outside the loop, assume the worst.
2871 if (L->contains(PredSucc))
2872 return CouldNotCompute;
2874 if (Pred == L->getHeader()) {
2881 return CouldNotCompute;
2884 // Procede to the next level to examine the exit condition expression.
2885 return ComputeBackedgeTakenCountFromExitCond(L, ExitBr->getCondition(),
2886 ExitBr->getSuccessor(0),
2887 ExitBr->getSuccessor(1));
2890 /// ComputeBackedgeTakenCountFromExitCond - Compute the number of times the
2891 /// backedge of the specified loop will execute if its exit condition
2892 /// were a conditional branch of ExitCond, TBB, and FBB.
2893 ScalarEvolution::BackedgeTakenInfo
2894 ScalarEvolution::ComputeBackedgeTakenCountFromExitCond(const Loop *L,
2898 // Check if the controlling expression for this loop is an and or or. In
2899 // such cases, an exact backedge-taken count may be infeasible, but a
2900 // maximum count may still be feasible.
2901 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(ExitCond)) {
2902 if (BO->getOpcode() == Instruction::And) {
2903 // Recurse on the operands of the and.
2904 BackedgeTakenInfo BTI0 =
2905 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
2906 BackedgeTakenInfo BTI1 =
2907 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
2908 const SCEV* BECount = CouldNotCompute;
2909 const SCEV* MaxBECount = CouldNotCompute;
2910 if (L->contains(TBB)) {
2911 // Both conditions must be true for the loop to continue executing.
2912 // Choose the less conservative count.
2913 if (BTI0.Exact == CouldNotCompute)
2914 BECount = BTI1.Exact;
2915 else if (BTI1.Exact == CouldNotCompute)
2916 BECount = BTI0.Exact;
2918 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
2919 if (BTI0.Max == CouldNotCompute)
2920 MaxBECount = BTI1.Max;
2921 else if (BTI1.Max == CouldNotCompute)
2922 MaxBECount = BTI0.Max;
2924 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
2926 // Both conditions must be true for the loop to exit.
2927 assert(L->contains(FBB) && "Loop block has no successor in loop!");
2928 if (BTI0.Exact != CouldNotCompute && BTI1.Exact != CouldNotCompute)
2929 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
2930 if (BTI0.Max != CouldNotCompute && BTI1.Max != CouldNotCompute)
2931 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
2934 return BackedgeTakenInfo(BECount, MaxBECount);
2936 if (BO->getOpcode() == Instruction::Or) {
2937 // Recurse on the operands of the or.
2938 BackedgeTakenInfo BTI0 =
2939 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(0), TBB, FBB);
2940 BackedgeTakenInfo BTI1 =
2941 ComputeBackedgeTakenCountFromExitCond(L, BO->getOperand(1), TBB, FBB);
2942 const SCEV* BECount = CouldNotCompute;
2943 const SCEV* MaxBECount = CouldNotCompute;
2944 if (L->contains(FBB)) {
2945 // Both conditions must be false for the loop to continue executing.
2946 // Choose the less conservative count.
2947 if (BTI0.Exact == CouldNotCompute)
2948 BECount = BTI1.Exact;
2949 else if (BTI1.Exact == CouldNotCompute)
2950 BECount = BTI0.Exact;
2952 BECount = getUMinFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
2953 if (BTI0.Max == CouldNotCompute)
2954 MaxBECount = BTI1.Max;
2955 else if (BTI1.Max == CouldNotCompute)
2956 MaxBECount = BTI0.Max;
2958 MaxBECount = getUMinFromMismatchedTypes(BTI0.Max, BTI1.Max);
2960 // Both conditions must be false for the loop to exit.
2961 assert(L->contains(TBB) && "Loop block has no successor in loop!");
2962 if (BTI0.Exact != CouldNotCompute && BTI1.Exact != CouldNotCompute)
2963 BECount = getUMaxFromMismatchedTypes(BTI0.Exact, BTI1.Exact);
2964 if (BTI0.Max != CouldNotCompute && BTI1.Max != CouldNotCompute)
2965 MaxBECount = getUMaxFromMismatchedTypes(BTI0.Max, BTI1.Max);
2968 return BackedgeTakenInfo(BECount, MaxBECount);
2972 // With an icmp, it may be feasible to compute an exact backedge-taken count.
2973 // Procede to the next level to examine the icmp.
2974 if (ICmpInst *ExitCondICmp = dyn_cast<ICmpInst>(ExitCond))
2975 return ComputeBackedgeTakenCountFromExitCondICmp(L, ExitCondICmp, TBB, FBB);
2977 // If it's not an integer or pointer comparison then compute it the hard way.
2978 return ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
2981 /// ComputeBackedgeTakenCountFromExitCondICmp - Compute the number of times the
2982 /// backedge of the specified loop will execute if its exit condition
2983 /// were a conditional branch of the ICmpInst ExitCond, TBB, and FBB.
2984 ScalarEvolution::BackedgeTakenInfo
2985 ScalarEvolution::ComputeBackedgeTakenCountFromExitCondICmp(const Loop *L,
2990 // If the condition was exit on true, convert the condition to exit on false
2991 ICmpInst::Predicate Cond;
2992 if (!L->contains(FBB))
2993 Cond = ExitCond->getPredicate();
2995 Cond = ExitCond->getInversePredicate();
2997 // Handle common loops like: for (X = "string"; *X; ++X)
2998 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2999 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
3001 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
3002 if (!isa<SCEVCouldNotCompute>(ItCnt)) {
3003 unsigned BitWidth = getTypeSizeInBits(ItCnt->getType());
3004 return BackedgeTakenInfo(ItCnt,
3005 isa<SCEVConstant>(ItCnt) ? ItCnt :
3006 getConstant(APInt::getMaxValue(BitWidth)-1));
3010 const SCEV* LHS = getSCEV(ExitCond->getOperand(0));
3011 const SCEV* RHS = getSCEV(ExitCond->getOperand(1));
3013 // Try to evaluate any dependencies out of the loop.
3014 LHS = getSCEVAtScope(LHS, L);
3015 RHS = getSCEVAtScope(RHS, L);
3017 // At this point, we would like to compute how many iterations of the
3018 // loop the predicate will return true for these inputs.
3019 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
3020 // If there is a loop-invariant, force it into the RHS.
3021 std::swap(LHS, RHS);
3022 Cond = ICmpInst::getSwappedPredicate(Cond);
3025 // If we have a comparison of a chrec against a constant, try to use value
3026 // ranges to answer this query.
3027 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
3028 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
3029 if (AddRec->getLoop() == L) {
3030 // Form the constant range.
3031 ConstantRange CompRange(
3032 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
3034 const SCEV* Ret = AddRec->getNumIterationsInRange(CompRange, *this);
3035 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
3039 case ICmpInst::ICMP_NE: { // while (X != Y)
3040 // Convert to: while (X-Y != 0)
3041 const SCEV* TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
3042 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3045 case ICmpInst::ICMP_EQ: {
3046 // Convert to: while (X-Y == 0) // while (X == Y)
3047 const SCEV* TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
3048 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
3051 case ICmpInst::ICMP_SLT: {
3052 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
3053 if (BTI.hasAnyInfo()) return BTI;
3056 case ICmpInst::ICMP_SGT: {
3057 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3058 getNotSCEV(RHS), L, true);
3059 if (BTI.hasAnyInfo()) return BTI;
3062 case ICmpInst::ICMP_ULT: {
3063 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
3064 if (BTI.hasAnyInfo()) return BTI;
3067 case ICmpInst::ICMP_UGT: {
3068 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
3069 getNotSCEV(RHS), L, false);
3070 if (BTI.hasAnyInfo()) return BTI;
3075 errs() << "ComputeBackedgeTakenCount ";
3076 if (ExitCond->getOperand(0)->getType()->isUnsigned())
3077 errs() << "[unsigned] ";
3078 errs() << *LHS << " "
3079 << Instruction::getOpcodeName(Instruction::ICmp)
3080 << " " << *RHS << "\n";
3085 ComputeBackedgeTakenCountExhaustively(L, ExitCond, !L->contains(TBB));
3088 static ConstantInt *
3089 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
3090 ScalarEvolution &SE) {
3091 const SCEV* InVal = SE.getConstant(C);
3092 const SCEV* Val = AddRec->evaluateAtIteration(InVal, SE);
3093 assert(isa<SCEVConstant>(Val) &&
3094 "Evaluation of SCEV at constant didn't fold correctly?");
3095 return cast<SCEVConstant>(Val)->getValue();
3098 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
3099 /// and a GEP expression (missing the pointer index) indexing into it, return
3100 /// the addressed element of the initializer or null if the index expression is
3103 GetAddressedElementFromGlobal(GlobalVariable *GV,
3104 const std::vector<ConstantInt*> &Indices) {
3105 Constant *Init = GV->getInitializer();
3106 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
3107 uint64_t Idx = Indices[i]->getZExtValue();
3108 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
3109 assert(Idx < CS->getNumOperands() && "Bad struct index!");
3110 Init = cast<Constant>(CS->getOperand(Idx));
3111 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
3112 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
3113 Init = cast<Constant>(CA->getOperand(Idx));
3114 } else if (isa<ConstantAggregateZero>(Init)) {
3115 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
3116 assert(Idx < STy->getNumElements() && "Bad struct index!");
3117 Init = Constant::getNullValue(STy->getElementType(Idx));
3118 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
3119 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
3120 Init = Constant::getNullValue(ATy->getElementType());
3122 assert(0 && "Unknown constant aggregate type!");
3126 return 0; // Unknown initializer type
3132 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
3133 /// 'icmp op load X, cst', try to see if we can compute the backedge
3134 /// execution count.
3135 const SCEV* ScalarEvolution::
3136 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
3138 ICmpInst::Predicate predicate) {
3139 if (LI->isVolatile()) return CouldNotCompute;
3141 // Check to see if the loaded pointer is a getelementptr of a global.
3142 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
3143 if (!GEP) return CouldNotCompute;
3145 // Make sure that it is really a constant global we are gepping, with an
3146 // initializer, and make sure the first IDX is really 0.
3147 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
3148 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
3149 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
3150 !cast<Constant>(GEP->getOperand(1))->isNullValue())
3151 return CouldNotCompute;
3153 // Okay, we allow one non-constant index into the GEP instruction.
3155 std::vector<ConstantInt*> Indexes;
3156 unsigned VarIdxNum = 0;
3157 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
3158 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
3159 Indexes.push_back(CI);
3160 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
3161 if (VarIdx) return CouldNotCompute; // Multiple non-constant idx's.
3162 VarIdx = GEP->getOperand(i);
3164 Indexes.push_back(0);
3167 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
3168 // Check to see if X is a loop variant variable value now.
3169 const SCEV* Idx = getSCEV(VarIdx);
3170 Idx = getSCEVAtScope(Idx, L);
3172 // We can only recognize very limited forms of loop index expressions, in
3173 // particular, only affine AddRec's like {C1,+,C2}.
3174 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
3175 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
3176 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
3177 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
3178 return CouldNotCompute;
3180 unsigned MaxSteps = MaxBruteForceIterations;
3181 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
3182 ConstantInt *ItCst =
3183 ConstantInt::get(cast<IntegerType>(IdxExpr->getType()), IterationNum);
3184 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
3186 // Form the GEP offset.
3187 Indexes[VarIdxNum] = Val;
3189 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
3190 if (Result == 0) break; // Cannot compute!
3192 // Evaluate the condition for this iteration.
3193 Result = ConstantExpr::getICmp(predicate, Result, RHS);
3194 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
3195 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
3197 errs() << "\n***\n*** Computed loop count " << *ItCst
3198 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
3201 ++NumArrayLenItCounts;
3202 return getConstant(ItCst); // Found terminating iteration!
3205 return CouldNotCompute;
3209 /// CanConstantFold - Return true if we can constant fold an instruction of the
3210 /// specified type, assuming that all operands were constants.
3211 static bool CanConstantFold(const Instruction *I) {
3212 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
3213 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
3216 if (const CallInst *CI = dyn_cast<CallInst>(I))
3217 if (const Function *F = CI->getCalledFunction())
3218 return canConstantFoldCallTo(F);
3222 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
3223 /// in the loop that V is derived from. We allow arbitrary operations along the
3224 /// way, but the operands of an operation must either be constants or a value
3225 /// derived from a constant PHI. If this expression does not fit with these
3226 /// constraints, return null.
3227 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
3228 // If this is not an instruction, or if this is an instruction outside of the
3229 // loop, it can't be derived from a loop PHI.
3230 Instruction *I = dyn_cast<Instruction>(V);
3231 if (I == 0 || !L->contains(I->getParent())) return 0;
3233 if (PHINode *PN = dyn_cast<PHINode>(I)) {
3234 if (L->getHeader() == I->getParent())
3237 // We don't currently keep track of the control flow needed to evaluate
3238 // PHIs, so we cannot handle PHIs inside of loops.
3242 // If we won't be able to constant fold this expression even if the operands
3243 // are constants, return early.
3244 if (!CanConstantFold(I)) return 0;
3246 // Otherwise, we can evaluate this instruction if all of its operands are
3247 // constant or derived from a PHI node themselves.
3249 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
3250 if (!(isa<Constant>(I->getOperand(Op)) ||
3251 isa<GlobalValue>(I->getOperand(Op)))) {
3252 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
3253 if (P == 0) return 0; // Not evolving from PHI
3257 return 0; // Evolving from multiple different PHIs.
3260 // This is a expression evolving from a constant PHI!
3264 /// EvaluateExpression - Given an expression that passes the
3265 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
3266 /// in the loop has the value PHIVal. If we can't fold this expression for some
3267 /// reason, return null.
3268 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
3269 if (isa<PHINode>(V)) return PHIVal;
3270 if (Constant *C = dyn_cast<Constant>(V)) return C;
3271 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
3272 Instruction *I = cast<Instruction>(V);
3274 std::vector<Constant*> Operands;
3275 Operands.resize(I->getNumOperands());
3277 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3278 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
3279 if (Operands[i] == 0) return 0;
3282 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3283 return ConstantFoldCompareInstOperands(CI->getPredicate(),
3284 &Operands[0], Operands.size());
3286 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3287 &Operands[0], Operands.size());
3290 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
3291 /// in the header of its containing loop, we know the loop executes a
3292 /// constant number of times, and the PHI node is just a recurrence
3293 /// involving constants, fold it.
3294 Constant *ScalarEvolution::
3295 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
3296 std::map<PHINode*, Constant*>::iterator I =
3297 ConstantEvolutionLoopExitValue.find(PN);
3298 if (I != ConstantEvolutionLoopExitValue.end())
3301 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
3302 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
3304 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
3306 // Since the loop is canonicalized, the PHI node must have two entries. One
3307 // entry must be a constant (coming in from outside of the loop), and the
3308 // second must be derived from the same PHI.
3309 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3310 Constant *StartCST =
3311 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3313 return RetVal = 0; // Must be a constant.
3315 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3316 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3318 return RetVal = 0; // Not derived from same PHI.
3320 // Execute the loop symbolically to determine the exit value.
3321 if (BEs.getActiveBits() >= 32)
3322 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
3324 unsigned NumIterations = BEs.getZExtValue(); // must be in range
3325 unsigned IterationNum = 0;
3326 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
3327 if (IterationNum == NumIterations)
3328 return RetVal = PHIVal; // Got exit value!
3330 // Compute the value of the PHI node for the next iteration.
3331 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3332 if (NextPHI == PHIVal)
3333 return RetVal = NextPHI; // Stopped evolving!
3335 return 0; // Couldn't evaluate!
3340 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
3341 /// constant number of times (the condition evolves only from constants),
3342 /// try to evaluate a few iterations of the loop until we get the exit
3343 /// condition gets a value of ExitWhen (true or false). If we cannot
3344 /// evaluate the trip count of the loop, return CouldNotCompute.
3345 const SCEV* ScalarEvolution::
3346 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
3347 PHINode *PN = getConstantEvolvingPHI(Cond, L);
3348 if (PN == 0) return CouldNotCompute;
3350 // Since the loop is canonicalized, the PHI node must have two entries. One
3351 // entry must be a constant (coming in from outside of the loop), and the
3352 // second must be derived from the same PHI.
3353 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
3354 Constant *StartCST =
3355 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
3356 if (StartCST == 0) return CouldNotCompute; // Must be a constant.
3358 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
3359 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
3360 if (PN2 != PN) return CouldNotCompute; // Not derived from same PHI.
3362 // Okay, we find a PHI node that defines the trip count of this loop. Execute
3363 // the loop symbolically to determine when the condition gets a value of
3365 unsigned IterationNum = 0;
3366 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
3367 for (Constant *PHIVal = StartCST;
3368 IterationNum != MaxIterations; ++IterationNum) {
3369 ConstantInt *CondVal =
3370 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
3372 // Couldn't symbolically evaluate.
3373 if (!CondVal) return CouldNotCompute;
3375 if (CondVal->getValue() == uint64_t(ExitWhen)) {
3376 ConstantEvolutionLoopExitValue[PN] = PHIVal;
3377 ++NumBruteForceTripCountsComputed;
3378 return getConstant(Type::Int32Ty, IterationNum);
3381 // Compute the value of the PHI node for the next iteration.
3382 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
3383 if (NextPHI == 0 || NextPHI == PHIVal)
3384 return CouldNotCompute; // Couldn't evaluate or not making progress...
3388 // Too many iterations were needed to evaluate.
3389 return CouldNotCompute;
3392 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
3393 /// at the specified scope in the program. The L value specifies a loop
3394 /// nest to evaluate the expression at, where null is the top-level or a
3395 /// specified loop is immediately inside of the loop.
3397 /// This method can be used to compute the exit value for a variable defined
3398 /// in a loop by querying what the value will hold in the parent loop.
3400 /// In the case that a relevant loop exit value cannot be computed, the
3401 /// original value V is returned.
3402 const SCEV* ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
3403 // FIXME: this should be turned into a virtual method on SCEV!
3405 if (isa<SCEVConstant>(V)) return V;
3407 // If this instruction is evolved from a constant-evolving PHI, compute the
3408 // exit value from the loop without using SCEVs.
3409 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
3410 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
3411 const Loop *LI = (*this->LI)[I->getParent()];
3412 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
3413 if (PHINode *PN = dyn_cast<PHINode>(I))
3414 if (PN->getParent() == LI->getHeader()) {
3415 // Okay, there is no closed form solution for the PHI node. Check
3416 // to see if the loop that contains it has a known backedge-taken
3417 // count. If so, we may be able to force computation of the exit
3419 const SCEV* BackedgeTakenCount = getBackedgeTakenCount(LI);
3420 if (const SCEVConstant *BTCC =
3421 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
3422 // Okay, we know how many times the containing loop executes. If
3423 // this is a constant evolving PHI node, get the final value at
3424 // the specified iteration number.
3425 Constant *RV = getConstantEvolutionLoopExitValue(PN,
3426 BTCC->getValue()->getValue(),
3428 if (RV) return getUnknown(RV);
3432 // Okay, this is an expression that we cannot symbolically evaluate
3433 // into a SCEV. Check to see if it's possible to symbolically evaluate
3434 // the arguments into constants, and if so, try to constant propagate the
3435 // result. This is particularly useful for computing loop exit values.
3436 if (CanConstantFold(I)) {
3437 // Check to see if we've folded this instruction at this loop before.
3438 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
3439 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
3440 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
3442 return Pair.first->second ? &*getUnknown(Pair.first->second) : V;
3444 std::vector<Constant*> Operands;
3445 Operands.reserve(I->getNumOperands());
3446 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
3447 Value *Op = I->getOperand(i);
3448 if (Constant *C = dyn_cast<Constant>(Op)) {
3449 Operands.push_back(C);
3451 // If any of the operands is non-constant and if they are
3452 // non-integer and non-pointer, don't even try to analyze them
3453 // with scev techniques.
3454 if (!isSCEVable(Op->getType()))
3457 const SCEV* OpV = getSCEVAtScope(getSCEV(Op), L);
3458 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
3459 Constant *C = SC->getValue();
3460 if (C->getType() != Op->getType())
3461 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3465 Operands.push_back(C);
3466 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
3467 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
3468 if (C->getType() != Op->getType())
3470 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
3474 Operands.push_back(C);
3484 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
3485 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
3486 &Operands[0], Operands.size());
3488 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3489 &Operands[0], Operands.size());
3490 Pair.first->second = C;
3491 return getUnknown(C);
3495 // This is some other type of SCEVUnknown, just return it.
3499 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3500 // Avoid performing the look-up in the common case where the specified
3501 // expression has no loop-variant portions.
3502 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3503 const SCEV* OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3504 if (OpAtScope != Comm->getOperand(i)) {
3505 // Okay, at least one of these operands is loop variant but might be
3506 // foldable. Build a new instance of the folded commutative expression.
3507 SmallVector<const SCEV*, 8> NewOps(Comm->op_begin(), Comm->op_begin()+i);
3508 NewOps.push_back(OpAtScope);
3510 for (++i; i != e; ++i) {
3511 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3512 NewOps.push_back(OpAtScope);
3514 if (isa<SCEVAddExpr>(Comm))
3515 return getAddExpr(NewOps);
3516 if (isa<SCEVMulExpr>(Comm))
3517 return getMulExpr(NewOps);
3518 if (isa<SCEVSMaxExpr>(Comm))
3519 return getSMaxExpr(NewOps);
3520 if (isa<SCEVUMaxExpr>(Comm))
3521 return getUMaxExpr(NewOps);
3522 assert(0 && "Unknown commutative SCEV type!");
3525 // If we got here, all operands are loop invariant.
3529 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3530 const SCEV* LHS = getSCEVAtScope(Div->getLHS(), L);
3531 const SCEV* RHS = getSCEVAtScope(Div->getRHS(), L);
3532 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3533 return Div; // must be loop invariant
3534 return getUDivExpr(LHS, RHS);
3537 // If this is a loop recurrence for a loop that does not contain L, then we
3538 // are dealing with the final value computed by the loop.
3539 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3540 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3541 // To evaluate this recurrence, we need to know how many times the AddRec
3542 // loop iterates. Compute this now.
3543 const SCEV* BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3544 if (BackedgeTakenCount == CouldNotCompute) return AddRec;
3546 // Then, evaluate the AddRec.
3547 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3552 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3553 const SCEV* Op = getSCEVAtScope(Cast->getOperand(), L);
3554 if (Op == Cast->getOperand())
3555 return Cast; // must be loop invariant
3556 return getZeroExtendExpr(Op, Cast->getType());
3559 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3560 const SCEV* Op = getSCEVAtScope(Cast->getOperand(), L);
3561 if (Op == Cast->getOperand())
3562 return Cast; // must be loop invariant
3563 return getSignExtendExpr(Op, Cast->getType());
3566 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3567 const SCEV* Op = getSCEVAtScope(Cast->getOperand(), L);
3568 if (Op == Cast->getOperand())
3569 return Cast; // must be loop invariant
3570 return getTruncateExpr(Op, Cast->getType());
3573 assert(0 && "Unknown SCEV type!");
3577 /// getSCEVAtScope - This is a convenience function which does
3578 /// getSCEVAtScope(getSCEV(V), L).
3579 const SCEV* ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3580 return getSCEVAtScope(getSCEV(V), L);
3583 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3584 /// following equation:
3586 /// A * X = B (mod N)
3588 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3589 /// A and B isn't important.
3591 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3592 static const SCEV* SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3593 ScalarEvolution &SE) {
3594 uint32_t BW = A.getBitWidth();
3595 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3596 assert(A != 0 && "A must be non-zero.");
3600 // The gcd of A and N may have only one prime factor: 2. The number of
3601 // trailing zeros in A is its multiplicity
3602 uint32_t Mult2 = A.countTrailingZeros();
3605 // 2. Check if B is divisible by D.
3607 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3608 // is not less than multiplicity of this prime factor for D.
3609 if (B.countTrailingZeros() < Mult2)
3610 return SE.getCouldNotCompute();
3612 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3615 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3616 // bit width during computations.
3617 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3618 APInt Mod(BW + 1, 0);
3619 Mod.set(BW - Mult2); // Mod = N / D
3620 APInt I = AD.multiplicativeInverse(Mod);
3622 // 4. Compute the minimum unsigned root of the equation:
3623 // I * (B / D) mod (N / D)
3624 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3626 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3628 return SE.getConstant(Result.trunc(BW));
3631 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3632 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
3633 /// might be the same) or two SCEVCouldNotCompute objects.
3635 static std::pair<const SCEV*,const SCEV*>
3636 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
3637 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
3638 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
3639 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
3640 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
3642 // We currently can only solve this if the coefficients are constants.
3643 if (!LC || !MC || !NC) {
3644 const SCEV *CNC = SE.getCouldNotCompute();
3645 return std::make_pair(CNC, CNC);
3648 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
3649 const APInt &L = LC->getValue()->getValue();
3650 const APInt &M = MC->getValue()->getValue();
3651 const APInt &N = NC->getValue()->getValue();
3652 APInt Two(BitWidth, 2);
3653 APInt Four(BitWidth, 4);
3656 using namespace APIntOps;
3658 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
3659 // The B coefficient is M-N/2
3663 // The A coefficient is N/2
3664 APInt A(N.sdiv(Two));
3666 // Compute the B^2-4ac term.
3669 SqrtTerm -= Four * (A * C);
3671 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
3672 // integer value or else APInt::sqrt() will assert.
3673 APInt SqrtVal(SqrtTerm.sqrt());
3675 // Compute the two solutions for the quadratic formula.
3676 // The divisions must be performed as signed divisions.
3678 APInt TwoA( A << 1 );
3679 if (TwoA.isMinValue()) {
3680 const SCEV *CNC = SE.getCouldNotCompute();
3681 return std::make_pair(CNC, CNC);
3684 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
3685 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
3687 return std::make_pair(SE.getConstant(Solution1),
3688 SE.getConstant(Solution2));
3689 } // end APIntOps namespace
3692 /// HowFarToZero - Return the number of times a backedge comparing the specified
3693 /// value to zero will execute. If not computable, return CouldNotCompute.
3694 const SCEV* ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
3695 // If the value is a constant
3696 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3697 // If the value is already zero, the branch will execute zero times.
3698 if (C->getValue()->isZero()) return C;
3699 return CouldNotCompute; // Otherwise it will loop infinitely.
3702 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
3703 if (!AddRec || AddRec->getLoop() != L)
3704 return CouldNotCompute;
3706 if (AddRec->isAffine()) {
3707 // If this is an affine expression, the execution count of this branch is
3708 // the minimum unsigned root of the following equation:
3710 // Start + Step*N = 0 (mod 2^BW)
3714 // Step*N = -Start (mod 2^BW)
3716 // where BW is the common bit width of Start and Step.
3718 // Get the initial value for the loop.
3719 const SCEV* Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
3720 const SCEV* Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
3722 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
3723 // For now we handle only constant steps.
3725 // First, handle unitary steps.
3726 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
3727 return getNegativeSCEV(Start); // N = -Start (as unsigned)
3728 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
3729 return Start; // N = Start (as unsigned)
3731 // Then, try to solve the above equation provided that Start is constant.
3732 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
3733 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
3734 -StartC->getValue()->getValue(),
3737 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
3738 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
3739 // the quadratic equation to solve it.
3740 std::pair<const SCEV*,const SCEV*> Roots = SolveQuadraticEquation(AddRec,
3742 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3743 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3746 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
3747 << " sol#2: " << *R2 << "\n";
3749 // Pick the smallest positive root value.
3750 if (ConstantInt *CB =
3751 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3752 R1->getValue(), R2->getValue()))) {
3753 if (CB->getZExtValue() == false)
3754 std::swap(R1, R2); // R1 is the minimum root now.
3756 // We can only use this value if the chrec ends up with an exact zero
3757 // value at this index. When solving for "X*X != 5", for example, we
3758 // should not accept a root of 2.
3759 const SCEV* Val = AddRec->evaluateAtIteration(R1, *this);
3761 return R1; // We found a quadratic root!
3766 return CouldNotCompute;
3769 /// HowFarToNonZero - Return the number of times a backedge checking the
3770 /// specified value for nonzero will execute. If not computable, return
3772 const SCEV* ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
3773 // Loops that look like: while (X == 0) are very strange indeed. We don't
3774 // handle them yet except for the trivial case. This could be expanded in the
3775 // future as needed.
3777 // If the value is a constant, check to see if it is known to be non-zero
3778 // already. If so, the backedge will execute zero times.
3779 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3780 if (!C->getValue()->isNullValue())
3781 return getIntegerSCEV(0, C->getType());
3782 return CouldNotCompute; // Otherwise it will loop infinitely.
3785 // We could implement others, but I really doubt anyone writes loops like
3786 // this, and if they did, they would already be constant folded.
3787 return CouldNotCompute;
3790 /// getLoopPredecessor - If the given loop's header has exactly one unique
3791 /// predecessor outside the loop, return it. Otherwise return null.
3793 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
3794 BasicBlock *Header = L->getHeader();
3795 BasicBlock *Pred = 0;
3796 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
3798 if (!L->contains(*PI)) {
3799 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
3805 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3806 /// (which may not be an immediate predecessor) which has exactly one
3807 /// successor from which BB is reachable, or null if no such block is
3811 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3812 // If the block has a unique predecessor, then there is no path from the
3813 // predecessor to the block that does not go through the direct edge
3814 // from the predecessor to the block.
3815 if (BasicBlock *Pred = BB->getSinglePredecessor())
3818 // A loop's header is defined to be a block that dominates the loop.
3819 // If the header has a unique predecessor outside the loop, it must be
3820 // a block that has exactly one successor that can reach the loop.
3821 if (Loop *L = LI->getLoopFor(BB))
3822 return getLoopPredecessor(L);
3827 /// HasSameValue - SCEV structural equivalence is usually sufficient for
3828 /// testing whether two expressions are equal, however for the purposes of
3829 /// looking for a condition guarding a loop, it can be useful to be a little
3830 /// more general, since a front-end may have replicated the controlling
3833 static bool HasSameValue(const SCEV* A, const SCEV* B) {
3834 // Quick check to see if they are the same SCEV.
3835 if (A == B) return true;
3837 // Otherwise, if they're both SCEVUnknown, it's possible that they hold
3838 // two different instructions with the same value. Check for this case.
3839 if (const SCEVUnknown *AU = dyn_cast<SCEVUnknown>(A))
3840 if (const SCEVUnknown *BU = dyn_cast<SCEVUnknown>(B))
3841 if (const Instruction *AI = dyn_cast<Instruction>(AU->getValue()))
3842 if (const Instruction *BI = dyn_cast<Instruction>(BU->getValue()))
3843 if (AI->isIdenticalTo(BI))
3846 // Otherwise assume they may have a different value.
3850 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
3851 /// a conditional between LHS and RHS. This is used to help avoid max
3852 /// expressions in loop trip counts.
3853 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3854 ICmpInst::Predicate Pred,
3855 const SCEV *LHS, const SCEV *RHS) {
3856 // Interpret a null as meaning no loop, where there is obviously no guard
3857 // (interprocedural conditions notwithstanding).
3858 if (!L) return false;
3860 BasicBlock *Predecessor = getLoopPredecessor(L);
3861 BasicBlock *PredecessorDest = L->getHeader();
3863 // Starting at the loop predecessor, climb up the predecessor chain, as long
3864 // as there are predecessors that can be found that have unique successors
3865 // leading to the original header.
3867 PredecessorDest = Predecessor,
3868 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
3870 BranchInst *LoopEntryPredicate =
3871 dyn_cast<BranchInst>(Predecessor->getTerminator());
3872 if (!LoopEntryPredicate ||
3873 LoopEntryPredicate->isUnconditional())
3876 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3879 // Now that we found a conditional branch that dominates the loop, check to
3880 // see if it is the comparison we are looking for.
3881 Value *PreCondLHS = ICI->getOperand(0);
3882 Value *PreCondRHS = ICI->getOperand(1);
3883 ICmpInst::Predicate Cond;
3884 if (LoopEntryPredicate->getSuccessor(0) == PredecessorDest)
3885 Cond = ICI->getPredicate();
3887 Cond = ICI->getInversePredicate();
3890 ; // An exact match.
3891 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3892 ; // The actual condition is beyond sufficient.
3894 // Check a few special cases.
3896 case ICmpInst::ICMP_UGT:
3897 if (Pred == ICmpInst::ICMP_ULT) {
3898 std::swap(PreCondLHS, PreCondRHS);
3899 Cond = ICmpInst::ICMP_ULT;
3903 case ICmpInst::ICMP_SGT:
3904 if (Pred == ICmpInst::ICMP_SLT) {
3905 std::swap(PreCondLHS, PreCondRHS);
3906 Cond = ICmpInst::ICMP_SLT;
3910 case ICmpInst::ICMP_NE:
3911 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3912 // so check for this case by checking if the NE is comparing against
3913 // a minimum or maximum constant.
3914 if (!ICmpInst::isTrueWhenEqual(Pred))
3915 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3916 const APInt &A = CI->getValue();
3918 case ICmpInst::ICMP_SLT:
3919 if (A.isMaxSignedValue()) break;
3921 case ICmpInst::ICMP_SGT:
3922 if (A.isMinSignedValue()) break;
3924 case ICmpInst::ICMP_ULT:
3925 if (A.isMaxValue()) break;
3927 case ICmpInst::ICMP_UGT:
3928 if (A.isMinValue()) break;
3933 Cond = ICmpInst::ICMP_NE;
3934 // NE is symmetric but the original comparison may not be. Swap
3935 // the operands if necessary so that they match below.
3936 if (isa<SCEVConstant>(LHS))
3937 std::swap(PreCondLHS, PreCondRHS);
3942 // We weren't able to reconcile the condition.
3946 if (!PreCondLHS->getType()->isInteger()) continue;
3948 const SCEV* PreCondLHSSCEV = getSCEV(PreCondLHS);
3949 const SCEV* PreCondRHSSCEV = getSCEV(PreCondRHS);
3950 if ((HasSameValue(LHS, PreCondLHSSCEV) &&
3951 HasSameValue(RHS, PreCondRHSSCEV)) ||
3952 (HasSameValue(LHS, getNotSCEV(PreCondRHSSCEV)) &&
3953 HasSameValue(RHS, getNotSCEV(PreCondLHSSCEV))))
3960 /// getBECount - Subtract the end and start values and divide by the step,
3961 /// rounding up, to get the number of times the backedge is executed. Return
3962 /// CouldNotCompute if an intermediate computation overflows.
3963 const SCEV* ScalarEvolution::getBECount(const SCEV* Start,
3966 const Type *Ty = Start->getType();
3967 const SCEV* NegOne = getIntegerSCEV(-1, Ty);
3968 const SCEV* Diff = getMinusSCEV(End, Start);
3969 const SCEV* RoundUp = getAddExpr(Step, NegOne);
3971 // Add an adjustment to the difference between End and Start so that
3972 // the division will effectively round up.
3973 const SCEV* Add = getAddExpr(Diff, RoundUp);
3975 // Check Add for unsigned overflow.
3976 // TODO: More sophisticated things could be done here.
3977 const Type *WideTy = IntegerType::get(getTypeSizeInBits(Ty) + 1);
3978 const SCEV* OperandExtendedAdd =
3979 getAddExpr(getZeroExtendExpr(Diff, WideTy),
3980 getZeroExtendExpr(RoundUp, WideTy));
3981 if (getZeroExtendExpr(Add, WideTy) != OperandExtendedAdd)
3982 return CouldNotCompute;
3984 return getUDivExpr(Add, Step);
3987 /// HowManyLessThans - Return the number of times a backedge containing the
3988 /// specified less-than comparison will execute. If not computable, return
3989 /// CouldNotCompute.
3990 ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3991 HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
3992 const Loop *L, bool isSigned) {
3993 // Only handle: "ADDREC < LoopInvariant".
3994 if (!RHS->isLoopInvariant(L)) return CouldNotCompute;
3996 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3997 if (!AddRec || AddRec->getLoop() != L)
3998 return CouldNotCompute;
4000 if (AddRec->isAffine()) {
4001 // FORNOW: We only support unit strides.
4002 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
4003 const SCEV* Step = AddRec->getStepRecurrence(*this);
4005 // TODO: handle non-constant strides.
4006 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
4007 if (!CStep || CStep->isZero())
4008 return CouldNotCompute;
4009 if (CStep->isOne()) {
4010 // With unit stride, the iteration never steps past the limit value.
4011 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
4012 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
4013 // Test whether a positive iteration iteration can step past the limit
4014 // value and past the maximum value for its type in a single step.
4016 APInt Max = APInt::getSignedMaxValue(BitWidth);
4017 if ((Max - CStep->getValue()->getValue())
4018 .slt(CLimit->getValue()->getValue()))
4019 return CouldNotCompute;
4021 APInt Max = APInt::getMaxValue(BitWidth);
4022 if ((Max - CStep->getValue()->getValue())
4023 .ult(CLimit->getValue()->getValue()))
4024 return CouldNotCompute;
4027 // TODO: handle non-constant limit values below.
4028 return CouldNotCompute;
4030 // TODO: handle negative strides below.
4031 return CouldNotCompute;
4033 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
4034 // m. So, we count the number of iterations in which {n,+,s} < m is true.
4035 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
4036 // treat m-n as signed nor unsigned due to overflow possibility.
4038 // First, we get the value of the LHS in the first iteration: n
4039 const SCEV* Start = AddRec->getOperand(0);
4041 // Determine the minimum constant start value.
4042 const SCEV* MinStart = isa<SCEVConstant>(Start) ? Start :
4043 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
4044 APInt::getMinValue(BitWidth));
4046 // If we know that the condition is true in order to enter the loop,
4047 // then we know that it will run exactly (m-n)/s times. Otherwise, we
4048 // only know that it will execute (max(m,n)-n)/s times. In both cases,
4049 // the division must round up.
4050 const SCEV* End = RHS;
4051 if (!isLoopGuardedByCond(L,
4052 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
4053 getMinusSCEV(Start, Step), RHS))
4054 End = isSigned ? getSMaxExpr(RHS, Start)
4055 : getUMaxExpr(RHS, Start);
4057 // Determine the maximum constant end value.
4058 const SCEV* MaxEnd =
4059 isa<SCEVConstant>(End) ? End :
4060 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth)
4061 .ashr(GetMinSignBits(End) - 1) :
4062 APInt::getMaxValue(BitWidth)
4063 .lshr(GetMinLeadingZeros(End)));
4065 // Finally, we subtract these two values and divide, rounding up, to get
4066 // the number of times the backedge is executed.
4067 const SCEV* BECount = getBECount(Start, End, Step);
4069 // The maximum backedge count is similar, except using the minimum start
4070 // value and the maximum end value.
4071 const SCEV* MaxBECount = getBECount(MinStart, MaxEnd, Step);;
4073 return BackedgeTakenInfo(BECount, MaxBECount);
4076 return CouldNotCompute;
4079 /// getNumIterationsInRange - Return the number of iterations of this loop that
4080 /// produce values in the specified constant range. Another way of looking at
4081 /// this is that it returns the first iteration number where the value is not in
4082 /// the condition, thus computing the exit count. If the iteration count can't
4083 /// be computed, an instance of SCEVCouldNotCompute is returned.
4084 const SCEV* SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
4085 ScalarEvolution &SE) const {
4086 if (Range.isFullSet()) // Infinite loop.
4087 return SE.getCouldNotCompute();
4089 // If the start is a non-zero constant, shift the range to simplify things.
4090 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
4091 if (!SC->getValue()->isZero()) {
4092 SmallVector<const SCEV*, 4> Operands(op_begin(), op_end());
4093 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
4094 const SCEV* Shifted = SE.getAddRecExpr(Operands, getLoop());
4095 if (const SCEVAddRecExpr *ShiftedAddRec =
4096 dyn_cast<SCEVAddRecExpr>(Shifted))
4097 return ShiftedAddRec->getNumIterationsInRange(
4098 Range.subtract(SC->getValue()->getValue()), SE);
4099 // This is strange and shouldn't happen.
4100 return SE.getCouldNotCompute();
4103 // The only time we can solve this is when we have all constant indices.
4104 // Otherwise, we cannot determine the overflow conditions.
4105 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
4106 if (!isa<SCEVConstant>(getOperand(i)))
4107 return SE.getCouldNotCompute();
4110 // Okay at this point we know that all elements of the chrec are constants and
4111 // that the start element is zero.
4113 // First check to see if the range contains zero. If not, the first
4115 unsigned BitWidth = SE.getTypeSizeInBits(getType());
4116 if (!Range.contains(APInt(BitWidth, 0)))
4117 return SE.getIntegerSCEV(0, getType());
4120 // If this is an affine expression then we have this situation:
4121 // Solve {0,+,A} in Range === Ax in Range
4123 // We know that zero is in the range. If A is positive then we know that
4124 // the upper value of the range must be the first possible exit value.
4125 // If A is negative then the lower of the range is the last possible loop
4126 // value. Also note that we already checked for a full range.
4127 APInt One(BitWidth,1);
4128 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
4129 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
4131 // The exit value should be (End+A)/A.
4132 APInt ExitVal = (End + A).udiv(A);
4133 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
4135 // Evaluate at the exit value. If we really did fall out of the valid
4136 // range, then we computed our trip count, otherwise wrap around or other
4137 // things must have happened.
4138 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
4139 if (Range.contains(Val->getValue()))
4140 return SE.getCouldNotCompute(); // Something strange happened
4142 // Ensure that the previous value is in the range. This is a sanity check.
4143 assert(Range.contains(
4144 EvaluateConstantChrecAtConstant(this,
4145 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
4146 "Linear scev computation is off in a bad way!");
4147 return SE.getConstant(ExitValue);
4148 } else if (isQuadratic()) {
4149 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
4150 // quadratic equation to solve it. To do this, we must frame our problem in
4151 // terms of figuring out when zero is crossed, instead of when
4152 // Range.getUpper() is crossed.
4153 SmallVector<const SCEV*, 4> NewOps(op_begin(), op_end());
4154 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
4155 const SCEV* NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
4157 // Next, solve the constructed addrec
4158 std::pair<const SCEV*,const SCEV*> Roots =
4159 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
4160 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
4161 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
4163 // Pick the smallest positive root value.
4164 if (ConstantInt *CB =
4165 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
4166 R1->getValue(), R2->getValue()))) {
4167 if (CB->getZExtValue() == false)
4168 std::swap(R1, R2); // R1 is the minimum root now.
4170 // Make sure the root is not off by one. The returned iteration should
4171 // not be in the range, but the previous one should be. When solving
4172 // for "X*X < 5", for example, we should not return a root of 2.
4173 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
4176 if (Range.contains(R1Val->getValue())) {
4177 // The next iteration must be out of the range...
4178 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
4180 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4181 if (!Range.contains(R1Val->getValue()))
4182 return SE.getConstant(NextVal);
4183 return SE.getCouldNotCompute(); // Something strange happened
4186 // If R1 was not in the range, then it is a good return value. Make
4187 // sure that R1-1 WAS in the range though, just in case.
4188 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
4189 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
4190 if (Range.contains(R1Val->getValue()))
4192 return SE.getCouldNotCompute(); // Something strange happened
4197 return SE.getCouldNotCompute();
4202 //===----------------------------------------------------------------------===//
4203 // SCEVCallbackVH Class Implementation
4204 //===----------------------------------------------------------------------===//
4206 void ScalarEvolution::SCEVCallbackVH::deleted() {
4207 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
4208 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
4209 SE->ConstantEvolutionLoopExitValue.erase(PN);
4210 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
4211 SE->ValuesAtScopes.erase(I);
4212 SE->Scalars.erase(getValPtr());
4213 // this now dangles!
4216 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
4217 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
4219 // Forget all the expressions associated with users of the old value,
4220 // so that future queries will recompute the expressions using the new
4222 SmallVector<User *, 16> Worklist;
4223 Value *Old = getValPtr();
4224 bool DeleteOld = false;
4225 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
4227 Worklist.push_back(*UI);
4228 while (!Worklist.empty()) {
4229 User *U = Worklist.pop_back_val();
4230 // Deleting the Old value will cause this to dangle. Postpone
4231 // that until everything else is done.
4236 if (PHINode *PN = dyn_cast<PHINode>(U))
4237 SE->ConstantEvolutionLoopExitValue.erase(PN);
4238 if (Instruction *I = dyn_cast<Instruction>(U))
4239 SE->ValuesAtScopes.erase(I);
4240 if (SE->Scalars.erase(U))
4241 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
4243 Worklist.push_back(*UI);
4246 if (PHINode *PN = dyn_cast<PHINode>(Old))
4247 SE->ConstantEvolutionLoopExitValue.erase(PN);
4248 if (Instruction *I = dyn_cast<Instruction>(Old))
4249 SE->ValuesAtScopes.erase(I);
4250 SE->Scalars.erase(Old);
4251 // this now dangles!
4256 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
4257 : CallbackVH(V), SE(se) {}
4259 //===----------------------------------------------------------------------===//
4260 // ScalarEvolution Class Implementation
4261 //===----------------------------------------------------------------------===//
4263 ScalarEvolution::ScalarEvolution()
4264 : FunctionPass(&ID), CouldNotCompute(new SCEVCouldNotCompute(0)) {
4267 bool ScalarEvolution::runOnFunction(Function &F) {
4269 LI = &getAnalysis<LoopInfo>();
4270 TD = getAnalysisIfAvailable<TargetData>();
4274 void ScalarEvolution::releaseMemory() {
4276 BackedgeTakenCounts.clear();
4277 ConstantEvolutionLoopExitValue.clear();
4278 ValuesAtScopes.clear();
4280 for (std::map<ConstantInt*, SCEVConstant*>::iterator
4281 I = SCEVConstants.begin(), E = SCEVConstants.end(); I != E; ++I)
4283 for (std::map<std::pair<const SCEV*, const Type*>,
4284 SCEVTruncateExpr*>::iterator I = SCEVTruncates.begin(),
4285 E = SCEVTruncates.end(); I != E; ++I)
4287 for (std::map<std::pair<const SCEV*, const Type*>,
4288 SCEVZeroExtendExpr*>::iterator I = SCEVZeroExtends.begin(),
4289 E = SCEVZeroExtends.end(); I != E; ++I)
4291 for (std::map<std::pair<unsigned, std::vector<const SCEV*> >,
4292 SCEVCommutativeExpr*>::iterator I = SCEVCommExprs.begin(),
4293 E = SCEVCommExprs.end(); I != E; ++I)
4295 for (std::map<std::pair<const SCEV*, const SCEV*>, SCEVUDivExpr*>::iterator
4296 I = SCEVUDivs.begin(), E = SCEVUDivs.end(); I != E; ++I)
4298 for (std::map<std::pair<const SCEV*, const Type*>,
4299 SCEVSignExtendExpr*>::iterator I = SCEVSignExtends.begin(),
4300 E = SCEVSignExtends.end(); I != E; ++I)
4302 for (std::map<std::pair<const Loop *, std::vector<const SCEV*> >,
4303 SCEVAddRecExpr*>::iterator I = SCEVAddRecExprs.begin(),
4304 E = SCEVAddRecExprs.end(); I != E; ++I)
4306 for (std::map<Value*, SCEVUnknown*>::iterator I = SCEVUnknowns.begin(),
4307 E = SCEVUnknowns.end(); I != E; ++I)
4310 SCEVConstants.clear();
4311 SCEVTruncates.clear();
4312 SCEVZeroExtends.clear();
4313 SCEVCommExprs.clear();
4315 SCEVSignExtends.clear();
4316 SCEVAddRecExprs.clear();
4317 SCEVUnknowns.clear();
4320 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
4321 AU.setPreservesAll();
4322 AU.addRequiredTransitive<LoopInfo>();
4325 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
4326 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
4329 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
4331 // Print all inner loops first
4332 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
4333 PrintLoopInfo(OS, SE, *I);
4335 OS << "Loop " << L->getHeader()->getName() << ": ";
4337 SmallVector<BasicBlock*, 8> ExitBlocks;
4338 L->getExitBlocks(ExitBlocks);
4339 if (ExitBlocks.size() != 1)
4340 OS << "<multiple exits> ";
4342 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
4343 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
4345 OS << "Unpredictable backedge-taken count. ";
4351 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
4352 // ScalarEvolution's implementaiton of the print method is to print
4353 // out SCEV values of all instructions that are interesting. Doing
4354 // this potentially causes it to create new SCEV objects though,
4355 // which technically conflicts with the const qualifier. This isn't
4356 // observable from outside the class though (the hasSCEV function
4357 // notwithstanding), so casting away the const isn't dangerous.
4358 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
4360 OS << "Classifying expressions for: " << F->getName() << "\n";
4361 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
4362 if (isSCEVable(I->getType())) {
4365 const SCEV* SV = SE.getSCEV(&*I);
4368 const Loop *L = LI->getLoopFor((*I).getParent());
4370 const SCEV* AtUse = SE.getSCEVAtScope(SV, L);
4377 OS << "\t\t" "Exits: ";
4378 const SCEV* ExitValue = SE.getSCEVAtScope(SV, L->getParentLoop());
4379 if (!ExitValue->isLoopInvariant(L)) {
4380 OS << "<<Unknown>>";
4389 OS << "Determining loop execution counts for: " << F->getName() << "\n";
4390 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
4391 PrintLoopInfo(OS, &SE, *I);
4394 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
4395 raw_os_ostream OS(o);