1 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
3 // The LLVM Compiler Infrastructure
5 // This file was developed by the LLVM research group and is distributed under
6 // the University of Illinois Open Source 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 // Orthogonal to the analysis of code above, this file also implements the
37 // ScalarEvolutionRewriter class, which is used to emit code that represents the
38 // various recurrences present in a loop, in canonical forms.
40 // TODO: We should use these routines and value representations to implement
41 // dependence analysis!
43 //===----------------------------------------------------------------------===//
45 // There are several good references for the techniques used in this analysis.
47 // Chains of recurrences -- a method to expedite the evaluation
48 // of closed-form functions
49 // Olaf Bachmann, Paul S. Wang, Eugene V. Zima
51 // On computational properties of chains of recurrences
54 // Symbolic Evaluation of Chains of Recurrences for Loop Optimization
55 // Robert A. van Engelen
57 // Efficient Symbolic Analysis for Optimizing Compilers
58 // Robert A. van Engelen
60 // Using the chains of recurrences algebra for data dependence testing and
61 // induction variable substitution
62 // MS Thesis, Johnie Birch
64 //===----------------------------------------------------------------------===//
66 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
67 #include "llvm/Constants.h"
68 #include "llvm/DerivedTypes.h"
69 #include "llvm/Instructions.h"
70 #include "llvm/Type.h"
71 #include "llvm/Value.h"
72 #include "llvm/Analysis/LoopInfo.h"
73 #include "llvm/Assembly/Writer.h"
74 #include "llvm/Transforms/Scalar.h"
75 #include "llvm/Transforms/Utils/Local.h"
76 #include "llvm/Support/CFG.h"
77 #include "llvm/Support/ConstantRange.h"
78 #include "llvm/Support/InstIterator.h"
79 #include "Support/CommandLine.h"
80 #include "Support/Statistic.h"
85 RegisterAnalysis<ScalarEvolution>
86 R("scalar-evolution", "Scalar Evolution Analysis Printer");
89 NumBruteForceEvaluations("scalar-evolution",
90 "Number of brute force evaluations needed to calculate high-order polynomial exit values");
92 NumTripCountsComputed("scalar-evolution",
93 "Number of loops with predictable loop counts");
95 NumTripCountsNotComputed("scalar-evolution",
96 "Number of loops without predictable loop counts");
98 NumBruteForceTripCountsComputed("scalar-evolution",
99 "Number of loops with trip counts computed by force");
102 MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
103 cl::desc("Maximum number of iterations SCEV will symbolically execute a constant derived loop"),
107 //===----------------------------------------------------------------------===//
108 // SCEV class definitions
109 //===----------------------------------------------------------------------===//
111 //===----------------------------------------------------------------------===//
112 // Implementation of the SCEV class.
115 /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
116 /// than the complexity of the RHS. If the SCEVs have identical complexity,
117 /// order them by their addresses. This comparator is used to canonicalize
119 struct SCEVComplexityCompare {
120 bool operator()(SCEV *LHS, SCEV *RHS) {
121 if (LHS->getSCEVType() < RHS->getSCEVType())
123 if (LHS->getSCEVType() == RHS->getSCEVType())
131 void SCEV::dump() const {
135 /// getValueRange - Return the tightest constant bounds that this value is
136 /// known to have. This method is only valid on integer SCEV objects.
137 ConstantRange SCEV::getValueRange() const {
138 const Type *Ty = getType();
139 assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
140 Ty = Ty->getUnsignedVersion();
141 // Default to a full range if no better information is available.
142 return ConstantRange(getType());
146 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
148 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
149 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
153 const Type *SCEVCouldNotCompute::getType() const {
154 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
158 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
159 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
163 Value *SCEVCouldNotCompute::expandCodeFor(ScalarEvolutionRewriter &SER,
164 Instruction *InsertPt) {
165 assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
170 void SCEVCouldNotCompute::print(std::ostream &OS) const {
171 OS << "***COULDNOTCOMPUTE***";
174 bool SCEVCouldNotCompute::classof(const SCEV *S) {
175 return S->getSCEVType() == scCouldNotCompute;
179 // SCEVConstants - Only allow the creation of one SCEVConstant for any
180 // particular value. Don't use a SCEVHandle here, or else the object will
182 static std::map<ConstantInt*, SCEVConstant*> SCEVConstants;
185 SCEVConstant::~SCEVConstant() {
186 SCEVConstants.erase(V);
189 SCEVHandle SCEVConstant::get(ConstantInt *V) {
190 // Make sure that SCEVConstant instances are all unsigned.
191 if (V->getType()->isSigned()) {
192 const Type *NewTy = V->getType()->getUnsignedVersion();
193 V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy));
196 SCEVConstant *&R = SCEVConstants[V];
197 if (R == 0) R = new SCEVConstant(V);
201 ConstantRange SCEVConstant::getValueRange() const {
202 return ConstantRange(V);
205 const Type *SCEVConstant::getType() const { return V->getType(); }
207 void SCEVConstant::print(std::ostream &OS) const {
208 WriteAsOperand(OS, V, false);
211 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
212 // particular input. Don't use a SCEVHandle here, or else the object will
214 static std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates;
216 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
217 : SCEV(scTruncate), Op(op), Ty(ty) {
218 assert(Op->getType()->isInteger() && Ty->isInteger() &&
220 "Cannot truncate non-integer value!");
221 assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() &&
222 "This is not a truncating conversion!");
225 SCEVTruncateExpr::~SCEVTruncateExpr() {
226 SCEVTruncates.erase(std::make_pair(Op, Ty));
229 ConstantRange SCEVTruncateExpr::getValueRange() const {
230 return getOperand()->getValueRange().truncate(getType());
233 void SCEVTruncateExpr::print(std::ostream &OS) const {
234 OS << "(truncate " << *Op << " to " << *Ty << ")";
237 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
238 // particular input. Don't use a SCEVHandle here, or else the object will never
240 static std::map<std::pair<SCEV*, const Type*>,
241 SCEVZeroExtendExpr*> SCEVZeroExtends;
243 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
244 : SCEV(scTruncate), Op(Op), Ty(ty) {
245 assert(Op->getType()->isInteger() && Ty->isInteger() &&
247 "Cannot zero extend non-integer value!");
248 assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() &&
249 "This is not an extending conversion!");
252 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
253 SCEVZeroExtends.erase(std::make_pair(Op, Ty));
256 ConstantRange SCEVZeroExtendExpr::getValueRange() const {
257 return getOperand()->getValueRange().zeroExtend(getType());
260 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
261 OS << "(zeroextend " << *Op << " to " << *Ty << ")";
264 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
265 // particular input. Don't use a SCEVHandle here, or else the object will never
267 static std::map<std::pair<unsigned, std::vector<SCEV*> >,
268 SCEVCommutativeExpr*> SCEVCommExprs;
270 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
271 SCEVCommExprs.erase(std::make_pair(getSCEVType(),
272 std::vector<SCEV*>(Operands.begin(),
276 void SCEVCommutativeExpr::print(std::ostream &OS) const {
277 assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
278 const char *OpStr = getOperationStr();
279 OS << "(" << *Operands[0];
280 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
281 OS << OpStr << *Operands[i];
285 // SCEVUDivs - Only allow the creation of one SCEVUDivExpr for any particular
286 // input. Don't use a SCEVHandle here, or else the object will never be
288 static std::map<std::pair<SCEV*, SCEV*>, SCEVUDivExpr*> SCEVUDivs;
290 SCEVUDivExpr::~SCEVUDivExpr() {
291 SCEVUDivs.erase(std::make_pair(LHS, RHS));
294 void SCEVUDivExpr::print(std::ostream &OS) const {
295 OS << "(" << *LHS << " /u " << *RHS << ")";
298 const Type *SCEVUDivExpr::getType() const {
299 const Type *Ty = LHS->getType();
300 if (Ty->isSigned()) Ty = Ty->getUnsignedVersion();
304 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
305 // particular input. Don't use a SCEVHandle here, or else the object will never
307 static std::map<std::pair<const Loop *, std::vector<SCEV*> >,
308 SCEVAddRecExpr*> SCEVAddRecExprs;
310 SCEVAddRecExpr::~SCEVAddRecExpr() {
311 SCEVAddRecExprs.erase(std::make_pair(L,
312 std::vector<SCEV*>(Operands.begin(),
316 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
317 // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
319 return !QueryLoop->contains(L->getHeader());
323 void SCEVAddRecExpr::print(std::ostream &OS) const {
324 OS << "{" << *Operands[0];
325 for (unsigned i = 1, e = Operands.size(); i != e; ++i)
326 OS << ",+," << *Operands[i];
327 OS << "}<" << L->getHeader()->getName() + ">";
330 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
331 // value. Don't use a SCEVHandle here, or else the object will never be
333 static std::map<Value*, SCEVUnknown*> SCEVUnknowns;
335 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns.erase(V); }
337 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
338 // All non-instruction values are loop invariant. All instructions are loop
339 // invariant if they are not contained in the specified loop.
340 if (Instruction *I = dyn_cast<Instruction>(V))
341 return !L->contains(I->getParent());
345 const Type *SCEVUnknown::getType() const {
349 void SCEVUnknown::print(std::ostream &OS) const {
350 WriteAsOperand(OS, V, false);
355 //===----------------------------------------------------------------------===//
356 // Simple SCEV method implementations
357 //===----------------------------------------------------------------------===//
359 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
360 /// specified signed integer value and return a SCEV for the constant.
361 static SCEVHandle getIntegerSCEV(int Val, const Type *Ty) {
364 C = Constant::getNullValue(Ty);
365 else if (Ty->isFloatingPoint())
366 C = ConstantFP::get(Ty, Val);
367 else if (Ty->isSigned())
368 C = ConstantSInt::get(Ty, Val);
370 C = ConstantSInt::get(Ty->getSignedVersion(), Val);
371 C = ConstantExpr::getCast(C, Ty);
373 return SCEVUnknown::get(C);
376 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
377 /// input value to the specified type. If the type must be extended, it is zero
379 static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
380 const Type *SrcTy = V->getType();
381 assert(SrcTy->isInteger() && Ty->isInteger() &&
382 "Cannot truncate or zero extend with non-integer arguments!");
383 if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize())
384 return V; // No conversion
385 if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize())
386 return SCEVTruncateExpr::get(V, Ty);
387 return SCEVZeroExtendExpr::get(V, Ty);
390 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
392 static SCEVHandle getNegativeSCEV(const SCEVHandle &V) {
393 if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
394 return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
396 return SCEVMulExpr::get(V, getIntegerSCEV(-1, V->getType()));
399 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
401 static SCEVHandle getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
403 return SCEVAddExpr::get(LHS, getNegativeSCEV(RHS));
407 /// Binomial - Evaluate N!/((N-M)!*M!) . Note that N is often large and M is
408 /// often very small, so we try to reduce the number of N! terms we need to
409 /// evaluate by evaluating this as (N!/(N-M)!)/M!
410 static ConstantInt *Binomial(ConstantInt *N, unsigned M) {
411 uint64_t NVal = N->getRawValue();
412 uint64_t FirstTerm = 1;
413 for (unsigned i = 0; i != M; ++i)
416 unsigned MFactorial = 1;
420 Constant *Result = ConstantUInt::get(Type::ULongTy, FirstTerm/MFactorial);
421 Result = ConstantExpr::getCast(Result, N->getType());
422 assert(isa<ConstantInt>(Result) && "Cast of integer not folded??");
423 return cast<ConstantInt>(Result);
426 /// PartialFact - Compute V!/(V-NumSteps)!
427 static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
428 // Handle this case efficiently, it is common to have constant iteration
429 // counts while computing loop exit values.
430 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
431 uint64_t Val = SC->getValue()->getRawValue();
433 for (; NumSteps; --NumSteps)
434 Result *= Val-(NumSteps-1);
435 Constant *Res = ConstantUInt::get(Type::ULongTy, Result);
436 return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType()));
439 const Type *Ty = V->getType();
441 return getIntegerSCEV(1, Ty);
443 SCEVHandle Result = V;
444 for (unsigned i = 1; i != NumSteps; ++i)
445 Result = SCEVMulExpr::get(Result, getMinusSCEV(V, getIntegerSCEV(i, Ty)));
450 /// evaluateAtIteration - Return the value of this chain of recurrences at
451 /// the specified iteration number. We can evaluate this recurrence by
452 /// multiplying each element in the chain by the binomial coefficient
453 /// corresponding to it. In other words, we can evaluate {A,+,B,+,C,+,D} as:
455 /// A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
457 /// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
458 /// Is the binomial equation safe using modular arithmetic??
460 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
461 SCEVHandle Result = getStart();
463 const Type *Ty = It->getType();
464 for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
465 SCEVHandle BC = PartialFact(It, i);
467 SCEVHandle Val = SCEVUDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
468 getIntegerSCEV(Divisor, Ty));
469 Result = SCEVAddExpr::get(Result, Val);
475 //===----------------------------------------------------------------------===//
476 // SCEV Expression folder implementations
477 //===----------------------------------------------------------------------===//
479 SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
480 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
481 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
483 // If the input value is a chrec scev made out of constants, truncate
484 // all of the constants.
485 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
486 std::vector<SCEVHandle> Operands;
487 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
488 // FIXME: This should allow truncation of other expression types!
489 if (isa<SCEVConstant>(AddRec->getOperand(i)))
490 Operands.push_back(get(AddRec->getOperand(i), Ty));
493 if (Operands.size() == AddRec->getNumOperands())
494 return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
497 SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)];
498 if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
502 SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
503 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
504 return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
506 // FIXME: If the input value is a chrec scev, and we can prove that the value
507 // did not overflow the old, smaller, value, we can zero extend all of the
508 // operands (often constants). This would allow analysis of something like
509 // this: for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
511 SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)];
512 if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
516 // get - Get a canonical add expression, or something simpler if possible.
517 SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
518 assert(!Ops.empty() && "Cannot get empty add!");
519 if (Ops.size() == 1) return Ops[0];
521 // Sort by complexity, this groups all similar expression types together.
522 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
524 // If there are any constants, fold them together.
526 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
528 assert(Idx < Ops.size());
529 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
530 // We found two constants, fold them together!
531 Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue());
532 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
533 Ops[0] = SCEVConstant::get(CI);
534 Ops.erase(Ops.begin()+1); // Erase the folded element
535 if (Ops.size() == 1) return Ops[0];
537 // If we couldn't fold the expression, move to the next constant. Note
538 // that this is impossible to happen in practice because we always
539 // constant fold constant ints to constant ints.
544 // If we are left with a constant zero being added, strip it off.
545 if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
546 Ops.erase(Ops.begin());
551 if (Ops.size() == 1) return Ops[0];
553 // Okay, check to see if the same value occurs in the operand list twice. If
554 // so, merge them together into an multiply expression. Since we sorted the
555 // list, these values are required to be adjacent.
556 const Type *Ty = Ops[0]->getType();
557 for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
558 if (Ops[i] == Ops[i+1]) { // X + Y + Y --> X + Y*2
559 // Found a match, merge the two values into a multiply, and add any
560 // remaining values to the result.
561 SCEVHandle Two = getIntegerSCEV(2, Ty);
562 SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
565 Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
567 return SCEVAddExpr::get(Ops);
570 // Okay, now we know the first non-constant operand. If there are add
571 // operands they would be next.
572 if (Idx < Ops.size()) {
573 bool DeletedAdd = false;
574 while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
575 // If we have an add, expand the add operands onto the end of the operands
577 Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
578 Ops.erase(Ops.begin()+Idx);
582 // If we deleted at least one add, we added operands to the end of the list,
583 // and they are not necessarily sorted. Recurse to resort and resimplify
584 // any operands we just aquired.
589 // Skip over the add expression until we get to a multiply.
590 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
593 // If we are adding something to a multiply expression, make sure the
594 // something is not already an operand of the multiply. If so, merge it into
596 for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
597 SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
598 for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
599 SCEV *MulOpSCEV = Mul->getOperand(MulOp);
600 for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
601 if (MulOpSCEV == Ops[AddOp] &&
602 (Mul->getNumOperands() != 2 || !isa<SCEVConstant>(MulOpSCEV))) {
603 // Fold W + X + (X * Y * Z) --> W + (X * ((Y*Z)+1))
604 SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
605 if (Mul->getNumOperands() != 2) {
606 // If the multiply has more than two operands, we must get the
608 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
609 MulOps.erase(MulOps.begin()+MulOp);
610 InnerMul = SCEVMulExpr::get(MulOps);
612 SCEVHandle One = getIntegerSCEV(1, Ty);
613 SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
614 SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
615 if (Ops.size() == 2) return OuterMul;
617 Ops.erase(Ops.begin()+AddOp);
618 Ops.erase(Ops.begin()+Idx-1);
620 Ops.erase(Ops.begin()+Idx);
621 Ops.erase(Ops.begin()+AddOp-1);
623 Ops.push_back(OuterMul);
624 return SCEVAddExpr::get(Ops);
627 // Check this multiply against other multiplies being added together.
628 for (unsigned OtherMulIdx = Idx+1;
629 OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
631 SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
632 // If MulOp occurs in OtherMul, we can fold the two multiplies
634 for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
635 OMulOp != e; ++OMulOp)
636 if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
637 // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
638 SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
639 if (Mul->getNumOperands() != 2) {
640 std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
641 MulOps.erase(MulOps.begin()+MulOp);
642 InnerMul1 = SCEVMulExpr::get(MulOps);
644 SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
645 if (OtherMul->getNumOperands() != 2) {
646 std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
648 MulOps.erase(MulOps.begin()+OMulOp);
649 InnerMul2 = SCEVMulExpr::get(MulOps);
651 SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
652 SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
653 if (Ops.size() == 2) return OuterMul;
654 Ops.erase(Ops.begin()+Idx);
655 Ops.erase(Ops.begin()+OtherMulIdx-1);
656 Ops.push_back(OuterMul);
657 return SCEVAddExpr::get(Ops);
663 // If there are any add recurrences in the operands list, see if any other
664 // added values are loop invariant. If so, we can fold them into the
666 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
669 // Scan over all recurrences, trying to fold loop invariants into them.
670 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
671 // Scan all of the other operands to this add and add them to the vector if
672 // they are loop invariant w.r.t. the recurrence.
673 std::vector<SCEVHandle> LIOps;
674 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
675 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
676 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
677 LIOps.push_back(Ops[i]);
678 Ops.erase(Ops.begin()+i);
682 // If we found some loop invariants, fold them into the recurrence.
683 if (!LIOps.empty()) {
684 // NLI + LI + { Start,+,Step} --> NLI + { LI+Start,+,Step }
685 LIOps.push_back(AddRec->getStart());
687 std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
688 AddRecOps[0] = SCEVAddExpr::get(LIOps);
690 SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
691 // If all of the other operands were loop invariant, we are done.
692 if (Ops.size() == 1) return NewRec;
694 // Otherwise, add the folded AddRec by the non-liv parts.
695 for (unsigned i = 0;; ++i)
696 if (Ops[i] == AddRec) {
700 return SCEVAddExpr::get(Ops);
703 // Okay, if there weren't any loop invariants to be folded, check to see if
704 // there are multiple AddRec's with the same loop induction variable being
705 // added together. If so, we can fold them.
706 for (unsigned OtherIdx = Idx+1;
707 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
708 if (OtherIdx != Idx) {
709 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
710 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
711 // Other + {A,+,B} + {C,+,D} --> Other + {A+C,+,B+D}
712 std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
713 for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
714 if (i >= NewOps.size()) {
715 NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
716 OtherAddRec->op_end());
719 NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
721 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
723 if (Ops.size() == 2) return NewAddRec;
725 Ops.erase(Ops.begin()+Idx);
726 Ops.erase(Ops.begin()+OtherIdx-1);
727 Ops.push_back(NewAddRec);
728 return SCEVAddExpr::get(Ops);
732 // Otherwise couldn't fold anything into this recurrence. Move onto the
736 // Okay, it looks like we really DO need an add expr. Check to see if we
737 // already have one, otherwise create a new one.
738 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
739 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr,
741 if (Result == 0) Result = new SCEVAddExpr(Ops);
746 SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
747 assert(!Ops.empty() && "Cannot get empty mul!");
749 // Sort by complexity, this groups all similar expression types together.
750 std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
752 // If there are any constants, fold them together.
754 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
756 // C1*(C2+V) -> C1*C2 + C1*V
758 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
759 if (Add->getNumOperands() == 2 &&
760 isa<SCEVConstant>(Add->getOperand(0)))
761 return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
762 SCEVMulExpr::get(LHSC, Add->getOperand(1)));
766 while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
767 // We found two constants, fold them together!
768 Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue());
769 if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
770 Ops[0] = SCEVConstant::get(CI);
771 Ops.erase(Ops.begin()+1); // Erase the folded element
772 if (Ops.size() == 1) return Ops[0];
774 // If we couldn't fold the expression, move to the next constant. Note
775 // that this is impossible to happen in practice because we always
776 // constant fold constant ints to constant ints.
781 // If we are left with a constant one being multiplied, strip it off.
782 if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
783 Ops.erase(Ops.begin());
785 } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
786 // If we have a multiply of zero, it will always be zero.
791 // Skip over the add expression until we get to a multiply.
792 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
798 // If there are mul operands inline them all into this expression.
799 if (Idx < Ops.size()) {
800 bool DeletedMul = false;
801 while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
802 // If we have an mul, expand the mul operands onto the end of the operands
804 Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
805 Ops.erase(Ops.begin()+Idx);
809 // If we deleted at least one mul, we added operands to the end of the list,
810 // and they are not necessarily sorted. Recurse to resort and resimplify
811 // any operands we just aquired.
816 // If there are any add recurrences in the operands list, see if any other
817 // added values are loop invariant. If so, we can fold them into the
819 while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
822 // Scan over all recurrences, trying to fold loop invariants into them.
823 for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
824 // Scan all of the other operands to this mul and add them to the vector if
825 // they are loop invariant w.r.t. the recurrence.
826 std::vector<SCEVHandle> LIOps;
827 SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
828 for (unsigned i = 0, e = Ops.size(); i != e; ++i)
829 if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
830 LIOps.push_back(Ops[i]);
831 Ops.erase(Ops.begin()+i);
835 // If we found some loop invariants, fold them into the recurrence.
836 if (!LIOps.empty()) {
837 // NLI * LI * { Start,+,Step} --> NLI * { LI*Start,+,LI*Step }
838 std::vector<SCEVHandle> NewOps;
839 NewOps.reserve(AddRec->getNumOperands());
840 if (LIOps.size() == 1) {
841 SCEV *Scale = LIOps[0];
842 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
843 NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
845 for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
846 std::vector<SCEVHandle> MulOps(LIOps);
847 MulOps.push_back(AddRec->getOperand(i));
848 NewOps.push_back(SCEVMulExpr::get(MulOps));
852 SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
854 // If all of the other operands were loop invariant, we are done.
855 if (Ops.size() == 1) return NewRec;
857 // Otherwise, multiply the folded AddRec by the non-liv parts.
858 for (unsigned i = 0;; ++i)
859 if (Ops[i] == AddRec) {
863 return SCEVMulExpr::get(Ops);
866 // Okay, if there weren't any loop invariants to be folded, check to see if
867 // there are multiple AddRec's with the same loop induction variable being
868 // multiplied together. If so, we can fold them.
869 for (unsigned OtherIdx = Idx+1;
870 OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
871 if (OtherIdx != Idx) {
872 SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
873 if (AddRec->getLoop() == OtherAddRec->getLoop()) {
874 // F * G --> {A,+,B} * {C,+,D} --> {A*C,+,F*D + G*B + B*D}
875 SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
876 SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
878 SCEVHandle B = F->getStepRecurrence();
879 SCEVHandle D = G->getStepRecurrence();
880 SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
881 SCEVMulExpr::get(G, B),
882 SCEVMulExpr::get(B, D));
883 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
885 if (Ops.size() == 2) return NewAddRec;
887 Ops.erase(Ops.begin()+Idx);
888 Ops.erase(Ops.begin()+OtherIdx-1);
889 Ops.push_back(NewAddRec);
890 return SCEVMulExpr::get(Ops);
894 // Otherwise couldn't fold anything into this recurrence. Move onto the
898 // Okay, it looks like we really DO need an mul expr. Check to see if we
899 // already have one, otherwise create a new one.
900 std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
901 SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr,
903 if (Result == 0) Result = new SCEVMulExpr(Ops);
907 SCEVHandle SCEVUDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
908 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
909 if (RHSC->getValue()->equalsInt(1))
910 return LHS; // X /u 1 --> x
911 if (RHSC->getValue()->isAllOnesValue())
912 return getNegativeSCEV(LHS); // X /u -1 --> -x
914 if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
915 Constant *LHSCV = LHSC->getValue();
916 Constant *RHSCV = RHSC->getValue();
917 if (LHSCV->getType()->isSigned())
918 LHSCV = ConstantExpr::getCast(LHSCV,
919 LHSCV->getType()->getUnsignedVersion());
920 if (RHSCV->getType()->isSigned())
921 RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType());
922 return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV));
926 // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
928 SCEVUDivExpr *&Result = SCEVUDivs[std::make_pair(LHS, RHS)];
929 if (Result == 0) Result = new SCEVUDivExpr(LHS, RHS);
934 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
935 /// specified loop. Simplify the expression as much as possible.
936 SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
937 const SCEVHandle &Step, const Loop *L) {
938 std::vector<SCEVHandle> Operands;
939 Operands.push_back(Start);
940 if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
941 if (StepChrec->getLoop() == L) {
942 Operands.insert(Operands.end(), StepChrec->op_begin(),
943 StepChrec->op_end());
944 return get(Operands, L);
947 Operands.push_back(Step);
948 return get(Operands, L);
951 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
952 /// specified loop. Simplify the expression as much as possible.
953 SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
955 if (Operands.size() == 1) return Operands[0];
957 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
958 if (StepC->getValue()->isNullValue()) {
960 return get(Operands, L); // { X,+,0 } --> X
963 SCEVAddRecExpr *&Result =
964 SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
966 if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
970 SCEVHandle SCEVUnknown::get(Value *V) {
971 if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
972 return SCEVConstant::get(CI);
973 SCEVUnknown *&Result = SCEVUnknowns[V];
974 if (Result == 0) Result = new SCEVUnknown(V);
979 //===----------------------------------------------------------------------===//
980 // Non-trivial closed-form SCEV Expanders
981 //===----------------------------------------------------------------------===//
983 Value *SCEVTruncateExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
984 Instruction *InsertPt) {
985 Value *V = SER.ExpandCodeFor(getOperand(), InsertPt);
986 return new CastInst(V, getType(), "tmp.", InsertPt);
989 Value *SCEVZeroExtendExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
990 Instruction *InsertPt) {
991 Value *V = SER.ExpandCodeFor(getOperand(), InsertPt,
992 getOperand()->getType()->getUnsignedVersion());
993 return new CastInst(V, getType(), "tmp.", InsertPt);
996 Value *SCEVAddExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
997 Instruction *InsertPt) {
998 const Type *Ty = getType();
999 Value *V = SER.ExpandCodeFor(getOperand(getNumOperands()-1), InsertPt, Ty);
1001 // Emit a bunch of add instructions
1002 for (int i = getNumOperands()-2; i >= 0; --i)
1003 V = BinaryOperator::create(Instruction::Add, V,
1004 SER.ExpandCodeFor(getOperand(i), InsertPt, Ty),
1009 Value *SCEVMulExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
1010 Instruction *InsertPt) {
1011 const Type *Ty = getType();
1012 int FirstOp = 0; // Set if we should emit a subtract.
1013 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getOperand(0)))
1014 if (SC->getValue()->isAllOnesValue())
1017 int i = getNumOperands()-2;
1018 Value *V = SER.ExpandCodeFor(getOperand(i+1), InsertPt, Ty);
1020 // Emit a bunch of multiply instructions
1021 for (; i >= FirstOp; --i)
1022 V = BinaryOperator::create(Instruction::Mul, V,
1023 SER.ExpandCodeFor(getOperand(i), InsertPt, Ty),
1025 // -1 * ... ---> 0 - ...
1027 V = BinaryOperator::create(Instruction::Sub, Constant::getNullValue(Ty), V,
1032 Value *SCEVUDivExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
1033 Instruction *InsertPt) {
1034 const Type *Ty = getType();
1035 Value *LHS = SER.ExpandCodeFor(getLHS(), InsertPt, Ty);
1036 Value *RHS = SER.ExpandCodeFor(getRHS(), InsertPt, Ty);
1037 return BinaryOperator::create(Instruction::Div, LHS, RHS, "tmp.", InsertPt);
1040 Value *SCEVAddRecExpr::expandCodeFor(ScalarEvolutionRewriter &SER,
1041 Instruction *InsertPt) {
1042 const Type *Ty = getType();
1043 // We cannot yet do fp recurrences, e.g. the xform of {X,+,F} --> X+{0,+,F}
1044 assert(Ty->isIntegral() && "Cannot expand fp recurrences yet!");
1046 // {X,+,F} --> X + {0,+,F}
1047 if (!isa<SCEVConstant>(getStart()) ||
1048 !cast<SCEVConstant>(getStart())->getValue()->isNullValue()) {
1049 Value *Start = SER.ExpandCodeFor(getStart(), InsertPt, Ty);
1050 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
1051 NewOps[0] = getIntegerSCEV(0, getType());
1052 Value *Rest = SER.ExpandCodeFor(SCEVAddRecExpr::get(NewOps, getLoop()),
1053 InsertPt, getType());
1055 // FIXME: look for an existing add to use.
1056 return BinaryOperator::create(Instruction::Add, Rest, Start, "tmp.",
1060 // {0,+,1} --> Insert a canonical induction variable into the loop!
1061 if (getNumOperands() == 2 && getOperand(1) == getIntegerSCEV(1, getType())) {
1062 // Create and insert the PHI node for the induction variable in the
1064 BasicBlock *Header = getLoop()->getHeader();
1065 PHINode *PN = new PHINode(Ty, "indvar", Header->begin());
1066 PN->addIncoming(Constant::getNullValue(Ty), L->getLoopPreheader());
1068 pred_iterator HPI = pred_begin(Header);
1069 assert(HPI != pred_end(Header) && "Loop with zero preds???");
1070 if (!getLoop()->contains(*HPI)) ++HPI;
1071 assert(HPI != pred_end(Header) && getLoop()->contains(*HPI) &&
1072 "No backedge in loop?");
1074 // Insert a unit add instruction right before the terminator corresponding
1075 // to the back-edge.
1076 Constant *One = Ty->isFloatingPoint() ? (Constant*)ConstantFP::get(Ty, 1.0)
1077 : (Constant*)ConstantInt::get(Ty, 1);
1078 Instruction *Add = BinaryOperator::create(Instruction::Add, PN, One,
1080 (*HPI)->getTerminator());
1082 pred_iterator PI = pred_begin(Header);
1083 if (*PI == L->getLoopPreheader())
1085 PN->addIncoming(Add, *PI);
1089 // Get the canonical induction variable I for this loop.
1090 Value *I = SER.GetOrInsertCanonicalInductionVariable(getLoop(), Ty);
1092 if (getNumOperands() == 2) { // {0,+,F} --> i*F
1093 Value *F = SER.ExpandCodeFor(getOperand(1), InsertPt, Ty);
1094 return BinaryOperator::create(Instruction::Mul, I, F, "tmp.", InsertPt);
1097 // If this is a chain of recurrences, turn it into a closed form, using the
1098 // folders, then expandCodeFor the closed form. This allows the folders to
1099 // simplify the expression without having to build a bunch of special code
1100 // into this folder.
1101 SCEVHandle IH = SCEVUnknown::get(I); // Get I as a "symbolic" SCEV.
1103 SCEVHandle V = evaluateAtIteration(IH);
1104 //std::cerr << "Evaluated: " << *this << "\n to: " << *V << "\n";
1106 return SER.ExpandCodeFor(V, InsertPt, Ty);
1110 //===----------------------------------------------------------------------===//
1111 // ScalarEvolutionsImpl Definition and Implementation
1112 //===----------------------------------------------------------------------===//
1114 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
1118 struct ScalarEvolutionsImpl {
1119 /// F - The function we are analyzing.
1123 /// LI - The loop information for the function we are currently analyzing.
1127 /// UnknownValue - This SCEV is used to represent unknown trip counts and
1129 SCEVHandle UnknownValue;
1131 /// Scalars - This is a cache of the scalars we have analyzed so far.
1133 std::map<Value*, SCEVHandle> Scalars;
1135 /// IterationCounts - Cache the iteration count of the loops for this
1136 /// function as they are computed.
1137 std::map<const Loop*, SCEVHandle> IterationCounts;
1139 /// ConstantEvolutionLoopExitValue - This map contains entries for all of
1140 /// the PHI instructions that we attempt to compute constant evolutions for.
1141 /// This allows us to avoid potentially expensive recomputation of these
1142 /// properties. An instruction maps to null if we are unable to compute its
1144 std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
1147 ScalarEvolutionsImpl(Function &f, LoopInfo &li)
1148 : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
1150 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1151 /// expression and create a new one.
1152 SCEVHandle getSCEV(Value *V);
1154 /// getSCEVAtScope - Compute the value of the specified expression within
1155 /// the indicated loop (which may be null to indicate in no loop). If the
1156 /// expression cannot be evaluated, return UnknownValue itself.
1157 SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
1160 /// hasLoopInvariantIterationCount - Return true if the specified loop has
1161 /// an analyzable loop-invariant iteration count.
1162 bool hasLoopInvariantIterationCount(const Loop *L);
1164 /// getIterationCount - If the specified loop has a predictable iteration
1165 /// count, return it. Note that it is not valid to call this method on a
1166 /// loop without a loop-invariant iteration count.
1167 SCEVHandle getIterationCount(const Loop *L);
1169 /// deleteInstructionFromRecords - This method should be called by the
1170 /// client before it removes an instruction from the program, to make sure
1171 /// that no dangling references are left around.
1172 void deleteInstructionFromRecords(Instruction *I);
1175 /// createSCEV - We know that there is no SCEV for the specified value.
1176 /// Analyze the expression.
1177 SCEVHandle createSCEV(Value *V);
1178 SCEVHandle createNodeForCast(CastInst *CI);
1180 /// createNodeForPHI - Provide the special handling we need to analyze PHI
1182 SCEVHandle createNodeForPHI(PHINode *PN);
1183 void UpdatePHIUserScalarEntries(Instruction *I, PHINode *PN,
1184 std::set<Instruction*> &UpdatedInsts);
1186 /// ComputeIterationCount - Compute the number of times the specified loop
1188 SCEVHandle ComputeIterationCount(const Loop *L);
1190 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1191 /// constant number of times (the condition evolves only from constants),
1192 /// try to evaluate a few iterations of the loop until we get the exit
1193 /// condition gets a value of ExitWhen (true or false). If we cannot
1194 /// evaluate the trip count of the loop, return UnknownValue.
1195 SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
1198 /// HowFarToZero - Return the number of times a backedge comparing the
1199 /// specified value to zero will execute. If not computable, return
1201 SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
1203 /// HowFarToNonZero - Return the number of times a backedge checking the
1204 /// specified value for nonzero will execute. If not computable, return
1206 SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
1208 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1209 /// in the header of its containing loop, we know the loop executes a
1210 /// constant number of times, and the PHI node is just a recurrence
1211 /// involving constants, fold it.
1212 Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its,
1217 //===----------------------------------------------------------------------===//
1218 // Basic SCEV Analysis and PHI Idiom Recognition Code
1221 /// deleteInstructionFromRecords - This method should be called by the
1222 /// client before it removes an instruction from the program, to make sure
1223 /// that no dangling references are left around.
1224 void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
1226 if (PHINode *PN = dyn_cast<PHINode>(I))
1227 ConstantEvolutionLoopExitValue.erase(PN);
1231 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
1232 /// expression and create a new one.
1233 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
1234 assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
1236 std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
1237 if (I != Scalars.end()) return I->second;
1238 SCEVHandle S = createSCEV(V);
1239 Scalars.insert(std::make_pair(V, S));
1244 /// UpdatePHIUserScalarEntries - After PHI node analysis, we have a bunch of
1245 /// entries in the scalar map that refer to the "symbolic" PHI value instead of
1246 /// the recurrence value. After we resolve the PHI we must loop over all of the
1247 /// using instructions that have scalar map entries and update them.
1248 void ScalarEvolutionsImpl::UpdatePHIUserScalarEntries(Instruction *I,
1250 std::set<Instruction*> &UpdatedInsts) {
1251 std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
1252 if (SI == Scalars.end()) return; // This scalar wasn't previous processed.
1253 if (UpdatedInsts.insert(I).second) {
1254 Scalars.erase(SI); // Remove the old entry
1255 getSCEV(I); // Calculate the new entry
1257 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
1259 UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN, UpdatedInsts);
1264 /// createNodeForPHI - PHI nodes have two cases. Either the PHI node exists in
1265 /// a loop header, making it a potential recurrence, or it doesn't.
1267 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
1268 if (PN->getNumIncomingValues() == 2) // The loops have been canonicalized.
1269 if (const Loop *L = LI.getLoopFor(PN->getParent()))
1270 if (L->getHeader() == PN->getParent()) {
1271 // If it lives in the loop header, it has two incoming values, one
1272 // from outside the loop, and one from inside.
1273 unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
1274 unsigned BackEdge = IncomingEdge^1;
1276 // While we are analyzing this PHI node, handle its value symbolically.
1277 SCEVHandle SymbolicName = SCEVUnknown::get(PN);
1278 assert(Scalars.find(PN) == Scalars.end() &&
1279 "PHI node already processed?");
1280 Scalars.insert(std::make_pair(PN, SymbolicName));
1282 // Using this symbolic name for the PHI, analyze the value coming around
1284 SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
1286 // NOTE: If BEValue is loop invariant, we know that the PHI node just
1287 // has a special value for the first iteration of the loop.
1289 // If the value coming around the backedge is an add with the symbolic
1290 // value we just inserted, then we found a simple induction variable!
1291 if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
1292 // If there is a single occurrence of the symbolic value, replace it
1293 // with a recurrence.
1294 unsigned FoundIndex = Add->getNumOperands();
1295 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1296 if (Add->getOperand(i) == SymbolicName)
1297 if (FoundIndex == e) {
1302 if (FoundIndex != Add->getNumOperands()) {
1303 // Create an add with everything but the specified operand.
1304 std::vector<SCEVHandle> Ops;
1305 for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
1306 if (i != FoundIndex)
1307 Ops.push_back(Add->getOperand(i));
1308 SCEVHandle Accum = SCEVAddExpr::get(Ops);
1310 // This is not a valid addrec if the step amount is varying each
1311 // loop iteration, but is not itself an addrec in this loop.
1312 if (Accum->isLoopInvariant(L) ||
1313 (isa<SCEVAddRecExpr>(Accum) &&
1314 cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
1315 SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
1316 SCEVHandle PHISCEV = SCEVAddRecExpr::get(StartVal, Accum, L);
1318 // Okay, for the entire analysis of this edge we assumed the PHI
1319 // to be symbolic. We now need to go back and update all of the
1320 // entries for the scalars that use the PHI (except for the PHI
1321 // itself) to use the new analyzed value instead of the "symbolic"
1323 Scalars.find(PN)->second = PHISCEV; // Update the PHI value
1324 std::set<Instruction*> UpdatedInsts;
1325 UpdatedInsts.insert(PN);
1326 for (Value::use_iterator UI = PN->use_begin(), E = PN->use_end();
1328 UpdatePHIUserScalarEntries(cast<Instruction>(*UI), PN,
1335 return SymbolicName;
1338 // If it's not a loop phi, we can't handle it yet.
1339 return SCEVUnknown::get(PN);
1342 /// createNodeForCast - Handle the various forms of casts that we support.
1344 SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) {
1345 const Type *SrcTy = CI->getOperand(0)->getType();
1346 const Type *DestTy = CI->getType();
1348 // If this is a noop cast (ie, conversion from int to uint), ignore it.
1349 if (SrcTy->isLosslesslyConvertibleTo(DestTy))
1350 return getSCEV(CI->getOperand(0));
1352 if (SrcTy->isInteger() && DestTy->isInteger()) {
1353 // Otherwise, if this is a truncating integer cast, we can represent this
1355 if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
1356 return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)),
1357 CI->getType()->getUnsignedVersion());
1358 if (SrcTy->isUnsigned() &&
1359 SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
1360 return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)),
1361 CI->getType()->getUnsignedVersion());
1364 // If this is an sign or zero extending cast and we can prove that the value
1365 // will never overflow, we could do similar transformations.
1367 // Otherwise, we can't handle this cast!
1368 return SCEVUnknown::get(CI);
1372 /// createSCEV - We know that there is no SCEV for the specified value.
1373 /// Analyze the expression.
1375 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
1376 if (Instruction *I = dyn_cast<Instruction>(V)) {
1377 switch (I->getOpcode()) {
1378 case Instruction::Add:
1379 return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
1380 getSCEV(I->getOperand(1)));
1381 case Instruction::Mul:
1382 return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
1383 getSCEV(I->getOperand(1)));
1384 case Instruction::Div:
1385 if (V->getType()->isInteger() && V->getType()->isUnsigned())
1386 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)),
1387 getSCEV(I->getOperand(1)));
1390 case Instruction::Sub:
1391 return getMinusSCEV(getSCEV(I->getOperand(0)), getSCEV(I->getOperand(1)));
1393 case Instruction::Shl:
1394 // Turn shift left of a constant amount into a multiply.
1395 if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
1396 Constant *X = ConstantInt::get(V->getType(), 1);
1397 X = ConstantExpr::getShl(X, SA);
1398 return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
1402 case Instruction::Shr:
1403 if (ConstantUInt *SA = dyn_cast<ConstantUInt>(I->getOperand(1)))
1404 if (V->getType()->isUnsigned()) {
1405 Constant *X = ConstantInt::get(V->getType(), 1);
1406 X = ConstantExpr::getShl(X, SA);
1407 return SCEVUDivExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
1411 case Instruction::Cast:
1412 return createNodeForCast(cast<CastInst>(I));
1414 case Instruction::PHI:
1415 return createNodeForPHI(cast<PHINode>(I));
1417 default: // We cannot analyze this expression.
1422 return SCEVUnknown::get(V);
1427 //===----------------------------------------------------------------------===//
1428 // Iteration Count Computation Code
1431 /// getIterationCount - If the specified loop has a predictable iteration
1432 /// count, return it. Note that it is not valid to call this method on a
1433 /// loop without a loop-invariant iteration count.
1434 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
1435 std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
1436 if (I == IterationCounts.end()) {
1437 SCEVHandle ItCount = ComputeIterationCount(L);
1438 I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
1439 if (ItCount != UnknownValue) {
1440 assert(ItCount->isLoopInvariant(L) &&
1441 "Computed trip count isn't loop invariant for loop!");
1442 ++NumTripCountsComputed;
1443 } else if (isa<PHINode>(L->getHeader()->begin())) {
1444 // Only count loops that have phi nodes as not being computable.
1445 ++NumTripCountsNotComputed;
1451 /// ComputeIterationCount - Compute the number of times the specified loop
1453 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
1454 // If the loop has a non-one exit block count, we can't analyze it.
1455 if (L->getExitBlocks().size() != 1) return UnknownValue;
1457 // Okay, there is one exit block. Try to find the condition that causes the
1458 // loop to be exited.
1459 BasicBlock *ExitBlock = L->getExitBlocks()[0];
1461 BasicBlock *ExitingBlock = 0;
1462 for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
1464 if (L->contains(*PI)) {
1465 if (ExitingBlock == 0)
1468 return UnknownValue; // More than one block exiting!
1470 assert(ExitingBlock && "No exits from loop, something is broken!");
1472 // Okay, we've computed the exiting block. See what condition causes us to
1475 // FIXME: we should be able to handle switch instructions (with a single exit)
1476 // FIXME: We should handle cast of int to bool as well
1477 BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
1478 if (ExitBr == 0) return UnknownValue;
1479 assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
1480 SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition());
1481 if (ExitCond == 0) // Not a setcc
1482 return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
1483 ExitBr->getSuccessor(0) == ExitBlock);
1485 SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
1486 SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
1488 // Try to evaluate any dependencies out of the loop.
1489 SCEVHandle Tmp = getSCEVAtScope(LHS, L);
1490 if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
1491 Tmp = getSCEVAtScope(RHS, L);
1492 if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
1494 // If the condition was exit on true, convert the condition to exit on false.
1495 Instruction::BinaryOps Cond;
1496 if (ExitBr->getSuccessor(1) == ExitBlock)
1497 Cond = ExitCond->getOpcode();
1499 Cond = ExitCond->getInverseCondition();
1501 // At this point, we would like to compute how many iterations of the loop the
1502 // predicate will return true for these inputs.
1503 if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
1504 // If there is a constant, force it into the RHS.
1505 std::swap(LHS, RHS);
1506 Cond = SetCondInst::getSwappedCondition(Cond);
1509 // FIXME: think about handling pointer comparisons! i.e.:
1510 // while (P != P+100) ++P;
1512 // If we have a comparison of a chrec against a constant, try to use value
1513 // ranges to answer this query.
1514 if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
1515 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
1516 if (AddRec->getLoop() == L) {
1517 // Form the comparison range using the constant of the correct type so
1518 // that the ConstantRange class knows to do a signed or unsigned
1520 ConstantInt *CompVal = RHSC->getValue();
1521 const Type *RealTy = ExitCond->getOperand(0)->getType();
1522 CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy));
1524 // Form the constant range.
1525 ConstantRange CompRange(Cond, CompVal);
1527 // Now that we have it, if it's signed, convert it to an unsigned
1529 if (CompRange.getLower()->getType()->isSigned()) {
1530 const Type *NewTy = RHSC->getValue()->getType();
1531 Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy);
1532 Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy);
1533 CompRange = ConstantRange(NewL, NewU);
1536 SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange);
1537 if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
1542 case Instruction::SetNE: // while (X != Y)
1543 // Convert to: while (X-Y != 0)
1544 if (LHS->getType()->isInteger()) {
1545 SCEVHandle TC = HowFarToZero(getMinusSCEV(LHS, RHS), L);
1546 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1549 case Instruction::SetEQ:
1550 // Convert to: while (X-Y == 0) // while (X == Y)
1551 if (LHS->getType()->isInteger()) {
1552 SCEVHandle TC = HowFarToNonZero(getMinusSCEV(LHS, RHS), L);
1553 if (!isa<SCEVCouldNotCompute>(TC)) return TC;
1558 std::cerr << "ComputeIterationCount ";
1559 if (ExitCond->getOperand(0)->getType()->isUnsigned())
1560 std::cerr << "[unsigned] ";
1561 std::cerr << *LHS << " "
1562 << Instruction::getOpcodeName(Cond) << " " << *RHS << "\n";
1567 return ComputeIterationCountExhaustively(L, ExitCond,
1568 ExitBr->getSuccessor(0) == ExitBlock);
1571 /// CanConstantFold - Return true if we can constant fold an instruction of the
1572 /// specified type, assuming that all operands were constants.
1573 static bool CanConstantFold(const Instruction *I) {
1574 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) ||
1575 isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
1578 if (const CallInst *CI = dyn_cast<CallInst>(I))
1579 if (const Function *F = CI->getCalledFunction())
1580 return canConstantFoldCallTo((Function*)F); // FIXME: elim cast
1584 /// ConstantFold - Constant fold an instruction of the specified type with the
1585 /// specified constant operands. This function may modify the operands vector.
1586 static Constant *ConstantFold(const Instruction *I,
1587 std::vector<Constant*> &Operands) {
1588 if (isa<BinaryOperator>(I) || isa<ShiftInst>(I))
1589 return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]);
1591 switch (I->getOpcode()) {
1592 case Instruction::Cast:
1593 return ConstantExpr::getCast(Operands[0], I->getType());
1594 case Instruction::Select:
1595 return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]);
1596 case Instruction::Call:
1597 if (ConstantPointerRef *CPR = dyn_cast<ConstantPointerRef>(Operands[0])) {
1598 Operands.erase(Operands.begin());
1599 return ConstantFoldCall(cast<Function>(CPR->getValue()), Operands);
1603 case Instruction::GetElementPtr:
1604 Constant *Base = Operands[0];
1605 Operands.erase(Operands.begin());
1606 return ConstantExpr::getGetElementPtr(Base, Operands);
1612 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
1613 /// in the loop that V is derived from. We allow arbitrary operations along the
1614 /// way, but the operands of an operation must either be constants or a value
1615 /// derived from a constant PHI. If this expression does not fit with these
1616 /// constraints, return null.
1617 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
1618 // If this is not an instruction, or if this is an instruction outside of the
1619 // loop, it can't be derived from a loop PHI.
1620 Instruction *I = dyn_cast<Instruction>(V);
1621 if (I == 0 || !L->contains(I->getParent())) return 0;
1623 if (PHINode *PN = dyn_cast<PHINode>(I))
1624 if (L->getHeader() == I->getParent())
1627 // We don't currently keep track of the control flow needed to evaluate
1628 // PHIs, so we cannot handle PHIs inside of loops.
1631 // If we won't be able to constant fold this expression even if the operands
1632 // are constants, return early.
1633 if (!CanConstantFold(I)) return 0;
1635 // Otherwise, we can evaluate this instruction if all of its operands are
1636 // constant or derived from a PHI node themselves.
1638 for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
1639 if (!(isa<Constant>(I->getOperand(Op)) ||
1640 isa<GlobalValue>(I->getOperand(Op)))) {
1641 PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
1642 if (P == 0) return 0; // Not evolving from PHI
1646 return 0; // Evolving from multiple different PHIs.
1649 // This is a expression evolving from a constant PHI!
1653 /// EvaluateExpression - Given an expression that passes the
1654 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
1655 /// in the loop has the value PHIVal. If we can't fold this expression for some
1656 /// reason, return null.
1657 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
1658 if (isa<PHINode>(V)) return PHIVal;
1659 if (Constant *C = dyn_cast<Constant>(V)) return C;
1660 if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
1661 return ConstantPointerRef::get(GV);
1662 Instruction *I = cast<Instruction>(V);
1664 std::vector<Constant*> Operands;
1665 Operands.resize(I->getNumOperands());
1667 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1668 Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
1669 if (Operands[i] == 0) return 0;
1672 return ConstantFold(I, Operands);
1675 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
1676 /// in the header of its containing loop, we know the loop executes a
1677 /// constant number of times, and the PHI node is just a recurrence
1678 /// involving constants, fold it.
1679 Constant *ScalarEvolutionsImpl::
1680 getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) {
1681 std::map<PHINode*, Constant*>::iterator I =
1682 ConstantEvolutionLoopExitValue.find(PN);
1683 if (I != ConstantEvolutionLoopExitValue.end())
1686 if (Its > MaxBruteForceIterations)
1687 return ConstantEvolutionLoopExitValue[PN] = 0; // Not going to evaluate it.
1689 Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
1691 // Since the loop is canonicalized, the PHI node must have two entries. One
1692 // entry must be a constant (coming in from outside of the loop), and the
1693 // second must be derived from the same PHI.
1694 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1695 Constant *StartCST =
1696 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1698 return RetVal = 0; // Must be a constant.
1700 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1701 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1703 return RetVal = 0; // Not derived from same PHI.
1705 // Execute the loop symbolically to determine the exit value.
1706 unsigned IterationNum = 0;
1707 unsigned NumIterations = Its;
1708 if (NumIterations != Its)
1709 return RetVal = 0; // More than 2^32 iterations??
1711 for (Constant *PHIVal = StartCST; ; ++IterationNum) {
1712 if (IterationNum == NumIterations)
1713 return RetVal = PHIVal; // Got exit value!
1715 // Compute the value of the PHI node for the next iteration.
1716 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1717 if (NextPHI == PHIVal)
1718 return RetVal = NextPHI; // Stopped evolving!
1720 return 0; // Couldn't evaluate!
1725 /// ComputeIterationCountExhaustively - If the trip is known to execute a
1726 /// constant number of times (the condition evolves only from constants),
1727 /// try to evaluate a few iterations of the loop until we get the exit
1728 /// condition gets a value of ExitWhen (true or false). If we cannot
1729 /// evaluate the trip count of the loop, return UnknownValue.
1730 SCEVHandle ScalarEvolutionsImpl::
1731 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
1732 PHINode *PN = getConstantEvolvingPHI(Cond, L);
1733 if (PN == 0) return UnknownValue;
1735 // Since the loop is canonicalized, the PHI node must have two entries. One
1736 // entry must be a constant (coming in from outside of the loop), and the
1737 // second must be derived from the same PHI.
1738 bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
1739 Constant *StartCST =
1740 dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
1741 if (StartCST == 0) return UnknownValue; // Must be a constant.
1743 Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
1744 PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
1745 if (PN2 != PN) return UnknownValue; // Not derived from same PHI.
1747 // Okay, we find a PHI node that defines the trip count of this loop. Execute
1748 // the loop symbolically to determine when the condition gets a value of
1750 unsigned IterationNum = 0;
1751 unsigned MaxIterations = MaxBruteForceIterations; // Limit analysis.
1752 for (Constant *PHIVal = StartCST;
1753 IterationNum != MaxIterations; ++IterationNum) {
1754 ConstantBool *CondVal =
1755 dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal));
1756 if (!CondVal) return UnknownValue; // Couldn't symbolically evaluate.
1758 if (CondVal->getValue() == ExitWhen) {
1759 ConstantEvolutionLoopExitValue[PN] = PHIVal;
1760 ++NumBruteForceTripCountsComputed;
1761 return SCEVConstant::get(ConstantUInt::get(Type::UIntTy, IterationNum));
1764 // Compute the value of the PHI node for the next iteration.
1765 Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
1766 if (NextPHI == 0 || NextPHI == PHIVal)
1767 return UnknownValue; // Couldn't evaluate or not making progress...
1771 // Too many iterations were needed to evaluate.
1772 return UnknownValue;
1775 /// getSCEVAtScope - Compute the value of the specified expression within the
1776 /// indicated loop (which may be null to indicate in no loop). If the
1777 /// expression cannot be evaluated, return UnknownValue.
1778 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
1779 // FIXME: this should be turned into a virtual method on SCEV!
1781 if (isa<SCEVConstant>(V)) return V;
1783 // If this instruction is evolves from a constant-evolving PHI, compute the
1784 // exit value from the loop without using SCEVs.
1785 if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
1786 if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
1787 const Loop *LI = this->LI[I->getParent()];
1788 if (LI && LI->getParentLoop() == L) // Looking for loop exit value.
1789 if (PHINode *PN = dyn_cast<PHINode>(I))
1790 if (PN->getParent() == LI->getHeader()) {
1791 // Okay, there is no closed form solution for the PHI node. Check
1792 // to see if the loop that contains it has a known iteration count.
1793 // If so, we may be able to force computation of the exit value.
1794 SCEVHandle IterationCount = getIterationCount(LI);
1795 if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
1796 // Okay, we know how many times the containing loop executes. If
1797 // this is a constant evolving PHI node, get the final value at
1798 // the specified iteration number.
1799 Constant *RV = getConstantEvolutionLoopExitValue(PN,
1800 ICC->getValue()->getRawValue(),
1802 if (RV) return SCEVUnknown::get(RV);
1806 // Okay, this is a some expression that we cannot symbolically evaluate
1807 // into a SCEV. Check to see if it's possible to symbolically evaluate
1808 // the arguments into constants, and if see, try to constant propagate the
1809 // result. This is particularly useful for computing loop exit values.
1810 if (CanConstantFold(I)) {
1811 std::vector<Constant*> Operands;
1812 Operands.reserve(I->getNumOperands());
1813 for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
1814 Value *Op = I->getOperand(i);
1815 if (Constant *C = dyn_cast<Constant>(Op)) {
1816 Operands.push_back(C);
1817 } else if (GlobalValue *GV = dyn_cast<GlobalValue>(Op)) {
1818 Operands.push_back(ConstantPointerRef::get(GV));
1820 SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
1821 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
1822 Operands.push_back(ConstantExpr::getCast(SC->getValue(),
1824 else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
1825 if (Constant *C = dyn_cast<Constant>(SU->getValue()))
1826 Operands.push_back(ConstantExpr::getCast(C, Op->getType()));
1834 return SCEVUnknown::get(ConstantFold(I, Operands));
1838 // This is some other type of SCEVUnknown, just return it.
1842 if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
1843 // Avoid performing the look-up in the common case where the specified
1844 // expression has no loop-variant portions.
1845 for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
1846 SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
1847 if (OpAtScope != Comm->getOperand(i)) {
1848 if (OpAtScope == UnknownValue) return UnknownValue;
1849 // Okay, at least one of these operands is loop variant but might be
1850 // foldable. Build a new instance of the folded commutative expression.
1851 std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
1852 NewOps.push_back(OpAtScope);
1854 for (++i; i != e; ++i) {
1855 OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
1856 if (OpAtScope == UnknownValue) return UnknownValue;
1857 NewOps.push_back(OpAtScope);
1859 if (isa<SCEVAddExpr>(Comm))
1860 return SCEVAddExpr::get(NewOps);
1861 assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
1862 return SCEVMulExpr::get(NewOps);
1865 // If we got here, all operands are loop invariant.
1869 if (SCEVUDivExpr *UDiv = dyn_cast<SCEVUDivExpr>(V)) {
1870 SCEVHandle LHS = getSCEVAtScope(UDiv->getLHS(), L);
1871 if (LHS == UnknownValue) return LHS;
1872 SCEVHandle RHS = getSCEVAtScope(UDiv->getRHS(), L);
1873 if (RHS == UnknownValue) return RHS;
1874 if (LHS == UDiv->getLHS() && RHS == UDiv->getRHS())
1875 return UDiv; // must be loop invariant
1876 return SCEVUDivExpr::get(LHS, RHS);
1879 // If this is a loop recurrence for a loop that does not contain L, then we
1880 // are dealing with the final value computed by the loop.
1881 if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
1882 if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
1883 // To evaluate this recurrence, we need to know how many times the AddRec
1884 // loop iterates. Compute this now.
1885 SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
1886 if (IterationCount == UnknownValue) return UnknownValue;
1887 IterationCount = getTruncateOrZeroExtend(IterationCount,
1890 // If the value is affine, simplify the expression evaluation to just
1891 // Start + Step*IterationCount.
1892 if (AddRec->isAffine())
1893 return SCEVAddExpr::get(AddRec->getStart(),
1894 SCEVMulExpr::get(IterationCount,
1895 AddRec->getOperand(1)));
1897 // Otherwise, evaluate it the hard way.
1898 return AddRec->evaluateAtIteration(IterationCount);
1900 return UnknownValue;
1903 //assert(0 && "Unknown SCEV type!");
1904 return UnknownValue;
1908 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
1909 /// given quadratic chrec {L,+,M,+,N}. This returns either the two roots (which
1910 /// might be the same) or two SCEVCouldNotCompute objects.
1912 static std::pair<SCEVHandle,SCEVHandle>
1913 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
1914 assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
1915 SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
1916 SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
1917 SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
1919 // We currently can only solve this if the coefficients are constants.
1920 if (!L || !M || !N) {
1921 SCEV *CNC = new SCEVCouldNotCompute();
1922 return std::make_pair(CNC, CNC);
1925 Constant *Two = ConstantInt::get(L->getValue()->getType(), 2);
1927 // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
1928 Constant *C = L->getValue();
1929 // The B coefficient is M-N/2
1930 Constant *B = ConstantExpr::getSub(M->getValue(),
1931 ConstantExpr::getDiv(N->getValue(),
1933 // The A coefficient is N/2
1934 Constant *A = ConstantExpr::getDiv(N->getValue(), Two);
1936 // Compute the B^2-4ac term.
1937 Constant *SqrtTerm =
1938 ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
1939 ConstantExpr::getMul(A, C));
1940 SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
1942 // Compute floor(sqrt(B^2-4ac))
1943 ConstantUInt *SqrtVal =
1944 cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm,
1945 SqrtTerm->getType()->getUnsignedVersion()));
1946 uint64_t SqrtValV = SqrtVal->getValue();
1947 uint64_t SqrtValV2 = (uint64_t)sqrt(SqrtValV);
1948 // The square root might not be precise for arbitrary 64-bit integer
1949 // values. Do some sanity checks to ensure it's correct.
1950 if (SqrtValV2*SqrtValV2 > SqrtValV ||
1951 (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
1952 SCEV *CNC = new SCEVCouldNotCompute();
1953 return std::make_pair(CNC, CNC);
1956 SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2);
1957 SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType());
1959 Constant *NegB = ConstantExpr::getNeg(B);
1960 Constant *TwoA = ConstantExpr::getMul(A, Two);
1962 // The divisions must be performed as signed divisions.
1963 const Type *SignedTy = NegB->getType()->getSignedVersion();
1964 NegB = ConstantExpr::getCast(NegB, SignedTy);
1965 TwoA = ConstantExpr::getCast(TwoA, SignedTy);
1966 SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy);
1968 Constant *Solution1 =
1969 ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
1970 Constant *Solution2 =
1971 ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
1972 return std::make_pair(SCEVUnknown::get(Solution1),
1973 SCEVUnknown::get(Solution2));
1976 /// HowFarToZero - Return the number of times a backedge comparing the specified
1977 /// value to zero will execute. If not computable, return UnknownValue
1978 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
1979 // If the value is a constant
1980 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
1981 // If the value is already zero, the branch will execute zero times.
1982 if (C->getValue()->isNullValue()) return C;
1983 return UnknownValue; // Otherwise it will loop infinitely.
1986 SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
1987 if (!AddRec || AddRec->getLoop() != L)
1988 return UnknownValue;
1990 if (AddRec->isAffine()) {
1991 // If this is an affine expression the execution count of this branch is
1994 // (0 - Start/Step) iff Start % Step == 0
1996 // Get the initial value for the loop.
1997 SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
1998 SCEVHandle Step = AddRec->getOperand(1);
2000 Step = getSCEVAtScope(Step, L->getParentLoop());
2002 // Figure out if Start % Step == 0.
2003 // FIXME: We should add DivExpr and RemExpr operations to our AST.
2004 if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
2005 if (StepC->getValue()->equalsInt(1)) // N % 1 == 0
2006 return getNegativeSCEV(Start); // 0 - Start/1 == -Start
2007 if (StepC->getValue()->isAllOnesValue()) // N % -1 == 0
2008 return Start; // 0 - Start/-1 == Start
2010 // Check to see if Start is divisible by SC with no remainder.
2011 if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
2012 ConstantInt *StartCC = StartC->getValue();
2013 Constant *StartNegC = ConstantExpr::getNeg(StartCC);
2014 Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue());
2015 if (Rem->isNullValue()) {
2016 Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue());
2017 return SCEVUnknown::get(Result);
2021 } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
2022 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
2023 // the quadratic equation to solve it.
2024 std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
2025 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2026 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2029 std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1
2030 << " sol#2: " << *R2 << "\n";
2032 // Pick the smallest positive root value.
2033 assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?");
2034 if (ConstantBool *CB =
2035 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
2037 if (CB != ConstantBool::True)
2038 std::swap(R1, R2); // R1 is the minimum root now.
2040 // We can only use this value if the chrec ends up with an exact zero
2041 // value at this index. When solving for "X*X != 5", for example, we
2042 // should not accept a root of 2.
2043 SCEVHandle Val = AddRec->evaluateAtIteration(R1);
2044 if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
2045 if (EvalVal->getValue()->isNullValue())
2046 return R1; // We found a quadratic root!
2051 return UnknownValue;
2054 /// HowFarToNonZero - Return the number of times a backedge checking the
2055 /// specified value for nonzero will execute. If not computable, return
2057 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
2058 // Loops that look like: while (X == 0) are very strange indeed. We don't
2059 // handle them yet except for the trivial case. This could be expanded in the
2060 // future as needed.
2062 // If the value is a constant, check to see if it is known to be non-zero
2063 // already. If so, the backedge will execute zero times.
2064 if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
2065 Constant *Zero = Constant::getNullValue(C->getValue()->getType());
2066 Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero);
2067 if (NonZero == ConstantBool::True)
2068 return getSCEV(Zero);
2069 return UnknownValue; // Otherwise it will loop infinitely.
2072 // We could implement others, but I really doubt anyone writes loops like
2073 // this, and if they did, they would already be constant folded.
2074 return UnknownValue;
2077 static ConstantInt *
2078 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
2079 SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
2080 SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
2081 assert(isa<SCEVConstant>(Val) &&
2082 "Evaluation of SCEV at constant didn't fold correctly?");
2083 return cast<SCEVConstant>(Val)->getValue();
2087 /// getNumIterationsInRange - Return the number of iterations of this loop that
2088 /// produce values in the specified constant range. Another way of looking at
2089 /// this is that it returns the first iteration number where the value is not in
2090 /// the condition, thus computing the exit count. If the iteration count can't
2091 /// be computed, an instance of SCEVCouldNotCompute is returned.
2092 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const {
2093 if (Range.isFullSet()) // Infinite loop.
2094 return new SCEVCouldNotCompute();
2096 // If the start is a non-zero constant, shift the range to simplify things.
2097 if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
2098 if (!SC->getValue()->isNullValue()) {
2099 std::vector<SCEVHandle> Operands(op_begin(), op_end());
2100 Operands[0] = getIntegerSCEV(0, SC->getType());
2101 SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
2102 if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
2103 return ShiftedAddRec->getNumIterationsInRange(
2104 Range.subtract(SC->getValue()));
2105 // This is strange and shouldn't happen.
2106 return new SCEVCouldNotCompute();
2109 // The only time we can solve this is when we have all constant indices.
2110 // Otherwise, we cannot determine the overflow conditions.
2111 for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
2112 if (!isa<SCEVConstant>(getOperand(i)))
2113 return new SCEVCouldNotCompute();
2116 // Okay at this point we know that all elements of the chrec are constants and
2117 // that the start element is zero.
2119 // First check to see if the range contains zero. If not, the first
2121 ConstantInt *Zero = ConstantInt::get(getType(), 0);
2122 if (!Range.contains(Zero)) return SCEVConstant::get(Zero);
2125 // If this is an affine expression then we have this situation:
2126 // Solve {0,+,A} in Range === Ax in Range
2128 // Since we know that zero is in the range, we know that the upper value of
2129 // the range must be the first possible exit value. Also note that we
2130 // already checked for a full range.
2131 ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
2132 ConstantInt *A = cast<SCEVConstant>(getOperand(1))->getValue();
2133 ConstantInt *One = ConstantInt::get(getType(), 1);
2135 // The exit value should be (Upper+A-1)/A.
2136 Constant *ExitValue = Upper;
2138 ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
2139 ExitValue = ConstantExpr::getDiv(ExitValue, A);
2141 assert(isa<ConstantInt>(ExitValue) &&
2142 "Constant folding of integers not implemented?");
2144 // Evaluate at the exit value. If we really did fall out of the valid
2145 // range, then we computed our trip count, otherwise wrap around or other
2146 // things must have happened.
2147 ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
2148 if (Range.contains(Val))
2149 return new SCEVCouldNotCompute(); // Something strange happened
2151 // Ensure that the previous value is in the range. This is a sanity check.
2152 assert(Range.contains(EvaluateConstantChrecAtConstant(this,
2153 ConstantExpr::getSub(ExitValue, One))) &&
2154 "Linear scev computation is off in a bad way!");
2155 return SCEVConstant::get(cast<ConstantInt>(ExitValue));
2156 } else if (isQuadratic()) {
2157 // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
2158 // quadratic equation to solve it. To do this, we must frame our problem in
2159 // terms of figuring out when zero is crossed, instead of when
2160 // Range.getUpper() is crossed.
2161 std::vector<SCEVHandle> NewOps(op_begin(), op_end());
2162 NewOps[0] = getNegativeSCEV(SCEVUnknown::get(Range.getUpper()));
2163 SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
2165 // Next, solve the constructed addrec
2166 std::pair<SCEVHandle,SCEVHandle> Roots =
2167 SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
2168 SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
2169 SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
2171 // Pick the smallest positive root value.
2172 assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?");
2173 if (ConstantBool *CB =
2174 dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
2176 if (CB != ConstantBool::True)
2177 std::swap(R1, R2); // R1 is the minimum root now.
2179 // Make sure the root is not off by one. The returned iteration should
2180 // not be in the range, but the previous one should be. When solving
2181 // for "X*X < 5", for example, we should not return a root of 2.
2182 ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
2184 if (Range.contains(R1Val)) {
2185 // The next iteration must be out of the range...
2187 ConstantExpr::getAdd(R1->getValue(),
2188 ConstantInt::get(R1->getType(), 1));
2190 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2191 if (!Range.contains(R1Val))
2192 return SCEVUnknown::get(NextVal);
2193 return new SCEVCouldNotCompute(); // Something strange happened
2196 // If R1 was not in the range, then it is a good return value. Make
2197 // sure that R1-1 WAS in the range though, just in case.
2199 ConstantExpr::getSub(R1->getValue(),
2200 ConstantInt::get(R1->getType(), 1));
2201 R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
2202 if (Range.contains(R1Val))
2204 return new SCEVCouldNotCompute(); // Something strange happened
2209 // Fallback, if this is a general polynomial, figure out the progression
2210 // through brute force: evaluate until we find an iteration that fails the
2211 // test. This is likely to be slow, but getting an accurate trip count is
2212 // incredibly important, we will be able to simplify the exit test a lot, and
2213 // we are almost guaranteed to get a trip count in this case.
2214 ConstantInt *TestVal = ConstantInt::get(getType(), 0);
2215 ConstantInt *One = ConstantInt::get(getType(), 1);
2216 ConstantInt *EndVal = TestVal; // Stop when we wrap around.
2218 ++NumBruteForceEvaluations;
2219 SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
2220 if (!isa<SCEVConstant>(Val)) // This shouldn't happen.
2221 return new SCEVCouldNotCompute();
2223 // Check to see if we found the value!
2224 if (!Range.contains(cast<SCEVConstant>(Val)->getValue()))
2225 return SCEVConstant::get(TestVal);
2227 // Increment to test the next index.
2228 TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
2229 } while (TestVal != EndVal);
2231 return new SCEVCouldNotCompute();
2236 //===----------------------------------------------------------------------===//
2237 // ScalarEvolution Class Implementation
2238 //===----------------------------------------------------------------------===//
2240 bool ScalarEvolution::runOnFunction(Function &F) {
2241 Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
2245 void ScalarEvolution::releaseMemory() {
2246 delete (ScalarEvolutionsImpl*)Impl;
2250 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
2251 AU.setPreservesAll();
2252 AU.addRequiredID(LoopSimplifyID);
2253 AU.addRequiredTransitive<LoopInfo>();
2256 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
2257 return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
2260 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
2261 return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
2264 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
2265 return !isa<SCEVCouldNotCompute>(getIterationCount(L));
2268 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
2269 return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
2272 void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
2273 return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
2277 /// shouldSubstituteIndVar - Return true if we should perform induction variable
2278 /// substitution for this variable. This is a hack because we don't have a
2279 /// strength reduction pass yet. When we do we will promote all vars, because
2280 /// we can strength reduce them later as desired.
2281 bool ScalarEvolution::shouldSubstituteIndVar(const SCEV *S) const {
2282 // Don't substitute high degree polynomials.
2283 if (const SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(S))
2284 if (AddRec->getNumOperands() > 3) return false;
2289 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
2291 // Print all inner loops first
2292 for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
2293 PrintLoopInfo(OS, SE, *I);
2295 std::cerr << "Loop " << L->getHeader()->getName() << ": ";
2296 if (L->getExitBlocks().size() != 1)
2297 std::cerr << "<multiple exits> ";
2299 if (SE->hasLoopInvariantIterationCount(L)) {
2300 std::cerr << *SE->getIterationCount(L) << " iterations! ";
2302 std::cerr << "Unpredictable iteration count. ";
2308 void ScalarEvolution::print(std::ostream &OS) const {
2309 Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
2310 LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
2312 OS << "Classifying expressions for: " << F.getName() << "\n";
2313 for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
2314 if ((*I)->getType()->isInteger()) {
2317 SCEVHandle SV = getSCEV(*I);
2321 if ((*I)->getType()->isIntegral()) {
2322 ConstantRange Bounds = SV->getValueRange();
2323 if (!Bounds.isFullSet())
2324 OS << "Bounds: " << Bounds << " ";
2327 if (const Loop *L = LI.getLoopFor((*I)->getParent())) {
2329 SCEVHandle ExitValue = getSCEVAtScope(*I, L->getParentLoop());
2330 if (isa<SCEVCouldNotCompute>(ExitValue)) {
2331 OS << "<<Unknown>>";
2341 OS << "Determining loop execution counts for: " << F.getName() << "\n";
2342 for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
2343 PrintLoopInfo(OS, this, *I);
2346 //===----------------------------------------------------------------------===//
2347 // ScalarEvolutionRewriter Class Implementation
2348 //===----------------------------------------------------------------------===//
2350 Value *ScalarEvolutionRewriter::
2351 GetOrInsertCanonicalInductionVariable(const Loop *L, const Type *Ty) {
2352 assert((Ty->isInteger() || Ty->isFloatingPoint()) &&
2353 "Can only insert integer or floating point induction variables!");
2355 // Check to see if we already inserted one.
2356 SCEVHandle H = SCEVAddRecExpr::get(getIntegerSCEV(0, Ty),
2357 getIntegerSCEV(1, Ty), L);
2358 return ExpandCodeFor(H, 0, Ty);
2361 /// ExpandCodeFor - Insert code to directly compute the specified SCEV
2362 /// expression into the program. The inserted code is inserted into the
2363 /// specified block.
2364 Value *ScalarEvolutionRewriter::ExpandCodeFor(SCEVHandle SH,
2365 Instruction *InsertPt,
2367 std::map<SCEVHandle, Value*>::iterator ExistVal =InsertedExpressions.find(SH);
2369 if (ExistVal != InsertedExpressions.end()) {
2370 V = ExistVal->second;
2372 // Ask the recurrence object to expand the code for itself.
2373 V = SH->expandCodeFor(*this, InsertPt);
2374 // Cache the generated result.
2375 InsertedExpressions.insert(std::make_pair(SH, V));
2378 if (Ty == 0 || V->getType() == Ty)
2380 if (Constant *C = dyn_cast<Constant>(V))
2381 return ConstantExpr::getCast(C, Ty);
2382 else if (Instruction *I = dyn_cast<Instruction>(V)) {
2383 // Check to see if there is already a cast. If there is, use it.
2384 for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
2386 if ((*UI)->getType() == Ty)
2387 if (CastInst *CI = dyn_cast<CastInst>(cast<Instruction>(*UI))) {
2388 BasicBlock::iterator It = I; ++It;
2389 while (isa<PHINode>(It)) ++It;
2390 if (It != BasicBlock::iterator(CI)) {
2391 // Splice the cast immediately after the operand in question.
2392 I->getParent()->getInstList().splice(It,
2393 CI->getParent()->getInstList(),
2399 BasicBlock::iterator IP = I; ++IP;
2400 if (InvokeInst *II = dyn_cast<InvokeInst>(I))
2401 IP = II->getNormalDest()->begin();
2402 while (isa<PHINode>(IP)) ++IP;
2403 return new CastInst(V, Ty, V->getName(), IP);
2405 // FIXME: check to see if there is already a cast!
2406 return new CastInst(V, Ty, V->getName(), InsertPt);