1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file is distributed under the University of Illinois Open Source
6 // License. See LICENSE.TXT for details.
8 //===----------------------------------------------------------------------===//
10 // This file contains the implementation of the scalar evolution analysis
11 // engine, which is used primarily to analyze expressions involving induction
12 // variables in loops.
14 // There are several aspects to this library. First is the representation of
15 // scalar expressions, which are represented as subclasses of the SCEV class.
16 // These classes are used to represent certain types of subexpressions that we
17 // can handle. These classes are reference counted, managed by the SCEVHandle
18 // class. We only create one SCEV of a particular shape, so pointer-comparisons
19 // for equality are legal.
21 // One important aspect of the SCEV objects is that they are never cyclic, even
22 // if there is a cycle in the dataflow for an expression (ie, a PHI node). If
23 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
24 // recurrence) then we represent it directly as a recurrence node, otherwise we
25 // represent it as a SCEVUnknown node.
27 // In addition to being able to represent expressions of various types, we also
28 // have folders that are used to build the *canonical* representation for a
29 // particular expression. These folders are capable of using a variety of
30 // rewrite rules to simplify the expressions.
32 // Once the folders are defined, we can implement the more interesting
33 // higher-level code, such as the code that recognizes PHI nodes of various
34 // types, computes the execution count of a loop, etc.
36 // TODO: We should use these routines and value representations to implement
37 // dependence analysis!
39 //===----------------------------------------------------------------------===//
41 // There are several good references for the techniques used in this analysis.
43 // Chains of recurrences -- a method to expedite the evaluation
44 // of closed-form functions
45 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
47 // On computational properties of chains of recurrences
50 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
51 // Robert A. van Engelen
53 // Efficient Symbolic Analysis for Optimizing Compilers
54 // Robert A. van Engelen
56 // Using the chains of recurrences algebra for data dependence testing and
57 // induction variable substitution
58 // MS Thesis, Johnie Birch
60 //===----------------------------------------------------------------------===//
62 #define DEBUG_TYPE "scalar-evolution"
63 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
64 #include "llvm/Constants.h"
65 #include "llvm/DerivedTypes.h"
66 #include "llvm/GlobalVariable.h"
67 #include "llvm/Instructions.h"
68 #include "llvm/Analysis/ConstantFolding.h"
69 #include "llvm/Analysis/Dominators.h"
70 #include "llvm/Analysis/LoopInfo.h"
71 #include "llvm/Assembly/Writer.h"
72 #include "llvm/Target/TargetData.h"
73 #include "llvm/Support/CommandLine.h"
74 #include "llvm/Support/Compiler.h"
75 #include "llvm/Support/ConstantRange.h"
76 #include "llvm/Support/GetElementPtrTypeIterator.h"
77 #include "llvm/Support/InstIterator.h"
78 #include "llvm/Support/ManagedStatic.h"
79 #include "llvm/Support/MathExtras.h"
80 #include "llvm/Support/raw_ostream.h"
81 #include "llvm/ADT/Statistic.h"
82 #include "llvm/ADT/STLExtras.h"
87 STATISTIC(NumArrayLenItCounts,
88 "Number of trip counts computed with array length");
89 STATISTIC(NumTripCountsComputed,
90 "Number of loops with predictable loop counts");
91 STATISTIC(NumTripCountsNotComputed,
92 "Number of loops without predictable loop counts");
93 STATISTIC(NumBruteForceTripCountsComputed,
94 "Number of loops with trip counts computed by force");
96 static cl::opt<unsigned>
97 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
98 cl::desc("Maximum number of iterations SCEV will "
99 "symbolically execute a constant derived loop"),
102 static RegisterPass<ScalarEvolution>
103 R("scalar-evolution", "Scalar Evolution Analysis", false, true);
104 char ScalarEvolution::ID = 0;
106 //===----------------------------------------------------------------------===//
107 // SCEV class definitions
108 //===----------------------------------------------------------------------===//
110 //===----------------------------------------------------------------------===//
111 // Implementation of the SCEV class.
114 void SCEV::dump() const {
119 void SCEV::print(std::ostream &o) const {
120 raw_os_ostream OS(o);
124 bool SCEV::isZero() const {
125 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
126 return SC->getValue()->isZero();
130 bool SCEV::isOne() const {
131 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(this))
132 return SC->getValue()->isOne();
136 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
137 SCEVCouldNotCompute::~SCEVCouldNotCompute() {}
139 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
140 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
144 const Type *SCEVCouldNotCompute::getType() const {
145 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
149 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
150 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
154 SCEVHandle SCEVCouldNotCompute::
155 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
156 const SCEVHandle &Conc,
157 ScalarEvolution &SE) const {
161 void SCEVCouldNotCompute::print(raw_ostream &OS) const {
162 OS << "***COULDNOTCOMPUTE***";
165 bool SCEVCouldNotCompute::classof(const SCEV *S) {
166 return S->getSCEVType() == scCouldNotCompute;
170 // SCEVConstants - Only allow the creation of one SCEVConstant for any
171 // particular value. Don't use a SCEVHandle here, or else the object will
173 static ManagedStatic<std::map<ConstantInt*, SCEVConstant*> > SCEVConstants;
176 SCEVConstant::~SCEVConstant() {
177 SCEVConstants->erase(V);
180 SCEVHandle ScalarEvolution::getConstant(ConstantInt *V) {
181 SCEVConstant *&R = (*SCEVConstants)[V];
182 if (R == 0) R = new SCEVConstant(V);
186 SCEVHandle ScalarEvolution::getConstant(const APInt& Val) {
187 return getConstant(ConstantInt::get(Val));
190 const Type *SCEVConstant::getType() const { return V->getType(); }
192 void SCEVConstant::print(raw_ostream &OS) const {
193 WriteAsOperand(OS, V, false);
196 SCEVCastExpr::SCEVCastExpr(unsigned SCEVTy,
197 const SCEVHandle &op, const Type *ty)
198 : SCEV(SCEVTy), Op(op), Ty(ty) {}
200 SCEVCastExpr::~SCEVCastExpr() {}
202 bool SCEVCastExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
203 return Op->dominates(BB, DT);
206 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
207 // particular input. Don't use a SCEVHandle here, or else the object will
209 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
210 SCEVTruncateExpr*> > SCEVTruncates;
212 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
213 : SCEVCastExpr(scTruncate, op, ty) {
214 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
215 (Ty->isInteger() || isa<PointerType>(Ty)) &&
216 "Cannot truncate non-integer value!");
219 SCEVTruncateExpr::~SCEVTruncateExpr() {
220 SCEVTruncates->erase(std::make_pair(Op, Ty));
223 void SCEVTruncateExpr::print(raw_ostream &OS) const {
224 OS << "(trunc " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
227 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
228 // particular input. Don't use a SCEVHandle here, or else the object will never
230 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
231 SCEVZeroExtendExpr*> > SCEVZeroExtends;
233 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
234 : SCEVCastExpr(scZeroExtend, op, ty) {
235 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
236 (Ty->isInteger() || isa<PointerType>(Ty)) &&
237 "Cannot zero extend non-integer value!");
240 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
241 SCEVZeroExtends->erase(std::make_pair(Op, Ty));
244 void SCEVZeroExtendExpr::print(raw_ostream &OS) const {
245 OS << "(zext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
248 // SCEVSignExtends - Only allow the creation of one SCEVSignExtendExpr for any
249 // particular input. Don't use a SCEVHandle here, or else the object will never
251 static ManagedStatic<std::map<std::pair<const SCEV*, const Type*>,
252 SCEVSignExtendExpr*> > SCEVSignExtends;
254 SCEVSignExtendExpr::SCEVSignExtendExpr(const SCEVHandle &op, const Type *ty)
255 : SCEVCastExpr(scSignExtend, op, ty) {
256 assert((Op->getType()->isInteger() || isa<PointerType>(Op->getType())) &&
257 (Ty->isInteger() || isa<PointerType>(Ty)) &&
258 "Cannot sign extend non-integer value!");
261 SCEVSignExtendExpr::~SCEVSignExtendExpr() {
262 SCEVSignExtends->erase(std::make_pair(Op, Ty));
265 void SCEVSignExtendExpr::print(raw_ostream &OS) const {
266 OS << "(sext " << *Op->getType() << " " << *Op << " to " << *Ty << ")";
269 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
270 // particular input. Don't use a SCEVHandle here, or else the object will never
272 static ManagedStatic<std::map<std::pair<unsigned, std::vector<const SCEV*> >,
273 SCEVCommutativeExpr*> > SCEVCommExprs;
275 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
276 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
277 SCEVCommExprs->erase(std::make_pair(getSCEVType(), SCEVOps));
280 void SCEVCommutativeExpr::print(raw_ostream &OS) const {
281 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
282 const char *OpStr = getOperationStr();
283 OS << "(" << *Operands[0];
284 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
285 OS << OpStr << *Operands[i];
289 SCEVHandle SCEVCommutativeExpr::
290 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
291 const SCEVHandle &Conc,
292 ScalarEvolution &SE) const {
293 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
295 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
296 if (H != getOperand(i)) {
297 std::vector<SCEVHandle> NewOps;
298 NewOps.reserve(getNumOperands());
299 for (unsigned j = 0; j != i; ++j)
300 NewOps.push_back(getOperand(j));
302 for (++i; i != e; ++i)
303 NewOps.push_back(getOperand(i)->
304 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
306 if (isa<SCEVAddExpr>(this))
307 return SE.getAddExpr(NewOps);
308 else if (isa<SCEVMulExpr>(this))
309 return SE.getMulExpr(NewOps);
310 else if (isa<SCEVSMaxExpr>(this))
311 return SE.getSMaxExpr(NewOps);
312 else if (isa<SCEVUMaxExpr>(this))
313 return SE.getUMaxExpr(NewOps);
315 assert(0 && "Unknown commutative expr!");
321 bool SCEVNAryExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
322 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
323 if (!getOperand(i)->dominates(BB, DT))
330 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
331 // input. Don't use a SCEVHandle here, or else the object will never be
333 static ManagedStatic<std::map<std::pair<const SCEV*, const SCEV*>,
334 SCEVUDivExpr*> > SCEVUDivs;
336 SCEVUDivExpr::~SCEVUDivExpr() {
337 SCEVUDivs->erase(std::make_pair(LHS, RHS));
340 bool SCEVUDivExpr::dominates(BasicBlock *BB, DominatorTree *DT) const {
341 return LHS->dominates(BB, DT) && RHS->dominates(BB, DT);
344 void SCEVUDivExpr::print(raw_ostream &OS) const {
345 OS << "(" << *LHS << " /u " << *RHS << ")";
348 const Type *SCEVUDivExpr::getType() const {
349 return LHS->getType();
352 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
353 // particular input. Don't use a SCEVHandle here, or else the object will never
355 static ManagedStatic<std::map<std::pair<const Loop *,
356 std::vector<const SCEV*> >,
357 SCEVAddRecExpr*> > SCEVAddRecExprs;
359 SCEVAddRecExpr::~SCEVAddRecExpr() {
360 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
361 SCEVAddRecExprs->erase(std::make_pair(L, SCEVOps));
364 SCEVHandle SCEVAddRecExpr::
365 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
366 const SCEVHandle &Conc,
367 ScalarEvolution &SE) const {
368 for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
370 getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc, SE);
371 if (H != getOperand(i)) {
372 std::vector<SCEVHandle> NewOps;
373 NewOps.reserve(getNumOperands());
374 for (unsigned j = 0; j != i; ++j)
375 NewOps.push_back(getOperand(j));
377 for (++i; i != e; ++i)
378 NewOps.push_back(getOperand(i)->
379 replaceSymbolicValuesWithConcrete(Sym, Conc, SE));
381 return SE.getAddRecExpr(NewOps, L);
388 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
389 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
390 // contain L and if the start is invariant.
391 // Add recurrences are never invariant in the function-body (null loop).
393 !QueryLoop->contains(L->getHeader()) &&
394 getOperand(0)->isLoopInvariant(QueryLoop);
398 void SCEVAddRecExpr::print(raw_ostream &OS) const {
399 OS << "{" << *Operands[0];
400 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
401 OS << ",+," << *Operands[i];
402 OS << "}<" << L->getHeader()->getName() + ">";
405 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
406 // value. Don't use a SCEVHandle here, or else the object will never be
408 static ManagedStatic<std::map<Value*, SCEVUnknown*> > SCEVUnknowns;
410 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns->erase(V); }
412 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
413 // All non-instruction values are loop invariant. All instructions are loop
414 // invariant if they are not contained in the specified loop.
415 // Instructions are never considered invariant in the function body
416 // (null loop) because they are defined within the "loop".
417 if (Instruction *I = dyn_cast<Instruction>(V))
418 return L && !L->contains(I->getParent());
422 bool SCEVUnknown::dominates(BasicBlock *BB, DominatorTree *DT) const {
423 if (Instruction *I = dyn_cast<Instruction>(getValue()))
424 return DT->dominates(I->getParent(), BB);
428 const Type *SCEVUnknown::getType() const {
432 void SCEVUnknown::print(raw_ostream &OS) const {
433 WriteAsOperand(OS, V, false);
436 //===----------------------------------------------------------------------===//
438 //===----------------------------------------------------------------------===//
441 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
442 /// than the complexity of the RHS. This comparator is used to canonicalize
444 class VISIBILITY_HIDDEN SCEVComplexityCompare {
447 explicit SCEVComplexityCompare(LoopInfo *li) : LI(li) {}
449 bool operator()(const SCEV *LHS, const SCEV *RHS) const {
450 // Primarily, sort the SCEVs by their getSCEVType().
451 if (LHS->getSCEVType() != RHS->getSCEVType())
452 return LHS->getSCEVType() < RHS->getSCEVType();
454 // Aside from the getSCEVType() ordering, the particular ordering
455 // isn't very important except that it's beneficial to be consistent,
456 // so that (a + b) and (b + a) don't end up as different expressions.
458 // Sort SCEVUnknown values with some loose heuristics. TODO: This is
459 // not as complete as it could be.
460 if (const SCEVUnknown *LU = dyn_cast<SCEVUnknown>(LHS)) {
461 const SCEVUnknown *RU = cast<SCEVUnknown>(RHS);
463 // Order pointer values after integer values. This helps SCEVExpander
465 if (isa<PointerType>(LU->getType()) && !isa<PointerType>(RU->getType()))
467 if (isa<PointerType>(RU->getType()) && !isa<PointerType>(LU->getType()))
470 // Compare getValueID values.
471 if (LU->getValue()->getValueID() != RU->getValue()->getValueID())
472 return LU->getValue()->getValueID() < RU->getValue()->getValueID();
474 // Sort arguments by their position.
475 if (const Argument *LA = dyn_cast<Argument>(LU->getValue())) {
476 const Argument *RA = cast<Argument>(RU->getValue());
477 return LA->getArgNo() < RA->getArgNo();
480 // For instructions, compare their loop depth, and their opcode.
481 // This is pretty loose.
482 if (Instruction *LV = dyn_cast<Instruction>(LU->getValue())) {
483 Instruction *RV = cast<Instruction>(RU->getValue());
485 // Compare loop depths.
486 if (LI->getLoopDepth(LV->getParent()) !=
487 LI->getLoopDepth(RV->getParent()))
488 return LI->getLoopDepth(LV->getParent()) <
489 LI->getLoopDepth(RV->getParent());
492 if (LV->getOpcode() != RV->getOpcode())
493 return LV->getOpcode() < RV->getOpcode();
495 // Compare the number of operands.
496 if (LV->getNumOperands() != RV->getNumOperands())
497 return LV->getNumOperands() < RV->getNumOperands();
503 // Constant sorting doesn't matter since they'll be folded.
504 if (isa<SCEVConstant>(LHS))
507 // Lexicographically compare n-ary expressions.
508 if (const SCEVNAryExpr *LC = dyn_cast<SCEVNAryExpr>(LHS)) {
509 const SCEVNAryExpr *RC = cast<SCEVNAryExpr>(RHS);
510 for (unsigned i = 0, e = LC->getNumOperands(); i != e; ++i) {
511 if (i >= RC->getNumOperands())
513 if (operator()(LC->getOperand(i), RC->getOperand(i)))
515 if (operator()(RC->getOperand(i), LC->getOperand(i)))
518 return LC->getNumOperands() < RC->getNumOperands();
521 // Lexicographically compare udiv expressions.
522 if (const SCEVUDivExpr *LC = dyn_cast<SCEVUDivExpr>(LHS)) {
523 const SCEVUDivExpr *RC = cast<SCEVUDivExpr>(RHS);
524 if (operator()(LC->getLHS(), RC->getLHS()))
526 if (operator()(RC->getLHS(), LC->getLHS()))
528 if (operator()(LC->getRHS(), RC->getRHS()))
530 if (operator()(RC->getRHS(), LC->getRHS()))
535 // Compare cast expressions by operand.
536 if (const SCEVCastExpr *LC = dyn_cast<SCEVCastExpr>(LHS)) {
537 const SCEVCastExpr *RC = cast<SCEVCastExpr>(RHS);
538 return operator()(LC->getOperand(), RC->getOperand());
541 assert(0 && "Unknown SCEV kind!");
547 /// GroupByComplexity - Given a list of SCEV objects, order them by their
548 /// complexity, and group objects of the same complexity together by value.
549 /// When this routine is finished, we know that any duplicates in the vector are
550 /// consecutive and that complexity is monotonically increasing.
552 /// Note that we go take special precautions to ensure that we get determinstic
553 /// results from this routine. In other words, we don't want the results of
554 /// this to depend on where the addresses of various SCEV objects happened to
557 static void GroupByComplexity(std::vector<SCEVHandle> &Ops,
559 if (Ops.size() < 2) return; // Noop
560 if (Ops.size() == 2) {
561 // This is the common case, which also happens to be trivially simple.
563 if (SCEVComplexityCompare(LI)(Ops[1], Ops[0]))
564 std::swap(Ops[0], Ops[1]);
568 // Do the rough sort by complexity.
569 std::stable_sort(Ops.begin(), Ops.end(), SCEVComplexityCompare(LI));
571 // Now that we are sorted by complexity, group elements of the same
572 // complexity. Note that this is, at worst, N^2, but the vector is likely to
573 // be extremely short in practice. Note that we take this approach because we
574 // do not want to depend on the addresses of the objects we are grouping.
575 for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
576 const SCEV *S = Ops[i];
577 unsigned Complexity = S->getSCEVType();
579 // If there are any objects of the same complexity and same value as this
581 for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
582 if (Ops[j] == S) { // Found a duplicate.
583 // Move it to immediately after i'th element.
584 std::swap(Ops[i+1], Ops[j]);
585 ++i; // no need to rescan it.
586 if (i == e-2) return; // Done!
594 //===----------------------------------------------------------------------===//
595 // Simple SCEV method implementations
596 //===----------------------------------------------------------------------===//
598 /// BinomialCoefficient - Compute BC(It, K). The result has width W.
600 static SCEVHandle BinomialCoefficient(SCEVHandle It, unsigned K,
602 const Type* ResultTy) {
603 // Handle the simplest case efficiently.
605 return SE.getTruncateOrZeroExtend(It, ResultTy);
607 // We are using the following formula for BC(It, K):
609 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / K!
611 // Suppose, W is the bitwidth of the return value. We must be prepared for
612 // overflow. Hence, we must assure that the result of our computation is
613 // equal to the accurate one modulo 2^W. Unfortunately, division isn't
614 // safe in modular arithmetic.
616 // However, this code doesn't use exactly that formula; the formula it uses
617 // is something like the following, where T is the number of factors of 2 in
618 // K! (i.e. trailing zeros in the binary representation of K!), and ^ is
621 // BC(It, K) = (It * (It - 1) * ... * (It - K + 1)) / 2^T / (K! / 2^T)
623 // This formula is trivially equivalent to the previous formula. However,
624 // this formula can be implemented much more efficiently. The trick is that
625 // K! / 2^T is odd, and exact division by an odd number *is* safe in modular
626 // arithmetic. To do exact division in modular arithmetic, all we have
627 // to do is multiply by the inverse. Therefore, this step can be done at
630 // The next issue is how to safely do the division by 2^T. The way this
631 // is done is by doing the multiplication step at a width of at least W + T
632 // bits. This way, the bottom W+T bits of the product are accurate. Then,
633 // when we perform the division by 2^T (which is equivalent to a right shift
634 // by T), the bottom W bits are accurate. Extra bits are okay; they'll get
635 // truncated out after the division by 2^T.
637 // In comparison to just directly using the first formula, this technique
638 // is much more efficient; using the first formula requires W * K bits,
639 // but this formula less than W + K bits. Also, the first formula requires
640 // a division step, whereas this formula only requires multiplies and shifts.
642 // It doesn't matter whether the subtraction step is done in the calculation
643 // width or the input iteration count's width; if the subtraction overflows,
644 // the result must be zero anyway. We prefer here to do it in the width of
645 // the induction variable because it helps a lot for certain cases; CodeGen
646 // isn't smart enough to ignore the overflow, which leads to much less
647 // efficient code if the width of the subtraction is wider than the native
650 // (It's possible to not widen at all by pulling out factors of 2 before
651 // the multiplication; for example, K=2 can be calculated as
652 // It/2*(It+(It*INT_MIN/INT_MIN)+-1). However, it requires
653 // extra arithmetic, so it's not an obvious win, and it gets
654 // much more complicated for K > 3.)
656 // Protection from insane SCEVs; this bound is conservative,
657 // but it probably doesn't matter.
659 return SE.getCouldNotCompute();
661 unsigned W = SE.getTypeSizeInBits(ResultTy);
663 // Calculate K! / 2^T and T; we divide out the factors of two before
664 // multiplying for calculating K! / 2^T to avoid overflow.
665 // Other overflow doesn't matter because we only care about the bottom
666 // W bits of the result.
667 APInt OddFactorial(W, 1);
669 for (unsigned i = 3; i <= K; ++i) {
671 unsigned TwoFactors = Mult.countTrailingZeros();
673 Mult = Mult.lshr(TwoFactors);
674 OddFactorial *= Mult;
677 // We need at least W + T bits for the multiplication step
678 unsigned CalculationBits = W + T;
680 // Calcuate 2^T, at width T+W.
681 APInt DivFactor = APInt(CalculationBits, 1).shl(T);
683 // Calculate the multiplicative inverse of K! / 2^T;
684 // this multiplication factor will perform the exact division by
686 APInt Mod = APInt::getSignedMinValue(W+1);
687 APInt MultiplyFactor = OddFactorial.zext(W+1);
688 MultiplyFactor = MultiplyFactor.multiplicativeInverse(Mod);
689 MultiplyFactor = MultiplyFactor.trunc(W);
691 // Calculate the product, at width T+W
692 const IntegerType *CalculationTy = IntegerType::get(CalculationBits);
693 SCEVHandle Dividend = SE.getTruncateOrZeroExtend(It, CalculationTy);
694 for (unsigned i = 1; i != K; ++i) {
695 SCEVHandle S = SE.getMinusSCEV(It, SE.getIntegerSCEV(i, It->getType()));
696 Dividend = SE.getMulExpr(Dividend,
697 SE.getTruncateOrZeroExtend(S, CalculationTy));
701 SCEVHandle DivResult = SE.getUDivExpr(Dividend, SE.getConstant(DivFactor));
703 // Truncate the result, and divide by K! / 2^T.
705 return SE.getMulExpr(SE.getConstant(MultiplyFactor),
706 SE.getTruncateOrZeroExtend(DivResult, ResultTy));
709 /// evaluateAtIteration - Return the value of this chain of recurrences at
710 /// the specified iteration number. We can evaluate this recurrence by
711 /// multiplying each element in the chain by the binomial coefficient
712 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
714 /// A*BC(It, 0) + B*BC(It, 1) + C*BC(It, 2) + D*BC(It, 3)
716 /// where BC(It, k) stands for binomial coefficient.
718 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It,
719 ScalarEvolution &SE) const {
720 SCEVHandle Result = getStart();
721 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
722 // The computation is correct in the face of overflow provided that the
723 // multiplication is performed _after_ the evaluation of the binomial
725 SCEVHandle Coeff = BinomialCoefficient(It, i, SE, getType());
726 if (isa<SCEVCouldNotCompute>(Coeff))
729 Result = SE.getAddExpr(Result, SE.getMulExpr(getOperand(i), Coeff));
734 //===----------------------------------------------------------------------===//
735 // SCEV Expression folder implementations
736 //===----------------------------------------------------------------------===//
738 SCEVHandle ScalarEvolution::getTruncateExpr(const SCEVHandle &Op,
740 assert(getTypeSizeInBits(Op->getType()) > getTypeSizeInBits(Ty) &&
741 "This is not a truncating conversion!");
742 assert(isSCEVable(Ty) &&
743 "This is not a conversion to a SCEVable type!");
744 Ty = getEffectiveSCEVType(Ty);
746 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
748 ConstantExpr::getTrunc(SC->getValue(), Ty));
750 // trunc(trunc(x)) --> trunc(x)
751 if (const SCEVTruncateExpr *ST = dyn_cast<SCEVTruncateExpr>(Op))
752 return getTruncateExpr(ST->getOperand(), Ty);
754 // trunc(sext(x)) --> sext(x) if widening or trunc(x) if narrowing
755 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
756 return getTruncateOrSignExtend(SS->getOperand(), Ty);
758 // trunc(zext(x)) --> zext(x) if widening or trunc(x) if narrowing
759 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
760 return getTruncateOrZeroExtend(SZ->getOperand(), Ty);
762 // If the input value is a chrec scev made out of constants, truncate
763 // all of the constants.
764 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
765 std::vector<SCEVHandle> Operands;
766 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
767 Operands.push_back(getTruncateExpr(AddRec->getOperand(i), Ty));
768 return getAddRecExpr(Operands, AddRec->getLoop());
771 SCEVTruncateExpr *&Result = (*SCEVTruncates)[std::make_pair(Op, Ty)];
772 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
776 SCEVHandle ScalarEvolution::getZeroExtendExpr(const SCEVHandle &Op,
778 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
779 "This is not an extending conversion!");
780 assert(isSCEVable(Ty) &&
781 "This is not a conversion to a SCEVable type!");
782 Ty = getEffectiveSCEVType(Ty);
784 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
785 const Type *IntTy = getEffectiveSCEVType(Ty);
786 Constant *C = ConstantExpr::getZExt(SC->getValue(), IntTy);
787 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
788 return getUnknown(C);
791 // zext(zext(x)) --> zext(x)
792 if (const SCEVZeroExtendExpr *SZ = dyn_cast<SCEVZeroExtendExpr>(Op))
793 return getZeroExtendExpr(SZ->getOperand(), Ty);
795 // If the input value is a chrec scev, and we can prove that the value
796 // did not overflow the old, smaller, value, we can zero extend all of the
797 // operands (often constants). This allows analysis of something like
798 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
799 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
800 if (AR->isAffine()) {
801 // Check whether the backedge-taken count is SCEVCouldNotCompute.
802 // Note that this serves two purposes: It filters out loops that are
803 // simply not analyzable, and it covers the case where this code is
804 // being called from within backedge-taken count analysis, such that
805 // attempting to ask for the backedge-taken count would likely result
806 // in infinite recursion. In the later case, the analysis code will
807 // cope with a conservative value, and it will take care to purge
808 // that value once it has finished.
809 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
810 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
811 // Manually compute the final value for AR, checking for
813 SCEVHandle Start = AR->getStart();
814 SCEVHandle Step = AR->getStepRecurrence(*this);
816 // Check whether the backedge-taken count can be losslessly casted to
817 // the addrec's type. The count is always unsigned.
818 SCEVHandle CastedMaxBECount =
819 getTruncateOrZeroExtend(MaxBECount, Start->getType());
820 SCEVHandle RecastedMaxBECount =
821 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
822 if (MaxBECount == RecastedMaxBECount) {
824 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
825 // Check whether Start+Step*MaxBECount has no unsigned overflow.
827 getMulExpr(CastedMaxBECount,
828 getTruncateOrZeroExtend(Step, Start->getType()));
829 SCEVHandle Add = getAddExpr(Start, ZMul);
830 SCEVHandle OperandExtendedAdd =
831 getAddExpr(getZeroExtendExpr(Start, WideTy),
832 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
833 getZeroExtendExpr(Step, WideTy)));
834 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
835 // Return the expression with the addrec on the outside.
836 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
837 getZeroExtendExpr(Step, Ty),
840 // Similar to above, only this time treat the step value as signed.
841 // This covers loops that count down.
843 getMulExpr(CastedMaxBECount,
844 getTruncateOrSignExtend(Step, Start->getType()));
845 Add = getAddExpr(Start, SMul);
847 getAddExpr(getZeroExtendExpr(Start, WideTy),
848 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
849 getSignExtendExpr(Step, WideTy)));
850 if (getZeroExtendExpr(Add, WideTy) == OperandExtendedAdd)
851 // Return the expression with the addrec on the outside.
852 return getAddRecExpr(getZeroExtendExpr(Start, Ty),
853 getSignExtendExpr(Step, Ty),
859 SCEVZeroExtendExpr *&Result = (*SCEVZeroExtends)[std::make_pair(Op, Ty)];
860 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
864 SCEVHandle ScalarEvolution::getSignExtendExpr(const SCEVHandle &Op,
866 assert(getTypeSizeInBits(Op->getType()) < getTypeSizeInBits(Ty) &&
867 "This is not an extending conversion!");
868 assert(isSCEVable(Ty) &&
869 "This is not a conversion to a SCEVable type!");
870 Ty = getEffectiveSCEVType(Ty);
872 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(Op)) {
873 const Type *IntTy = getEffectiveSCEVType(Ty);
874 Constant *C = ConstantExpr::getSExt(SC->getValue(), IntTy);
875 if (IntTy != Ty) C = ConstantExpr::getIntToPtr(C, Ty);
876 return getUnknown(C);
879 // sext(sext(x)) --> sext(x)
880 if (const SCEVSignExtendExpr *SS = dyn_cast<SCEVSignExtendExpr>(Op))
881 return getSignExtendExpr(SS->getOperand(), Ty);
883 // If the input value is a chrec scev, and we can prove that the value
884 // did not overflow the old, smaller, value, we can sign extend all of the
885 // operands (often constants). This allows analysis of something like
886 // this: for (signed char X = 0; X < 100; ++X) { int Y = X; }
887 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Op))
888 if (AR->isAffine()) {
889 // Check whether the backedge-taken count is SCEVCouldNotCompute.
890 // Note that this serves two purposes: It filters out loops that are
891 // simply not analyzable, and it covers the case where this code is
892 // being called from within backedge-taken count analysis, such that
893 // attempting to ask for the backedge-taken count would likely result
894 // in infinite recursion. In the later case, the analysis code will
895 // cope with a conservative value, and it will take care to purge
896 // that value once it has finished.
897 SCEVHandle MaxBECount = getMaxBackedgeTakenCount(AR->getLoop());
898 if (!isa<SCEVCouldNotCompute>(MaxBECount)) {
899 // Manually compute the final value for AR, checking for
901 SCEVHandle Start = AR->getStart();
902 SCEVHandle Step = AR->getStepRecurrence(*this);
904 // Check whether the backedge-taken count can be losslessly casted to
905 // the addrec's type. The count is always unsigned.
906 SCEVHandle CastedMaxBECount =
907 getTruncateOrZeroExtend(MaxBECount, Start->getType());
908 SCEVHandle RecastedMaxBECount =
909 getTruncateOrZeroExtend(CastedMaxBECount, MaxBECount->getType());
910 if (MaxBECount == RecastedMaxBECount) {
912 IntegerType::get(getTypeSizeInBits(Start->getType()) * 2);
913 // Check whether Start+Step*MaxBECount has no signed overflow.
915 getMulExpr(CastedMaxBECount,
916 getTruncateOrSignExtend(Step, Start->getType()));
917 SCEVHandle Add = getAddExpr(Start, SMul);
918 SCEVHandle OperandExtendedAdd =
919 getAddExpr(getSignExtendExpr(Start, WideTy),
920 getMulExpr(getZeroExtendExpr(CastedMaxBECount, WideTy),
921 getSignExtendExpr(Step, WideTy)));
922 if (getSignExtendExpr(Add, WideTy) == OperandExtendedAdd)
923 // Return the expression with the addrec on the outside.
924 return getAddRecExpr(getSignExtendExpr(Start, Ty),
925 getSignExtendExpr(Step, Ty),
931 SCEVSignExtendExpr *&Result = (*SCEVSignExtends)[std::make_pair(Op, Ty)];
932 if (Result == 0) Result = new SCEVSignExtendExpr(Op, Ty);
936 // get - Get a canonical add expression, or something simpler if possible.
937 SCEVHandle ScalarEvolution::getAddExpr(std::vector<SCEVHandle> &Ops) {
938 assert(!Ops.empty() && "Cannot get empty add!");
939 if (Ops.size() == 1) return Ops[0];
941 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
942 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
943 getEffectiveSCEVType(Ops[0]->getType()) &&
944 "SCEVAddExpr operand types don't match!");
947 // Sort by complexity, this groups all similar expression types together.
948 GroupByComplexity(Ops, LI);
950 // If there are any constants, fold them together.
952 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
954 assert(Idx < Ops.size());
955 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
956 // We found two constants, fold them together!
957 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() +
958 RHSC->getValue()->getValue());
959 Ops[0] = getConstant(Fold);
960 Ops.erase(Ops.begin()+1); // Erase the folded element
961 if (Ops.size() == 1) return Ops[0];
962 LHSC = cast<SCEVConstant>(Ops[0]);
965 // If we are left with a constant zero being added, strip it off.
966 if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
967 Ops.erase(Ops.begin());
972 if (Ops.size() == 1) return Ops[0];
974 // Okay, check to see if the same value occurs in the operand list twice. If
975 // so, merge them together into an multiply expression. Since we sorted the
976 // list, these values are required to be adjacent.
977 const Type *Ty = Ops[0]->getType();
978 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
979 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
980 // Found a match, merge the two values into a multiply, and add any
981 // remaining values to the result.
982 SCEVHandle Two = getIntegerSCEV(2, Ty);
983 SCEVHandle Mul = getMulExpr(Ops[i], Two);
986 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
988 return getAddExpr(Ops);
991 // Check for truncates. If all the operands are truncated from the same
992 // type, see if factoring out the truncate would permit the result to be
993 // folded. eg., trunc(x) + m*trunc(n) --> trunc(x + trunc(m)*n)
994 // if the contents of the resulting outer trunc fold to something simple.
995 for (; Idx < Ops.size() && isa<SCEVTruncateExpr>(Ops[Idx]); ++Idx) {
996 const SCEVTruncateExpr *Trunc = cast<SCEVTruncateExpr>(Ops[Idx]);
997 const Type *DstType = Trunc->getType();
998 const Type *SrcType = Trunc->getOperand()->getType();
999 std::vector<SCEVHandle> LargeOps;
1001 // Check all the operands to see if they can be represented in the
1002 // source type of the truncate.
1003 for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
1004 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(Ops[i])) {
1005 if (T->getOperand()->getType() != SrcType) {
1009 LargeOps.push_back(T->getOperand());
1010 } else if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[i])) {
1011 // This could be either sign or zero extension, but sign extension
1012 // is much more likely to be foldable here.
1013 LargeOps.push_back(getSignExtendExpr(C, SrcType));
1014 } else if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Ops[i])) {
1015 std::vector<SCEVHandle> LargeMulOps;
1016 for (unsigned j = 0, f = M->getNumOperands(); j != f && Ok; ++j) {
1017 if (const SCEVTruncateExpr *T =
1018 dyn_cast<SCEVTruncateExpr>(M->getOperand(j))) {
1019 if (T->getOperand()->getType() != SrcType) {
1023 LargeMulOps.push_back(T->getOperand());
1024 } else if (const SCEVConstant *C =
1025 dyn_cast<SCEVConstant>(M->getOperand(j))) {
1026 // This could be either sign or zero extension, but sign extension
1027 // is much more likely to be foldable here.
1028 LargeMulOps.push_back(getSignExtendExpr(C, SrcType));
1035 LargeOps.push_back(getMulExpr(LargeMulOps));
1042 // Evaluate the expression in the larger type.
1043 SCEVHandle Fold = getAddExpr(LargeOps);
1044 // If it folds to something simple, use it. Otherwise, don't.
1045 if (isa<SCEVConstant>(Fold) || isa<SCEVUnknown>(Fold))
1046 return getTruncateExpr(Fold, DstType);
1050 // Skip past any other cast SCEVs.
1051 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddExpr)
1054 // If there are add operands they would be next.
1055 if (Idx < Ops.size()) {
1056 bool DeletedAdd = false;
1057 while (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
1058 // If we have an add, expand the add operands onto the end of the operands
1060 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
1061 Ops.erase(Ops.begin()+Idx);
1065 // If we deleted at least one add, we added operands to the end of the list,
1066 // and they are not necessarily sorted. Recurse to resort and resimplify
1067 // any operands we just aquired.
1069 return getAddExpr(Ops);
1072 // Skip over the add expression until we get to a multiply.
1073 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1076 // If we are adding something to a multiply expression, make sure the
1077 // something is not already an operand of the multiply. If so, merge it into
1079 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
1080 const SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
1081 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
1082 const SCEV *MulOpSCEV = Mul->getOperand(MulOp);
1083 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
1084 if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
1085 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
1086 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
1087 if (Mul->getNumOperands() != 2) {
1088 // If the multiply has more than two operands, we must get the
1090 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1091 MulOps.erase(MulOps.begin()+MulOp);
1092 InnerMul = getMulExpr(MulOps);
1094 SCEVHandle One = getIntegerSCEV(1, Ty);
1095 SCEVHandle AddOne = getAddExpr(InnerMul, One);
1096 SCEVHandle OuterMul = getMulExpr(AddOne, Ops[AddOp]);
1097 if (Ops.size() == 2) return OuterMul;
1099 Ops.erase(Ops.begin()+AddOp);
1100 Ops.erase(Ops.begin()+Idx-1);
1102 Ops.erase(Ops.begin()+Idx);
1103 Ops.erase(Ops.begin()+AddOp-1);
1105 Ops.push_back(OuterMul);
1106 return getAddExpr(Ops);
1109 // Check this multiply against other multiplies being added together.
1110 for (unsigned OtherMulIdx = Idx+1;
1111 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
1113 const SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
1114 // If MulOp occurs in OtherMul, we can fold the two multiplies
1116 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
1117 OMulOp != e; ++OMulOp)
1118 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
1119 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
1120 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
1121 if (Mul->getNumOperands() != 2) {
1122 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
1123 MulOps.erase(MulOps.begin()+MulOp);
1124 InnerMul1 = getMulExpr(MulOps);
1126 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
1127 if (OtherMul->getNumOperands() != 2) {
1128 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
1129 OtherMul->op_end());
1130 MulOps.erase(MulOps.begin()+OMulOp);
1131 InnerMul2 = getMulExpr(MulOps);
1133 SCEVHandle InnerMulSum = getAddExpr(InnerMul1,InnerMul2);
1134 SCEVHandle OuterMul = getMulExpr(MulOpSCEV, InnerMulSum);
1135 if (Ops.size() == 2) return OuterMul;
1136 Ops.erase(Ops.begin()+Idx);
1137 Ops.erase(Ops.begin()+OtherMulIdx-1);
1138 Ops.push_back(OuterMul);
1139 return getAddExpr(Ops);
1145 // If there are any add recurrences in the operands list, see if any other
1146 // added values are loop invariant. If so, we can fold them into the
1148 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1151 // Scan over all recurrences, trying to fold loop invariants into them.
1152 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1153 // Scan all of the other operands to this add and add them to the vector if
1154 // they are loop invariant w.r.t. the recurrence.
1155 std::vector<SCEVHandle> LIOps;
1156 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1157 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1158 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1159 LIOps.push_back(Ops[i]);
1160 Ops.erase(Ops.begin()+i);
1164 // If we found some loop invariants, fold them into the recurrence.
1165 if (!LIOps.empty()) {
1166 // NLI + LI + {Start,+,Step} --> NLI + {LI+Start,+,Step}
1167 LIOps.push_back(AddRec->getStart());
1169 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
1170 AddRecOps[0] = getAddExpr(LIOps);
1172 SCEVHandle NewRec = getAddRecExpr(AddRecOps, AddRec->getLoop());
1173 // If all of the other operands were loop invariant, we are done.
1174 if (Ops.size() == 1) return NewRec;
1176 // Otherwise, add the folded AddRec by the non-liv parts.
1177 for (unsigned i = 0;; ++i)
1178 if (Ops[i] == AddRec) {
1182 return getAddExpr(Ops);
1185 // Okay, if there weren't any loop invariants to be folded, check to see if
1186 // there are multiple AddRec's with the same loop induction variable being
1187 // added together. If so, we can fold them.
1188 for (unsigned OtherIdx = Idx+1;
1189 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1190 if (OtherIdx != Idx) {
1191 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1192 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1193 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
1194 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
1195 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
1196 if (i >= NewOps.size()) {
1197 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
1198 OtherAddRec->op_end());
1201 NewOps[i] = getAddExpr(NewOps[i], OtherAddRec->getOperand(i));
1203 SCEVHandle NewAddRec = getAddRecExpr(NewOps, AddRec->getLoop());
1205 if (Ops.size() == 2) return NewAddRec;
1207 Ops.erase(Ops.begin()+Idx);
1208 Ops.erase(Ops.begin()+OtherIdx-1);
1209 Ops.push_back(NewAddRec);
1210 return getAddExpr(Ops);
1214 // Otherwise couldn't fold anything into this recurrence. Move onto the
1218 // Okay, it looks like we really DO need an add expr. Check to see if we
1219 // already have one, otherwise create a new one.
1220 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1221 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scAddExpr,
1223 if (Result == 0) Result = new SCEVAddExpr(Ops);
1228 SCEVHandle ScalarEvolution::getMulExpr(std::vector<SCEVHandle> &Ops) {
1229 assert(!Ops.empty() && "Cannot get empty mul!");
1231 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1232 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1233 getEffectiveSCEVType(Ops[0]->getType()) &&
1234 "SCEVMulExpr operand types don't match!");
1237 // Sort by complexity, this groups all similar expression types together.
1238 GroupByComplexity(Ops, LI);
1240 // If there are any constants, fold them together.
1242 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1244 // C1*(C2+V) -> C1*C2 + C1*V
1245 if (Ops.size() == 2)
1246 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
1247 if (Add->getNumOperands() == 2 &&
1248 isa<SCEVConstant>(Add->getOperand(0)))
1249 return getAddExpr(getMulExpr(LHSC, Add->getOperand(0)),
1250 getMulExpr(LHSC, Add->getOperand(1)));
1254 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1255 // We found two constants, fold them together!
1256 ConstantInt *Fold = ConstantInt::get(LHSC->getValue()->getValue() *
1257 RHSC->getValue()->getValue());
1258 Ops[0] = getConstant(Fold);
1259 Ops.erase(Ops.begin()+1); // Erase the folded element
1260 if (Ops.size() == 1) return Ops[0];
1261 LHSC = cast<SCEVConstant>(Ops[0]);
1264 // If we are left with a constant one being multiplied, strip it off.
1265 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
1266 Ops.erase(Ops.begin());
1268 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isZero()) {
1269 // If we have a multiply of zero, it will always be zero.
1274 // Skip over the add expression until we get to a multiply.
1275 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
1278 if (Ops.size() == 1)
1281 // If there are mul operands inline them all into this expression.
1282 if (Idx < Ops.size()) {
1283 bool DeletedMul = false;
1284 while (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
1285 // If we have an mul, expand the mul operands onto the end of the operands
1287 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
1288 Ops.erase(Ops.begin()+Idx);
1292 // If we deleted at least one mul, we added operands to the end of the list,
1293 // and they are not necessarily sorted. Recurse to resort and resimplify
1294 // any operands we just aquired.
1296 return getMulExpr(Ops);
1299 // If there are any add recurrences in the operands list, see if any other
1300 // added values are loop invariant. If so, we can fold them into the
1302 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
1305 // Scan over all recurrences, trying to fold loop invariants into them.
1306 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
1307 // Scan all of the other operands to this mul and add them to the vector if
1308 // they are loop invariant w.r.t. the recurrence.
1309 std::vector<SCEVHandle> LIOps;
1310 const SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
1311 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
1312 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
1313 LIOps.push_back(Ops[i]);
1314 Ops.erase(Ops.begin()+i);
1318 // If we found some loop invariants, fold them into the recurrence.
1319 if (!LIOps.empty()) {
1320 // NLI * LI * {Start,+,Step} --> NLI * {LI*Start,+,LI*Step}
1321 std::vector<SCEVHandle> NewOps;
1322 NewOps.reserve(AddRec->getNumOperands());
1323 if (LIOps.size() == 1) {
1324 const SCEV *Scale = LIOps[0];
1325 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
1326 NewOps.push_back(getMulExpr(Scale, AddRec->getOperand(i)));
1328 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
1329 std::vector<SCEVHandle> MulOps(LIOps);
1330 MulOps.push_back(AddRec->getOperand(i));
1331 NewOps.push_back(getMulExpr(MulOps));
1335 SCEVHandle NewRec = getAddRecExpr(NewOps, AddRec->getLoop());
1337 // If all of the other operands were loop invariant, we are done.
1338 if (Ops.size() == 1) return NewRec;
1340 // Otherwise, multiply the folded AddRec by the non-liv parts.
1341 for (unsigned i = 0;; ++i)
1342 if (Ops[i] == AddRec) {
1346 return getMulExpr(Ops);
1349 // Okay, if there weren't any loop invariants to be folded, check to see if
1350 // there are multiple AddRec's with the same loop induction variable being
1351 // multiplied together. If so, we can fold them.
1352 for (unsigned OtherIdx = Idx+1;
1353 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
1354 if (OtherIdx != Idx) {
1355 const SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
1356 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
1357 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
1358 const SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
1359 SCEVHandle NewStart = getMulExpr(F->getStart(),
1361 SCEVHandle B = F->getStepRecurrence(*this);
1362 SCEVHandle D = G->getStepRecurrence(*this);
1363 SCEVHandle NewStep = getAddExpr(getMulExpr(F, D),
1366 SCEVHandle NewAddRec = getAddRecExpr(NewStart, NewStep,
1368 if (Ops.size() == 2) return NewAddRec;
1370 Ops.erase(Ops.begin()+Idx);
1371 Ops.erase(Ops.begin()+OtherIdx-1);
1372 Ops.push_back(NewAddRec);
1373 return getMulExpr(Ops);
1377 // Otherwise couldn't fold anything into this recurrence. Move onto the
1381 // Okay, it looks like we really DO need an mul expr. Check to see if we
1382 // already have one, otherwise create a new one.
1383 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1384 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scMulExpr,
1387 Result = new SCEVMulExpr(Ops);
1391 SCEVHandle ScalarEvolution::getUDivExpr(const SCEVHandle &LHS,
1392 const SCEVHandle &RHS) {
1393 assert(getEffectiveSCEVType(LHS->getType()) ==
1394 getEffectiveSCEVType(RHS->getType()) &&
1395 "SCEVUDivExpr operand types don't match!");
1397 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
1398 if (RHSC->getValue()->equalsInt(1))
1399 return LHS; // X udiv 1 --> x
1401 return getIntegerSCEV(0, LHS->getType()); // value is undefined
1403 // Determine if the division can be folded into the operands of
1405 // TODO: Generalize this to non-constants by using known-bits information.
1406 const Type *Ty = LHS->getType();
1407 unsigned LZ = RHSC->getValue()->getValue().countLeadingZeros();
1408 unsigned MaxShiftAmt = getTypeSizeInBits(Ty) - LZ;
1409 // For non-power-of-two values, effectively round the value up to the
1410 // nearest power of two.
1411 if (!RHSC->getValue()->getValue().isPowerOf2())
1413 const IntegerType *ExtTy =
1414 IntegerType::get(getTypeSizeInBits(Ty) + MaxShiftAmt);
1415 // {X,+,N}/C --> {X/C,+,N/C} if safe and N/C can be folded.
1416 if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(LHS))
1417 if (const SCEVConstant *Step =
1418 dyn_cast<SCEVConstant>(AR->getStepRecurrence(*this)))
1419 if (!Step->getValue()->getValue()
1420 .urem(RHSC->getValue()->getValue()) &&
1421 getZeroExtendExpr(AR, ExtTy) ==
1422 getAddRecExpr(getZeroExtendExpr(AR->getStart(), ExtTy),
1423 getZeroExtendExpr(Step, ExtTy),
1425 std::vector<SCEVHandle> Operands;
1426 for (unsigned i = 0, e = AR->getNumOperands(); i != e; ++i)
1427 Operands.push_back(getUDivExpr(AR->getOperand(i), RHS));
1428 return getAddRecExpr(Operands, AR->getLoop());
1430 // (A*B)/C --> A*(B/C) if safe and B/C can be folded.
1431 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(LHS)) {
1432 std::vector<SCEVHandle> Operands;
1433 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i)
1434 Operands.push_back(getZeroExtendExpr(M->getOperand(i), ExtTy));
1435 if (getZeroExtendExpr(M, ExtTy) == getMulExpr(Operands))
1436 // Find an operand that's safely divisible.
1437 for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
1438 SCEVHandle Op = M->getOperand(i);
1439 SCEVHandle Div = getUDivExpr(Op, RHSC);
1440 if (!isa<SCEVUDivExpr>(Div) && getMulExpr(Div, RHSC) == Op) {
1441 Operands = M->getOperands();
1443 return getMulExpr(Operands);
1447 // (A+B)/C --> (A/C + B/C) if safe and A/C and B/C can be folded.
1448 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(LHS)) {
1449 std::vector<SCEVHandle> Operands;
1450 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i)
1451 Operands.push_back(getZeroExtendExpr(A->getOperand(i), ExtTy));
1452 if (getZeroExtendExpr(A, ExtTy) == getAddExpr(Operands)) {
1454 for (unsigned i = 0, e = A->getNumOperands(); i != e; ++i) {
1455 SCEVHandle Op = getUDivExpr(A->getOperand(i), RHS);
1456 if (isa<SCEVUDivExpr>(Op) || getMulExpr(Op, RHS) != A->getOperand(i))
1458 Operands.push_back(Op);
1460 if (Operands.size() == A->getNumOperands())
1461 return getAddExpr(Operands);
1465 // Fold if both operands are constant.
1466 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
1467 Constant *LHSCV = LHSC->getValue();
1468 Constant *RHSCV = RHSC->getValue();
1469 return getUnknown(ConstantExpr::getUDiv(LHSCV, RHSCV));
1473 SCEVUDivExpr *&Result = (*SCEVUDivs)[std::make_pair(LHS, RHS)];
1474 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
1479 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1480 /// specified loop. Simplify the expression as much as possible.
1481 SCEVHandle ScalarEvolution::getAddRecExpr(const SCEVHandle &Start,
1482 const SCEVHandle &Step, const Loop *L) {
1483 std::vector<SCEVHandle> Operands;
1484 Operands.push_back(Start);
1485 if (const SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
1486 if (StepChrec->getLoop() == L) {
1487 Operands.insert(Operands.end(), StepChrec->op_begin(),
1488 StepChrec->op_end());
1489 return getAddRecExpr(Operands, L);
1492 Operands.push_back(Step);
1493 return getAddRecExpr(Operands, L);
1496 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
1497 /// specified loop. Simplify the expression as much as possible.
1498 SCEVHandle ScalarEvolution::getAddRecExpr(std::vector<SCEVHandle> &Operands,
1500 if (Operands.size() == 1) return Operands[0];
1502 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
1503 assert(getEffectiveSCEVType(Operands[i]->getType()) ==
1504 getEffectiveSCEVType(Operands[0]->getType()) &&
1505 "SCEVAddRecExpr operand types don't match!");
1508 if (Operands.back()->isZero()) {
1509 Operands.pop_back();
1510 return getAddRecExpr(Operands, L); // {X,+,0} --> X
1513 // Canonicalize nested AddRecs in by nesting them in order of loop depth.
1514 if (const SCEVAddRecExpr *NestedAR = dyn_cast<SCEVAddRecExpr>(Operands[0])) {
1515 const Loop* NestedLoop = NestedAR->getLoop();
1516 if (L->getLoopDepth() < NestedLoop->getLoopDepth()) {
1517 std::vector<SCEVHandle> NestedOperands(NestedAR->op_begin(),
1518 NestedAR->op_end());
1519 SCEVHandle NestedARHandle(NestedAR);
1520 Operands[0] = NestedAR->getStart();
1521 NestedOperands[0] = getAddRecExpr(Operands, L);
1522 return getAddRecExpr(NestedOperands, NestedLoop);
1526 std::vector<const SCEV*> SCEVOps(Operands.begin(), Operands.end());
1527 SCEVAddRecExpr *&Result = (*SCEVAddRecExprs)[std::make_pair(L, SCEVOps)];
1528 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
1532 SCEVHandle ScalarEvolution::getSMaxExpr(const SCEVHandle &LHS,
1533 const SCEVHandle &RHS) {
1534 std::vector<SCEVHandle> Ops;
1537 return getSMaxExpr(Ops);
1540 SCEVHandle ScalarEvolution::getSMaxExpr(std::vector<SCEVHandle> Ops) {
1541 assert(!Ops.empty() && "Cannot get empty smax!");
1542 if (Ops.size() == 1) return Ops[0];
1544 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1545 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1546 getEffectiveSCEVType(Ops[0]->getType()) &&
1547 "SCEVSMaxExpr operand types don't match!");
1550 // Sort by complexity, this groups all similar expression types together.
1551 GroupByComplexity(Ops, LI);
1553 // If there are any constants, fold them together.
1555 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1557 assert(Idx < Ops.size());
1558 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1559 // We found two constants, fold them together!
1560 ConstantInt *Fold = ConstantInt::get(
1561 APIntOps::smax(LHSC->getValue()->getValue(),
1562 RHSC->getValue()->getValue()));
1563 Ops[0] = getConstant(Fold);
1564 Ops.erase(Ops.begin()+1); // Erase the folded element
1565 if (Ops.size() == 1) return Ops[0];
1566 LHSC = cast<SCEVConstant>(Ops[0]);
1569 // If we are left with a constant -inf, strip it off.
1570 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(true)) {
1571 Ops.erase(Ops.begin());
1576 if (Ops.size() == 1) return Ops[0];
1578 // Find the first SMax
1579 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scSMaxExpr)
1582 // Check to see if one of the operands is an SMax. If so, expand its operands
1583 // onto our operand list, and recurse to simplify.
1584 if (Idx < Ops.size()) {
1585 bool DeletedSMax = false;
1586 while (const SCEVSMaxExpr *SMax = dyn_cast<SCEVSMaxExpr>(Ops[Idx])) {
1587 Ops.insert(Ops.end(), SMax->op_begin(), SMax->op_end());
1588 Ops.erase(Ops.begin()+Idx);
1593 return getSMaxExpr(Ops);
1596 // Okay, check to see if the same value occurs in the operand list twice. If
1597 // so, delete one. Since we sorted the list, these values are required to
1599 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1600 if (Ops[i] == Ops[i+1]) { // X smax Y smax Y --> X smax Y
1601 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1605 if (Ops.size() == 1) return Ops[0];
1607 assert(!Ops.empty() && "Reduced smax down to nothing!");
1609 // Okay, it looks like we really DO need an smax expr. Check to see if we
1610 // already have one, otherwise create a new one.
1611 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1612 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scSMaxExpr,
1614 if (Result == 0) Result = new SCEVSMaxExpr(Ops);
1618 SCEVHandle ScalarEvolution::getUMaxExpr(const SCEVHandle &LHS,
1619 const SCEVHandle &RHS) {
1620 std::vector<SCEVHandle> Ops;
1623 return getUMaxExpr(Ops);
1626 SCEVHandle ScalarEvolution::getUMaxExpr(std::vector<SCEVHandle> Ops) {
1627 assert(!Ops.empty() && "Cannot get empty umax!");
1628 if (Ops.size() == 1) return Ops[0];
1630 for (unsigned i = 1, e = Ops.size(); i != e; ++i)
1631 assert(getEffectiveSCEVType(Ops[i]->getType()) ==
1632 getEffectiveSCEVType(Ops[0]->getType()) &&
1633 "SCEVUMaxExpr operand types don't match!");
1636 // Sort by complexity, this groups all similar expression types together.
1637 GroupByComplexity(Ops, LI);
1639 // If there are any constants, fold them together.
1641 if (const SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
1643 assert(Idx < Ops.size());
1644 while (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
1645 // We found two constants, fold them together!
1646 ConstantInt *Fold = ConstantInt::get(
1647 APIntOps::umax(LHSC->getValue()->getValue(),
1648 RHSC->getValue()->getValue()));
1649 Ops[0] = getConstant(Fold);
1650 Ops.erase(Ops.begin()+1); // Erase the folded element
1651 if (Ops.size() == 1) return Ops[0];
1652 LHSC = cast<SCEVConstant>(Ops[0]);
1655 // If we are left with a constant zero, strip it off.
1656 if (cast<SCEVConstant>(Ops[0])->getValue()->isMinValue(false)) {
1657 Ops.erase(Ops.begin());
1662 if (Ops.size() == 1) return Ops[0];
1664 // Find the first UMax
1665 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scUMaxExpr)
1668 // Check to see if one of the operands is a UMax. If so, expand its operands
1669 // onto our operand list, and recurse to simplify.
1670 if (Idx < Ops.size()) {
1671 bool DeletedUMax = false;
1672 while (const SCEVUMaxExpr *UMax = dyn_cast<SCEVUMaxExpr>(Ops[Idx])) {
1673 Ops.insert(Ops.end(), UMax->op_begin(), UMax->op_end());
1674 Ops.erase(Ops.begin()+Idx);
1679 return getUMaxExpr(Ops);
1682 // Okay, check to see if the same value occurs in the operand list twice. If
1683 // so, delete one. Since we sorted the list, these values are required to
1685 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
1686 if (Ops[i] == Ops[i+1]) { // X umax Y umax Y --> X umax Y
1687 Ops.erase(Ops.begin()+i, Ops.begin()+i+1);
1691 if (Ops.size() == 1) return Ops[0];
1693 assert(!Ops.empty() && "Reduced umax down to nothing!");
1695 // Okay, it looks like we really DO need a umax expr. Check to see if we
1696 // already have one, otherwise create a new one.
1697 std::vector<const SCEV*> SCEVOps(Ops.begin(), Ops.end());
1698 SCEVCommutativeExpr *&Result = (*SCEVCommExprs)[std::make_pair(scUMaxExpr,
1700 if (Result == 0) Result = new SCEVUMaxExpr(Ops);
1704 SCEVHandle ScalarEvolution::getUnknown(Value *V) {
1705 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
1706 return getConstant(CI);
1707 if (isa<ConstantPointerNull>(V))
1708 return getIntegerSCEV(0, V->getType());
1709 SCEVUnknown *&Result = (*SCEVUnknowns)[V];
1710 if (Result == 0) Result = new SCEVUnknown(V);
1714 //===----------------------------------------------------------------------===//
1715 // Basic SCEV Analysis and PHI Idiom Recognition Code
1718 /// isSCEVable - Test if values of the given type are analyzable within
1719 /// the SCEV framework. This primarily includes integer types, and it
1720 /// can optionally include pointer types if the ScalarEvolution class
1721 /// has access to target-specific information.
1722 bool ScalarEvolution::isSCEVable(const Type *Ty) const {
1723 // Integers are always SCEVable.
1724 if (Ty->isInteger())
1727 // Pointers are SCEVable if TargetData information is available
1728 // to provide pointer size information.
1729 if (isa<PointerType>(Ty))
1732 // Otherwise it's not SCEVable.
1736 /// getTypeSizeInBits - Return the size in bits of the specified type,
1737 /// for which isSCEVable must return true.
1738 uint64_t ScalarEvolution::getTypeSizeInBits(const Type *Ty) const {
1739 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1741 // If we have a TargetData, use it!
1743 return TD->getTypeSizeInBits(Ty);
1745 // Otherwise, we support only integer types.
1746 assert(Ty->isInteger() && "isSCEVable permitted a non-SCEVable type!");
1747 return Ty->getPrimitiveSizeInBits();
1750 /// getEffectiveSCEVType - Return a type with the same bitwidth as
1751 /// the given type and which represents how SCEV will treat the given
1752 /// type, for which isSCEVable must return true. For pointer types,
1753 /// this is the pointer-sized integer type.
1754 const Type *ScalarEvolution::getEffectiveSCEVType(const Type *Ty) const {
1755 assert(isSCEVable(Ty) && "Type is not SCEVable!");
1757 if (Ty->isInteger())
1760 assert(isa<PointerType>(Ty) && "Unexpected non-pointer non-integer type!");
1761 return TD->getIntPtrType();
1764 SCEVHandle ScalarEvolution::getCouldNotCompute() {
1765 return UnknownValue;
1768 /// hasSCEV - Return true if the SCEV for this value has already been
1770 bool ScalarEvolution::hasSCEV(Value *V) const {
1771 return Scalars.count(V);
1774 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1775 /// expression and create a new one.
1776 SCEVHandle ScalarEvolution::getSCEV(Value *V) {
1777 assert(isSCEVable(V->getType()) && "Value is not SCEVable!");
1779 std::map<SCEVCallbackVH, SCEVHandle>::iterator I = Scalars.find(V);
1780 if (I != Scalars.end()) return I->second;
1781 SCEVHandle S = createSCEV(V);
1782 Scalars.insert(std::make_pair(SCEVCallbackVH(V, this), S));
1786 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
1787 /// specified signed integer value and return a SCEV for the constant.
1788 SCEVHandle ScalarEvolution::getIntegerSCEV(int Val, const Type *Ty) {
1789 Ty = getEffectiveSCEVType(Ty);
1792 C = Constant::getNullValue(Ty);
1793 else if (Ty->isFloatingPoint())
1794 C = ConstantFP::get(APFloat(Ty==Type::FloatTy ? APFloat::IEEEsingle :
1795 APFloat::IEEEdouble, Val));
1797 C = ConstantInt::get(Ty, Val);
1798 return getUnknown(C);
1801 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
1803 SCEVHandle ScalarEvolution::getNegativeSCEV(const SCEVHandle &V) {
1804 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1805 return getUnknown(ConstantExpr::getNeg(VC->getValue()));
1807 const Type *Ty = V->getType();
1808 Ty = getEffectiveSCEVType(Ty);
1809 return getMulExpr(V, getConstant(ConstantInt::getAllOnesValue(Ty)));
1812 /// getNotSCEV - Return a SCEV corresponding to ~V = -1-V
1813 SCEVHandle ScalarEvolution::getNotSCEV(const SCEVHandle &V) {
1814 if (const SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
1815 return getUnknown(ConstantExpr::getNot(VC->getValue()));
1817 const Type *Ty = V->getType();
1818 Ty = getEffectiveSCEVType(Ty);
1819 SCEVHandle AllOnes = getConstant(ConstantInt::getAllOnesValue(Ty));
1820 return getMinusSCEV(AllOnes, V);
1823 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
1825 SCEVHandle ScalarEvolution::getMinusSCEV(const SCEVHandle &LHS,
1826 const SCEVHandle &RHS) {
1828 return getAddExpr(LHS, getNegativeSCEV(RHS));
1831 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
1832 /// input value to the specified type. If the type must be extended, it is zero
1835 ScalarEvolution::getTruncateOrZeroExtend(const SCEVHandle &V,
1837 const Type *SrcTy = V->getType();
1838 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1839 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1840 "Cannot truncate or zero extend with non-integer arguments!");
1841 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1842 return V; // No conversion
1843 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1844 return getTruncateExpr(V, Ty);
1845 return getZeroExtendExpr(V, Ty);
1848 /// getTruncateOrSignExtend - Return a SCEV corresponding to a conversion of the
1849 /// input value to the specified type. If the type must be extended, it is sign
1852 ScalarEvolution::getTruncateOrSignExtend(const SCEVHandle &V,
1854 const Type *SrcTy = V->getType();
1855 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1856 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1857 "Cannot truncate or zero extend with non-integer arguments!");
1858 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1859 return V; // No conversion
1860 if (getTypeSizeInBits(SrcTy) > getTypeSizeInBits(Ty))
1861 return getTruncateExpr(V, Ty);
1862 return getSignExtendExpr(V, Ty);
1865 /// getNoopOrZeroExtend - Return a SCEV corresponding to a conversion of the
1866 /// input value to the specified type. If the type must be extended, it is zero
1867 /// extended. The conversion must not be narrowing.
1869 ScalarEvolution::getNoopOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
1870 const Type *SrcTy = V->getType();
1871 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1872 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1873 "Cannot noop or zero extend with non-integer arguments!");
1874 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1875 "getNoopOrZeroExtend cannot truncate!");
1876 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1877 return V; // No conversion
1878 return getZeroExtendExpr(V, Ty);
1881 /// getNoopOrSignExtend - Return a SCEV corresponding to a conversion of the
1882 /// input value to the specified type. If the type must be extended, it is sign
1883 /// extended. The conversion must not be narrowing.
1885 ScalarEvolution::getNoopOrSignExtend(const SCEVHandle &V, const Type *Ty) {
1886 const Type *SrcTy = V->getType();
1887 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1888 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1889 "Cannot noop or sign extend with non-integer arguments!");
1890 assert(getTypeSizeInBits(SrcTy) <= getTypeSizeInBits(Ty) &&
1891 "getNoopOrSignExtend cannot truncate!");
1892 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1893 return V; // No conversion
1894 return getSignExtendExpr(V, Ty);
1897 /// getTruncateOrNoop - Return a SCEV corresponding to a conversion of the
1898 /// input value to the specified type. The conversion must not be widening.
1900 ScalarEvolution::getTruncateOrNoop(const SCEVHandle &V, const Type *Ty) {
1901 const Type *SrcTy = V->getType();
1902 assert((SrcTy->isInteger() || (TD && isa<PointerType>(SrcTy))) &&
1903 (Ty->isInteger() || (TD && isa<PointerType>(Ty))) &&
1904 "Cannot truncate or noop with non-integer arguments!");
1905 assert(getTypeSizeInBits(SrcTy) >= getTypeSizeInBits(Ty) &&
1906 "getTruncateOrNoop cannot extend!");
1907 if (getTypeSizeInBits(SrcTy) == getTypeSizeInBits(Ty))
1908 return V; // No conversion
1909 return getTruncateExpr(V, Ty);
1912 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
1913 /// the specified instruction and replaces any references to the symbolic value
1914 /// SymName with the specified value. This is used during PHI resolution.
1915 void ScalarEvolution::
1916 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
1917 const SCEVHandle &NewVal) {
1918 std::map<SCEVCallbackVH, SCEVHandle>::iterator SI =
1919 Scalars.find(SCEVCallbackVH(I, this));
1920 if (SI == Scalars.end()) return;
1923 SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal, *this);
1924 if (NV == SI->second) return; // No change.
1926 SI->second = NV; // Update the scalars map!
1928 // Any instruction values that use this instruction might also need to be
1930 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1932 ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
1935 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1936 /// a loop header, making it a potential recurrence, or it doesn't.
1938 SCEVHandle ScalarEvolution::createNodeForPHI(PHINode *PN) {
1939 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1940 if (const Loop *L = LI->getLoopFor(PN->getParent()))
1941 if (L->getHeader() == PN->getParent()) {
1942 // If it lives in the loop header, it has two incoming values, one
1943 // from outside the loop, and one from inside.
1944 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1945 unsigned BackEdge = IncomingEdge^1;
1947 // While we are analyzing this PHI node, handle its value symbolically.
1948 SCEVHandle SymbolicName = getUnknown(PN);
1949 assert(Scalars.find(PN) == Scalars.end() &&
1950 "PHI node already processed?");
1951 Scalars.insert(std::make_pair(SCEVCallbackVH(PN, this), SymbolicName));
1953 // Using this symbolic name for the PHI, analyze the value coming around
1955 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1957 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1958 // has a special value for the first iteration of the loop.
1960 // If the value coming around the backedge is an add with the symbolic
1961 // value we just inserted, then we found a simple induction variable!
1962 if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1963 // If there is a single occurrence of the symbolic value, replace it
1964 // with a recurrence.
1965 unsigned FoundIndex = Add->getNumOperands();
1966 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1967 if (Add->getOperand(i) == SymbolicName)
1968 if (FoundIndex == e) {
1973 if (FoundIndex != Add->getNumOperands()) {
1974 // Create an add with everything but the specified operand.
1975 std::vector<SCEVHandle> Ops;
1976 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1977 if (i != FoundIndex)
1978 Ops.push_back(Add->getOperand(i));
1979 SCEVHandle Accum = getAddExpr(Ops);
1981 // This is not a valid addrec if the step amount is varying each
1982 // loop iteration, but is not itself an addrec in this loop.
1983 if (Accum->isLoopInvariant(L) ||
1984 (isa<SCEVAddRecExpr>(Accum) &&
1985 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1986 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1987 SCEVHandle PHISCEV = getAddRecExpr(StartVal, Accum, L);
1989 // Okay, for the entire analysis of this edge we assumed the PHI
1990 // to be symbolic. We now need to go back and update all of the
1991 // entries for the scalars that use the PHI (except for the PHI
1992 // itself) to use the new analyzed value instead of the "symbolic"
1994 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
1998 } else if (const SCEVAddRecExpr *AddRec =
1999 dyn_cast<SCEVAddRecExpr>(BEValue)) {
2000 // Otherwise, this could be a loop like this:
2001 // i = 0; for (j = 1; ..; ++j) { .... i = j; }
2002 // In this case, j = {1,+,1} and BEValue is j.
2003 // Because the other in-value of i (0) fits the evolution of BEValue
2004 // i really is an addrec evolution.
2005 if (AddRec->getLoop() == L && AddRec->isAffine()) {
2006 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
2008 // If StartVal = j.start - j.stride, we can use StartVal as the
2009 // initial step of the addrec evolution.
2010 if (StartVal == getMinusSCEV(AddRec->getOperand(0),
2011 AddRec->getOperand(1))) {
2012 SCEVHandle PHISCEV =
2013 getAddRecExpr(StartVal, AddRec->getOperand(1), L);
2015 // Okay, for the entire analysis of this edge we assumed the PHI
2016 // to be symbolic. We now need to go back and update all of the
2017 // entries for the scalars that use the PHI (except for the PHI
2018 // itself) to use the new analyzed value instead of the "symbolic"
2020 ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
2026 return SymbolicName;
2029 // If it's not a loop phi, we can't handle it yet.
2030 return getUnknown(PN);
2033 /// createNodeForGEP - Expand GEP instructions into add and multiply
2034 /// operations. This allows them to be analyzed by regular SCEV code.
2036 SCEVHandle ScalarEvolution::createNodeForGEP(User *GEP) {
2038 const Type *IntPtrTy = TD->getIntPtrType();
2039 Value *Base = GEP->getOperand(0);
2040 // Don't attempt to analyze GEPs over unsized objects.
2041 if (!cast<PointerType>(Base->getType())->getElementType()->isSized())
2042 return getUnknown(GEP);
2043 SCEVHandle TotalOffset = getIntegerSCEV(0, IntPtrTy);
2044 gep_type_iterator GTI = gep_type_begin(GEP);
2045 for (GetElementPtrInst::op_iterator I = next(GEP->op_begin()),
2049 // Compute the (potentially symbolic) offset in bytes for this index.
2050 if (const StructType *STy = dyn_cast<StructType>(*GTI++)) {
2051 // For a struct, add the member offset.
2052 const StructLayout &SL = *TD->getStructLayout(STy);
2053 unsigned FieldNo = cast<ConstantInt>(Index)->getZExtValue();
2054 uint64_t Offset = SL.getElementOffset(FieldNo);
2055 TotalOffset = getAddExpr(TotalOffset,
2056 getIntegerSCEV(Offset, IntPtrTy));
2058 // For an array, add the element offset, explicitly scaled.
2059 SCEVHandle LocalOffset = getSCEV(Index);
2060 if (!isa<PointerType>(LocalOffset->getType()))
2061 // Getelementptr indicies are signed.
2062 LocalOffset = getTruncateOrSignExtend(LocalOffset,
2065 getMulExpr(LocalOffset,
2066 getIntegerSCEV(TD->getTypeAllocSize(*GTI),
2068 TotalOffset = getAddExpr(TotalOffset, LocalOffset);
2071 return getAddExpr(getSCEV(Base), TotalOffset);
2074 /// GetMinTrailingZeros - Determine the minimum number of zero bits that S is
2075 /// guaranteed to end in (at every loop iteration). It is, at the same time,
2076 /// the minimum number of times S is divisible by 2. For example, given {4,+,8}
2077 /// it returns 2. If S is guaranteed to be 0, it returns the bitwidth of S.
2078 static uint32_t GetMinTrailingZeros(SCEVHandle S, const ScalarEvolution &SE) {
2079 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S))
2080 return C->getValue()->getValue().countTrailingZeros();
2082 if (const SCEVTruncateExpr *T = dyn_cast<SCEVTruncateExpr>(S))
2083 return std::min(GetMinTrailingZeros(T->getOperand(), SE),
2084 (uint32_t)SE.getTypeSizeInBits(T->getType()));
2086 if (const SCEVZeroExtendExpr *E = dyn_cast<SCEVZeroExtendExpr>(S)) {
2087 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2088 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2089 SE.getTypeSizeInBits(E->getType()) : OpRes;
2092 if (const SCEVSignExtendExpr *E = dyn_cast<SCEVSignExtendExpr>(S)) {
2093 uint32_t OpRes = GetMinTrailingZeros(E->getOperand(), SE);
2094 return OpRes == SE.getTypeSizeInBits(E->getOperand()->getType()) ?
2095 SE.getTypeSizeInBits(E->getType()) : OpRes;
2098 if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(S)) {
2099 // The result is the min of all operands results.
2100 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2101 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2102 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2106 if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
2107 // The result is the sum of all operands results.
2108 uint32_t SumOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2109 uint32_t BitWidth = SE.getTypeSizeInBits(M->getType());
2110 for (unsigned i = 1, e = M->getNumOperands();
2111 SumOpRes != BitWidth && i != e; ++i)
2112 SumOpRes = std::min(SumOpRes + GetMinTrailingZeros(M->getOperand(i), SE),
2117 if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
2118 // The result is the min of all operands results.
2119 uint32_t MinOpRes = GetMinTrailingZeros(A->getOperand(0), SE);
2120 for (unsigned i = 1, e = A->getNumOperands(); MinOpRes && i != e; ++i)
2121 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(A->getOperand(i), SE));
2125 if (const SCEVSMaxExpr *M = dyn_cast<SCEVSMaxExpr>(S)) {
2126 // The result is the min of all operands results.
2127 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2128 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2129 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2133 if (const SCEVUMaxExpr *M = dyn_cast<SCEVUMaxExpr>(S)) {
2134 // The result is the min of all operands results.
2135 uint32_t MinOpRes = GetMinTrailingZeros(M->getOperand(0), SE);
2136 for (unsigned i = 1, e = M->getNumOperands(); MinOpRes && i != e; ++i)
2137 MinOpRes = std::min(MinOpRes, GetMinTrailingZeros(M->getOperand(i), SE));
2141 // SCEVUDivExpr, SCEVUnknown
2145 /// createSCEV - We know that there is no SCEV for the specified value.
2146 /// Analyze the expression.
2148 SCEVHandle ScalarEvolution::createSCEV(Value *V) {
2149 if (!isSCEVable(V->getType()))
2150 return getUnknown(V);
2152 unsigned Opcode = Instruction::UserOp1;
2153 if (Instruction *I = dyn_cast<Instruction>(V))
2154 Opcode = I->getOpcode();
2155 else if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
2156 Opcode = CE->getOpcode();
2158 return getUnknown(V);
2160 User *U = cast<User>(V);
2162 case Instruction::Add:
2163 return getAddExpr(getSCEV(U->getOperand(0)),
2164 getSCEV(U->getOperand(1)));
2165 case Instruction::Mul:
2166 return getMulExpr(getSCEV(U->getOperand(0)),
2167 getSCEV(U->getOperand(1)));
2168 case Instruction::UDiv:
2169 return getUDivExpr(getSCEV(U->getOperand(0)),
2170 getSCEV(U->getOperand(1)));
2171 case Instruction::Sub:
2172 return getMinusSCEV(getSCEV(U->getOperand(0)),
2173 getSCEV(U->getOperand(1)));
2174 case Instruction::And:
2175 // For an expression like x&255 that merely masks off the high bits,
2176 // use zext(trunc(x)) as the SCEV expression.
2177 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2178 if (CI->isNullValue())
2179 return getSCEV(U->getOperand(1));
2180 if (CI->isAllOnesValue())
2181 return getSCEV(U->getOperand(0));
2182 const APInt &A = CI->getValue();
2183 unsigned Ones = A.countTrailingOnes();
2184 if (APIntOps::isMask(Ones, A))
2186 getZeroExtendExpr(getTruncateExpr(getSCEV(U->getOperand(0)),
2187 IntegerType::get(Ones)),
2191 case Instruction::Or:
2192 // If the RHS of the Or is a constant, we may have something like:
2193 // X*4+1 which got turned into X*4|1. Handle this as an Add so loop
2194 // optimizations will transparently handle this case.
2196 // In order for this transformation to be safe, the LHS must be of the
2197 // form X*(2^n) and the Or constant must be less than 2^n.
2198 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2199 SCEVHandle LHS = getSCEV(U->getOperand(0));
2200 const APInt &CIVal = CI->getValue();
2201 if (GetMinTrailingZeros(LHS, *this) >=
2202 (CIVal.getBitWidth() - CIVal.countLeadingZeros()))
2203 return getAddExpr(LHS, getSCEV(U->getOperand(1)));
2206 case Instruction::Xor:
2207 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1))) {
2208 // If the RHS of the xor is a signbit, then this is just an add.
2209 // Instcombine turns add of signbit into xor as a strength reduction step.
2210 if (CI->getValue().isSignBit())
2211 return getAddExpr(getSCEV(U->getOperand(0)),
2212 getSCEV(U->getOperand(1)));
2214 // If the RHS of xor is -1, then this is a not operation.
2215 if (CI->isAllOnesValue())
2216 return getNotSCEV(getSCEV(U->getOperand(0)));
2218 // Model xor(and(x, C), C) as and(~x, C), if C is a low-bits mask.
2219 // This is a variant of the check for xor with -1, and it handles
2220 // the case where instcombine has trimmed non-demanded bits out
2221 // of an xor with -1.
2222 if (BinaryOperator *BO = dyn_cast<BinaryOperator>(U->getOperand(0)))
2223 if (ConstantInt *LCI = dyn_cast<ConstantInt>(BO->getOperand(1)))
2224 if (BO->getOpcode() == Instruction::And &&
2225 LCI->getValue() == CI->getValue())
2226 if (const SCEVZeroExtendExpr *Z =
2227 dyn_cast<SCEVZeroExtendExpr>(getSCEV(U->getOperand(0))))
2228 return getZeroExtendExpr(getNotSCEV(Z->getOperand()),
2233 case Instruction::Shl:
2234 // Turn shift left of a constant amount into a multiply.
2235 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2236 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2237 Constant *X = ConstantInt::get(
2238 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2239 return getMulExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2243 case Instruction::LShr:
2244 // Turn logical shift right of a constant into a unsigned divide.
2245 if (ConstantInt *SA = dyn_cast<ConstantInt>(U->getOperand(1))) {
2246 uint32_t BitWidth = cast<IntegerType>(V->getType())->getBitWidth();
2247 Constant *X = ConstantInt::get(
2248 APInt(BitWidth, 1).shl(SA->getLimitedValue(BitWidth)));
2249 return getUDivExpr(getSCEV(U->getOperand(0)), getSCEV(X));
2253 case Instruction::AShr:
2254 // For a two-shift sext-inreg, use sext(trunc(x)) as the SCEV expression.
2255 if (ConstantInt *CI = dyn_cast<ConstantInt>(U->getOperand(1)))
2256 if (Instruction *L = dyn_cast<Instruction>(U->getOperand(0)))
2257 if (L->getOpcode() == Instruction::Shl &&
2258 L->getOperand(1) == U->getOperand(1)) {
2259 unsigned BitWidth = getTypeSizeInBits(U->getType());
2260 uint64_t Amt = BitWidth - CI->getZExtValue();
2261 if (Amt == BitWidth)
2262 return getSCEV(L->getOperand(0)); // shift by zero --> noop
2264 return getIntegerSCEV(0, U->getType()); // value is undefined
2266 getSignExtendExpr(getTruncateExpr(getSCEV(L->getOperand(0)),
2267 IntegerType::get(Amt)),
2272 case Instruction::Trunc:
2273 return getTruncateExpr(getSCEV(U->getOperand(0)), U->getType());
2275 case Instruction::ZExt:
2276 return getZeroExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2278 case Instruction::SExt:
2279 return getSignExtendExpr(getSCEV(U->getOperand(0)), U->getType());
2281 case Instruction::BitCast:
2282 // BitCasts are no-op casts so we just eliminate the cast.
2283 if (isSCEVable(U->getType()) && isSCEVable(U->getOperand(0)->getType()))
2284 return getSCEV(U->getOperand(0));
2287 case Instruction::IntToPtr:
2288 if (!TD) break; // Without TD we can't analyze pointers.
2289 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2290 TD->getIntPtrType());
2292 case Instruction::PtrToInt:
2293 if (!TD) break; // Without TD we can't analyze pointers.
2294 return getTruncateOrZeroExtend(getSCEV(U->getOperand(0)),
2297 case Instruction::GetElementPtr:
2298 if (!TD) break; // Without TD we can't analyze pointers.
2299 return createNodeForGEP(U);
2301 case Instruction::PHI:
2302 return createNodeForPHI(cast<PHINode>(U));
2304 case Instruction::Select:
2305 // This could be a smax or umax that was lowered earlier.
2306 // Try to recover it.
2307 if (ICmpInst *ICI = dyn_cast<ICmpInst>(U->getOperand(0))) {
2308 Value *LHS = ICI->getOperand(0);
2309 Value *RHS = ICI->getOperand(1);
2310 switch (ICI->getPredicate()) {
2311 case ICmpInst::ICMP_SLT:
2312 case ICmpInst::ICMP_SLE:
2313 std::swap(LHS, RHS);
2315 case ICmpInst::ICMP_SGT:
2316 case ICmpInst::ICMP_SGE:
2317 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2318 return getSMaxExpr(getSCEV(LHS), getSCEV(RHS));
2319 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2320 // ~smax(~x, ~y) == smin(x, y).
2321 return getNotSCEV(getSMaxExpr(
2322 getNotSCEV(getSCEV(LHS)),
2323 getNotSCEV(getSCEV(RHS))));
2325 case ICmpInst::ICMP_ULT:
2326 case ICmpInst::ICMP_ULE:
2327 std::swap(LHS, RHS);
2329 case ICmpInst::ICMP_UGT:
2330 case ICmpInst::ICMP_UGE:
2331 if (LHS == U->getOperand(1) && RHS == U->getOperand(2))
2332 return getUMaxExpr(getSCEV(LHS), getSCEV(RHS));
2333 else if (LHS == U->getOperand(2) && RHS == U->getOperand(1))
2334 // ~umax(~x, ~y) == umin(x, y)
2335 return getNotSCEV(getUMaxExpr(getNotSCEV(getSCEV(LHS)),
2336 getNotSCEV(getSCEV(RHS))));
2343 default: // We cannot analyze this expression.
2347 return getUnknown(V);
2352 //===----------------------------------------------------------------------===//
2353 // Iteration Count Computation Code
2356 /// getBackedgeTakenCount - If the specified loop has a predictable
2357 /// backedge-taken count, return it, otherwise return a SCEVCouldNotCompute
2358 /// object. The backedge-taken count is the number of times the loop header
2359 /// will be branched to from within the loop. This is one less than the
2360 /// trip count of the loop, since it doesn't count the first iteration,
2361 /// when the header is branched to from outside the loop.
2363 /// Note that it is not valid to call this method on a loop without a
2364 /// loop-invariant backedge-taken count (see
2365 /// hasLoopInvariantBackedgeTakenCount).
2367 SCEVHandle ScalarEvolution::getBackedgeTakenCount(const Loop *L) {
2368 return getBackedgeTakenInfo(L).Exact;
2371 /// getMaxBackedgeTakenCount - Similar to getBackedgeTakenCount, except
2372 /// return the least SCEV value that is known never to be less than the
2373 /// actual backedge taken count.
2374 SCEVHandle ScalarEvolution::getMaxBackedgeTakenCount(const Loop *L) {
2375 return getBackedgeTakenInfo(L).Max;
2378 const ScalarEvolution::BackedgeTakenInfo &
2379 ScalarEvolution::getBackedgeTakenInfo(const Loop *L) {
2380 // Initially insert a CouldNotCompute for this loop. If the insertion
2381 // succeeds, procede to actually compute a backedge-taken count and
2382 // update the value. The temporary CouldNotCompute value tells SCEV
2383 // code elsewhere that it shouldn't attempt to request a new
2384 // backedge-taken count, which could result in infinite recursion.
2385 std::pair<std::map<const Loop*, BackedgeTakenInfo>::iterator, bool> Pair =
2386 BackedgeTakenCounts.insert(std::make_pair(L, getCouldNotCompute()));
2388 BackedgeTakenInfo ItCount = ComputeBackedgeTakenCount(L);
2389 if (ItCount.Exact != UnknownValue) {
2390 assert(ItCount.Exact->isLoopInvariant(L) &&
2391 ItCount.Max->isLoopInvariant(L) &&
2392 "Computed trip count isn't loop invariant for loop!");
2393 ++NumTripCountsComputed;
2395 // Update the value in the map.
2396 Pair.first->second = ItCount;
2397 } else if (isa<PHINode>(L->getHeader()->begin())) {
2398 // Only count loops that have phi nodes as not being computable.
2399 ++NumTripCountsNotComputed;
2402 // Now that we know more about the trip count for this loop, forget any
2403 // existing SCEV values for PHI nodes in this loop since they are only
2404 // conservative estimates made without the benefit
2405 // of trip count information.
2406 if (ItCount.hasAnyInfo())
2409 return Pair.first->second;
2412 /// forgetLoopBackedgeTakenCount - This method should be called by the
2413 /// client when it has changed a loop in a way that may effect
2414 /// ScalarEvolution's ability to compute a trip count, or if the loop
2416 void ScalarEvolution::forgetLoopBackedgeTakenCount(const Loop *L) {
2417 BackedgeTakenCounts.erase(L);
2421 /// forgetLoopPHIs - Delete the memoized SCEVs associated with the
2422 /// PHI nodes in the given loop. This is used when the trip count of
2423 /// the loop may have changed.
2424 void ScalarEvolution::forgetLoopPHIs(const Loop *L) {
2425 BasicBlock *Header = L->getHeader();
2427 // Push all Loop-header PHIs onto the Worklist stack, except those
2428 // that are presently represented via a SCEVUnknown. SCEVUnknown for
2429 // a PHI either means that it has an unrecognized structure, or it's
2430 // a PHI that's in the progress of being computed by createNodeForPHI.
2431 // In the former case, additional loop trip count information isn't
2432 // going to change anything. In the later case, createNodeForPHI will
2433 // perform the necessary updates on its own when it gets to that point.
2434 SmallVector<Instruction *, 16> Worklist;
2435 for (BasicBlock::iterator I = Header->begin();
2436 PHINode *PN = dyn_cast<PHINode>(I); ++I) {
2437 std::map<SCEVCallbackVH, SCEVHandle>::iterator It = Scalars.find((Value*)I);
2438 if (It != Scalars.end() && !isa<SCEVUnknown>(It->second))
2439 Worklist.push_back(PN);
2442 while (!Worklist.empty()) {
2443 Instruction *I = Worklist.pop_back_val();
2444 if (Scalars.erase(I))
2445 for (Value::use_iterator UI = I->use_begin(), UE = I->use_end();
2447 Worklist.push_back(cast<Instruction>(UI));
2451 /// ComputeBackedgeTakenCount - Compute the number of times the backedge
2452 /// of the specified loop will execute.
2453 ScalarEvolution::BackedgeTakenInfo
2454 ScalarEvolution::ComputeBackedgeTakenCount(const Loop *L) {
2455 // If the loop has a non-one exit block count, we can't analyze it.
2456 SmallVector<BasicBlock*, 8> ExitBlocks;
2457 L->getExitBlocks(ExitBlocks);
2458 if (ExitBlocks.size() != 1) return UnknownValue;
2460 // Okay, there is one exit block. Try to find the condition that causes the
2461 // loop to be exited.
2462 BasicBlock *ExitBlock = ExitBlocks[0];
2464 BasicBlock *ExitingBlock = 0;
2465 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
2467 if (L->contains(*PI)) {
2468 if (ExitingBlock == 0)
2471 return UnknownValue; // More than one block exiting!
2473 assert(ExitingBlock && "No exits from loop, something is broken!");
2475 // Okay, we've computed the exiting block. See what condition causes us to
2478 // FIXME: we should be able to handle switch instructions (with a single exit)
2479 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
2480 if (ExitBr == 0) return UnknownValue;
2481 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
2483 // At this point, we know we have a conditional branch that determines whether
2484 // the loop is exited. However, we don't know if the branch is executed each
2485 // time through the loop. If not, then the execution count of the branch will
2486 // not be equal to the trip count of the loop.
2488 // Currently we check for this by checking to see if the Exit branch goes to
2489 // the loop header. If so, we know it will always execute the same number of
2490 // times as the loop. We also handle the case where the exit block *is* the
2491 // loop header. This is common for un-rotated loops. More extensive analysis
2492 // could be done to handle more cases here.
2493 if (ExitBr->getSuccessor(0) != L->getHeader() &&
2494 ExitBr->getSuccessor(1) != L->getHeader() &&
2495 ExitBr->getParent() != L->getHeader())
2496 return UnknownValue;
2498 ICmpInst *ExitCond = dyn_cast<ICmpInst>(ExitBr->getCondition());
2500 // If it's not an integer or pointer comparison then compute it the hard way.
2502 return ComputeBackedgeTakenCountExhaustively(L, ExitBr->getCondition(),
2503 ExitBr->getSuccessor(0) == ExitBlock);
2505 // If the condition was exit on true, convert the condition to exit on false
2506 ICmpInst::Predicate Cond;
2507 if (ExitBr->getSuccessor(1) == ExitBlock)
2508 Cond = ExitCond->getPredicate();
2510 Cond = ExitCond->getInversePredicate();
2512 // Handle common loops like: for (X = "string"; *X; ++X)
2513 if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
2514 if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
2516 ComputeLoadConstantCompareBackedgeTakenCount(LI, RHS, L, Cond);
2517 if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
2520 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
2521 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
2523 // Try to evaluate any dependencies out of the loop.
2524 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
2525 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
2526 Tmp = getSCEVAtScope(RHS, L);
2527 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
2529 // At this point, we would like to compute how many iterations of the
2530 // loop the predicate will return true for these inputs.
2531 if (LHS->isLoopInvariant(L) && !RHS->isLoopInvariant(L)) {
2532 // If there is a loop-invariant, force it into the RHS.
2533 std::swap(LHS, RHS);
2534 Cond = ICmpInst::getSwappedPredicate(Cond);
2537 // If we have a comparison of a chrec against a constant, try to use value
2538 // ranges to answer this query.
2539 if (const SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
2540 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
2541 if (AddRec->getLoop() == L) {
2542 // Form the constant range.
2543 ConstantRange CompRange(
2544 ICmpInst::makeConstantRange(Cond, RHSC->getValue()->getValue()));
2546 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange, *this);
2547 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
2551 case ICmpInst::ICMP_NE: { // while (X != Y)
2552 // Convert to: while (X-Y != 0)
2553 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
2554 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2557 case ICmpInst::ICMP_EQ: {
2558 // Convert to: while (X-Y == 0) // while (X == Y)
2559 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
2560 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
2563 case ICmpInst::ICMP_SLT: {
2564 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, true);
2565 if (BTI.hasAnyInfo()) return BTI;
2568 case ICmpInst::ICMP_SGT: {
2569 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2570 getNotSCEV(RHS), L, true);
2571 if (BTI.hasAnyInfo()) return BTI;
2574 case ICmpInst::ICMP_ULT: {
2575 BackedgeTakenInfo BTI = HowManyLessThans(LHS, RHS, L, false);
2576 if (BTI.hasAnyInfo()) return BTI;
2579 case ICmpInst::ICMP_UGT: {
2580 BackedgeTakenInfo BTI = HowManyLessThans(getNotSCEV(LHS),
2581 getNotSCEV(RHS), L, false);
2582 if (BTI.hasAnyInfo()) return BTI;
2587 errs() << "ComputeBackedgeTakenCount ";
2588 if (ExitCond->getOperand(0)->getType()->isUnsigned())
2589 errs() << "[unsigned] ";
2590 errs() << *LHS << " "
2591 << Instruction::getOpcodeName(Instruction::ICmp)
2592 << " " << *RHS << "\n";
2597 ComputeBackedgeTakenCountExhaustively(L, ExitCond,
2598 ExitBr->getSuccessor(0) == ExitBlock);
2601 static ConstantInt *
2602 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, ConstantInt *C,
2603 ScalarEvolution &SE) {
2604 SCEVHandle InVal = SE.getConstant(C);
2605 SCEVHandle Val = AddRec->evaluateAtIteration(InVal, SE);
2606 assert(isa<SCEVConstant>(Val) &&
2607 "Evaluation of SCEV at constant didn't fold correctly?");
2608 return cast<SCEVConstant>(Val)->getValue();
2611 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
2612 /// and a GEP expression (missing the pointer index) indexing into it, return
2613 /// the addressed element of the initializer or null if the index expression is
2616 GetAddressedElementFromGlobal(GlobalVariable *GV,
2617 const std::vector<ConstantInt*> &Indices) {
2618 Constant *Init = GV->getInitializer();
2619 for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
2620 uint64_t Idx = Indices[i]->getZExtValue();
2621 if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
2622 assert(Idx < CS->getNumOperands() && "Bad struct index!");
2623 Init = cast<Constant>(CS->getOperand(Idx));
2624 } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
2625 if (Idx >= CA->getNumOperands()) return 0; // Bogus program
2626 Init = cast<Constant>(CA->getOperand(Idx));
2627 } else if (isa<ConstantAggregateZero>(Init)) {
2628 if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
2629 assert(Idx < STy->getNumElements() && "Bad struct index!");
2630 Init = Constant::getNullValue(STy->getElementType(Idx));
2631 } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
2632 if (Idx >= ATy->getNumElements()) return 0; // Bogus program
2633 Init = Constant::getNullValue(ATy->getElementType());
2635 assert(0 && "Unknown constant aggregate type!");
2639 return 0; // Unknown initializer type
2645 /// ComputeLoadConstantCompareBackedgeTakenCount - Given an exit condition of
2646 /// 'icmp op load X, cst', try to see if we can compute the backedge
2647 /// execution count.
2648 SCEVHandle ScalarEvolution::
2649 ComputeLoadConstantCompareBackedgeTakenCount(LoadInst *LI, Constant *RHS,
2651 ICmpInst::Predicate predicate) {
2652 if (LI->isVolatile()) return UnknownValue;
2654 // Check to see if the loaded pointer is a getelementptr of a global.
2655 GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
2656 if (!GEP) return UnknownValue;
2658 // Make sure that it is really a constant global we are gepping, with an
2659 // initializer, and make sure the first IDX is really 0.
2660 GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
2661 if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
2662 GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
2663 !cast<Constant>(GEP->getOperand(1))->isNullValue())
2664 return UnknownValue;
2666 // Okay, we allow one non-constant index into the GEP instruction.
2668 std::vector<ConstantInt*> Indexes;
2669 unsigned VarIdxNum = 0;
2670 for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
2671 if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
2672 Indexes.push_back(CI);
2673 } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
2674 if (VarIdx) return UnknownValue; // Multiple non-constant idx's.
2675 VarIdx = GEP->getOperand(i);
2677 Indexes.push_back(0);
2680 // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
2681 // Check to see if X is a loop variant variable value now.
2682 SCEVHandle Idx = getSCEV(VarIdx);
2683 SCEVHandle Tmp = getSCEVAtScope(Idx, L);
2684 if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
2686 // We can only recognize very limited forms of loop index expressions, in
2687 // particular, only affine AddRec's like {C1,+,C2}.
2688 const SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
2689 if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
2690 !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
2691 !isa<SCEVConstant>(IdxExpr->getOperand(1)))
2692 return UnknownValue;
2694 unsigned MaxSteps = MaxBruteForceIterations;
2695 for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
2696 ConstantInt *ItCst =
2697 ConstantInt::get(IdxExpr->getType(), IterationNum);
2698 ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst, *this);
2700 // Form the GEP offset.
2701 Indexes[VarIdxNum] = Val;
2703 Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
2704 if (Result == 0) break; // Cannot compute!
2706 // Evaluate the condition for this iteration.
2707 Result = ConstantExpr::getICmp(predicate, Result, RHS);
2708 if (!isa<ConstantInt>(Result)) break; // Couldn't decide for sure
2709 if (cast<ConstantInt>(Result)->getValue().isMinValue()) {
2711 errs() << "\n***\n*** Computed loop count " << *ItCst
2712 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
2715 ++NumArrayLenItCounts;
2716 return getConstant(ItCst); // Found terminating iteration!
2719 return UnknownValue;
2723 /// CanConstantFold - Return true if we can constant fold an instruction of the
2724 /// specified type, assuming that all operands were constants.
2725 static bool CanConstantFold(const Instruction *I) {
2726 if (isa<BinaryOperator>(I) || isa<CmpInst>(I) ||
2727 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
2730 if (const CallInst *CI = dyn_cast<CallInst>(I))
2731 if (const Function *F = CI->getCalledFunction())
2732 return canConstantFoldCallTo(F);
2736 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
2737 /// in the loop that V is derived from. We allow arbitrary operations along the
2738 /// way, but the operands of an operation must either be constants or a value
2739 /// derived from a constant PHI. If this expression does not fit with these
2740 /// constraints, return null.
2741 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
2742 // If this is not an instruction, or if this is an instruction outside of the
2743 // loop, it can't be derived from a loop PHI.
2744 Instruction *I = dyn_cast<Instruction>(V);
2745 if (I == 0 || !L->contains(I->getParent())) return 0;
2747 if (PHINode *PN = dyn_cast<PHINode>(I)) {
2748 if (L->getHeader() == I->getParent())
2751 // We don't currently keep track of the control flow needed to evaluate
2752 // PHIs, so we cannot handle PHIs inside of loops.
2756 // If we won't be able to constant fold this expression even if the operands
2757 // are constants, return early.
2758 if (!CanConstantFold(I)) return 0;
2760 // Otherwise, we can evaluate this instruction if all of its operands are
2761 // constant or derived from a PHI node themselves.
2763 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
2764 if (!(isa<Constant>(I->getOperand(Op)) ||
2765 isa<GlobalValue>(I->getOperand(Op)))) {
2766 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
2767 if (P == 0) return 0; // Not evolving from PHI
2771 return 0; // Evolving from multiple different PHIs.
2774 // This is a expression evolving from a constant PHI!
2778 /// EvaluateExpression - Given an expression that passes the
2779 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
2780 /// in the loop has the value PHIVal. If we can't fold this expression for some
2781 /// reason, return null.
2782 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
2783 if (isa<PHINode>(V)) return PHIVal;
2784 if (Constant *C = dyn_cast<Constant>(V)) return C;
2785 if (GlobalValue *GV = dyn_cast<GlobalValue>(V)) return GV;
2786 Instruction *I = cast<Instruction>(V);
2788 std::vector<Constant*> Operands;
2789 Operands.resize(I->getNumOperands());
2791 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2792 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
2793 if (Operands[i] == 0) return 0;
2796 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2797 return ConstantFoldCompareInstOperands(CI->getPredicate(),
2798 &Operands[0], Operands.size());
2800 return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
2801 &Operands[0], Operands.size());
2804 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
2805 /// in the header of its containing loop, we know the loop executes a
2806 /// constant number of times, and the PHI node is just a recurrence
2807 /// involving constants, fold it.
2808 Constant *ScalarEvolution::
2809 getConstantEvolutionLoopExitValue(PHINode *PN, const APInt& BEs, const Loop *L){
2810 std::map<PHINode*, Constant*>::iterator I =
2811 ConstantEvolutionLoopExitValue.find(PN);
2812 if (I != ConstantEvolutionLoopExitValue.end())
2815 if (BEs.ugt(APInt(BEs.getBitWidth(),MaxBruteForceIterations)))
2816 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
2818 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
2820 // Since the loop is canonicalized, the PHI node must have two entries. One
2821 // entry must be a constant (coming in from outside of the loop), and the
2822 // second must be derived from the same PHI.
2823 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2824 Constant *StartCST =
2825 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2827 return RetVal = 0; // Must be a constant.
2829 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2830 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2832 return RetVal = 0; // Not derived from same PHI.
2834 // Execute the loop symbolically to determine the exit value.
2835 if (BEs.getActiveBits() >= 32)
2836 return RetVal = 0; // More than 2^32-1 iterations?? Not doing it!
2838 unsigned NumIterations = BEs.getZExtValue(); // must be in range
2839 unsigned IterationNum = 0;
2840 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
2841 if (IterationNum == NumIterations)
2842 return RetVal = PHIVal; // Got exit value!
2844 // Compute the value of the PHI node for the next iteration.
2845 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2846 if (NextPHI == PHIVal)
2847 return RetVal = NextPHI; // Stopped evolving!
2849 return 0; // Couldn't evaluate!
2854 /// ComputeBackedgeTakenCountExhaustively - If the trip is known to execute a
2855 /// constant number of times (the condition evolves only from constants),
2856 /// try to evaluate a few iterations of the loop until we get the exit
2857 /// condition gets a value of ExitWhen (true or false). If we cannot
2858 /// evaluate the trip count of the loop, return UnknownValue.
2859 SCEVHandle ScalarEvolution::
2860 ComputeBackedgeTakenCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
2861 PHINode *PN = getConstantEvolvingPHI(Cond, L);
2862 if (PN == 0) return UnknownValue;
2864 // Since the loop is canonicalized, the PHI node must have two entries. One
2865 // entry must be a constant (coming in from outside of the loop), and the
2866 // second must be derived from the same PHI.
2867 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
2868 Constant *StartCST =
2869 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
2870 if (StartCST == 0) return UnknownValue; // Must be a constant.
2872 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
2873 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
2874 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
2876 // Okay, we find a PHI node that defines the trip count of this loop. Execute
2877 // the loop symbolically to determine when the condition gets a value of
2879 unsigned IterationNum = 0;
2880 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
2881 for (Constant *PHIVal = StartCST;
2882 IterationNum != MaxIterations; ++IterationNum) {
2883 ConstantInt *CondVal =
2884 dyn_cast_or_null<ConstantInt>(EvaluateExpression(Cond, PHIVal));
2886 // Couldn't symbolically evaluate.
2887 if (!CondVal) return UnknownValue;
2889 if (CondVal->getValue() == uint64_t(ExitWhen)) {
2890 ConstantEvolutionLoopExitValue[PN] = PHIVal;
2891 ++NumBruteForceTripCountsComputed;
2892 return getConstant(ConstantInt::get(Type::Int32Ty, IterationNum));
2895 // Compute the value of the PHI node for the next iteration.
2896 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
2897 if (NextPHI == 0 || NextPHI == PHIVal)
2898 return UnknownValue; // Couldn't evaluate or not making progress...
2902 // Too many iterations were needed to evaluate.
2903 return UnknownValue;
2906 /// getSCEVAtScope - Return a SCEV expression handle for the specified value
2907 /// at the specified scope in the program. The L value specifies a loop
2908 /// nest to evaluate the expression at, where null is the top-level or a
2909 /// specified loop is immediately inside of the loop.
2911 /// This method can be used to compute the exit value for a variable defined
2912 /// in a loop by querying what the value will hold in the parent loop.
2914 /// If this value is not computable at this scope, a SCEVCouldNotCompute
2915 /// object is returned.
2916 SCEVHandle ScalarEvolution::getSCEVAtScope(const SCEV *V, const Loop *L) {
2917 // FIXME: this should be turned into a virtual method on SCEV!
2919 if (isa<SCEVConstant>(V)) return V;
2921 // If this instruction is evolved from a constant-evolving PHI, compute the
2922 // exit value from the loop without using SCEVs.
2923 if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
2924 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
2925 const Loop *LI = (*this->LI)[I->getParent()];
2926 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
2927 if (PHINode *PN = dyn_cast<PHINode>(I))
2928 if (PN->getParent() == LI->getHeader()) {
2929 // Okay, there is no closed form solution for the PHI node. Check
2930 // to see if the loop that contains it has a known backedge-taken
2931 // count. If so, we may be able to force computation of the exit
2933 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(LI);
2934 if (const SCEVConstant *BTCC =
2935 dyn_cast<SCEVConstant>(BackedgeTakenCount)) {
2936 // Okay, we know how many times the containing loop executes. If
2937 // this is a constant evolving PHI node, get the final value at
2938 // the specified iteration number.
2939 Constant *RV = getConstantEvolutionLoopExitValue(PN,
2940 BTCC->getValue()->getValue(),
2942 if (RV) return getUnknown(RV);
2946 // Okay, this is an expression that we cannot symbolically evaluate
2947 // into a SCEV. Check to see if it's possible to symbolically evaluate
2948 // the arguments into constants, and if so, try to constant propagate the
2949 // result. This is particularly useful for computing loop exit values.
2950 if (CanConstantFold(I)) {
2951 // Check to see if we've folded this instruction at this loop before.
2952 std::map<const Loop *, Constant *> &Values = ValuesAtScopes[I];
2953 std::pair<std::map<const Loop *, Constant *>::iterator, bool> Pair =
2954 Values.insert(std::make_pair(L, static_cast<Constant *>(0)));
2956 return Pair.first->second ? &*getUnknown(Pair.first->second) : V;
2958 std::vector<Constant*> Operands;
2959 Operands.reserve(I->getNumOperands());
2960 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
2961 Value *Op = I->getOperand(i);
2962 if (Constant *C = dyn_cast<Constant>(Op)) {
2963 Operands.push_back(C);
2965 // If any of the operands is non-constant and if they are
2966 // non-integer and non-pointer, don't even try to analyze them
2967 // with scev techniques.
2968 if (!isSCEVable(Op->getType()))
2971 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
2972 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV)) {
2973 Constant *C = SC->getValue();
2974 if (C->getType() != Op->getType())
2975 C = ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2979 Operands.push_back(C);
2980 } else if (const SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
2981 if (Constant *C = dyn_cast<Constant>(SU->getValue())) {
2982 if (C->getType() != Op->getType())
2984 ConstantExpr::getCast(CastInst::getCastOpcode(C, false,
2988 Operands.push_back(C);
2998 if (const CmpInst *CI = dyn_cast<CmpInst>(I))
2999 C = ConstantFoldCompareInstOperands(CI->getPredicate(),
3000 &Operands[0], Operands.size());
3002 C = ConstantFoldInstOperands(I->getOpcode(), I->getType(),
3003 &Operands[0], Operands.size());
3004 Pair.first->second = C;
3005 return getUnknown(C);
3009 // This is some other type of SCEVUnknown, just return it.
3013 if (const SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
3014 // Avoid performing the look-up in the common case where the specified
3015 // expression has no loop-variant portions.
3016 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
3017 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3018 if (OpAtScope != Comm->getOperand(i)) {
3019 if (OpAtScope == UnknownValue) return UnknownValue;
3020 // Okay, at least one of these operands is loop variant but might be
3021 // foldable. Build a new instance of the folded commutative expression.
3022 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
3023 NewOps.push_back(OpAtScope);
3025 for (++i; i != e; ++i) {
3026 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
3027 if (OpAtScope == UnknownValue) return UnknownValue;
3028 NewOps.push_back(OpAtScope);
3030 if (isa<SCEVAddExpr>(Comm))
3031 return getAddExpr(NewOps);
3032 if (isa<SCEVMulExpr>(Comm))
3033 return getMulExpr(NewOps);
3034 if (isa<SCEVSMaxExpr>(Comm))
3035 return getSMaxExpr(NewOps);
3036 if (isa<SCEVUMaxExpr>(Comm))
3037 return getUMaxExpr(NewOps);
3038 assert(0 && "Unknown commutative SCEV type!");
3041 // If we got here, all operands are loop invariant.
3045 if (const SCEVUDivExpr *Div = dyn_cast<SCEVUDivExpr>(V)) {
3046 SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
3047 if (LHS == UnknownValue) return LHS;
3048 SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
3049 if (RHS == UnknownValue) return RHS;
3050 if (LHS == Div->getLHS() && RHS == Div->getRHS())
3051 return Div; // must be loop invariant
3052 return getUDivExpr(LHS, RHS);
3055 // If this is a loop recurrence for a loop that does not contain L, then we
3056 // are dealing with the final value computed by the loop.
3057 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
3058 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
3059 // To evaluate this recurrence, we need to know how many times the AddRec
3060 // loop iterates. Compute this now.
3061 SCEVHandle BackedgeTakenCount = getBackedgeTakenCount(AddRec->getLoop());
3062 if (BackedgeTakenCount == UnknownValue) return UnknownValue;
3064 // Then, evaluate the AddRec.
3065 return AddRec->evaluateAtIteration(BackedgeTakenCount, *this);
3067 return UnknownValue;
3070 if (const SCEVZeroExtendExpr *Cast = dyn_cast<SCEVZeroExtendExpr>(V)) {
3071 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3072 if (Op == UnknownValue) return Op;
3073 if (Op == Cast->getOperand())
3074 return Cast; // must be loop invariant
3075 return getZeroExtendExpr(Op, Cast->getType());
3078 if (const SCEVSignExtendExpr *Cast = dyn_cast<SCEVSignExtendExpr>(V)) {
3079 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3080 if (Op == UnknownValue) return Op;
3081 if (Op == Cast->getOperand())
3082 return Cast; // must be loop invariant
3083 return getSignExtendExpr(Op, Cast->getType());
3086 if (const SCEVTruncateExpr *Cast = dyn_cast<SCEVTruncateExpr>(V)) {
3087 SCEVHandle Op = getSCEVAtScope(Cast->getOperand(), L);
3088 if (Op == UnknownValue) return Op;
3089 if (Op == Cast->getOperand())
3090 return Cast; // must be loop invariant
3091 return getTruncateExpr(Op, Cast->getType());
3094 assert(0 && "Unknown SCEV type!");
3098 /// getSCEVAtScope - This is a convenience function which does
3099 /// getSCEVAtScope(getSCEV(V), L).
3100 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) {
3101 return getSCEVAtScope(getSCEV(V), L);
3104 /// SolveLinEquationWithOverflow - Finds the minimum unsigned root of the
3105 /// following equation:
3107 /// A * X = B (mod N)
3109 /// where N = 2^BW and BW is the common bit width of A and B. The signedness of
3110 /// A and B isn't important.
3112 /// If the equation does not have a solution, SCEVCouldNotCompute is returned.
3113 static SCEVHandle SolveLinEquationWithOverflow(const APInt &A, const APInt &B,
3114 ScalarEvolution &SE) {
3115 uint32_t BW = A.getBitWidth();
3116 assert(BW == B.getBitWidth() && "Bit widths must be the same.");
3117 assert(A != 0 && "A must be non-zero.");
3121 // The gcd of A and N may have only one prime factor: 2. The number of
3122 // trailing zeros in A is its multiplicity
3123 uint32_t Mult2 = A.countTrailingZeros();
3126 // 2. Check if B is divisible by D.
3128 // B is divisible by D if and only if the multiplicity of prime factor 2 for B
3129 // is not less than multiplicity of this prime factor for D.
3130 if (B.countTrailingZeros() < Mult2)
3131 return SE.getCouldNotCompute();
3133 // 3. Compute I: the multiplicative inverse of (A / D) in arithmetic
3136 // (N / D) may need BW+1 bits in its representation. Hence, we'll use this
3137 // bit width during computations.
3138 APInt AD = A.lshr(Mult2).zext(BW + 1); // AD = A / D
3139 APInt Mod(BW + 1, 0);
3140 Mod.set(BW - Mult2); // Mod = N / D
3141 APInt I = AD.multiplicativeInverse(Mod);
3143 // 4. Compute the minimum unsigned root of the equation:
3144 // I * (B / D) mod (N / D)
3145 APInt Result = (I * B.lshr(Mult2).zext(BW + 1)).urem(Mod);
3147 // The result is guaranteed to be less than 2^BW so we may truncate it to BW
3149 return SE.getConstant(Result.trunc(BW));
3152 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
3153 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
3154 /// might be the same) or two SCEVCouldNotCompute objects.
3156 static std::pair<SCEVHandle,SCEVHandle>
3157 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec, ScalarEvolution &SE) {
3158 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
3159 const SCEVConstant *LC = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
3160 const SCEVConstant *MC = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
3161 const SCEVConstant *NC = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
3163 // We currently can only solve this if the coefficients are constants.
3164 if (!LC || !MC || !NC) {
3165 const SCEV *CNC = SE.getCouldNotCompute();
3166 return std::make_pair(CNC, CNC);
3169 uint32_t BitWidth = LC->getValue()->getValue().getBitWidth();
3170 const APInt &L = LC->getValue()->getValue();
3171 const APInt &M = MC->getValue()->getValue();
3172 const APInt &N = NC->getValue()->getValue();
3173 APInt Two(BitWidth, 2);
3174 APInt Four(BitWidth, 4);
3177 using namespace APIntOps;
3179 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
3180 // The B coefficient is M-N/2
3184 // The A coefficient is N/2
3185 APInt A(N.sdiv(Two));
3187 // Compute the B^2-4ac term.
3190 SqrtTerm -= Four * (A * C);
3192 // Compute sqrt(B^2-4ac). This is guaranteed to be the nearest
3193 // integer value or else APInt::sqrt() will assert.
3194 APInt SqrtVal(SqrtTerm.sqrt());
3196 // Compute the two solutions for the quadratic formula.
3197 // The divisions must be performed as signed divisions.
3199 APInt TwoA( A << 1 );
3200 if (TwoA.isMinValue()) {
3201 const SCEV *CNC = SE.getCouldNotCompute();
3202 return std::make_pair(CNC, CNC);
3205 ConstantInt *Solution1 = ConstantInt::get((NegB + SqrtVal).sdiv(TwoA));
3206 ConstantInt *Solution2 = ConstantInt::get((NegB - SqrtVal).sdiv(TwoA));
3208 return std::make_pair(SE.getConstant(Solution1),
3209 SE.getConstant(Solution2));
3210 } // end APIntOps namespace
3213 /// HowFarToZero - Return the number of times a backedge comparing the specified
3214 /// value to zero will execute. If not computable, return UnknownValue
3215 SCEVHandle ScalarEvolution::HowFarToZero(const SCEV *V, const Loop *L) {
3216 // If the value is a constant
3217 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3218 // If the value is already zero, the branch will execute zero times.
3219 if (C->getValue()->isZero()) return C;
3220 return UnknownValue; // Otherwise it will loop infinitely.
3223 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
3224 if (!AddRec || AddRec->getLoop() != L)
3225 return UnknownValue;
3227 if (AddRec->isAffine()) {
3228 // If this is an affine expression, the execution count of this branch is
3229 // the minimum unsigned root of the following equation:
3231 // Start + Step*N = 0 (mod 2^BW)
3235 // Step*N = -Start (mod 2^BW)
3237 // where BW is the common bit width of Start and Step.
3239 // Get the initial value for the loop.
3240 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
3241 if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
3243 SCEVHandle Step = getSCEVAtScope(AddRec->getOperand(1), L->getParentLoop());
3245 if (const SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
3246 // For now we handle only constant steps.
3248 // First, handle unitary steps.
3249 if (StepC->getValue()->equalsInt(1)) // 1*N = -Start (mod 2^BW), so:
3250 return getNegativeSCEV(Start); // N = -Start (as unsigned)
3251 if (StepC->getValue()->isAllOnesValue()) // -1*N = -Start (mod 2^BW), so:
3252 return Start; // N = Start (as unsigned)
3254 // Then, try to solve the above equation provided that Start is constant.
3255 if (const SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start))
3256 return SolveLinEquationWithOverflow(StepC->getValue()->getValue(),
3257 -StartC->getValue()->getValue(),
3260 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
3261 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
3262 // the quadratic equation to solve it.
3263 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec,
3265 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3266 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3269 errs() << "HFTZ: " << *V << " - sol#1: " << *R1
3270 << " sol#2: " << *R2 << "\n";
3272 // Pick the smallest positive root value.
3273 if (ConstantInt *CB =
3274 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3275 R1->getValue(), R2->getValue()))) {
3276 if (CB->getZExtValue() == false)
3277 std::swap(R1, R2); // R1 is the minimum root now.
3279 // We can only use this value if the chrec ends up with an exact zero
3280 // value at this index. When solving for "X*X != 5", for example, we
3281 // should not accept a root of 2.
3282 SCEVHandle Val = AddRec->evaluateAtIteration(R1, *this);
3284 return R1; // We found a quadratic root!
3289 return UnknownValue;
3292 /// HowFarToNonZero - Return the number of times a backedge checking the
3293 /// specified value for nonzero will execute. If not computable, return
3295 SCEVHandle ScalarEvolution::HowFarToNonZero(const SCEV *V, const Loop *L) {
3296 // Loops that look like: while (X == 0) are very strange indeed. We don't
3297 // handle them yet except for the trivial case. This could be expanded in the
3298 // future as needed.
3300 // If the value is a constant, check to see if it is known to be non-zero
3301 // already. If so, the backedge will execute zero times.
3302 if (const SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
3303 if (!C->getValue()->isNullValue())
3304 return getIntegerSCEV(0, C->getType());
3305 return UnknownValue; // Otherwise it will loop infinitely.
3308 // We could implement others, but I really doubt anyone writes loops like
3309 // this, and if they did, they would already be constant folded.
3310 return UnknownValue;
3313 /// getLoopPredecessor - If the given loop's header has exactly one unique
3314 /// predecessor outside the loop, return it. Otherwise return null.
3316 BasicBlock *ScalarEvolution::getLoopPredecessor(const Loop *L) {
3317 BasicBlock *Header = L->getHeader();
3318 BasicBlock *Pred = 0;
3319 for (pred_iterator PI = pred_begin(Header), E = pred_end(Header);
3321 if (!L->contains(*PI)) {
3322 if (Pred && Pred != *PI) return 0; // Multiple predecessors.
3328 /// getPredecessorWithUniqueSuccessorForBB - Return a predecessor of BB
3329 /// (which may not be an immediate predecessor) which has exactly one
3330 /// successor from which BB is reachable, or null if no such block is
3334 ScalarEvolution::getPredecessorWithUniqueSuccessorForBB(BasicBlock *BB) {
3335 // If the block has a unique predecessor, then there is no path from the
3336 // predecessor to the block that does not go through the direct edge
3337 // from the predecessor to the block.
3338 if (BasicBlock *Pred = BB->getSinglePredecessor())
3341 // A loop's header is defined to be a block that dominates the loop.
3342 // If the header has a unique predecessor outside the loop, it must be
3343 // a block that has exactly one successor that can reach the loop.
3344 if (Loop *L = LI->getLoopFor(BB))
3345 return getLoopPredecessor(L);
3350 /// isLoopGuardedByCond - Test whether entry to the loop is protected by
3351 /// a conditional between LHS and RHS. This is used to help avoid max
3352 /// expressions in loop trip counts.
3353 bool ScalarEvolution::isLoopGuardedByCond(const Loop *L,
3354 ICmpInst::Predicate Pred,
3355 const SCEV *LHS, const SCEV *RHS) {
3356 // Interpret a null as meaning no loop, where there is obviously no guard
3357 // (interprocedural conditions notwithstanding).
3358 if (!L) return false;
3360 BasicBlock *Predecessor = getLoopPredecessor(L);
3361 BasicBlock *PredecessorDest = L->getHeader();
3363 // Starting at the loop predecessor, climb up the predecessor chain, as long
3364 // as there are predecessors that can be found that have unique successors
3365 // leading to the original header.
3367 PredecessorDest = Predecessor,
3368 Predecessor = getPredecessorWithUniqueSuccessorForBB(Predecessor)) {
3370 BranchInst *LoopEntryPredicate =
3371 dyn_cast<BranchInst>(Predecessor->getTerminator());
3372 if (!LoopEntryPredicate ||
3373 LoopEntryPredicate->isUnconditional())
3376 ICmpInst *ICI = dyn_cast<ICmpInst>(LoopEntryPredicate->getCondition());
3379 // Now that we found a conditional branch that dominates the loop, check to
3380 // see if it is the comparison we are looking for.
3381 Value *PreCondLHS = ICI->getOperand(0);
3382 Value *PreCondRHS = ICI->getOperand(1);
3383 ICmpInst::Predicate Cond;
3384 if (LoopEntryPredicate->getSuccessor(0) == PredecessorDest)
3385 Cond = ICI->getPredicate();
3387 Cond = ICI->getInversePredicate();
3390 ; // An exact match.
3391 else if (!ICmpInst::isTrueWhenEqual(Cond) && Pred == ICmpInst::ICMP_NE)
3392 ; // The actual condition is beyond sufficient.
3394 // Check a few special cases.
3396 case ICmpInst::ICMP_UGT:
3397 if (Pred == ICmpInst::ICMP_ULT) {
3398 std::swap(PreCondLHS, PreCondRHS);
3399 Cond = ICmpInst::ICMP_ULT;
3403 case ICmpInst::ICMP_SGT:
3404 if (Pred == ICmpInst::ICMP_SLT) {
3405 std::swap(PreCondLHS, PreCondRHS);
3406 Cond = ICmpInst::ICMP_SLT;
3410 case ICmpInst::ICMP_NE:
3411 // Expressions like (x >u 0) are often canonicalized to (x != 0),
3412 // so check for this case by checking if the NE is comparing against
3413 // a minimum or maximum constant.
3414 if (!ICmpInst::isTrueWhenEqual(Pred))
3415 if (ConstantInt *CI = dyn_cast<ConstantInt>(PreCondRHS)) {
3416 const APInt &A = CI->getValue();
3418 case ICmpInst::ICMP_SLT:
3419 if (A.isMaxSignedValue()) break;
3421 case ICmpInst::ICMP_SGT:
3422 if (A.isMinSignedValue()) break;
3424 case ICmpInst::ICMP_ULT:
3425 if (A.isMaxValue()) break;
3427 case ICmpInst::ICMP_UGT:
3428 if (A.isMinValue()) break;
3433 Cond = ICmpInst::ICMP_NE;
3434 // NE is symmetric but the original comparison may not be. Swap
3435 // the operands if necessary so that they match below.
3436 if (isa<SCEVConstant>(LHS))
3437 std::swap(PreCondLHS, PreCondRHS);
3442 // We weren't able to reconcile the condition.
3446 if (!PreCondLHS->getType()->isInteger()) continue;
3448 SCEVHandle PreCondLHSSCEV = getSCEV(PreCondLHS);
3449 SCEVHandle PreCondRHSSCEV = getSCEV(PreCondRHS);
3450 if ((LHS == PreCondLHSSCEV && RHS == PreCondRHSSCEV) ||
3451 (LHS == getNotSCEV(PreCondRHSSCEV) &&
3452 RHS == getNotSCEV(PreCondLHSSCEV)))
3459 /// HowManyLessThans - Return the number of times a backedge containing the
3460 /// specified less-than comparison will execute. If not computable, return
3462 ScalarEvolution::BackedgeTakenInfo ScalarEvolution::
3463 HowManyLessThans(const SCEV *LHS, const SCEV *RHS,
3464 const Loop *L, bool isSigned) {
3465 // Only handle: "ADDREC < LoopInvariant".
3466 if (!RHS->isLoopInvariant(L)) return UnknownValue;
3468 const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
3469 if (!AddRec || AddRec->getLoop() != L)
3470 return UnknownValue;
3472 if (AddRec->isAffine()) {
3473 // FORNOW: We only support unit strides.
3474 unsigned BitWidth = getTypeSizeInBits(AddRec->getType());
3475 SCEVHandle Step = AddRec->getStepRecurrence(*this);
3476 SCEVHandle NegOne = getIntegerSCEV(-1, AddRec->getType());
3478 // TODO: handle non-constant strides.
3479 const SCEVConstant *CStep = dyn_cast<SCEVConstant>(Step);
3480 if (!CStep || CStep->isZero())
3481 return UnknownValue;
3482 if (CStep->isOne()) {
3483 // With unit stride, the iteration never steps past the limit value.
3484 } else if (CStep->getValue()->getValue().isStrictlyPositive()) {
3485 if (const SCEVConstant *CLimit = dyn_cast<SCEVConstant>(RHS)) {
3486 // Test whether a positive iteration iteration can step past the limit
3487 // value and past the maximum value for its type in a single step.
3489 APInt Max = APInt::getSignedMaxValue(BitWidth);
3490 if ((Max - CStep->getValue()->getValue())
3491 .slt(CLimit->getValue()->getValue()))
3492 return UnknownValue;
3494 APInt Max = APInt::getMaxValue(BitWidth);
3495 if ((Max - CStep->getValue()->getValue())
3496 .ult(CLimit->getValue()->getValue()))
3497 return UnknownValue;
3500 // TODO: handle non-constant limit values below.
3501 return UnknownValue;
3503 // TODO: handle negative strides below.
3504 return UnknownValue;
3506 // We know the LHS is of the form {n,+,s} and the RHS is some loop-invariant
3507 // m. So, we count the number of iterations in which {n,+,s} < m is true.
3508 // Note that we cannot simply return max(m-n,0)/s because it's not safe to
3509 // treat m-n as signed nor unsigned due to overflow possibility.
3511 // First, we get the value of the LHS in the first iteration: n
3512 SCEVHandle Start = AddRec->getOperand(0);
3514 // Determine the minimum constant start value.
3515 SCEVHandle MinStart = isa<SCEVConstant>(Start) ? Start :
3516 getConstant(isSigned ? APInt::getSignedMinValue(BitWidth) :
3517 APInt::getMinValue(BitWidth));
3519 // If we know that the condition is true in order to enter the loop,
3520 // then we know that it will run exactly (m-n)/s times. Otherwise, we
3521 // only know if will execute (max(m,n)-n)/s times. In both cases, the
3522 // division must round up.
3523 SCEVHandle End = RHS;
3524 if (!isLoopGuardedByCond(L,
3525 isSigned ? ICmpInst::ICMP_SLT : ICmpInst::ICMP_ULT,
3526 getMinusSCEV(Start, Step), RHS))
3527 End = isSigned ? getSMaxExpr(RHS, Start)
3528 : getUMaxExpr(RHS, Start);
3530 // Determine the maximum constant end value.
3531 SCEVHandle MaxEnd = isa<SCEVConstant>(End) ? End :
3532 getConstant(isSigned ? APInt::getSignedMaxValue(BitWidth) :
3533 APInt::getMaxValue(BitWidth));
3535 // Finally, we subtract these two values and divide, rounding up, to get
3536 // the number of times the backedge is executed.
3537 SCEVHandle BECount = getUDivExpr(getAddExpr(getMinusSCEV(End, Start),
3538 getAddExpr(Step, NegOne)),
3541 // The maximum backedge count is similar, except using the minimum start
3542 // value and the maximum end value.
3543 SCEVHandle MaxBECount = getUDivExpr(getAddExpr(getMinusSCEV(MaxEnd,
3545 getAddExpr(Step, NegOne)),
3548 return BackedgeTakenInfo(BECount, MaxBECount);
3551 return UnknownValue;
3554 /// getNumIterationsInRange - Return the number of iterations of this loop that
3555 /// produce values in the specified constant range. Another way of looking at
3556 /// this is that it returns the first iteration number where the value is not in
3557 /// the condition, thus computing the exit count. If the iteration count can't
3558 /// be computed, an instance of SCEVCouldNotCompute is returned.
3559 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
3560 ScalarEvolution &SE) const {
3561 if (Range.isFullSet()) // Infinite loop.
3562 return SE.getCouldNotCompute();
3564 // If the start is a non-zero constant, shift the range to simplify things.
3565 if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
3566 if (!SC->getValue()->isZero()) {
3567 std::vector<SCEVHandle> Operands(op_begin(), op_end());
3568 Operands[0] = SE.getIntegerSCEV(0, SC->getType());
3569 SCEVHandle Shifted = SE.getAddRecExpr(Operands, getLoop());
3570 if (const SCEVAddRecExpr *ShiftedAddRec =
3571 dyn_cast<SCEVAddRecExpr>(Shifted))
3572 return ShiftedAddRec->getNumIterationsInRange(
3573 Range.subtract(SC->getValue()->getValue()), SE);
3574 // This is strange and shouldn't happen.
3575 return SE.getCouldNotCompute();
3578 // The only time we can solve this is when we have all constant indices.
3579 // Otherwise, we cannot determine the overflow conditions.
3580 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
3581 if (!isa<SCEVConstant>(getOperand(i)))
3582 return SE.getCouldNotCompute();
3585 // Okay at this point we know that all elements of the chrec are constants and
3586 // that the start element is zero.
3588 // First check to see if the range contains zero. If not, the first
3590 unsigned BitWidth = SE.getTypeSizeInBits(getType());
3591 if (!Range.contains(APInt(BitWidth, 0)))
3592 return SE.getConstant(ConstantInt::get(getType(),0));
3595 // If this is an affine expression then we have this situation:
3596 // Solve {0,+,A} in Range === Ax in Range
3598 // We know that zero is in the range. If A is positive then we know that
3599 // the upper value of the range must be the first possible exit value.
3600 // If A is negative then the lower of the range is the last possible loop
3601 // value. Also note that we already checked for a full range.
3602 APInt One(BitWidth,1);
3603 APInt A = cast<SCEVConstant>(getOperand(1))->getValue()->getValue();
3604 APInt End = A.sge(One) ? (Range.getUpper() - One) : Range.getLower();
3606 // The exit value should be (End+A)/A.
3607 APInt ExitVal = (End + A).udiv(A);
3608 ConstantInt *ExitValue = ConstantInt::get(ExitVal);
3610 // Evaluate at the exit value. If we really did fall out of the valid
3611 // range, then we computed our trip count, otherwise wrap around or other
3612 // things must have happened.
3613 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue, SE);
3614 if (Range.contains(Val->getValue()))
3615 return SE.getCouldNotCompute(); // Something strange happened
3617 // Ensure that the previous value is in the range. This is a sanity check.
3618 assert(Range.contains(
3619 EvaluateConstantChrecAtConstant(this,
3620 ConstantInt::get(ExitVal - One), SE)->getValue()) &&
3621 "Linear scev computation is off in a bad way!");
3622 return SE.getConstant(ExitValue);
3623 } else if (isQuadratic()) {
3624 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
3625 // quadratic equation to solve it. To do this, we must frame our problem in
3626 // terms of figuring out when zero is crossed, instead of when
3627 // Range.getUpper() is crossed.
3628 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
3629 NewOps[0] = SE.getNegativeSCEV(SE.getConstant(Range.getUpper()));
3630 SCEVHandle NewAddRec = SE.getAddRecExpr(NewOps, getLoop());
3632 // Next, solve the constructed addrec
3633 std::pair<SCEVHandle,SCEVHandle> Roots =
3634 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec), SE);
3635 const SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
3636 const SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
3638 // Pick the smallest positive root value.
3639 if (ConstantInt *CB =
3640 dyn_cast<ConstantInt>(ConstantExpr::getICmp(ICmpInst::ICMP_ULT,
3641 R1->getValue(), R2->getValue()))) {
3642 if (CB->getZExtValue() == false)
3643 std::swap(R1, R2); // R1 is the minimum root now.
3645 // Make sure the root is not off by one. The returned iteration should
3646 // not be in the range, but the previous one should be. When solving
3647 // for "X*X < 5", for example, we should not return a root of 2.
3648 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
3651 if (Range.contains(R1Val->getValue())) {
3652 // The next iteration must be out of the range...
3653 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()+1);
3655 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3656 if (!Range.contains(R1Val->getValue()))
3657 return SE.getConstant(NextVal);
3658 return SE.getCouldNotCompute(); // Something strange happened
3661 // If R1 was not in the range, then it is a good return value. Make
3662 // sure that R1-1 WAS in the range though, just in case.
3663 ConstantInt *NextVal = ConstantInt::get(R1->getValue()->getValue()-1);
3664 R1Val = EvaluateConstantChrecAtConstant(this, NextVal, SE);
3665 if (Range.contains(R1Val->getValue()))
3667 return SE.getCouldNotCompute(); // Something strange happened
3672 return SE.getCouldNotCompute();
3677 //===----------------------------------------------------------------------===//
3678 // SCEVCallbackVH Class Implementation
3679 //===----------------------------------------------------------------------===//
3681 void ScalarEvolution::SCEVCallbackVH::deleted() {
3682 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3683 if (PHINode *PN = dyn_cast<PHINode>(getValPtr()))
3684 SE->ConstantEvolutionLoopExitValue.erase(PN);
3685 if (Instruction *I = dyn_cast<Instruction>(getValPtr()))
3686 SE->ValuesAtScopes.erase(I);
3687 SE->Scalars.erase(getValPtr());
3688 // this now dangles!
3691 void ScalarEvolution::SCEVCallbackVH::allUsesReplacedWith(Value *) {
3692 assert(SE && "SCEVCallbackVH called with a non-null ScalarEvolution!");
3694 // Forget all the expressions associated with users of the old value,
3695 // so that future queries will recompute the expressions using the new
3697 SmallVector<User *, 16> Worklist;
3698 Value *Old = getValPtr();
3699 bool DeleteOld = false;
3700 for (Value::use_iterator UI = Old->use_begin(), UE = Old->use_end();
3702 Worklist.push_back(*UI);
3703 while (!Worklist.empty()) {
3704 User *U = Worklist.pop_back_val();
3705 // Deleting the Old value will cause this to dangle. Postpone
3706 // that until everything else is done.
3711 if (PHINode *PN = dyn_cast<PHINode>(U))
3712 SE->ConstantEvolutionLoopExitValue.erase(PN);
3713 if (Instruction *I = dyn_cast<Instruction>(U))
3714 SE->ValuesAtScopes.erase(I);
3715 if (SE->Scalars.erase(U))
3716 for (Value::use_iterator UI = U->use_begin(), UE = U->use_end();
3718 Worklist.push_back(*UI);
3721 if (PHINode *PN = dyn_cast<PHINode>(Old))
3722 SE->ConstantEvolutionLoopExitValue.erase(PN);
3723 if (Instruction *I = dyn_cast<Instruction>(Old))
3724 SE->ValuesAtScopes.erase(I);
3725 SE->Scalars.erase(Old);
3726 // this now dangles!
3731 ScalarEvolution::SCEVCallbackVH::SCEVCallbackVH(Value *V, ScalarEvolution *se)
3732 : CallbackVH(V), SE(se) {}
3734 //===----------------------------------------------------------------------===//
3735 // ScalarEvolution Class Implementation
3736 //===----------------------------------------------------------------------===//
3738 ScalarEvolution::ScalarEvolution()
3739 : FunctionPass(&ID), UnknownValue(new SCEVCouldNotCompute()) {
3742 bool ScalarEvolution::runOnFunction(Function &F) {
3744 LI = &getAnalysis<LoopInfo>();
3745 TD = getAnalysisIfAvailable<TargetData>();
3749 void ScalarEvolution::releaseMemory() {
3751 BackedgeTakenCounts.clear();
3752 ConstantEvolutionLoopExitValue.clear();
3753 ValuesAtScopes.clear();
3756 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
3757 AU.setPreservesAll();
3758 AU.addRequiredTransitive<LoopInfo>();
3761 bool ScalarEvolution::hasLoopInvariantBackedgeTakenCount(const Loop *L) {
3762 return !isa<SCEVCouldNotCompute>(getBackedgeTakenCount(L));
3765 static void PrintLoopInfo(raw_ostream &OS, ScalarEvolution *SE,
3767 // Print all inner loops first
3768 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
3769 PrintLoopInfo(OS, SE, *I);
3771 OS << "Loop " << L->getHeader()->getName() << ": ";
3773 SmallVector<BasicBlock*, 8> ExitBlocks;
3774 L->getExitBlocks(ExitBlocks);
3775 if (ExitBlocks.size() != 1)
3776 OS << "<multiple exits> ";
3778 if (SE->hasLoopInvariantBackedgeTakenCount(L)) {
3779 OS << "backedge-taken count is " << *SE->getBackedgeTakenCount(L);
3781 OS << "Unpredictable backedge-taken count. ";
3787 void ScalarEvolution::print(raw_ostream &OS, const Module* ) const {
3788 // ScalarEvolution's implementaiton of the print method is to print
3789 // out SCEV values of all instructions that are interesting. Doing
3790 // this potentially causes it to create new SCEV objects though,
3791 // which technically conflicts with the const qualifier. This isn't
3792 // observable from outside the class though (the hasSCEV function
3793 // notwithstanding), so casting away the const isn't dangerous.
3794 ScalarEvolution &SE = *const_cast<ScalarEvolution*>(this);
3796 OS << "Classifying expressions for: " << F->getName() << "\n";
3797 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
3798 if (isSCEVable(I->getType())) {
3801 SCEVHandle SV = SE.getSCEV(&*I);
3805 if (const Loop *L = LI->getLoopFor((*I).getParent())) {
3807 SCEVHandle ExitValue = SE.getSCEVAtScope(&*I, L->getParentLoop());
3808 if (isa<SCEVCouldNotCompute>(ExitValue)) {
3809 OS << "<<Unknown>>";
3819 OS << "Determining loop execution counts for: " << F->getName() << "\n";
3820 for (LoopInfo::iterator I = LI->begin(), E = LI->end(); I != E; ++I)
3821 PrintLoopInfo(OS, &SE, *I);
3824 void ScalarEvolution::print(std::ostream &o, const Module *M) const {
3825 raw_os_ostream OS(o);