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ScalarEvolution.cpp

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00001 //===- ScalarEvolution.cpp - Scalar Evolution Analysis ----------*- C++ -*-===//
00002 //
00003 //                     The LLVM Compiler Infrastructure
00004 //
00005 // This file was developed by the LLVM research group and is distributed under
00006 // the University of Illinois Open Source License. See LICENSE.TXT for details.
00007 //
00008 //===----------------------------------------------------------------------===//
00009 //
00010 // This file contains the implementation of the scalar evolution analysis
00011 // engine, which is used primarily to analyze expressions involving induction
00012 // variables in loops.
00013 //
00014 // There are several aspects to this library.  First is the representation of
00015 // scalar expressions, which are represented as subclasses of the SCEV class.
00016 // These classes are used to represent certain types of subexpressions that we
00017 // can handle.  These classes are reference counted, managed by the SCEVHandle
00018 // class.  We only create one SCEV of a particular shape, so pointer-comparisons
00019 // for equality are legal.
00020 //
00021 // One important aspect of the SCEV objects is that they are never cyclic, even
00022 // if there is a cycle in the dataflow for an expression (ie, a PHI node).  If
00023 // the PHI node is one of the idioms that we can represent (e.g., a polynomial
00024 // recurrence) then we represent it directly as a recurrence node, otherwise we
00025 // represent it as a SCEVUnknown node.
00026 //
00027 // In addition to being able to represent expressions of various types, we also
00028 // have folders that are used to build the *canonical* representation for a
00029 // particular expression.  These folders are capable of using a variety of
00030 // rewrite rules to simplify the expressions.
00031 //
00032 // Once the folders are defined, we can implement the more interesting
00033 // higher-level code, such as the code that recognizes PHI nodes of various
00034 // types, computes the execution count of a loop, etc.
00035 //
00036 // TODO: We should use these routines and value representations to implement
00037 // dependence analysis!
00038 //
00039 //===----------------------------------------------------------------------===//
00040 //
00041 // There are several good references for the techniques used in this analysis.
00042 //
00043 //  Chains of recurrences -- a method to expedite the evaluation
00044 //  of closed-form functions
00045 //  Olaf Bachmann, Paul S. Wang, Eugene V. Zima
00046 //
00047 //  On computational properties of chains of recurrences
00048 //  Eugene V. Zima
00049 //
00050 //  Symbolic Evaluation of Chains of Recurrences for Loop Optimization
00051 //  Robert A. van Engelen
00052 //
00053 //  Efficient Symbolic Analysis for Optimizing Compilers
00054 //  Robert A. van Engelen
00055 //
00056 //  Using the chains of recurrences algebra for data dependence testing and
00057 //  induction variable substitution
00058 //  MS Thesis, Johnie Birch
00059 //
00060 //===----------------------------------------------------------------------===//
00061 
00062 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
00063 #include "llvm/Constants.h"
00064 #include "llvm/DerivedTypes.h"
00065 #include "llvm/GlobalVariable.h"
00066 #include "llvm/Instructions.h"
00067 #include "llvm/Analysis/ConstantFolding.h"
00068 #include "llvm/Analysis/LoopInfo.h"
00069 #include "llvm/Assembly/Writer.h"
00070 #include "llvm/Transforms/Scalar.h"
00071 #include "llvm/Support/CFG.h"
00072 #include "llvm/Support/CommandLine.h"
00073 #include "llvm/Support/ConstantRange.h"
00074 #include "llvm/Support/InstIterator.h"
00075 #include "llvm/Support/Visibility.h"
00076 #include "llvm/ADT/Statistic.h"
00077 #include <cmath>
00078 #include <iostream>
00079 #include <algorithm>
00080 using namespace llvm;
00081 
00082 namespace {
00083   RegisterAnalysis<ScalarEvolution>
00084   R("scalar-evolution", "Scalar Evolution Analysis");
00085 
00086   Statistic<>
00087   NumBruteForceEvaluations("scalar-evolution",
00088                            "Number of brute force evaluations needed to "
00089                            "calculate high-order polynomial exit values");
00090   Statistic<>
00091   NumArrayLenItCounts("scalar-evolution",
00092                       "Number of trip counts computed with array length");
00093   Statistic<>
00094   NumTripCountsComputed("scalar-evolution",
00095                         "Number of loops with predictable loop counts");
00096   Statistic<>
00097   NumTripCountsNotComputed("scalar-evolution",
00098                            "Number of loops without predictable loop counts");
00099   Statistic<>
00100   NumBruteForceTripCountsComputed("scalar-evolution",
00101                         "Number of loops with trip counts computed by force");
00102 
00103   cl::opt<unsigned>
00104   MaxBruteForceIterations("scalar-evolution-max-iterations", cl::ReallyHidden,
00105                           cl::desc("Maximum number of iterations SCEV will "
00106                               "symbolically execute a constant derived loop"),
00107                           cl::init(100));
00108 }
00109 
00110 //===----------------------------------------------------------------------===//
00111 //                           SCEV class definitions
00112 //===----------------------------------------------------------------------===//
00113 
00114 //===----------------------------------------------------------------------===//
00115 // Implementation of the SCEV class.
00116 //
00117 SCEV::~SCEV() {}
00118 void SCEV::dump() const {
00119   print(std::cerr);
00120 }
00121 
00122 /// getValueRange - Return the tightest constant bounds that this value is
00123 /// known to have.  This method is only valid on integer SCEV objects.
00124 ConstantRange SCEV::getValueRange() const {
00125   const Type *Ty = getType();
00126   assert(Ty->isInteger() && "Can't get range for a non-integer SCEV!");
00127   Ty = Ty->getUnsignedVersion();
00128   // Default to a full range if no better information is available.
00129   return ConstantRange(getType());
00130 }
00131 
00132 
00133 SCEVCouldNotCompute::SCEVCouldNotCompute() : SCEV(scCouldNotCompute) {}
00134 
00135 bool SCEVCouldNotCompute::isLoopInvariant(const Loop *L) const {
00136   assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
00137   return false;
00138 }
00139 
00140 const Type *SCEVCouldNotCompute::getType() const {
00141   assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
00142   return 0;
00143 }
00144 
00145 bool SCEVCouldNotCompute::hasComputableLoopEvolution(const Loop *L) const {
00146   assert(0 && "Attempt to use a SCEVCouldNotCompute object!");
00147   return false;
00148 }
00149 
00150 SCEVHandle SCEVCouldNotCompute::
00151 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
00152                                   const SCEVHandle &Conc) const {
00153   return this;
00154 }
00155 
00156 void SCEVCouldNotCompute::print(std::ostream &OS) const {
00157   OS << "***COULDNOTCOMPUTE***";
00158 }
00159 
00160 bool SCEVCouldNotCompute::classof(const SCEV *S) {
00161   return S->getSCEVType() == scCouldNotCompute;
00162 }
00163 
00164 
00165 // SCEVConstants - Only allow the creation of one SCEVConstant for any
00166 // particular value.  Don't use a SCEVHandle here, or else the object will
00167 // never be deleted!
00168 static std::map<ConstantInt*, SCEVConstant*> SCEVConstants;
00169 
00170 
00171 SCEVConstant::~SCEVConstant() {
00172   SCEVConstants.erase(V);
00173 }
00174 
00175 SCEVHandle SCEVConstant::get(ConstantInt *V) {
00176   // Make sure that SCEVConstant instances are all unsigned.
00177   if (V->getType()->isSigned()) {
00178     const Type *NewTy = V->getType()->getUnsignedVersion();
00179     V = cast<ConstantUInt>(ConstantExpr::getCast(V, NewTy));
00180   }
00181 
00182   SCEVConstant *&R = SCEVConstants[V];
00183   if (R == 0) R = new SCEVConstant(V);
00184   return R;
00185 }
00186 
00187 ConstantRange SCEVConstant::getValueRange() const {
00188   return ConstantRange(V);
00189 }
00190 
00191 const Type *SCEVConstant::getType() const { return V->getType(); }
00192 
00193 void SCEVConstant::print(std::ostream &OS) const {
00194   WriteAsOperand(OS, V, false);
00195 }
00196 
00197 // SCEVTruncates - Only allow the creation of one SCEVTruncateExpr for any
00198 // particular input.  Don't use a SCEVHandle here, or else the object will
00199 // never be deleted!
00200 static std::map<std::pair<SCEV*, const Type*>, SCEVTruncateExpr*> SCEVTruncates;
00201 
00202 SCEVTruncateExpr::SCEVTruncateExpr(const SCEVHandle &op, const Type *ty)
00203   : SCEV(scTruncate), Op(op), Ty(ty) {
00204   assert(Op->getType()->isInteger() && Ty->isInteger() &&
00205          Ty->isUnsigned() &&
00206          "Cannot truncate non-integer value!");
00207   assert(Op->getType()->getPrimitiveSize() > Ty->getPrimitiveSize() &&
00208          "This is not a truncating conversion!");
00209 }
00210 
00211 SCEVTruncateExpr::~SCEVTruncateExpr() {
00212   SCEVTruncates.erase(std::make_pair(Op, Ty));
00213 }
00214 
00215 ConstantRange SCEVTruncateExpr::getValueRange() const {
00216   return getOperand()->getValueRange().truncate(getType());
00217 }
00218 
00219 void SCEVTruncateExpr::print(std::ostream &OS) const {
00220   OS << "(truncate " << *Op << " to " << *Ty << ")";
00221 }
00222 
00223 // SCEVZeroExtends - Only allow the creation of one SCEVZeroExtendExpr for any
00224 // particular input.  Don't use a SCEVHandle here, or else the object will never
00225 // be deleted!
00226 static std::map<std::pair<SCEV*, const Type*>,
00227                 SCEVZeroExtendExpr*> SCEVZeroExtends;
00228 
00229 SCEVZeroExtendExpr::SCEVZeroExtendExpr(const SCEVHandle &op, const Type *ty)
00230   : SCEV(scTruncate), Op(op), Ty(ty) {
00231   assert(Op->getType()->isInteger() && Ty->isInteger() &&
00232          Ty->isUnsigned() &&
00233          "Cannot zero extend non-integer value!");
00234   assert(Op->getType()->getPrimitiveSize() < Ty->getPrimitiveSize() &&
00235          "This is not an extending conversion!");
00236 }
00237 
00238 SCEVZeroExtendExpr::~SCEVZeroExtendExpr() {
00239   SCEVZeroExtends.erase(std::make_pair(Op, Ty));
00240 }
00241 
00242 ConstantRange SCEVZeroExtendExpr::getValueRange() const {
00243   return getOperand()->getValueRange().zeroExtend(getType());
00244 }
00245 
00246 void SCEVZeroExtendExpr::print(std::ostream &OS) const {
00247   OS << "(zeroextend " << *Op << " to " << *Ty << ")";
00248 }
00249 
00250 // SCEVCommExprs - Only allow the creation of one SCEVCommutativeExpr for any
00251 // particular input.  Don't use a SCEVHandle here, or else the object will never
00252 // be deleted!
00253 static std::map<std::pair<unsigned, std::vector<SCEV*> >,
00254                 SCEVCommutativeExpr*> SCEVCommExprs;
00255 
00256 SCEVCommutativeExpr::~SCEVCommutativeExpr() {
00257   SCEVCommExprs.erase(std::make_pair(getSCEVType(),
00258                                      std::vector<SCEV*>(Operands.begin(),
00259                                                         Operands.end())));
00260 }
00261 
00262 void SCEVCommutativeExpr::print(std::ostream &OS) const {
00263   assert(Operands.size() > 1 && "This plus expr shouldn't exist!");
00264   const char *OpStr = getOperationStr();
00265   OS << "(" << *Operands[0];
00266   for (unsigned i = 1, e = Operands.size(); i != e; ++i)
00267     OS << OpStr << *Operands[i];
00268   OS << ")";
00269 }
00270 
00271 SCEVHandle SCEVCommutativeExpr::
00272 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
00273                                   const SCEVHandle &Conc) const {
00274   for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
00275     SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
00276     if (H != getOperand(i)) {
00277       std::vector<SCEVHandle> NewOps;
00278       NewOps.reserve(getNumOperands());
00279       for (unsigned j = 0; j != i; ++j)
00280         NewOps.push_back(getOperand(j));
00281       NewOps.push_back(H);
00282       for (++i; i != e; ++i)
00283         NewOps.push_back(getOperand(i)->
00284                          replaceSymbolicValuesWithConcrete(Sym, Conc));
00285 
00286       if (isa<SCEVAddExpr>(this))
00287         return SCEVAddExpr::get(NewOps);
00288       else if (isa<SCEVMulExpr>(this))
00289         return SCEVMulExpr::get(NewOps);
00290       else
00291         assert(0 && "Unknown commutative expr!");
00292     }
00293   }
00294   return this;
00295 }
00296 
00297 
00298 // SCEVSDivs - Only allow the creation of one SCEVSDivExpr for any particular
00299 // input.  Don't use a SCEVHandle here, or else the object will never be
00300 // deleted!
00301 static std::map<std::pair<SCEV*, SCEV*>, SCEVSDivExpr*> SCEVSDivs;
00302 
00303 SCEVSDivExpr::~SCEVSDivExpr() {
00304   SCEVSDivs.erase(std::make_pair(LHS, RHS));
00305 }
00306 
00307 void SCEVSDivExpr::print(std::ostream &OS) const {
00308   OS << "(" << *LHS << " /s " << *RHS << ")";
00309 }
00310 
00311 const Type *SCEVSDivExpr::getType() const {
00312   const Type *Ty = LHS->getType();
00313   if (Ty->isUnsigned()) Ty = Ty->getSignedVersion();
00314   return Ty;
00315 }
00316 
00317 // SCEVAddRecExprs - Only allow the creation of one SCEVAddRecExpr for any
00318 // particular input.  Don't use a SCEVHandle here, or else the object will never
00319 // be deleted!
00320 static std::map<std::pair<const Loop *, std::vector<SCEV*> >,
00321                 SCEVAddRecExpr*> SCEVAddRecExprs;
00322 
00323 SCEVAddRecExpr::~SCEVAddRecExpr() {
00324   SCEVAddRecExprs.erase(std::make_pair(L,
00325                                        std::vector<SCEV*>(Operands.begin(),
00326                                                           Operands.end())));
00327 }
00328 
00329 SCEVHandle SCEVAddRecExpr::
00330 replaceSymbolicValuesWithConcrete(const SCEVHandle &Sym,
00331                                   const SCEVHandle &Conc) const {
00332   for (unsigned i = 0, e = getNumOperands(); i != e; ++i) {
00333     SCEVHandle H = getOperand(i)->replaceSymbolicValuesWithConcrete(Sym, Conc);
00334     if (H != getOperand(i)) {
00335       std::vector<SCEVHandle> NewOps;
00336       NewOps.reserve(getNumOperands());
00337       for (unsigned j = 0; j != i; ++j)
00338         NewOps.push_back(getOperand(j));
00339       NewOps.push_back(H);
00340       for (++i; i != e; ++i)
00341         NewOps.push_back(getOperand(i)->
00342                          replaceSymbolicValuesWithConcrete(Sym, Conc));
00343 
00344       return get(NewOps, L);
00345     }
00346   }
00347   return this;
00348 }
00349 
00350 
00351 bool SCEVAddRecExpr::isLoopInvariant(const Loop *QueryLoop) const {
00352   // This recurrence is invariant w.r.t to QueryLoop iff QueryLoop doesn't
00353   // contain L and if the start is invariant.
00354   return !QueryLoop->contains(L->getHeader()) &&
00355          getOperand(0)->isLoopInvariant(QueryLoop);
00356 }
00357 
00358 
00359 void SCEVAddRecExpr::print(std::ostream &OS) const {
00360   OS << "{" << *Operands[0];
00361   for (unsigned i = 1, e = Operands.size(); i != e; ++i)
00362     OS << ",+," << *Operands[i];
00363   OS << "}<" << L->getHeader()->getName() + ">";
00364 }
00365 
00366 // SCEVUnknowns - Only allow the creation of one SCEVUnknown for any particular
00367 // value.  Don't use a SCEVHandle here, or else the object will never be
00368 // deleted!
00369 static std::map<Value*, SCEVUnknown*> SCEVUnknowns;
00370 
00371 SCEVUnknown::~SCEVUnknown() { SCEVUnknowns.erase(V); }
00372 
00373 bool SCEVUnknown::isLoopInvariant(const Loop *L) const {
00374   // All non-instruction values are loop invariant.  All instructions are loop
00375   // invariant if they are not contained in the specified loop.
00376   if (Instruction *I = dyn_cast<Instruction>(V))
00377     return !L->contains(I->getParent());
00378   return true;
00379 }
00380 
00381 const Type *SCEVUnknown::getType() const {
00382   return V->getType();
00383 }
00384 
00385 void SCEVUnknown::print(std::ostream &OS) const {
00386   WriteAsOperand(OS, V, false);
00387 }
00388 
00389 //===----------------------------------------------------------------------===//
00390 //                               SCEV Utilities
00391 //===----------------------------------------------------------------------===//
00392 
00393 namespace {
00394   /// SCEVComplexityCompare - Return true if the complexity of the LHS is less
00395   /// than the complexity of the RHS.  This comparator is used to canonicalize
00396   /// expressions.
00397   struct VISIBILITY_HIDDEN SCEVComplexityCompare {
00398     bool operator()(SCEV *LHS, SCEV *RHS) {
00399       return LHS->getSCEVType() < RHS->getSCEVType();
00400     }
00401   };
00402 }
00403 
00404 /// GroupByComplexity - Given a list of SCEV objects, order them by their
00405 /// complexity, and group objects of the same complexity together by value.
00406 /// When this routine is finished, we know that any duplicates in the vector are
00407 /// consecutive and that complexity is monotonically increasing.
00408 ///
00409 /// Note that we go take special precautions to ensure that we get determinstic
00410 /// results from this routine.  In other words, we don't want the results of
00411 /// this to depend on where the addresses of various SCEV objects happened to
00412 /// land in memory.
00413 ///
00414 static void GroupByComplexity(std::vector<SCEVHandle> &Ops) {
00415   if (Ops.size() < 2) return;  // Noop
00416   if (Ops.size() == 2) {
00417     // This is the common case, which also happens to be trivially simple.
00418     // Special case it.
00419     if (Ops[0]->getSCEVType() > Ops[1]->getSCEVType())
00420       std::swap(Ops[0], Ops[1]);
00421     return;
00422   }
00423 
00424   // Do the rough sort by complexity.
00425   std::sort(Ops.begin(), Ops.end(), SCEVComplexityCompare());
00426 
00427   // Now that we are sorted by complexity, group elements of the same
00428   // complexity.  Note that this is, at worst, N^2, but the vector is likely to
00429   // be extremely short in practice.  Note that we take this approach because we
00430   // do not want to depend on the addresses of the objects we are grouping.
00431   for (unsigned i = 0, e = Ops.size(); i != e-2; ++i) {
00432     SCEV *S = Ops[i];
00433     unsigned Complexity = S->getSCEVType();
00434 
00435     // If there are any objects of the same complexity and same value as this
00436     // one, group them.
00437     for (unsigned j = i+1; j != e && Ops[j]->getSCEVType() == Complexity; ++j) {
00438       if (Ops[j] == S) { // Found a duplicate.
00439         // Move it to immediately after i'th element.
00440         std::swap(Ops[i+1], Ops[j]);
00441         ++i;   // no need to rescan it.
00442         if (i == e-2) return;  // Done!
00443       }
00444     }
00445   }
00446 }
00447 
00448 
00449 
00450 //===----------------------------------------------------------------------===//
00451 //                      Simple SCEV method implementations
00452 //===----------------------------------------------------------------------===//
00453 
00454 /// getIntegerSCEV - Given an integer or FP type, create a constant for the
00455 /// specified signed integer value and return a SCEV for the constant.
00456 SCEVHandle SCEVUnknown::getIntegerSCEV(int Val, const Type *Ty) {
00457   Constant *C;
00458   if (Val == 0)
00459     C = Constant::getNullValue(Ty);
00460   else if (Ty->isFloatingPoint())
00461     C = ConstantFP::get(Ty, Val);
00462   else if (Ty->isSigned())
00463     C = ConstantSInt::get(Ty, Val);
00464   else {
00465     C = ConstantSInt::get(Ty->getSignedVersion(), Val);
00466     C = ConstantExpr::getCast(C, Ty);
00467   }
00468   return SCEVUnknown::get(C);
00469 }
00470 
00471 /// getTruncateOrZeroExtend - Return a SCEV corresponding to a conversion of the
00472 /// input value to the specified type.  If the type must be extended, it is zero
00473 /// extended.
00474 static SCEVHandle getTruncateOrZeroExtend(const SCEVHandle &V, const Type *Ty) {
00475   const Type *SrcTy = V->getType();
00476   assert(SrcTy->isInteger() && Ty->isInteger() &&
00477          "Cannot truncate or zero extend with non-integer arguments!");
00478   if (SrcTy->getPrimitiveSize() == Ty->getPrimitiveSize())
00479     return V;  // No conversion
00480   if (SrcTy->getPrimitiveSize() > Ty->getPrimitiveSize())
00481     return SCEVTruncateExpr::get(V, Ty);
00482   return SCEVZeroExtendExpr::get(V, Ty);
00483 }
00484 
00485 /// getNegativeSCEV - Return a SCEV corresponding to -V = -1*V
00486 ///
00487 SCEVHandle SCEV::getNegativeSCEV(const SCEVHandle &V) {
00488   if (SCEVConstant *VC = dyn_cast<SCEVConstant>(V))
00489     return SCEVUnknown::get(ConstantExpr::getNeg(VC->getValue()));
00490 
00491   return SCEVMulExpr::get(V, SCEVUnknown::getIntegerSCEV(-1, V->getType()));
00492 }
00493 
00494 /// getMinusSCEV - Return a SCEV corresponding to LHS - RHS.
00495 ///
00496 SCEVHandle SCEV::getMinusSCEV(const SCEVHandle &LHS, const SCEVHandle &RHS) {
00497   // X - Y --> X + -Y
00498   return SCEVAddExpr::get(LHS, SCEV::getNegativeSCEV(RHS));
00499 }
00500 
00501 
00502 /// PartialFact - Compute V!/(V-NumSteps)!
00503 static SCEVHandle PartialFact(SCEVHandle V, unsigned NumSteps) {
00504   // Handle this case efficiently, it is common to have constant iteration
00505   // counts while computing loop exit values.
00506   if (SCEVConstant *SC = dyn_cast<SCEVConstant>(V)) {
00507     uint64_t Val = SC->getValue()->getRawValue();
00508     uint64_t Result = 1;
00509     for (; NumSteps; --NumSteps)
00510       Result *= Val-(NumSteps-1);
00511     Constant *Res = ConstantUInt::get(Type::ULongTy, Result);
00512     return SCEVUnknown::get(ConstantExpr::getCast(Res, V->getType()));
00513   }
00514 
00515   const Type *Ty = V->getType();
00516   if (NumSteps == 0)
00517     return SCEVUnknown::getIntegerSCEV(1, Ty);
00518 
00519   SCEVHandle Result = V;
00520   for (unsigned i = 1; i != NumSteps; ++i)
00521     Result = SCEVMulExpr::get(Result, SCEV::getMinusSCEV(V,
00522                                           SCEVUnknown::getIntegerSCEV(i, Ty)));
00523   return Result;
00524 }
00525 
00526 
00527 /// evaluateAtIteration - Return the value of this chain of recurrences at
00528 /// the specified iteration number.  We can evaluate this recurrence by
00529 /// multiplying each element in the chain by the binomial coefficient
00530 /// corresponding to it.  In other words, we can evaluate {A,+,B,+,C,+,D} as:
00531 ///
00532 ///   A*choose(It, 0) + B*choose(It, 1) + C*choose(It, 2) + D*choose(It, 3)
00533 ///
00534 /// FIXME/VERIFY: I don't trust that this is correct in the face of overflow.
00535 /// Is the binomial equation safe using modular arithmetic??
00536 ///
00537 SCEVHandle SCEVAddRecExpr::evaluateAtIteration(SCEVHandle It) const {
00538   SCEVHandle Result = getStart();
00539   int Divisor = 1;
00540   const Type *Ty = It->getType();
00541   for (unsigned i = 1, e = getNumOperands(); i != e; ++i) {
00542     SCEVHandle BC = PartialFact(It, i);
00543     Divisor *= i;
00544     SCEVHandle Val = SCEVSDivExpr::get(SCEVMulExpr::get(BC, getOperand(i)),
00545                                        SCEVUnknown::getIntegerSCEV(Divisor,Ty));
00546     Result = SCEVAddExpr::get(Result, Val);
00547   }
00548   return Result;
00549 }
00550 
00551 
00552 //===----------------------------------------------------------------------===//
00553 //                    SCEV Expression folder implementations
00554 //===----------------------------------------------------------------------===//
00555 
00556 SCEVHandle SCEVTruncateExpr::get(const SCEVHandle &Op, const Type *Ty) {
00557   if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
00558     return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
00559 
00560   // If the input value is a chrec scev made out of constants, truncate
00561   // all of the constants.
00562   if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(Op)) {
00563     std::vector<SCEVHandle> Operands;
00564     for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
00565       // FIXME: This should allow truncation of other expression types!
00566       if (isa<SCEVConstant>(AddRec->getOperand(i)))
00567         Operands.push_back(get(AddRec->getOperand(i), Ty));
00568       else
00569         break;
00570     if (Operands.size() == AddRec->getNumOperands())
00571       return SCEVAddRecExpr::get(Operands, AddRec->getLoop());
00572   }
00573 
00574   SCEVTruncateExpr *&Result = SCEVTruncates[std::make_pair(Op, Ty)];
00575   if (Result == 0) Result = new SCEVTruncateExpr(Op, Ty);
00576   return Result;
00577 }
00578 
00579 SCEVHandle SCEVZeroExtendExpr::get(const SCEVHandle &Op, const Type *Ty) {
00580   if (SCEVConstant *SC = dyn_cast<SCEVConstant>(Op))
00581     return SCEVUnknown::get(ConstantExpr::getCast(SC->getValue(), Ty));
00582 
00583   // FIXME: If the input value is a chrec scev, and we can prove that the value
00584   // did not overflow the old, smaller, value, we can zero extend all of the
00585   // operands (often constants).  This would allow analysis of something like
00586   // this:  for (unsigned char X = 0; X < 100; ++X) { int Y = X; }
00587 
00588   SCEVZeroExtendExpr *&Result = SCEVZeroExtends[std::make_pair(Op, Ty)];
00589   if (Result == 0) Result = new SCEVZeroExtendExpr(Op, Ty);
00590   return Result;
00591 }
00592 
00593 // get - Get a canonical add expression, or something simpler if possible.
00594 SCEVHandle SCEVAddExpr::get(std::vector<SCEVHandle> &Ops) {
00595   assert(!Ops.empty() && "Cannot get empty add!");
00596   if (Ops.size() == 1) return Ops[0];
00597 
00598   // Sort by complexity, this groups all similar expression types together.
00599   GroupByComplexity(Ops);
00600 
00601   // If there are any constants, fold them together.
00602   unsigned Idx = 0;
00603   if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
00604     ++Idx;
00605     assert(Idx < Ops.size());
00606     while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
00607       // We found two constants, fold them together!
00608       Constant *Fold = ConstantExpr::getAdd(LHSC->getValue(), RHSC->getValue());
00609       if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
00610         Ops[0] = SCEVConstant::get(CI);
00611         Ops.erase(Ops.begin()+1);  // Erase the folded element
00612         if (Ops.size() == 1) return Ops[0];
00613         LHSC = cast<SCEVConstant>(Ops[0]);
00614       } else {
00615         // If we couldn't fold the expression, move to the next constant.  Note
00616         // that this is impossible to happen in practice because we always
00617         // constant fold constant ints to constant ints.
00618         ++Idx;
00619       }
00620     }
00621 
00622     // If we are left with a constant zero being added, strip it off.
00623     if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
00624       Ops.erase(Ops.begin());
00625       --Idx;
00626     }
00627   }
00628 
00629   if (Ops.size() == 1) return Ops[0];
00630 
00631   // Okay, check to see if the same value occurs in the operand list twice.  If
00632   // so, merge them together into an multiply expression.  Since we sorted the
00633   // list, these values are required to be adjacent.
00634   const Type *Ty = Ops[0]->getType();
00635   for (unsigned i = 0, e = Ops.size()-1; i != e; ++i)
00636     if (Ops[i] == Ops[i+1]) {      //  X + Y + Y  -->  X + Y*2
00637       // Found a match, merge the two values into a multiply, and add any
00638       // remaining values to the result.
00639       SCEVHandle Two = SCEVUnknown::getIntegerSCEV(2, Ty);
00640       SCEVHandle Mul = SCEVMulExpr::get(Ops[i], Two);
00641       if (Ops.size() == 2)
00642         return Mul;
00643       Ops.erase(Ops.begin()+i, Ops.begin()+i+2);
00644       Ops.push_back(Mul);
00645       return SCEVAddExpr::get(Ops);
00646     }
00647 
00648   // Okay, now we know the first non-constant operand.  If there are add
00649   // operands they would be next.
00650   if (Idx < Ops.size()) {
00651     bool DeletedAdd = false;
00652     while (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[Idx])) {
00653       // If we have an add, expand the add operands onto the end of the operands
00654       // list.
00655       Ops.insert(Ops.end(), Add->op_begin(), Add->op_end());
00656       Ops.erase(Ops.begin()+Idx);
00657       DeletedAdd = true;
00658     }
00659 
00660     // If we deleted at least one add, we added operands to the end of the list,
00661     // and they are not necessarily sorted.  Recurse to resort and resimplify
00662     // any operands we just aquired.
00663     if (DeletedAdd)
00664       return get(Ops);
00665   }
00666 
00667   // Skip over the add expression until we get to a multiply.
00668   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
00669     ++Idx;
00670 
00671   // If we are adding something to a multiply expression, make sure the
00672   // something is not already an operand of the multiply.  If so, merge it into
00673   // the multiply.
00674   for (; Idx < Ops.size() && isa<SCEVMulExpr>(Ops[Idx]); ++Idx) {
00675     SCEVMulExpr *Mul = cast<SCEVMulExpr>(Ops[Idx]);
00676     for (unsigned MulOp = 0, e = Mul->getNumOperands(); MulOp != e; ++MulOp) {
00677       SCEV *MulOpSCEV = Mul->getOperand(MulOp);
00678       for (unsigned AddOp = 0, e = Ops.size(); AddOp != e; ++AddOp)
00679         if (MulOpSCEV == Ops[AddOp] && !isa<SCEVConstant>(MulOpSCEV)) {
00680           // Fold W + X + (X * Y * Z)  -->  W + (X * ((Y*Z)+1))
00681           SCEVHandle InnerMul = Mul->getOperand(MulOp == 0);
00682           if (Mul->getNumOperands() != 2) {
00683             // If the multiply has more than two operands, we must get the
00684             // Y*Z term.
00685             std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
00686             MulOps.erase(MulOps.begin()+MulOp);
00687             InnerMul = SCEVMulExpr::get(MulOps);
00688           }
00689           SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, Ty);
00690           SCEVHandle AddOne = SCEVAddExpr::get(InnerMul, One);
00691           SCEVHandle OuterMul = SCEVMulExpr::get(AddOne, Ops[AddOp]);
00692           if (Ops.size() == 2) return OuterMul;
00693           if (AddOp < Idx) {
00694             Ops.erase(Ops.begin()+AddOp);
00695             Ops.erase(Ops.begin()+Idx-1);
00696           } else {
00697             Ops.erase(Ops.begin()+Idx);
00698             Ops.erase(Ops.begin()+AddOp-1);
00699           }
00700           Ops.push_back(OuterMul);
00701           return SCEVAddExpr::get(Ops);
00702         }
00703 
00704       // Check this multiply against other multiplies being added together.
00705       for (unsigned OtherMulIdx = Idx+1;
00706            OtherMulIdx < Ops.size() && isa<SCEVMulExpr>(Ops[OtherMulIdx]);
00707            ++OtherMulIdx) {
00708         SCEVMulExpr *OtherMul = cast<SCEVMulExpr>(Ops[OtherMulIdx]);
00709         // If MulOp occurs in OtherMul, we can fold the two multiplies
00710         // together.
00711         for (unsigned OMulOp = 0, e = OtherMul->getNumOperands();
00712              OMulOp != e; ++OMulOp)
00713           if (OtherMul->getOperand(OMulOp) == MulOpSCEV) {
00714             // Fold X + (A*B*C) + (A*D*E) --> X + (A*(B*C+D*E))
00715             SCEVHandle InnerMul1 = Mul->getOperand(MulOp == 0);
00716             if (Mul->getNumOperands() != 2) {
00717               std::vector<SCEVHandle> MulOps(Mul->op_begin(), Mul->op_end());
00718               MulOps.erase(MulOps.begin()+MulOp);
00719               InnerMul1 = SCEVMulExpr::get(MulOps);
00720             }
00721             SCEVHandle InnerMul2 = OtherMul->getOperand(OMulOp == 0);
00722             if (OtherMul->getNumOperands() != 2) {
00723               std::vector<SCEVHandle> MulOps(OtherMul->op_begin(),
00724                                              OtherMul->op_end());
00725               MulOps.erase(MulOps.begin()+OMulOp);
00726               InnerMul2 = SCEVMulExpr::get(MulOps);
00727             }
00728             SCEVHandle InnerMulSum = SCEVAddExpr::get(InnerMul1,InnerMul2);
00729             SCEVHandle OuterMul = SCEVMulExpr::get(MulOpSCEV, InnerMulSum);
00730             if (Ops.size() == 2) return OuterMul;
00731             Ops.erase(Ops.begin()+Idx);
00732             Ops.erase(Ops.begin()+OtherMulIdx-1);
00733             Ops.push_back(OuterMul);
00734             return SCEVAddExpr::get(Ops);
00735           }
00736       }
00737     }
00738   }
00739 
00740   // If there are any add recurrences in the operands list, see if any other
00741   // added values are loop invariant.  If so, we can fold them into the
00742   // recurrence.
00743   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
00744     ++Idx;
00745 
00746   // Scan over all recurrences, trying to fold loop invariants into them.
00747   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
00748     // Scan all of the other operands to this add and add them to the vector if
00749     // they are loop invariant w.r.t. the recurrence.
00750     std::vector<SCEVHandle> LIOps;
00751     SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
00752     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
00753       if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
00754         LIOps.push_back(Ops[i]);
00755         Ops.erase(Ops.begin()+i);
00756         --i; --e;
00757       }
00758 
00759     // If we found some loop invariants, fold them into the recurrence.
00760     if (!LIOps.empty()) {
00761       //  NLI + LI + { Start,+,Step}  -->  NLI + { LI+Start,+,Step }
00762       LIOps.push_back(AddRec->getStart());
00763 
00764       std::vector<SCEVHandle> AddRecOps(AddRec->op_begin(), AddRec->op_end());
00765       AddRecOps[0] = SCEVAddExpr::get(LIOps);
00766 
00767       SCEVHandle NewRec = SCEVAddRecExpr::get(AddRecOps, AddRec->getLoop());
00768       // If all of the other operands were loop invariant, we are done.
00769       if (Ops.size() == 1) return NewRec;
00770 
00771       // Otherwise, add the folded AddRec by the non-liv parts.
00772       for (unsigned i = 0;; ++i)
00773         if (Ops[i] == AddRec) {
00774           Ops[i] = NewRec;
00775           break;
00776         }
00777       return SCEVAddExpr::get(Ops);
00778     }
00779 
00780     // Okay, if there weren't any loop invariants to be folded, check to see if
00781     // there are multiple AddRec's with the same loop induction variable being
00782     // added together.  If so, we can fold them.
00783     for (unsigned OtherIdx = Idx+1;
00784          OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
00785       if (OtherIdx != Idx) {
00786         SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
00787         if (AddRec->getLoop() == OtherAddRec->getLoop()) {
00788           // Other + {A,+,B} + {C,+,D}  -->  Other + {A+C,+,B+D}
00789           std::vector<SCEVHandle> NewOps(AddRec->op_begin(), AddRec->op_end());
00790           for (unsigned i = 0, e = OtherAddRec->getNumOperands(); i != e; ++i) {
00791             if (i >= NewOps.size()) {
00792               NewOps.insert(NewOps.end(), OtherAddRec->op_begin()+i,
00793                             OtherAddRec->op_end());
00794               break;
00795             }
00796             NewOps[i] = SCEVAddExpr::get(NewOps[i], OtherAddRec->getOperand(i));
00797           }
00798           SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
00799 
00800           if (Ops.size() == 2) return NewAddRec;
00801 
00802           Ops.erase(Ops.begin()+Idx);
00803           Ops.erase(Ops.begin()+OtherIdx-1);
00804           Ops.push_back(NewAddRec);
00805           return SCEVAddExpr::get(Ops);
00806         }
00807       }
00808 
00809     // Otherwise couldn't fold anything into this recurrence.  Move onto the
00810     // next one.
00811   }
00812 
00813   // Okay, it looks like we really DO need an add expr.  Check to see if we
00814   // already have one, otherwise create a new one.
00815   std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
00816   SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scAddExpr,
00817                                                               SCEVOps)];
00818   if (Result == 0) Result = new SCEVAddExpr(Ops);
00819   return Result;
00820 }
00821 
00822 
00823 SCEVHandle SCEVMulExpr::get(std::vector<SCEVHandle> &Ops) {
00824   assert(!Ops.empty() && "Cannot get empty mul!");
00825 
00826   // Sort by complexity, this groups all similar expression types together.
00827   GroupByComplexity(Ops);
00828 
00829   // If there are any constants, fold them together.
00830   unsigned Idx = 0;
00831   if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(Ops[0])) {
00832 
00833     // C1*(C2+V) -> C1*C2 + C1*V
00834     if (Ops.size() == 2)
00835       if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Ops[1]))
00836         if (Add->getNumOperands() == 2 &&
00837             isa<SCEVConstant>(Add->getOperand(0)))
00838           return SCEVAddExpr::get(SCEVMulExpr::get(LHSC, Add->getOperand(0)),
00839                                   SCEVMulExpr::get(LHSC, Add->getOperand(1)));
00840 
00841 
00842     ++Idx;
00843     while (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(Ops[Idx])) {
00844       // We found two constants, fold them together!
00845       Constant *Fold = ConstantExpr::getMul(LHSC->getValue(), RHSC->getValue());
00846       if (ConstantInt *CI = dyn_cast<ConstantInt>(Fold)) {
00847         Ops[0] = SCEVConstant::get(CI);
00848         Ops.erase(Ops.begin()+1);  // Erase the folded element
00849         if (Ops.size() == 1) return Ops[0];
00850         LHSC = cast<SCEVConstant>(Ops[0]);
00851       } else {
00852         // If we couldn't fold the expression, move to the next constant.  Note
00853         // that this is impossible to happen in practice because we always
00854         // constant fold constant ints to constant ints.
00855         ++Idx;
00856       }
00857     }
00858 
00859     // If we are left with a constant one being multiplied, strip it off.
00860     if (cast<SCEVConstant>(Ops[0])->getValue()->equalsInt(1)) {
00861       Ops.erase(Ops.begin());
00862       --Idx;
00863     } else if (cast<SCEVConstant>(Ops[0])->getValue()->isNullValue()) {
00864       // If we have a multiply of zero, it will always be zero.
00865       return Ops[0];
00866     }
00867   }
00868 
00869   // Skip over the add expression until we get to a multiply.
00870   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scMulExpr)
00871     ++Idx;
00872 
00873   if (Ops.size() == 1)
00874     return Ops[0];
00875 
00876   // If there are mul operands inline them all into this expression.
00877   if (Idx < Ops.size()) {
00878     bool DeletedMul = false;
00879     while (SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(Ops[Idx])) {
00880       // If we have an mul, expand the mul operands onto the end of the operands
00881       // list.
00882       Ops.insert(Ops.end(), Mul->op_begin(), Mul->op_end());
00883       Ops.erase(Ops.begin()+Idx);
00884       DeletedMul = true;
00885     }
00886 
00887     // If we deleted at least one mul, we added operands to the end of the list,
00888     // and they are not necessarily sorted.  Recurse to resort and resimplify
00889     // any operands we just aquired.
00890     if (DeletedMul)
00891       return get(Ops);
00892   }
00893 
00894   // If there are any add recurrences in the operands list, see if any other
00895   // added values are loop invariant.  If so, we can fold them into the
00896   // recurrence.
00897   while (Idx < Ops.size() && Ops[Idx]->getSCEVType() < scAddRecExpr)
00898     ++Idx;
00899 
00900   // Scan over all recurrences, trying to fold loop invariants into them.
00901   for (; Idx < Ops.size() && isa<SCEVAddRecExpr>(Ops[Idx]); ++Idx) {
00902     // Scan all of the other operands to this mul and add them to the vector if
00903     // they are loop invariant w.r.t. the recurrence.
00904     std::vector<SCEVHandle> LIOps;
00905     SCEVAddRecExpr *AddRec = cast<SCEVAddRecExpr>(Ops[Idx]);
00906     for (unsigned i = 0, e = Ops.size(); i != e; ++i)
00907       if (Ops[i]->isLoopInvariant(AddRec->getLoop())) {
00908         LIOps.push_back(Ops[i]);
00909         Ops.erase(Ops.begin()+i);
00910         --i; --e;
00911       }
00912 
00913     // If we found some loop invariants, fold them into the recurrence.
00914     if (!LIOps.empty()) {
00915       //  NLI * LI * { Start,+,Step}  -->  NLI * { LI*Start,+,LI*Step }
00916       std::vector<SCEVHandle> NewOps;
00917       NewOps.reserve(AddRec->getNumOperands());
00918       if (LIOps.size() == 1) {
00919         SCEV *Scale = LIOps[0];
00920         for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i)
00921           NewOps.push_back(SCEVMulExpr::get(Scale, AddRec->getOperand(i)));
00922       } else {
00923         for (unsigned i = 0, e = AddRec->getNumOperands(); i != e; ++i) {
00924           std::vector<SCEVHandle> MulOps(LIOps);
00925           MulOps.push_back(AddRec->getOperand(i));
00926           NewOps.push_back(SCEVMulExpr::get(MulOps));
00927         }
00928       }
00929 
00930       SCEVHandle NewRec = SCEVAddRecExpr::get(NewOps, AddRec->getLoop());
00931 
00932       // If all of the other operands were loop invariant, we are done.
00933       if (Ops.size() == 1) return NewRec;
00934 
00935       // Otherwise, multiply the folded AddRec by the non-liv parts.
00936       for (unsigned i = 0;; ++i)
00937         if (Ops[i] == AddRec) {
00938           Ops[i] = NewRec;
00939           break;
00940         }
00941       return SCEVMulExpr::get(Ops);
00942     }
00943 
00944     // Okay, if there weren't any loop invariants to be folded, check to see if
00945     // there are multiple AddRec's with the same loop induction variable being
00946     // multiplied together.  If so, we can fold them.
00947     for (unsigned OtherIdx = Idx+1;
00948          OtherIdx < Ops.size() && isa<SCEVAddRecExpr>(Ops[OtherIdx]);++OtherIdx)
00949       if (OtherIdx != Idx) {
00950         SCEVAddRecExpr *OtherAddRec = cast<SCEVAddRecExpr>(Ops[OtherIdx]);
00951         if (AddRec->getLoop() == OtherAddRec->getLoop()) {
00952           // F * G  -->  {A,+,B} * {C,+,D}  -->  {A*C,+,F*D + G*B + B*D}
00953           SCEVAddRecExpr *F = AddRec, *G = OtherAddRec;
00954           SCEVHandle NewStart = SCEVMulExpr::get(F->getStart(),
00955                                                  G->getStart());
00956           SCEVHandle B = F->getStepRecurrence();
00957           SCEVHandle D = G->getStepRecurrence();
00958           SCEVHandle NewStep = SCEVAddExpr::get(SCEVMulExpr::get(F, D),
00959                                                 SCEVMulExpr::get(G, B),
00960                                                 SCEVMulExpr::get(B, D));
00961           SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewStart, NewStep,
00962                                                      F->getLoop());
00963           if (Ops.size() == 2) return NewAddRec;
00964 
00965           Ops.erase(Ops.begin()+Idx);
00966           Ops.erase(Ops.begin()+OtherIdx-1);
00967           Ops.push_back(NewAddRec);
00968           return SCEVMulExpr::get(Ops);
00969         }
00970       }
00971 
00972     // Otherwise couldn't fold anything into this recurrence.  Move onto the
00973     // next one.
00974   }
00975 
00976   // Okay, it looks like we really DO need an mul expr.  Check to see if we
00977   // already have one, otherwise create a new one.
00978   std::vector<SCEV*> SCEVOps(Ops.begin(), Ops.end());
00979   SCEVCommutativeExpr *&Result = SCEVCommExprs[std::make_pair(scMulExpr,
00980                                                               SCEVOps)];
00981   if (Result == 0)
00982     Result = new SCEVMulExpr(Ops);
00983   return Result;
00984 }
00985 
00986 SCEVHandle SCEVSDivExpr::get(const SCEVHandle &LHS, const SCEVHandle &RHS) {
00987   if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS)) {
00988     if (RHSC->getValue()->equalsInt(1))
00989       return LHS;                            // X /s 1 --> x
00990     if (RHSC->getValue()->isAllOnesValue())
00991       return SCEV::getNegativeSCEV(LHS);           // X /s -1  -->  -x
00992 
00993     if (SCEVConstant *LHSC = dyn_cast<SCEVConstant>(LHS)) {
00994       Constant *LHSCV = LHSC->getValue();
00995       Constant *RHSCV = RHSC->getValue();
00996       if (LHSCV->getType()->isUnsigned())
00997         LHSCV = ConstantExpr::getCast(LHSCV,
00998                                       LHSCV->getType()->getSignedVersion());
00999       if (RHSCV->getType()->isUnsigned())
01000         RHSCV = ConstantExpr::getCast(RHSCV, LHSCV->getType());
01001       return SCEVUnknown::get(ConstantExpr::getDiv(LHSCV, RHSCV));
01002     }
01003   }
01004 
01005   // FIXME: implement folding of (X*4)/4 when we know X*4 doesn't overflow.
01006 
01007   SCEVSDivExpr *&Result = SCEVSDivs[std::make_pair(LHS, RHS)];
01008   if (Result == 0) Result = new SCEVSDivExpr(LHS, RHS);
01009   return Result;
01010 }
01011 
01012 
01013 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
01014 /// specified loop.  Simplify the expression as much as possible.
01015 SCEVHandle SCEVAddRecExpr::get(const SCEVHandle &Start,
01016                                const SCEVHandle &Step, const Loop *L) {
01017   std::vector<SCEVHandle> Operands;
01018   Operands.push_back(Start);
01019   if (SCEVAddRecExpr *StepChrec = dyn_cast<SCEVAddRecExpr>(Step))
01020     if (StepChrec->getLoop() == L) {
01021       Operands.insert(Operands.end(), StepChrec->op_begin(),
01022                       StepChrec->op_end());
01023       return get(Operands, L);
01024     }
01025 
01026   Operands.push_back(Step);
01027   return get(Operands, L);
01028 }
01029 
01030 /// SCEVAddRecExpr::get - Get a add recurrence expression for the
01031 /// specified loop.  Simplify the expression as much as possible.
01032 SCEVHandle SCEVAddRecExpr::get(std::vector<SCEVHandle> &Operands,
01033                                const Loop *L) {
01034   if (Operands.size() == 1) return Operands[0];
01035 
01036   if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Operands.back()))
01037     if (StepC->getValue()->isNullValue()) {
01038       Operands.pop_back();
01039       return get(Operands, L);             // { X,+,0 }  -->  X
01040     }
01041 
01042   SCEVAddRecExpr *&Result =
01043     SCEVAddRecExprs[std::make_pair(L, std::vector<SCEV*>(Operands.begin(),
01044                                                          Operands.end()))];
01045   if (Result == 0) Result = new SCEVAddRecExpr(Operands, L);
01046   return Result;
01047 }
01048 
01049 SCEVHandle SCEVUnknown::get(Value *V) {
01050   if (ConstantInt *CI = dyn_cast<ConstantInt>(V))
01051     return SCEVConstant::get(CI);
01052   SCEVUnknown *&Result = SCEVUnknowns[V];
01053   if (Result == 0) Result = new SCEVUnknown(V);
01054   return Result;
01055 }
01056 
01057 
01058 //===----------------------------------------------------------------------===//
01059 //             ScalarEvolutionsImpl Definition and Implementation
01060 //===----------------------------------------------------------------------===//
01061 //
01062 /// ScalarEvolutionsImpl - This class implements the main driver for the scalar
01063 /// evolution code.
01064 ///
01065 namespace {
01066   struct VISIBILITY_HIDDEN ScalarEvolutionsImpl {
01067     /// F - The function we are analyzing.
01068     ///
01069     Function &F;
01070 
01071     /// LI - The loop information for the function we are currently analyzing.
01072     ///
01073     LoopInfo &LI;
01074 
01075     /// UnknownValue - This SCEV is used to represent unknown trip counts and
01076     /// things.
01077     SCEVHandle UnknownValue;
01078 
01079     /// Scalars - This is a cache of the scalars we have analyzed so far.
01080     ///
01081     std::map<Value*, SCEVHandle> Scalars;
01082 
01083     /// IterationCounts - Cache the iteration count of the loops for this
01084     /// function as they are computed.
01085     std::map<const Loop*, SCEVHandle> IterationCounts;
01086 
01087     /// ConstantEvolutionLoopExitValue - This map contains entries for all of
01088     /// the PHI instructions that we attempt to compute constant evolutions for.
01089     /// This allows us to avoid potentially expensive recomputation of these
01090     /// properties.  An instruction maps to null if we are unable to compute its
01091     /// exit value.
01092     std::map<PHINode*, Constant*> ConstantEvolutionLoopExitValue;
01093 
01094   public:
01095     ScalarEvolutionsImpl(Function &f, LoopInfo &li)
01096       : F(f), LI(li), UnknownValue(new SCEVCouldNotCompute()) {}
01097 
01098     /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
01099     /// expression and create a new one.
01100     SCEVHandle getSCEV(Value *V);
01101 
01102     /// hasSCEV - Return true if the SCEV for this value has already been
01103     /// computed.
01104     bool hasSCEV(Value *V) const {
01105       return Scalars.count(V);
01106     }
01107 
01108     /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
01109     /// the specified value.
01110     void setSCEV(Value *V, const SCEVHandle &H) {
01111       bool isNew = Scalars.insert(std::make_pair(V, H)).second;
01112       assert(isNew && "This entry already existed!");
01113     }
01114 
01115 
01116     /// getSCEVAtScope - Compute the value of the specified expression within
01117     /// the indicated loop (which may be null to indicate in no loop).  If the
01118     /// expression cannot be evaluated, return UnknownValue itself.
01119     SCEVHandle getSCEVAtScope(SCEV *V, const Loop *L);
01120 
01121 
01122     /// hasLoopInvariantIterationCount - Return true if the specified loop has
01123     /// an analyzable loop-invariant iteration count.
01124     bool hasLoopInvariantIterationCount(const Loop *L);
01125 
01126     /// getIterationCount - If the specified loop has a predictable iteration
01127     /// count, return it.  Note that it is not valid to call this method on a
01128     /// loop without a loop-invariant iteration count.
01129     SCEVHandle getIterationCount(const Loop *L);
01130 
01131     /// deleteInstructionFromRecords - This method should be called by the
01132     /// client before it removes an instruction from the program, to make sure
01133     /// that no dangling references are left around.
01134     void deleteInstructionFromRecords(Instruction *I);
01135 
01136   private:
01137     /// createSCEV - We know that there is no SCEV for the specified value.
01138     /// Analyze the expression.
01139     SCEVHandle createSCEV(Value *V);
01140     SCEVHandle createNodeForCast(CastInst *CI);
01141 
01142     /// createNodeForPHI - Provide the special handling we need to analyze PHI
01143     /// SCEVs.
01144     SCEVHandle createNodeForPHI(PHINode *PN);
01145 
01146     /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value
01147     /// for the specified instruction and replaces any references to the
01148     /// symbolic value SymName with the specified value.  This is used during
01149     /// PHI resolution.
01150     void ReplaceSymbolicValueWithConcrete(Instruction *I,
01151                                           const SCEVHandle &SymName,
01152                                           const SCEVHandle &NewVal);
01153 
01154     /// ComputeIterationCount - Compute the number of times the specified loop
01155     /// will iterate.
01156     SCEVHandle ComputeIterationCount(const Loop *L);
01157 
01158     /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
01159     /// 'setcc load X, cst', try to se if we can compute the trip count.
01160     SCEVHandle ComputeLoadConstantCompareIterationCount(LoadInst *LI,
01161                                                         Constant *RHS,
01162                                                         const Loop *L,
01163                                                         unsigned SetCCOpcode);
01164 
01165     /// ComputeIterationCountExhaustively - If the trip is known to execute a
01166     /// constant number of times (the condition evolves only from constants),
01167     /// try to evaluate a few iterations of the loop until we get the exit
01168     /// condition gets a value of ExitWhen (true or false).  If we cannot
01169     /// evaluate the trip count of the loop, return UnknownValue.
01170     SCEVHandle ComputeIterationCountExhaustively(const Loop *L, Value *Cond,
01171                                                  bool ExitWhen);
01172 
01173     /// HowFarToZero - Return the number of times a backedge comparing the
01174     /// specified value to zero will execute.  If not computable, return
01175     /// UnknownValue.
01176     SCEVHandle HowFarToZero(SCEV *V, const Loop *L);
01177 
01178     /// HowFarToNonZero - Return the number of times a backedge checking the
01179     /// specified value for nonzero will execute.  If not computable, return
01180     /// UnknownValue.
01181     SCEVHandle HowFarToNonZero(SCEV *V, const Loop *L);
01182 
01183     /// HowManyLessThans - Return the number of times a backedge containing the
01184     /// specified less-than comparison will execute.  If not computable, return
01185     /// UnknownValue.
01186     SCEVHandle HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L);
01187 
01188     /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
01189     /// in the header of its containing loop, we know the loop executes a
01190     /// constant number of times, and the PHI node is just a recurrence
01191     /// involving constants, fold it.
01192     Constant *getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its,
01193                                                 const Loop *L);
01194   };
01195 }
01196 
01197 //===----------------------------------------------------------------------===//
01198 //            Basic SCEV Analysis and PHI Idiom Recognition Code
01199 //
01200 
01201 /// deleteInstructionFromRecords - This method should be called by the
01202 /// client before it removes an instruction from the program, to make sure
01203 /// that no dangling references are left around.
01204 void ScalarEvolutionsImpl::deleteInstructionFromRecords(Instruction *I) {
01205   Scalars.erase(I);
01206   if (PHINode *PN = dyn_cast<PHINode>(I))
01207     ConstantEvolutionLoopExitValue.erase(PN);
01208 }
01209 
01210 
01211 /// getSCEV - Return an existing SCEV if it exists, otherwise analyze the
01212 /// expression and create a new one.
01213 SCEVHandle ScalarEvolutionsImpl::getSCEV(Value *V) {
01214   assert(V->getType() != Type::VoidTy && "Can't analyze void expressions!");
01215 
01216   std::map<Value*, SCEVHandle>::iterator I = Scalars.find(V);
01217   if (I != Scalars.end()) return I->second;
01218   SCEVHandle S = createSCEV(V);
01219   Scalars.insert(std::make_pair(V, S));
01220   return S;
01221 }
01222 
01223 /// ReplaceSymbolicValueWithConcrete - This looks up the computed SCEV value for
01224 /// the specified instruction and replaces any references to the symbolic value
01225 /// SymName with the specified value.  This is used during PHI resolution.
01226 void ScalarEvolutionsImpl::
01227 ReplaceSymbolicValueWithConcrete(Instruction *I, const SCEVHandle &SymName,
01228                                  const SCEVHandle &NewVal) {
01229   std::map<Value*, SCEVHandle>::iterator SI = Scalars.find(I);
01230   if (SI == Scalars.end()) return;
01231 
01232   SCEVHandle NV =
01233     SI->second->replaceSymbolicValuesWithConcrete(SymName, NewVal);
01234   if (NV == SI->second) return;  // No change.
01235 
01236   SI->second = NV;       // Update the scalars map!
01237 
01238   // Any instruction values that use this instruction might also need to be
01239   // updated!
01240   for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
01241        UI != E; ++UI)
01242     ReplaceSymbolicValueWithConcrete(cast<Instruction>(*UI), SymName, NewVal);
01243 }
01244 
01245 /// createNodeForPHI - PHI nodes have two cases.  Either the PHI node exists in
01246 /// a loop header, making it a potential recurrence, or it doesn't.
01247 ///
01248 SCEVHandle ScalarEvolutionsImpl::createNodeForPHI(PHINode *PN) {
01249   if (PN->getNumIncomingValues() == 2)  // The loops have been canonicalized.
01250     if (const Loop *L = LI.getLoopFor(PN->getParent()))
01251       if (L->getHeader() == PN->getParent()) {
01252         // If it lives in the loop header, it has two incoming values, one
01253         // from outside the loop, and one from inside.
01254         unsigned IncomingEdge = L->contains(PN->getIncomingBlock(0));
01255         unsigned BackEdge     = IncomingEdge^1;
01256 
01257         // While we are analyzing this PHI node, handle its value symbolically.
01258         SCEVHandle SymbolicName = SCEVUnknown::get(PN);
01259         assert(Scalars.find(PN) == Scalars.end() &&
01260                "PHI node already processed?");
01261         Scalars.insert(std::make_pair(PN, SymbolicName));
01262 
01263         // Using this symbolic name for the PHI, analyze the value coming around
01264         // the back-edge.
01265         SCEVHandle BEValue = getSCEV(PN->getIncomingValue(BackEdge));
01266 
01267         // NOTE: If BEValue is loop invariant, we know that the PHI node just
01268         // has a special value for the first iteration of the loop.
01269 
01270         // If the value coming around the backedge is an add with the symbolic
01271         // value we just inserted, then we found a simple induction variable!
01272         if (SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(BEValue)) {
01273           // If there is a single occurrence of the symbolic value, replace it
01274           // with a recurrence.
01275           unsigned FoundIndex = Add->getNumOperands();
01276           for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
01277             if (Add->getOperand(i) == SymbolicName)
01278               if (FoundIndex == e) {
01279                 FoundIndex = i;
01280                 break;
01281               }
01282 
01283           if (FoundIndex != Add->getNumOperands()) {
01284             // Create an add with everything but the specified operand.
01285             std::vector<SCEVHandle> Ops;
01286             for (unsigned i = 0, e = Add->getNumOperands(); i != e; ++i)
01287               if (i != FoundIndex)
01288                 Ops.push_back(Add->getOperand(i));
01289             SCEVHandle Accum = SCEVAddExpr::get(Ops);
01290 
01291             // This is not a valid addrec if the step amount is varying each
01292             // loop iteration, but is not itself an addrec in this loop.
01293             if (Accum->isLoopInvariant(L) ||
01294                 (isa<SCEVAddRecExpr>(Accum) &&
01295                  cast<SCEVAddRecExpr>(Accum)->getLoop() == L)) {
01296               SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
01297               SCEVHandle PHISCEV  = SCEVAddRecExpr::get(StartVal, Accum, L);
01298 
01299               // Okay, for the entire analysis of this edge we assumed the PHI
01300               // to be symbolic.  We now need to go back and update all of the
01301               // entries for the scalars that use the PHI (except for the PHI
01302               // itself) to use the new analyzed value instead of the "symbolic"
01303               // value.
01304               ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
01305               return PHISCEV;
01306             }
01307           }
01308         } else if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(BEValue)) {
01309           // Otherwise, this could be a loop like this:
01310           //     i = 0;  for (j = 1; ..; ++j) { ....  i = j; }
01311           // In this case, j = {1,+,1}  and BEValue is j.
01312           // Because the other in-value of i (0) fits the evolution of BEValue
01313           // i really is an addrec evolution.
01314           if (AddRec->getLoop() == L && AddRec->isAffine()) {
01315             SCEVHandle StartVal = getSCEV(PN->getIncomingValue(IncomingEdge));
01316 
01317             // If StartVal = j.start - j.stride, we can use StartVal as the
01318             // initial step of the addrec evolution.
01319             if (StartVal == SCEV::getMinusSCEV(AddRec->getOperand(0),
01320                                                AddRec->getOperand(1))) {
01321               SCEVHandle PHISCEV = 
01322                  SCEVAddRecExpr::get(StartVal, AddRec->getOperand(1), L);
01323 
01324               // Okay, for the entire analysis of this edge we assumed the PHI
01325               // to be symbolic.  We now need to go back and update all of the
01326               // entries for the scalars that use the PHI (except for the PHI
01327               // itself) to use the new analyzed value instead of the "symbolic"
01328               // value.
01329               ReplaceSymbolicValueWithConcrete(PN, SymbolicName, PHISCEV);
01330               return PHISCEV;
01331             }
01332           }
01333         }
01334 
01335         return SymbolicName;
01336       }
01337 
01338   // If it's not a loop phi, we can't handle it yet.
01339   return SCEVUnknown::get(PN);
01340 }
01341 
01342 /// createNodeForCast - Handle the various forms of casts that we support.
01343 ///
01344 SCEVHandle ScalarEvolutionsImpl::createNodeForCast(CastInst *CI) {
01345   const Type *SrcTy = CI->getOperand(0)->getType();
01346   const Type *DestTy = CI->getType();
01347 
01348   // If this is a noop cast (ie, conversion from int to uint), ignore it.
01349   if (SrcTy->isLosslesslyConvertibleTo(DestTy))
01350     return getSCEV(CI->getOperand(0));
01351 
01352   if (SrcTy->isInteger() && DestTy->isInteger()) {
01353     // Otherwise, if this is a truncating integer cast, we can represent this
01354     // cast.
01355     if (SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
01356       return SCEVTruncateExpr::get(getSCEV(CI->getOperand(0)),
01357                                    CI->getType()->getUnsignedVersion());
01358     if (SrcTy->isUnsigned() &&
01359         SrcTy->getPrimitiveSize() > DestTy->getPrimitiveSize())
01360       return SCEVZeroExtendExpr::get(getSCEV(CI->getOperand(0)),
01361                                      CI->getType()->getUnsignedVersion());
01362   }
01363 
01364   // If this is an sign or zero extending cast and we can prove that the value
01365   // will never overflow, we could do similar transformations.
01366 
01367   // Otherwise, we can't handle this cast!
01368   return SCEVUnknown::get(CI);
01369 }
01370 
01371 
01372 /// createSCEV - We know that there is no SCEV for the specified value.
01373 /// Analyze the expression.
01374 ///
01375 SCEVHandle ScalarEvolutionsImpl::createSCEV(Value *V) {
01376   if (Instruction *I = dyn_cast<Instruction>(V)) {
01377     switch (I->getOpcode()) {
01378     case Instruction::Add:
01379       return SCEVAddExpr::get(getSCEV(I->getOperand(0)),
01380                               getSCEV(I->getOperand(1)));
01381     case Instruction::Mul:
01382       return SCEVMulExpr::get(getSCEV(I->getOperand(0)),
01383                               getSCEV(I->getOperand(1)));
01384     case Instruction::Div:
01385       if (V->getType()->isInteger() && V->getType()->isSigned())
01386         return SCEVSDivExpr::get(getSCEV(I->getOperand(0)),
01387                                  getSCEV(I->getOperand(1)));
01388       break;
01389 
01390     case Instruction::Sub:
01391       return SCEV::getMinusSCEV(getSCEV(I->getOperand(0)),
01392                                 getSCEV(I->getOperand(1)));
01393 
01394     case Instruction::Shl:
01395       // Turn shift left of a constant amount into a multiply.
01396       if (ConstantInt *SA = dyn_cast<ConstantInt>(I->getOperand(1))) {
01397         Constant *X = ConstantInt::get(V->getType(), 1);
01398         X = ConstantExpr::getShl(X, SA);
01399         return SCEVMulExpr::get(getSCEV(I->getOperand(0)), getSCEV(X));
01400       }
01401       break;
01402 
01403     case Instruction::Cast:
01404       return createNodeForCast(cast<CastInst>(I));
01405 
01406     case Instruction::PHI:
01407       return createNodeForPHI(cast<PHINode>(I));
01408 
01409     default: // We cannot analyze this expression.
01410       break;
01411     }
01412   }
01413 
01414   return SCEVUnknown::get(V);
01415 }
01416 
01417 
01418 
01419 //===----------------------------------------------------------------------===//
01420 //                   Iteration Count Computation Code
01421 //
01422 
01423 /// getIterationCount - If the specified loop has a predictable iteration
01424 /// count, return it.  Note that it is not valid to call this method on a
01425 /// loop without a loop-invariant iteration count.
01426 SCEVHandle ScalarEvolutionsImpl::getIterationCount(const Loop *L) {
01427   std::map<const Loop*, SCEVHandle>::iterator I = IterationCounts.find(L);
01428   if (I == IterationCounts.end()) {
01429     SCEVHandle ItCount = ComputeIterationCount(L);
01430     I = IterationCounts.insert(std::make_pair(L, ItCount)).first;
01431     if (ItCount != UnknownValue) {
01432       assert(ItCount->isLoopInvariant(L) &&
01433              "Computed trip count isn't loop invariant for loop!");
01434       ++NumTripCountsComputed;
01435     } else if (isa<PHINode>(L->getHeader()->begin())) {
01436       // Only count loops that have phi nodes as not being computable.
01437       ++NumTripCountsNotComputed;
01438     }
01439   }
01440   return I->second;
01441 }
01442 
01443 /// ComputeIterationCount - Compute the number of times the specified loop
01444 /// will iterate.
01445 SCEVHandle ScalarEvolutionsImpl::ComputeIterationCount(const Loop *L) {
01446   // If the loop has a non-one exit block count, we can't analyze it.
01447   std::vector<BasicBlock*> ExitBlocks;
01448   L->getExitBlocks(ExitBlocks);
01449   if (ExitBlocks.size() != 1) return UnknownValue;
01450 
01451   // Okay, there is one exit block.  Try to find the condition that causes the
01452   // loop to be exited.
01453   BasicBlock *ExitBlock = ExitBlocks[0];
01454 
01455   BasicBlock *ExitingBlock = 0;
01456   for (pred_iterator PI = pred_begin(ExitBlock), E = pred_end(ExitBlock);
01457        PI != E; ++PI)
01458     if (L->contains(*PI)) {
01459       if (ExitingBlock == 0)
01460         ExitingBlock = *PI;
01461       else
01462         return UnknownValue;   // More than one block exiting!
01463     }
01464   assert(ExitingBlock && "No exits from loop, something is broken!");
01465 
01466   // Okay, we've computed the exiting block.  See what condition causes us to
01467   // exit.
01468   //
01469   // FIXME: we should be able to handle switch instructions (with a single exit)
01470   // FIXME: We should handle cast of int to bool as well
01471   BranchInst *ExitBr = dyn_cast<BranchInst>(ExitingBlock->getTerminator());
01472   if (ExitBr == 0) return UnknownValue;
01473   assert(ExitBr->isConditional() && "If unconditional, it can't be in loop!");
01474   SetCondInst *ExitCond = dyn_cast<SetCondInst>(ExitBr->getCondition());
01475   if (ExitCond == 0)  // Not a setcc
01476     return ComputeIterationCountExhaustively(L, ExitBr->getCondition(),
01477                                           ExitBr->getSuccessor(0) == ExitBlock);
01478 
01479   // If the condition was exit on true, convert the condition to exit on false.
01480   Instruction::BinaryOps Cond;
01481   if (ExitBr->getSuccessor(1) == ExitBlock)
01482     Cond = ExitCond->getOpcode();
01483   else
01484     Cond = ExitCond->getInverseCondition();
01485 
01486   // Handle common loops like: for (X = "string"; *X; ++X)
01487   if (LoadInst *LI = dyn_cast<LoadInst>(ExitCond->getOperand(0)))
01488     if (Constant *RHS = dyn_cast<Constant>(ExitCond->getOperand(1))) {
01489       SCEVHandle ItCnt =
01490         ComputeLoadConstantCompareIterationCount(LI, RHS, L, Cond);
01491       if (!isa<SCEVCouldNotCompute>(ItCnt)) return ItCnt;
01492     }
01493 
01494   SCEVHandle LHS = getSCEV(ExitCond->getOperand(0));
01495   SCEVHandle RHS = getSCEV(ExitCond->getOperand(1));
01496 
01497   // Try to evaluate any dependencies out of the loop.
01498   SCEVHandle Tmp = getSCEVAtScope(LHS, L);
01499   if (!isa<SCEVCouldNotCompute>(Tmp)) LHS = Tmp;
01500   Tmp = getSCEVAtScope(RHS, L);
01501   if (!isa<SCEVCouldNotCompute>(Tmp)) RHS = Tmp;
01502 
01503   // At this point, we would like to compute how many iterations of the loop the
01504   // predicate will return true for these inputs.
01505   if (isa<SCEVConstant>(LHS) && !isa<SCEVConstant>(RHS)) {
01506     // If there is a constant, force it into the RHS.
01507     std::swap(LHS, RHS);
01508     Cond = SetCondInst::getSwappedCondition(Cond);
01509   }
01510 
01511   // FIXME: think about handling pointer comparisons!  i.e.:
01512   // while (P != P+100) ++P;
01513 
01514   // If we have a comparison of a chrec against a constant, try to use value
01515   // ranges to answer this query.
01516   if (SCEVConstant *RHSC = dyn_cast<SCEVConstant>(RHS))
01517     if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS))
01518       if (AddRec->getLoop() == L) {
01519         // Form the comparison range using the constant of the correct type so
01520         // that the ConstantRange class knows to do a signed or unsigned
01521         // comparison.
01522         ConstantInt *CompVal = RHSC->getValue();
01523         const Type *RealTy = ExitCond->getOperand(0)->getType();
01524         CompVal = dyn_cast<ConstantInt>(ConstantExpr::getCast(CompVal, RealTy));
01525         if (CompVal) {
01526           // Form the constant range.
01527           ConstantRange CompRange(Cond, CompVal);
01528 
01529           // Now that we have it, if it's signed, convert it to an unsigned
01530           // range.
01531           if (CompRange.getLower()->getType()->isSigned()) {
01532             const Type *NewTy = RHSC->getValue()->getType();
01533             Constant *NewL = ConstantExpr::getCast(CompRange.getLower(), NewTy);
01534             Constant *NewU = ConstantExpr::getCast(CompRange.getUpper(), NewTy);
01535             CompRange = ConstantRange(NewL, NewU);
01536           }
01537 
01538           SCEVHandle Ret = AddRec->getNumIterationsInRange(CompRange);
01539           if (!isa<SCEVCouldNotCompute>(Ret)) return Ret;
01540         }
01541       }
01542 
01543   switch (Cond) {
01544   case Instruction::SetNE:                     // while (X != Y)
01545     // Convert to: while (X-Y != 0)
01546     if (LHS->getType()->isInteger()) {
01547       SCEVHandle TC = HowFarToZero(SCEV::getMinusSCEV(LHS, RHS), L);
01548       if (!isa<SCEVCouldNotCompute>(TC)) return TC;
01549     }
01550     break;
01551   case Instruction::SetEQ:
01552     // Convert to: while (X-Y == 0)           // while (X == Y)
01553     if (LHS->getType()->isInteger()) {
01554       SCEVHandle TC = HowFarToNonZero(SCEV::getMinusSCEV(LHS, RHS), L);
01555       if (!isa<SCEVCouldNotCompute>(TC)) return TC;
01556     }
01557     break;
01558   case Instruction::SetLT:
01559     if (LHS->getType()->isInteger() && 
01560         ExitCond->getOperand(0)->getType()->isSigned()) {
01561       SCEVHandle TC = HowManyLessThans(LHS, RHS, L);
01562       if (!isa<SCEVCouldNotCompute>(TC)) return TC;
01563     }
01564     break;
01565   case Instruction::SetGT:
01566     if (LHS->getType()->isInteger() &&
01567         ExitCond->getOperand(0)->getType()->isSigned()) {
01568       SCEVHandle TC = HowManyLessThans(RHS, LHS, L);
01569       if (!isa<SCEVCouldNotCompute>(TC)) return TC;
01570     }
01571     break;
01572   default:
01573 #if 0
01574     std::cerr << "ComputeIterationCount ";
01575     if (ExitCond->getOperand(0)->getType()->isUnsigned())
01576       std::cerr << "[unsigned] ";
01577     std::cerr << *LHS << "   "
01578               << Instruction::getOpcodeName(Cond) << "   " << *RHS << "\n";
01579 #endif
01580     break;
01581   }
01582 
01583   return ComputeIterationCountExhaustively(L, ExitCond,
01584                                          ExitBr->getSuccessor(0) == ExitBlock);
01585 }
01586 
01587 static ConstantInt *
01588 EvaluateConstantChrecAtConstant(const SCEVAddRecExpr *AddRec, Constant *C) {
01589   SCEVHandle InVal = SCEVConstant::get(cast<ConstantInt>(C));
01590   SCEVHandle Val = AddRec->evaluateAtIteration(InVal);
01591   assert(isa<SCEVConstant>(Val) &&
01592          "Evaluation of SCEV at constant didn't fold correctly?");
01593   return cast<SCEVConstant>(Val)->getValue();
01594 }
01595 
01596 /// GetAddressedElementFromGlobal - Given a global variable with an initializer
01597 /// and a GEP expression (missing the pointer index) indexing into it, return
01598 /// the addressed element of the initializer or null if the index expression is
01599 /// invalid.
01600 static Constant *
01601 GetAddressedElementFromGlobal(GlobalVariable *GV,
01602                               const std::vector<ConstantInt*> &Indices) {
01603   Constant *Init = GV->getInitializer();
01604   for (unsigned i = 0, e = Indices.size(); i != e; ++i) {
01605     uint64_t Idx = Indices[i]->getRawValue();
01606     if (ConstantStruct *CS = dyn_cast<ConstantStruct>(Init)) {
01607       assert(Idx < CS->getNumOperands() && "Bad struct index!");
01608       Init = cast<Constant>(CS->getOperand(Idx));
01609     } else if (ConstantArray *CA = dyn_cast<ConstantArray>(Init)) {
01610       if (Idx >= CA->getNumOperands()) return 0;  // Bogus program
01611       Init = cast<Constant>(CA->getOperand(Idx));
01612     } else if (isa<ConstantAggregateZero>(Init)) {
01613       if (const StructType *STy = dyn_cast<StructType>(Init->getType())) {
01614         assert(Idx < STy->getNumElements() && "Bad struct index!");
01615         Init = Constant::getNullValue(STy->getElementType(Idx));
01616       } else if (const ArrayType *ATy = dyn_cast<ArrayType>(Init->getType())) {
01617         if (Idx >= ATy->getNumElements()) return 0;  // Bogus program
01618         Init = Constant::getNullValue(ATy->getElementType());
01619       } else {
01620         assert(0 && "Unknown constant aggregate type!");
01621       }
01622       return 0;
01623     } else {
01624       return 0; // Unknown initializer type
01625     }
01626   }
01627   return Init;
01628 }
01629 
01630 /// ComputeLoadConstantCompareIterationCount - Given an exit condition of
01631 /// 'setcc load X, cst', try to se if we can compute the trip count.
01632 SCEVHandle ScalarEvolutionsImpl::
01633 ComputeLoadConstantCompareIterationCount(LoadInst *LI, Constant *RHS,
01634                                          const Loop *L, unsigned SetCCOpcode) {
01635   if (LI->isVolatile()) return UnknownValue;
01636 
01637   // Check to see if the loaded pointer is a getelementptr of a global.
01638   GetElementPtrInst *GEP = dyn_cast<GetElementPtrInst>(LI->getOperand(0));
01639   if (!GEP) return UnknownValue;
01640 
01641   // Make sure that it is really a constant global we are gepping, with an
01642   // initializer, and make sure the first IDX is really 0.
01643   GlobalVariable *GV = dyn_cast<GlobalVariable>(GEP->getOperand(0));
01644   if (!GV || !GV->isConstant() || !GV->hasInitializer() ||
01645       GEP->getNumOperands() < 3 || !isa<Constant>(GEP->getOperand(1)) ||
01646       !cast<Constant>(GEP->getOperand(1))->isNullValue())
01647     return UnknownValue;
01648 
01649   // Okay, we allow one non-constant index into the GEP instruction.
01650   Value *VarIdx = 0;
01651   std::vector<ConstantInt*> Indexes;
01652   unsigned VarIdxNum = 0;
01653   for (unsigned i = 2, e = GEP->getNumOperands(); i != e; ++i)
01654     if (ConstantInt *CI = dyn_cast<ConstantInt>(GEP->getOperand(i))) {
01655       Indexes.push_back(CI);
01656     } else if (!isa<ConstantInt>(GEP->getOperand(i))) {
01657       if (VarIdx) return UnknownValue;  // Multiple non-constant idx's.
01658       VarIdx = GEP->getOperand(i);
01659       VarIdxNum = i-2;
01660       Indexes.push_back(0);
01661     }
01662 
01663   // Okay, we know we have a (load (gep GV, 0, X)) comparison with a constant.
01664   // Check to see if X is a loop variant variable value now.
01665   SCEVHandle Idx = getSCEV(VarIdx);
01666   SCEVHandle Tmp = getSCEVAtScope(Idx, L);
01667   if (!isa<SCEVCouldNotCompute>(Tmp)) Idx = Tmp;
01668 
01669   // We can only recognize very limited forms of loop index expressions, in
01670   // particular, only affine AddRec's like {C1,+,C2}.
01671   SCEVAddRecExpr *IdxExpr = dyn_cast<SCEVAddRecExpr>(Idx);
01672   if (!IdxExpr || !IdxExpr->isAffine() || IdxExpr->isLoopInvariant(L) ||
01673       !isa<SCEVConstant>(IdxExpr->getOperand(0)) ||
01674       !isa<SCEVConstant>(IdxExpr->getOperand(1)))
01675     return UnknownValue;
01676 
01677   unsigned MaxSteps = MaxBruteForceIterations;
01678   for (unsigned IterationNum = 0; IterationNum != MaxSteps; ++IterationNum) {
01679     ConstantUInt *ItCst =
01680       ConstantUInt::get(IdxExpr->getType()->getUnsignedVersion(), IterationNum);
01681     ConstantInt *Val = EvaluateConstantChrecAtConstant(IdxExpr, ItCst);
01682 
01683     // Form the GEP offset.
01684     Indexes[VarIdxNum] = Val;
01685 
01686     Constant *Result = GetAddressedElementFromGlobal(GV, Indexes);
01687     if (Result == 0) break;  // Cannot compute!
01688 
01689     // Evaluate the condition for this iteration.
01690     Result = ConstantExpr::get(SetCCOpcode, Result, RHS);
01691     if (!isa<ConstantBool>(Result)) break;  // Couldn't decide for sure
01692     if (Result == ConstantBool::False) {
01693 #if 0
01694       std::cerr << "\n***\n*** Computed loop count " << *ItCst
01695                 << "\n*** From global " << *GV << "*** BB: " << *L->getHeader()
01696                 << "***\n";
01697 #endif
01698       ++NumArrayLenItCounts;
01699       return SCEVConstant::get(ItCst);   // Found terminating iteration!
01700     }
01701   }
01702   return UnknownValue;
01703 }
01704 
01705 
01706 /// CanConstantFold - Return true if we can constant fold an instruction of the
01707 /// specified type, assuming that all operands were constants.
01708 static bool CanConstantFold(const Instruction *I) {
01709   if (isa<BinaryOperator>(I) || isa<ShiftInst>(I) ||
01710       isa<SelectInst>(I) || isa<CastInst>(I) || isa<GetElementPtrInst>(I))
01711     return true;
01712 
01713   if (const CallInst *CI = dyn_cast<CallInst>(I))
01714     if (const Function *F = CI->getCalledFunction())
01715       return canConstantFoldCallTo((Function*)F);  // FIXME: elim cast
01716   return false;
01717 }
01718 
01719 /// ConstantFold - Constant fold an instruction of the specified type with the
01720 /// specified constant operands.  This function may modify the operands vector.
01721 static Constant *ConstantFold(const Instruction *I,
01722                               std::vector<Constant*> &Operands) {
01723   if (isa<BinaryOperator>(I) || isa<ShiftInst>(I))
01724     return ConstantExpr::get(I->getOpcode(), Operands[0], Operands[1]);
01725 
01726   switch (I->getOpcode()) {
01727   case Instruction::Cast:
01728     return ConstantExpr::getCast(Operands[0], I->getType());
01729   case Instruction::Select:
01730     return ConstantExpr::getSelect(Operands[0], Operands[1], Operands[2]);
01731   case Instruction::Call:
01732     if (Function *GV = dyn_cast<Function>(Operands[0])) {
01733       Operands.erase(Operands.begin());
01734       return ConstantFoldCall(cast<Function>(GV), Operands);
01735     }
01736 
01737     return 0;
01738   case Instruction::GetElementPtr:
01739     Constant *Base = Operands[0];
01740     Operands.erase(Operands.begin());
01741     return ConstantExpr::getGetElementPtr(Base, Operands);
01742   }
01743   return 0;
01744 }
01745 
01746 
01747 /// getConstantEvolvingPHI - Given an LLVM value and a loop, return a PHI node
01748 /// in the loop that V is derived from.  We allow arbitrary operations along the
01749 /// way, but the operands of an operation must either be constants or a value
01750 /// derived from a constant PHI.  If this expression does not fit with these
01751 /// constraints, return null.
01752 static PHINode *getConstantEvolvingPHI(Value *V, const Loop *L) {
01753   // If this is not an instruction, or if this is an instruction outside of the
01754   // loop, it can't be derived from a loop PHI.
01755   Instruction *I = dyn_cast<Instruction>(V);
01756   if (I == 0 || !L->contains(I->getParent())) return 0;
01757 
01758   if (PHINode *PN = dyn_cast<PHINode>(I))
01759     if (L->getHeader() == I->getParent())
01760       return PN;
01761     else
01762       // We don't currently keep track of the control flow needed to evaluate
01763       // PHIs, so we cannot handle PHIs inside of loops.
01764       return 0;
01765 
01766   // If we won't be able to constant fold this expression even if the operands
01767   // are constants, return early.
01768   if (!CanConstantFold(I)) return 0;
01769 
01770   // Otherwise, we can evaluate this instruction if all of its operands are
01771   // constant or derived from a PHI node themselves.
01772   PHINode *PHI = 0;
01773   for (unsigned Op = 0, e = I->getNumOperands(); Op != e; ++Op)
01774     if (!(isa<Constant>(I->getOperand(Op)) ||
01775           isa<GlobalValue>(I->getOperand(Op)))) {
01776       PHINode *P = getConstantEvolvingPHI(I->getOperand(Op), L);
01777       if (P == 0) return 0;  // Not evolving from PHI
01778       if (PHI == 0)
01779         PHI = P;
01780       else if (PHI != P)
01781         return 0;  // Evolving from multiple different PHIs.
01782     }
01783 
01784   // This is a expression evolving from a constant PHI!
01785   return PHI;
01786 }
01787 
01788 /// EvaluateExpression - Given an expression that passes the
01789 /// getConstantEvolvingPHI predicate, evaluate its value assuming the PHI node
01790 /// in the loop has the value PHIVal.  If we can't fold this expression for some
01791 /// reason, return null.
01792 static Constant *EvaluateExpression(Value *V, Constant *PHIVal) {
01793   if (isa<PHINode>(V)) return PHIVal;
01794   if (GlobalValue *GV = dyn_cast<GlobalValue>(V))
01795     return GV;
01796   if (Constant *C = dyn_cast<Constant>(V)) return C;
01797   Instruction *I = cast<Instruction>(V);
01798 
01799   std::vector<Constant*> Operands;
01800   Operands.resize(I->getNumOperands());
01801 
01802   for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
01803     Operands[i] = EvaluateExpression(I->getOperand(i), PHIVal);
01804     if (Operands[i] == 0) return 0;
01805   }
01806 
01807   return ConstantFold(I, Operands);
01808 }
01809 
01810 /// getConstantEvolutionLoopExitValue - If we know that the specified Phi is
01811 /// in the header of its containing loop, we know the loop executes a
01812 /// constant number of times, and the PHI node is just a recurrence
01813 /// involving constants, fold it.
01814 Constant *ScalarEvolutionsImpl::
01815 getConstantEvolutionLoopExitValue(PHINode *PN, uint64_t Its, const Loop *L) {
01816   std::map<PHINode*, Constant*>::iterator I =
01817     ConstantEvolutionLoopExitValue.find(PN);
01818   if (I != ConstantEvolutionLoopExitValue.end())
01819     return I->second;
01820 
01821   if (Its > MaxBruteForceIterations)
01822     return ConstantEvolutionLoopExitValue[PN] = 0;  // Not going to evaluate it.
01823 
01824   Constant *&RetVal = ConstantEvolutionLoopExitValue[PN];
01825 
01826   // Since the loop is canonicalized, the PHI node must have two entries.  One
01827   // entry must be a constant (coming in from outside of the loop), and the
01828   // second must be derived from the same PHI.
01829   bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
01830   Constant *StartCST =
01831     dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
01832   if (StartCST == 0)
01833     return RetVal = 0;  // Must be a constant.
01834 
01835   Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
01836   PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
01837   if (PN2 != PN)
01838     return RetVal = 0;  // Not derived from same PHI.
01839 
01840   // Execute the loop symbolically to determine the exit value.
01841   unsigned IterationNum = 0;
01842   unsigned NumIterations = Its;
01843   if (NumIterations != Its)
01844     return RetVal = 0;  // More than 2^32 iterations??
01845 
01846   for (Constant *PHIVal = StartCST; ; ++IterationNum) {
01847     if (IterationNum == NumIterations)
01848       return RetVal = PHIVal;  // Got exit value!
01849 
01850     // Compute the value of the PHI node for the next iteration.
01851     Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
01852     if (NextPHI == PHIVal)
01853       return RetVal = NextPHI;  // Stopped evolving!
01854     if (NextPHI == 0)
01855       return 0;        // Couldn't evaluate!
01856     PHIVal = NextPHI;
01857   }
01858 }
01859 
01860 /// ComputeIterationCountExhaustively - If the trip is known to execute a
01861 /// constant number of times (the condition evolves only from constants),
01862 /// try to evaluate a few iterations of the loop until we get the exit
01863 /// condition gets a value of ExitWhen (true or false).  If we cannot
01864 /// evaluate the trip count of the loop, return UnknownValue.
01865 SCEVHandle ScalarEvolutionsImpl::
01866 ComputeIterationCountExhaustively(const Loop *L, Value *Cond, bool ExitWhen) {
01867   PHINode *PN = getConstantEvolvingPHI(Cond, L);
01868   if (PN == 0) return UnknownValue;
01869 
01870   // Since the loop is canonicalized, the PHI node must have two entries.  One
01871   // entry must be a constant (coming in from outside of the loop), and the
01872   // second must be derived from the same PHI.
01873   bool SecondIsBackedge = L->contains(PN->getIncomingBlock(1));
01874   Constant *StartCST =
01875     dyn_cast<Constant>(PN->getIncomingValue(!SecondIsBackedge));
01876   if (StartCST == 0) return UnknownValue;  // Must be a constant.
01877 
01878   Value *BEValue = PN->getIncomingValue(SecondIsBackedge);
01879   PHINode *PN2 = getConstantEvolvingPHI(BEValue, L);
01880   if (PN2 != PN) return UnknownValue;  // Not derived from same PHI.
01881 
01882   // Okay, we find a PHI node that defines the trip count of this loop.  Execute
01883   // the loop symbolically to determine when the condition gets a value of
01884   // "ExitWhen".
01885   unsigned IterationNum = 0;
01886   unsigned MaxIterations = MaxBruteForceIterations;   // Limit analysis.
01887   for (Constant *PHIVal = StartCST;
01888        IterationNum != MaxIterations; ++IterationNum) {
01889     ConstantBool *CondVal =
01890       dyn_cast_or_null<ConstantBool>(EvaluateExpression(Cond, PHIVal));
01891     if (!CondVal) return UnknownValue;     // Couldn't symbolically evaluate.
01892 
01893     if (CondVal->getValue() == ExitWhen) {
01894       ConstantEvolutionLoopExitValue[PN] = PHIVal;
01895       ++NumBruteForceTripCountsComputed;
01896       return SCEVConstant::get(ConstantUInt::get(Type::UIntTy, IterationNum));
01897     }
01898 
01899     // Compute the value of the PHI node for the next iteration.
01900     Constant *NextPHI = EvaluateExpression(BEValue, PHIVal);
01901     if (NextPHI == 0 || NextPHI == PHIVal)
01902       return UnknownValue;  // Couldn't evaluate or not making progress...
01903     PHIVal = NextPHI;
01904   }
01905 
01906   // Too many iterations were needed to evaluate.
01907   return UnknownValue;
01908 }
01909 
01910 /// getSCEVAtScope - Compute the value of the specified expression within the
01911 /// indicated loop (which may be null to indicate in no loop).  If the
01912 /// expression cannot be evaluated, return UnknownValue.
01913 SCEVHandle ScalarEvolutionsImpl::getSCEVAtScope(SCEV *V, const Loop *L) {
01914   // FIXME: this should be turned into a virtual method on SCEV!
01915 
01916   if (isa<SCEVConstant>(V)) return V;
01917 
01918   // If this instruction is evolves from a constant-evolving PHI, compute the
01919   // exit value from the loop without using SCEVs.
01920   if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(V)) {
01921     if (Instruction *I = dyn_cast<Instruction>(SU->getValue())) {
01922       const Loop *LI = this->LI[I->getParent()];
01923       if (LI && LI->getParentLoop() == L)  // Looking for loop exit value.
01924         if (PHINode *PN = dyn_cast<PHINode>(I))
01925           if (PN->getParent() == LI->getHeader()) {
01926             // Okay, there is no closed form solution for the PHI node.  Check
01927             // to see if the loop that contains it has a known iteration count.
01928             // If so, we may be able to force computation of the exit value.
01929             SCEVHandle IterationCount = getIterationCount(LI);
01930             if (SCEVConstant *ICC = dyn_cast<SCEVConstant>(IterationCount)) {
01931               // Okay, we know how many times the containing loop executes.  If
01932               // this is a constant evolving PHI node, get the final value at
01933               // the specified iteration number.
01934               Constant *RV = getConstantEvolutionLoopExitValue(PN,
01935                                                ICC->getValue()->getRawValue(),
01936                                                                LI);
01937               if (RV) return SCEVUnknown::get(RV);
01938             }
01939           }
01940 
01941       // Okay, this is a some expression that we cannot symbolically evaluate
01942       // into a SCEV.  Check to see if it's possible to symbolically evaluate
01943       // the arguments into constants, and if see, try to constant propagate the
01944       // result.  This is particularly useful for computing loop exit values.
01945       if (CanConstantFold(I)) {
01946         std::vector<Constant*> Operands;
01947         Operands.reserve(I->getNumOperands());
01948         for (unsigned i = 0, e = I->getNumOperands(); i != e; ++i) {
01949           Value *Op = I->getOperand(i);
01950           if (Constant *C = dyn_cast<Constant>(Op)) {
01951             Operands.push_back(C);
01952           } else {
01953             SCEVHandle OpV = getSCEVAtScope(getSCEV(Op), L);
01954             if (SCEVConstant *SC = dyn_cast<SCEVConstant>(OpV))
01955               Operands.push_back(ConstantExpr::getCast(SC->getValue(),
01956                                                        Op->getType()));
01957             else if (SCEVUnknown *SU = dyn_cast<SCEVUnknown>(OpV)) {
01958               if (Constant *C = dyn_cast<Constant>(SU->getValue()))
01959                 Operands.push_back(ConstantExpr::getCast(C, Op->getType()));
01960               else
01961                 return V;
01962             } else {
01963               return V;
01964             }
01965           }
01966         }
01967         return SCEVUnknown::get(ConstantFold(I, Operands));
01968       }
01969     }
01970 
01971     // This is some other type of SCEVUnknown, just return it.
01972     return V;
01973   }
01974 
01975   if (SCEVCommutativeExpr *Comm = dyn_cast<SCEVCommutativeExpr>(V)) {
01976     // Avoid performing the look-up in the common case where the specified
01977     // expression has no loop-variant portions.
01978     for (unsigned i = 0, e = Comm->getNumOperands(); i != e; ++i) {
01979       SCEVHandle OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
01980       if (OpAtScope != Comm->getOperand(i)) {
01981         if (OpAtScope == UnknownValue) return UnknownValue;
01982         // Okay, at least one of these operands is loop variant but might be
01983         // foldable.  Build a new instance of the folded commutative expression.
01984         std::vector<SCEVHandle> NewOps(Comm->op_begin(), Comm->op_begin()+i);
01985         NewOps.push_back(OpAtScope);
01986 
01987         for (++i; i != e; ++i) {
01988           OpAtScope = getSCEVAtScope(Comm->getOperand(i), L);
01989           if (OpAtScope == UnknownValue) return UnknownValue;
01990           NewOps.push_back(OpAtScope);
01991         }
01992         if (isa<SCEVAddExpr>(Comm))
01993           return SCEVAddExpr::get(NewOps);
01994         assert(isa<SCEVMulExpr>(Comm) && "Only know about add and mul!");
01995         return SCEVMulExpr::get(NewOps);
01996       }
01997     }
01998     // If we got here, all operands are loop invariant.
01999     return Comm;
02000   }
02001 
02002   if (SCEVSDivExpr *Div = dyn_cast<SCEVSDivExpr>(V)) {
02003     SCEVHandle LHS = getSCEVAtScope(Div->getLHS(), L);
02004     if (LHS == UnknownValue) return LHS;
02005     SCEVHandle RHS = getSCEVAtScope(Div->getRHS(), L);
02006     if (RHS == UnknownValue) return RHS;
02007     if (LHS == Div->getLHS() && RHS == Div->getRHS())
02008       return Div;   // must be loop invariant
02009     return SCEVSDivExpr::get(LHS, RHS);
02010   }
02011 
02012   // If this is a loop recurrence for a loop that does not contain L, then we
02013   // are dealing with the final value computed by the loop.
02014   if (SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V)) {
02015     if (!L || !AddRec->getLoop()->contains(L->getHeader())) {
02016       // To evaluate this recurrence, we need to know how many times the AddRec
02017       // loop iterates.  Compute this now.
02018       SCEVHandle IterationCount = getIterationCount(AddRec->getLoop());
02019       if (IterationCount == UnknownValue) return UnknownValue;
02020       IterationCount = getTruncateOrZeroExtend(IterationCount,
02021                                                AddRec->getType());
02022 
02023       // If the value is affine, simplify the expression evaluation to just
02024       // Start + Step*IterationCount.
02025       if (AddRec->isAffine())
02026         return SCEVAddExpr::get(AddRec->getStart(),
02027                                 SCEVMulExpr::get(IterationCount,
02028                                                  AddRec->getOperand(1)));
02029 
02030       // Otherwise, evaluate it the hard way.
02031       return AddRec->evaluateAtIteration(IterationCount);
02032     }
02033     return UnknownValue;
02034   }
02035 
02036   //assert(0 && "Unknown SCEV type!");
02037   return UnknownValue;
02038 }
02039 
02040 
02041 /// SolveQuadraticEquation - Find the roots of the quadratic equation for the
02042 /// given quadratic chrec {L,+,M,+,N}.  This returns either the two roots (which
02043 /// might be the same) or two SCEVCouldNotCompute objects.
02044 ///
02045 static std::pair<SCEVHandle,SCEVHandle>
02046 SolveQuadraticEquation(const SCEVAddRecExpr *AddRec) {
02047   assert(AddRec->getNumOperands() == 3 && "This is not a quadratic chrec!");
02048   SCEVConstant *L = dyn_cast<SCEVConstant>(AddRec->getOperand(0));
02049   SCEVConstant *M = dyn_cast<SCEVConstant>(AddRec->getOperand(1));
02050   SCEVConstant *N = dyn_cast<SCEVConstant>(AddRec->getOperand(2));
02051 
02052   // We currently can only solve this if the coefficients are constants.
02053   if (!L || !M || !N) {
02054     SCEV *CNC = new SCEVCouldNotCompute();
02055     return std::make_pair(CNC, CNC);
02056   }
02057 
02058   Constant *Two = ConstantInt::get(L->getValue()->getType(), 2);
02059 
02060   // Convert from chrec coefficients to polynomial coefficients AX^2+BX+C
02061   Constant *C = L->getValue();
02062   // The B coefficient is M-N/2
02063   Constant *B = ConstantExpr::getSub(M->getValue(),
02064                                      ConstantExpr::getDiv(N->getValue(),
02065                                                           Two));
02066   // The A coefficient is N/2
02067   Constant *A = ConstantExpr::getDiv(N->getValue(), Two);
02068 
02069   // Compute the B^2-4ac term.
02070   Constant *SqrtTerm =
02071     ConstantExpr::getMul(ConstantInt::get(C->getType(), 4),
02072                          ConstantExpr::getMul(A, C));
02073   SqrtTerm = ConstantExpr::getSub(ConstantExpr::getMul(B, B), SqrtTerm);
02074 
02075   // Compute floor(sqrt(B^2-4ac))
02076   ConstantUInt *SqrtVal =
02077     cast<ConstantUInt>(ConstantExpr::getCast(SqrtTerm,
02078                                    SqrtTerm->getType()->getUnsignedVersion()));
02079   uint64_t SqrtValV = SqrtVal->getValue();
02080   uint64_t SqrtValV2 = (uint64_t)sqrt((double)SqrtValV);
02081   // The square root might not be precise for arbitrary 64-bit integer
02082   // values.  Do some sanity checks to ensure it's correct.
02083   if (SqrtValV2*SqrtValV2 > SqrtValV ||
02084       (SqrtValV2+1)*(SqrtValV2+1) <= SqrtValV) {
02085     SCEV *CNC = new SCEVCouldNotCompute();
02086     return std::make_pair(CNC, CNC);
02087   }
02088 
02089   SqrtVal = ConstantUInt::get(Type::ULongTy, SqrtValV2);
02090   SqrtTerm = ConstantExpr::getCast(SqrtVal, SqrtTerm->getType());
02091 
02092   Constant *NegB = ConstantExpr::getNeg(B);
02093   Constant *TwoA = ConstantExpr::getMul(A, Two);
02094 
02095   // The divisions must be performed as signed divisions.
02096   const Type *SignedTy = NegB->getType()->getSignedVersion();
02097   NegB = ConstantExpr::getCast(NegB, SignedTy);
02098   TwoA = ConstantExpr::getCast(TwoA, SignedTy);
02099   SqrtTerm = ConstantExpr::getCast(SqrtTerm, SignedTy);
02100 
02101   Constant *Solution1 =
02102     ConstantExpr::getDiv(ConstantExpr::getAdd(NegB, SqrtTerm), TwoA);
02103   Constant *Solution2 =
02104     ConstantExpr::getDiv(ConstantExpr::getSub(NegB, SqrtTerm), TwoA);
02105   return std::make_pair(SCEVUnknown::get(Solution1),
02106                         SCEVUnknown::get(Solution2));
02107 }
02108 
02109 /// HowFarToZero - Return the number of times a backedge comparing the specified
02110 /// value to zero will execute.  If not computable, return UnknownValue
02111 SCEVHandle ScalarEvolutionsImpl::HowFarToZero(SCEV *V, const Loop *L) {
02112   // If the value is a constant
02113   if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
02114     // If the value is already zero, the branch will execute zero times.
02115     if (C->getValue()->isNullValue()) return C;
02116     return UnknownValue;  // Otherwise it will loop infinitely.
02117   }
02118 
02119   SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(V);
02120   if (!AddRec || AddRec->getLoop() != L)
02121     return UnknownValue;
02122 
02123   if (AddRec->isAffine()) {
02124     // If this is an affine expression the execution count of this branch is
02125     // equal to:
02126     //
02127     //     (0 - Start/Step)    iff   Start % Step == 0
02128     //
02129     // Get the initial value for the loop.
02130     SCEVHandle Start = getSCEVAtScope(AddRec->getStart(), L->getParentLoop());
02131     if (isa<SCEVCouldNotCompute>(Start)) return UnknownValue;
02132     SCEVHandle Step = AddRec->getOperand(1);
02133 
02134     Step = getSCEVAtScope(Step, L->getParentLoop());
02135 
02136     // Figure out if Start % Step == 0.
02137     // FIXME: We should add DivExpr and RemExpr operations to our AST.
02138     if (SCEVConstant *StepC = dyn_cast<SCEVConstant>(Step)) {
02139       if (StepC->getValue()->equalsInt(1))      // N % 1 == 0
02140         return SCEV::getNegativeSCEV(Start);  // 0 - Start/1 == -Start
02141       if (StepC->getValue()->isAllOnesValue())  // N % -1 == 0
02142         return Start;                   // 0 - Start/-1 == Start
02143 
02144       // Check to see if Start is divisible by SC with no remainder.
02145       if (SCEVConstant *StartC = dyn_cast<SCEVConstant>(Start)) {
02146         ConstantInt *StartCC = StartC->getValue();
02147         Constant *StartNegC = ConstantExpr::getNeg(StartCC);
02148         Constant *Rem = ConstantExpr::getRem(StartNegC, StepC->getValue());
02149         if (Rem->isNullValue()) {
02150           Constant *Result =ConstantExpr::getDiv(StartNegC,StepC->getValue());
02151           return SCEVUnknown::get(Result);
02152         }
02153       }
02154     }
02155   } else if (AddRec->isQuadratic() && AddRec->getType()->isInteger()) {
02156     // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of
02157     // the quadratic equation to solve it.
02158     std::pair<SCEVHandle,SCEVHandle> Roots = SolveQuadraticEquation(AddRec);
02159     SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
02160     SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
02161     if (R1) {
02162 #if 0
02163       std::cerr << "HFTZ: " << *V << " - sol#1: " << *R1
02164                 << "  sol#2: " << *R2 << "\n";
02165 #endif
02166       // Pick the smallest positive root value.
02167       assert(R1->getType()->isUnsigned()&&"Didn't canonicalize to unsigned?");
02168       if (ConstantBool *CB =
02169           dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
02170                                                         R2->getValue()))) {
02171         if (CB != ConstantBool::True)
02172           std::swap(R1, R2);   // R1 is the minimum root now.
02173 
02174         // We can only use this value if the chrec ends up with an exact zero
02175         // value at this index.  When solving for "X*X != 5", for example, we
02176         // should not accept a root of 2.
02177         SCEVHandle Val = AddRec->evaluateAtIteration(R1);
02178         if (SCEVConstant *EvalVal = dyn_cast<SCEVConstant>(Val))
02179           if (EvalVal->getValue()->isNullValue())
02180             return R1;  // We found a quadratic root!
02181       }
02182     }
02183   }
02184 
02185   return UnknownValue;
02186 }
02187 
02188 /// HowFarToNonZero - Return the number of times a backedge checking the
02189 /// specified value for nonzero will execute.  If not computable, return
02190 /// UnknownValue
02191 SCEVHandle ScalarEvolutionsImpl::HowFarToNonZero(SCEV *V, const Loop *L) {
02192   // Loops that look like: while (X == 0) are very strange indeed.  We don't
02193   // handle them yet except for the trivial case.  This could be expanded in the
02194   // future as needed.
02195 
02196   // If the value is a constant, check to see if it is known to be non-zero
02197   // already.  If so, the backedge will execute zero times.
02198   if (SCEVConstant *C = dyn_cast<SCEVConstant>(V)) {
02199     Constant *Zero = Constant::getNullValue(C->getValue()->getType());
02200     Constant *NonZero = ConstantExpr::getSetNE(C->getValue(), Zero);
02201     if (NonZero == ConstantBool::True)
02202       return getSCEV(Zero);
02203     return UnknownValue;  // Otherwise it will loop infinitely.
02204   }
02205 
02206   // We could implement others, but I really doubt anyone writes loops like
02207   // this, and if they did, they would already be constant folded.
02208   return UnknownValue;
02209 }
02210 
02211 /// HowManyLessThans - Return the number of times a backedge containing the
02212 /// specified less-than comparison will execute.  If not computable, return
02213 /// UnknownValue.
02214 SCEVHandle ScalarEvolutionsImpl::
02215 HowManyLessThans(SCEV *LHS, SCEV *RHS, const Loop *L) {
02216   // Only handle:  "ADDREC < LoopInvariant".
02217   if (!RHS->isLoopInvariant(L)) return UnknownValue;
02218 
02219   SCEVAddRecExpr *AddRec = dyn_cast<SCEVAddRecExpr>(LHS);
02220   if (!AddRec || AddRec->getLoop() != L)
02221     return UnknownValue;
02222 
02223   if (AddRec->isAffine()) {
02224     // FORNOW: We only support unit strides.
02225     SCEVHandle One = SCEVUnknown::getIntegerSCEV(1, RHS->getType());
02226     if (AddRec->getOperand(1) != One)
02227       return UnknownValue;
02228 
02229     // The number of iterations for "[n,+,1] < m", is m-n.  However, we don't
02230     // know that m is >= n on input to the loop.  If it is, the condition return
02231     // true zero times.  What we really should return, for full generality, is
02232     // SMAX(0, m-n).  Since we cannot check this, we will instead check for a
02233     // canonical loop form: most do-loops will have a check that dominates the
02234     // loop, that only enters the loop if [n-1]<m.  If we can find this check,
02235     // we know that the SMAX will evaluate to m-n, because we know that m >= n.
02236 
02237     // Search for the check.
02238     BasicBlock *Preheader = L->getLoopPreheader();
02239     BasicBlock *PreheaderDest = L->getHeader();
02240     if (Preheader == 0) return UnknownValue;
02241 
02242     BranchInst *LoopEntryPredicate =
02243       dyn_cast<BranchInst>(Preheader->getTerminator());
02244     if (!LoopEntryPredicate) return UnknownValue;
02245 
02246     // This might be a critical edge broken out.  If the loop preheader ends in
02247     // an unconditional branch to the loop, check to see if the preheader has a
02248     // single predecessor, and if so, look for its terminator.
02249     while (LoopEntryPredicate->isUnconditional()) {
02250       PreheaderDest = Preheader;
02251       Preheader = Preheader->getSinglePredecessor();
02252       if (!Preheader) return UnknownValue;  // Multiple preds.
02253       
02254       LoopEntryPredicate =
02255         dyn_cast<BranchInst>(Preheader->getTerminator());
02256       if (!LoopEntryPredicate) return UnknownValue;
02257     }
02258 
02259     // Now that we found a conditional branch that dominates the loop, check to
02260     // see if it is the comparison we are looking for.
02261     SetCondInst *SCI =dyn_cast<SetCondInst>(LoopEntryPredicate->getCondition());
02262     if (!SCI) return UnknownValue;
02263     Value *PreCondLHS = SCI->getOperand(0);
02264     Value *PreCondRHS = SCI->getOperand(1);
02265     Instruction::BinaryOps Cond;
02266     if (LoopEntryPredicate->getSuccessor(0) == PreheaderDest)
02267       Cond = SCI->getOpcode();
02268     else
02269       Cond = SCI->getInverseCondition();
02270     
02271     switch (Cond) {
02272     case Instruction::SetGT:
02273       std::swap(PreCondLHS, PreCondRHS);
02274       Cond = Instruction::SetLT;
02275       // Fall Through.
02276     case Instruction::SetLT:
02277       if (PreCondLHS->getType()->isInteger() &&
02278           PreCondLHS->getType()->isSigned()) { 
02279         if (RHS != getSCEV(PreCondRHS))
02280           return UnknownValue;  // Not a comparison against 'm'.
02281 
02282         if (SCEV::getMinusSCEV(AddRec->getOperand(0), One)
02283                     != getSCEV(PreCondLHS))
02284           return UnknownValue;  // Not a comparison against 'n-1'.
02285         break;
02286       } else {
02287         return UnknownValue;
02288       }
02289     default: break;
02290     }
02291 
02292     //std::cerr << "Computed Loop Trip Count as: " <<
02293     //  *SCEV::getMinusSCEV(RHS, AddRec->getOperand(0)) << "\n";
02294     return SCEV::getMinusSCEV(RHS, AddRec->getOperand(0));
02295   }
02296 
02297   return UnknownValue;
02298 }
02299 
02300 /// getNumIterationsInRange - Return the number of iterations of this loop that
02301 /// produce values in the specified constant range.  Another way of looking at
02302 /// this is that it returns the first iteration number where the value is not in
02303 /// the condition, thus computing the exit count. If the iteration count can't
02304 /// be computed, an instance of SCEVCouldNotCompute is returned.
02305 SCEVHandle SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range) const {
02306   if (Range.isFullSet())  // Infinite loop.
02307     return new SCEVCouldNotCompute();
02308 
02309   // If the start is a non-zero constant, shift the range to simplify things.
02310   if (SCEVConstant *SC = dyn_cast<SCEVConstant>(getStart()))
02311     if (!SC->getValue()->isNullValue()) {
02312       std::vector<SCEVHandle> Operands(op_begin(), op_end());
02313       Operands[0] = SCEVUnknown::getIntegerSCEV(0, SC->getType());
02314       SCEVHandle Shifted = SCEVAddRecExpr::get(Operands, getLoop());
02315       if (SCEVAddRecExpr *ShiftedAddRec = dyn_cast<SCEVAddRecExpr>(Shifted))
02316         return ShiftedAddRec->getNumIterationsInRange(
02317                                               Range.subtract(SC->getValue()));
02318       // This is strange and shouldn't happen.
02319       return new SCEVCouldNotCompute();
02320     }
02321 
02322   // The only time we can solve this is when we have all constant indices.
02323   // Otherwise, we cannot determine the overflow conditions.
02324   for (unsigned i = 0, e = getNumOperands(); i != e; ++i)
02325     if (!isa<SCEVConstant>(getOperand(i)))
02326       return new SCEVCouldNotCompute();
02327 
02328 
02329   // Okay at this point we know that all elements of the chrec are constants and
02330   // that the start element is zero.
02331 
02332   // First check to see if the range contains zero.  If not, the first
02333   // iteration exits.
02334   ConstantInt *Zero = ConstantInt::get(getType(), 0);
02335   if (!Range.contains(Zero)) return SCEVConstant::get(Zero);
02336 
02337   if (isAffine()) {
02338     // If this is an affine expression then we have this situation:
02339     //   Solve {0,+,A} in Range  ===  Ax in Range
02340 
02341     // Since we know that zero is in the range, we know that the upper value of
02342     // the range must be the first possible exit value.  Also note that we
02343     // already checked for a full range.
02344     ConstantInt *Upper = cast<ConstantInt>(Range.getUpper());
02345     ConstantInt *A     = cast<SCEVConstant>(getOperand(1))->getValue();
02346     ConstantInt *One   = ConstantInt::get(getType(), 1);
02347 
02348     // The exit value should be (Upper+A-1)/A.
02349     Constant *ExitValue = Upper;
02350     if (A != One) {
02351       ExitValue = ConstantExpr::getSub(ConstantExpr::getAdd(Upper, A), One);
02352       ExitValue = ConstantExpr::getDiv(ExitValue, A);
02353     }
02354     assert(isa<ConstantInt>(ExitValue) &&
02355            "Constant folding of integers not implemented?");
02356 
02357     // Evaluate at the exit value.  If we really did fall out of the valid
02358     // range, then we computed our trip count, otherwise wrap around or other
02359     // things must have happened.
02360     ConstantInt *Val = EvaluateConstantChrecAtConstant(this, ExitValue);
02361     if (Range.contains(Val))
02362       return new SCEVCouldNotCompute();  // Something strange happened
02363 
02364     // Ensure that the previous value is in the range.  This is a sanity check.
02365     assert(Range.contains(EvaluateConstantChrecAtConstant(this,
02366                               ConstantExpr::getSub(ExitValue, One))) &&
02367            "Linear scev computation is off in a bad way!");
02368     return SCEVConstant::get(cast<ConstantInt>(ExitValue));
02369   } else if (isQuadratic()) {
02370     // If this is a quadratic (3-term) AddRec {L,+,M,+,N}, find the roots of the
02371     // quadratic equation to solve it.  To do this, we must frame our problem in
02372     // terms of figuring out when zero is crossed, instead of when
02373     // Range.getUpper() is crossed.
02374     std::vector<SCEVHandle> NewOps(op_begin(), op_end());
02375     NewOps[0] = SCEV::getNegativeSCEV(SCEVUnknown::get(Range.getUpper()));
02376     SCEVHandle NewAddRec = SCEVAddRecExpr::get(NewOps, getLoop());
02377 
02378     // Next, solve the constructed addrec
02379     std::pair<SCEVHandle,SCEVHandle> Roots =
02380       SolveQuadraticEquation(cast<SCEVAddRecExpr>(NewAddRec));
02381     SCEVConstant *R1 = dyn_cast<SCEVConstant>(Roots.first);
02382     SCEVConstant *R2 = dyn_cast<SCEVConstant>(Roots.second);
02383     if (R1) {
02384       // Pick the smallest positive root value.
02385       assert(R1->getType()->isUnsigned() && "Didn't canonicalize to unsigned?");
02386       if (ConstantBool *CB =
02387           dyn_cast<ConstantBool>(ConstantExpr::getSetLT(R1->getValue(),
02388                                                         R2->getValue()))) {
02389         if (CB != ConstantBool::True)
02390           std::swap(R1, R2);   // R1 is the minimum root now.
02391 
02392         // Make sure the root is not off by one.  The returned iteration should
02393         // not be in the range, but the previous one should be.  When solving
02394         // for "X*X < 5", for example, we should not return a root of 2.
02395         ConstantInt *R1Val = EvaluateConstantChrecAtConstant(this,
02396                                                              R1->getValue());
02397         if (Range.contains(R1Val)) {
02398           // The next iteration must be out of the range...
02399           Constant *NextVal =
02400             ConstantExpr::getAdd(R1->getValue(),
02401                                  ConstantInt::get(R1->getType(), 1));
02402 
02403           R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
02404           if (!Range.contains(R1Val))
02405             return SCEVUnknown::get(NextVal);
02406           return new SCEVCouldNotCompute();  // Something strange happened
02407         }
02408 
02409         // If R1 was not in the range, then it is a good return value.  Make
02410         // sure that R1-1 WAS in the range though, just in case.
02411         Constant *NextVal =
02412           ConstantExpr::getSub(R1->getValue(),
02413                                ConstantInt::get(R1->getType(), 1));
02414         R1Val = EvaluateConstantChrecAtConstant(this, NextVal);
02415         if (Range.contains(R1Val))
02416           return R1;
02417         return new SCEVCouldNotCompute();  // Something strange happened
02418       }
02419     }
02420   }
02421 
02422   // Fallback, if this is a general polynomial, figure out the progression
02423   // through brute force: evaluate until we find an iteration that fails the
02424   // test.  This is likely to be slow, but getting an accurate trip count is
02425   // incredibly important, we will be able to simplify the exit test a lot, and
02426   // we are almost guaranteed to get a trip count in this case.
02427   ConstantInt *TestVal = ConstantInt::get(getType(), 0);
02428   ConstantInt *One     = ConstantInt::get(getType(), 1);
02429   ConstantInt *EndVal  = TestVal;  // Stop when we wrap around.
02430   do {
02431     ++NumBruteForceEvaluations;
02432     SCEVHandle Val = evaluateAtIteration(SCEVConstant::get(TestVal));
02433     if (!isa<SCEVConstant>(Val))  // This shouldn't happen.
02434       return new SCEVCouldNotCompute();
02435 
02436     // Check to see if we found the value!
02437     if (!Range.contains(cast<SCEVConstant>(Val)->getValue()))
02438       return SCEVConstant::get(TestVal);
02439 
02440     // Increment to test the next index.
02441     TestVal = cast<ConstantInt>(ConstantExpr::getAdd(TestVal, One));
02442   } while (TestVal != EndVal);
02443 
02444   return new SCEVCouldNotCompute();
02445 }
02446 
02447 
02448 
02449 //===----------------------------------------------------------------------===//
02450 //                   ScalarEvolution Class Implementation
02451 //===----------------------------------------------------------------------===//
02452 
02453 bool ScalarEvolution::runOnFunction(Function &F) {
02454   Impl = new ScalarEvolutionsImpl(F, getAnalysis<LoopInfo>());
02455   return false;
02456 }
02457 
02458 void ScalarEvolution::releaseMemory() {
02459   delete (ScalarEvolutionsImpl*)Impl;
02460   Impl = 0;
02461 }
02462 
02463 void ScalarEvolution::getAnalysisUsage(AnalysisUsage &AU) const {
02464   AU.setPreservesAll();
02465   AU.addRequiredTransitive<LoopInfo>();
02466 }
02467 
02468 SCEVHandle ScalarEvolution::getSCEV(Value *V) const {
02469   return ((ScalarEvolutionsImpl*)Impl)->getSCEV(V);
02470 }
02471 
02472 /// hasSCEV - Return true if the SCEV for this value has already been
02473 /// computed.
02474 bool ScalarEvolution::hasSCEV(Value *V) const {
02475   return ((ScalarEvolutionsImpl*)Impl)->hasSCEV(V);
02476 }
02477 
02478 
02479 /// setSCEV - Insert the specified SCEV into the map of current SCEVs for
02480 /// the specified value.
02481 void ScalarEvolution::setSCEV(Value *V, const SCEVHandle &H) {
02482   ((ScalarEvolutionsImpl*)Impl)->setSCEV(V, H);
02483 }
02484 
02485 
02486 SCEVHandle ScalarEvolution::getIterationCount(const Loop *L) const {
02487   return ((ScalarEvolutionsImpl*)Impl)->getIterationCount(L);
02488 }
02489 
02490 bool ScalarEvolution::hasLoopInvariantIterationCount(const Loop *L) const {
02491   return !isa<SCEVCouldNotCompute>(getIterationCount(L));
02492 }
02493 
02494 SCEVHandle ScalarEvolution::getSCEVAtScope(Value *V, const Loop *L) const {
02495   return ((ScalarEvolutionsImpl*)Impl)->getSCEVAtScope(getSCEV(V), L);
02496 }
02497 
02498 void ScalarEvolution::deleteInstructionFromRecords(Instruction *I) const {
02499   return ((ScalarEvolutionsImpl*)Impl)->deleteInstructionFromRecords(I);
02500 }
02501 
02502 static void PrintLoopInfo(std::ostream &OS, const ScalarEvolution *SE,
02503                           const Loop *L) {
02504   // Print all inner loops first
02505   for (Loop::iterator I = L->begin(), E = L->end(); I != E; ++I)
02506     PrintLoopInfo(OS, SE, *I);
02507 
02508   std::cerr << "Loop " << L->getHeader()->getName() << ": ";
02509 
02510   std::vector<BasicBlock*> ExitBlocks;
02511   L->getExitBlocks(ExitBlocks);
02512   if (ExitBlocks.size() != 1)
02513     std::cerr << "<multiple exits> ";
02514 
02515   if (SE->hasLoopInvariantIterationCount(L)) {
02516     std::cerr << *SE->getIterationCount(L) << " iterations! ";
02517   } else {
02518     std::cerr << "Unpredictable iteration count. ";
02519   }
02520 
02521   std::cerr << "\n";
02522 }
02523 
02524 void ScalarEvolution::print(std::ostream &OS, const Module* ) const {
02525   Function &F = ((ScalarEvolutionsImpl*)Impl)->F;
02526   LoopInfo &LI = ((ScalarEvolutionsImpl*)Impl)->LI;
02527 
02528   OS << "Classifying expressions for: " << F.getName() << "\n";
02529   for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I)
02530     if (I->getType()->isInteger()) {
02531       OS << *I;
02532       OS << "  --> ";
02533       SCEVHandle SV = getSCEV(&*I);
02534       SV->print(OS);
02535       OS << "\t\t";
02536 
02537       if ((*I).getType()->isIntegral()) {
02538         ConstantRange Bounds = SV->getValueRange();
02539         if (!Bounds.isFullSet())
02540           OS << "Bounds: " << Bounds << " ";
02541       }
02542 
02543       if (const Loop *L = LI.getLoopFor((*I).getParent())) {
02544         OS << "Exits: ";
02545         SCEVHandle ExitValue = getSCEVAtScope(&*I, L->getParentLoop());
02546         if (isa<SCEVCouldNotCompute>(ExitValue)) {
02547           OS << "<<Unknown>>";
02548         } else {
02549           OS << *ExitValue;
02550         }
02551       }
02552 
02553 
02554       OS << "\n";
02555     }
02556 
02557   OS << "Determining loop execution counts for: " << F.getName() << "\n";
02558   for (LoopInfo::iterator I = LI.begin(), E = LI.end(); I != E; ++I)
02559     PrintLoopInfo(OS, this, *I);
02560 }
02561