lib/Analysis/ScalarEvolutionExpander.cpp

   1 //===- ScalarEvolutionExpander.cpp - Scalar Evolution Analysis --*- C++ -*-===//
   2 //
   3 //                     The LLVM Compiler Infrastructure
   4 //
   5 // This file is distributed under the University of Illinois Open Source
   6 // License. See LICENSE.TXT for details.
   7 //
   8 //===----------------------------------------------------------------------===//
   9 //
  10 // This file contains the implementation of the scalar evolution expander,
  11 // which is used to generate the code corresponding to a given scalar evolution
  12 // expression.
  13 //
  14 //===----------------------------------------------------------------------===//
  15
  16 #include "llvm/Analysis/ScalarEvolutionExpander.h"
  17 #include "llvm/Analysis/LoopInfo.h"
  18 #include "llvm/LLVMContext.h"
  19 #include "llvm/Target/TargetData.h"
  20 #include "llvm/ADT/STLExtras.h"
  21 using namespace llvm;
  22
  23 /// InsertNoopCastOfTo - Insert a cast of V to the specified type,
  24 /// which must be possible with a noop cast, doing what we can to share
  25 /// the casts.
  26 Value *SCEVExpander::InsertNoopCastOfTo(Value *V, const Type *Ty) {
  27   Instruction::CastOps Op = CastInst::getCastOpcode(V, false, Ty, false);
  28   assert((Op == Instruction::BitCast ||
  29           Op == Instruction::PtrToInt ||
  30           Op == Instruction::IntToPtr) &&
  31          "InsertNoopCastOfTo cannot perform non-noop casts!");
  32   assert(SE.getTypeSizeInBits(V->getType()) == SE.getTypeSizeInBits(Ty) &&
  33          "InsertNoopCastOfTo cannot change sizes!");
  34
  35   // Short-circuit unnecessary bitcasts.
  36   if (Op == Instruction::BitCast && V->getType() == Ty)
  37     return V;
  38
  39   // Short-circuit unnecessary inttoptr<->ptrtoint casts.
  40   if ((Op == Instruction::PtrToInt || Op == Instruction::IntToPtr) &&
  41       SE.getTypeSizeInBits(Ty) == SE.getTypeSizeInBits(V->getType())) {
  42     if (CastInst *CI = dyn_cast<CastInst>(V))
  43       if ((CI->getOpcode() == Instruction::PtrToInt ||
  44            CI->getOpcode() == Instruction::IntToPtr) &&
  45           SE.getTypeSizeInBits(CI->getType()) ==
  46           SE.getTypeSizeInBits(CI->getOperand(0)->getType()))
  47         return CI->getOperand(0);
  48     if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
  49       if ((CE->getOpcode() == Instruction::PtrToInt ||
  50            CE->getOpcode() == Instruction::IntToPtr) &&
  51           SE.getTypeSizeInBits(CE->getType()) ==
  52           SE.getTypeSizeInBits(CE->getOperand(0)->getType()))
  53         return CE->getOperand(0);
  54   }
  55
  56   // FIXME: keep track of the cast instruction.
  57   if (Constant *C = dyn_cast<Constant>(V))
  58     return getContext().getConstantExprCast(Op, C, Ty);
  59
  60   if (Argument *A = dyn_cast<Argument>(V)) {
  61     // Check to see if there is already a cast!
  62     for (Value::use_iterator UI = A->use_begin(), E = A->use_end();
  63          UI != E; ++UI)
  64       if ((*UI)->getType() == Ty)
  65         if (CastInst *CI = dyn_cast<CastInst>(cast<Instruction>(*UI)))
  66           if (CI->getOpcode() == Op) {
  67             // If the cast isn't the first instruction of the function, move it.
  68             if (BasicBlock::iterator(CI) !=
  69                 A->getParent()->getEntryBlock().begin()) {
  70               // Recreate the cast at the beginning of the entry block.
  71               // The old cast is left in place in case it is being used
  72               // as an insert point.
  73               Instruction *NewCI =
  74                 CastInst::Create(Op, V, Ty, "",
  75                                  A->getParent()->getEntryBlock().begin());
  76               NewCI->takeName(CI);
  77               CI->replaceAllUsesWith(NewCI);
  78               return NewCI;
  79             }
  80             return CI;
  81           }
  82
  83     Instruction *I = CastInst::Create(Op, V, Ty, V->getName(),
  84                                       A->getParent()->getEntryBlock().begin());
  85     InsertedValues.insert(I);
  86     return I;
  87   }
  88
  89   Instruction *I = cast<Instruction>(V);
  90
  91   // Check to see if there is already a cast.  If there is, use it.
  92   for (Value::use_iterator UI = I->use_begin(), E = I->use_end();
  93        UI != E; ++UI) {
  94     if ((*UI)->getType() == Ty)
  95       if (CastInst *CI = dyn_cast<CastInst>(cast<Instruction>(*UI)))
  96         if (CI->getOpcode() == Op) {
  97           BasicBlock::iterator It = I; ++It;
  98           if (isa<InvokeInst>(I))
  99             It = cast<InvokeInst>(I)->getNormalDest()->begin();
 100           while (isa<PHINode>(It)) ++It;
 101           if (It != BasicBlock::iterator(CI)) {
 102             // Recreate the cast at the beginning of the entry block.
 103             // The old cast is left in place in case it is being used
 104             // as an insert point.
 105             Instruction *NewCI = CastInst::Create(Op, V, Ty, "", It);
 106             NewCI->takeName(CI);
 107             CI->replaceAllUsesWith(NewCI);
 108             return NewCI;
 109           }
 110           return CI;
 111         }
 112   }
 113   BasicBlock::iterator IP = I; ++IP;
 114   if (InvokeInst *II = dyn_cast<InvokeInst>(I))
 115     IP = II->getNormalDest()->begin();
 116   while (isa<PHINode>(IP)) ++IP;
 117   Instruction *CI = CastInst::Create(Op, V, Ty, V->getName(), IP);
 118   InsertedValues.insert(CI);
 119   return CI;
 120 }
 121
 122 /// InsertBinop - Insert the specified binary operator, doing a small amount
 123 /// of work to avoid inserting an obviously redundant operation.
 124 Value *SCEVExpander::InsertBinop(Instruction::BinaryOps Opcode,
 125                                  Value *LHS, Value *RHS) {
 126   // Fold a binop with constant operands.
 127   if (Constant *CLHS = dyn_cast<Constant>(LHS))
 128     if (Constant *CRHS = dyn_cast<Constant>(RHS))
 129       return getContext().getConstantExpr(Opcode, CLHS, CRHS);
 130
 131   // Do a quick scan to see if we have this binop nearby.  If so, reuse it.
 132   unsigned ScanLimit = 6;
 133   BasicBlock::iterator BlockBegin = Builder.GetInsertBlock()->begin();
 134   // Scanning starts from the last instruction before the insertion point.
 135   BasicBlock::iterator IP = Builder.GetInsertPoint();
 136   if (IP != BlockBegin) {
 137     --IP;
 138     for (; ScanLimit; --IP, --ScanLimit) {
 139       if (IP->getOpcode() == (unsigned)Opcode && IP->getOperand(0) == LHS &&
 140           IP->getOperand(1) == RHS)
 141         return IP;
 142       if (IP == BlockBegin) break;
 143     }
 144   }
 145
 146   // If we haven't found this binop, insert it.
 147   Value *BO = Builder.CreateBinOp(Opcode, LHS, RHS, "tmp");
 148   InsertedValues.insert(BO);
 149   return BO;
 150 }
 151
 152 /// FactorOutConstant - Test if S is divisible by Factor, using signed
 153 /// division. If so, update S with Factor divided out and return true.
 154 /// S need not be evenly divisble if a reasonable remainder can be
 155 /// computed.
 156 /// TODO: When ScalarEvolution gets a SCEVSDivExpr, this can be made
 157 /// unnecessary; in its place, just signed-divide Ops[i] by the scale and
 158 /// check to see if the divide was folded.
 159 static bool FactorOutConstant(const SCEV *&S,
 160                               const SCEV *&Remainder,
 161                               const APInt &Factor,
 162                               ScalarEvolution &SE) {
 163   // Everything is divisible by one.
 164   if (Factor == 1)
 165     return true;
 166
 167   // For a Constant, check for a multiple of the given factor.
 168   if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
 169     ConstantInt *CI =
 170       ConstantInt::get(SE.getContext(), C->getValue()->getValue().sdiv(Factor));
 171     // If the quotient is zero and the remainder is non-zero, reject
 172     // the value at this scale. It will be considered for subsequent
 173     // smaller scales.
 174     if (C->isZero() || !CI->isZero()) {
 175       const SCEV *Div = SE.getConstant(CI);
 176       S = Div;
 177       Remainder =
 178         SE.getAddExpr(Remainder,
 179                       SE.getConstant(C->getValue()->getValue().srem(Factor)));
 180       return true;
 181     }
 182   }
 183
 184   // In a Mul, check if there is a constant operand which is a multiple
 185   // of the given factor.
 186   if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S))
 187     if (const SCEVConstant *C = dyn_cast<SCEVConstant>(M->getOperand(0)))
 188       if (!C->getValue()->getValue().srem(Factor)) {
 189         const SmallVectorImpl<const SCEV *> &MOperands = M->getOperands();
 190         SmallVector<const SCEV *, 4> NewMulOps(MOperands.begin(),
 191                                                MOperands.end());
 192         NewMulOps[0] =
 193           SE.getConstant(C->getValue()->getValue().sdiv(Factor));
 194         S = SE.getMulExpr(NewMulOps);
 195         return true;
 196       }
 197
 198   // In an AddRec, check if both start and step are divisible.
 199   if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
 200     const SCEV *Step = A->getStepRecurrence(SE);
 201     const SCEV *StepRem = SE.getIntegerSCEV(0, Step->getType());
 202     if (!FactorOutConstant(Step, StepRem, Factor, SE))
 203       return false;
 204     if (!StepRem->isZero())
 205       return false;
 206     const SCEV *Start = A->getStart();
 207     if (!FactorOutConstant(Start, Remainder, Factor, SE))
 208       return false;
 209     S = SE.getAddRecExpr(Start, Step, A->getLoop());
 210     return true;
 211   }
 212
 213   return false;
 214 }
 215
 216 /// expandAddToGEP - Expand a SCEVAddExpr with a pointer type into a GEP
 217 /// instead of using ptrtoint+arithmetic+inttoptr. This helps
 218 /// BasicAliasAnalysis analyze the result.
 219 ///
 220 /// Design note: This depends on ScalarEvolution not recognizing inttoptr
 221 /// and ptrtoint operators, as they may introduce pointer arithmetic
 222 /// which may not be safely converted into getelementptr.
 223 ///
 224 /// Design note: It might seem desirable for this function to be more
 225 /// loop-aware. If some of the indices are loop-invariant while others
 226 /// aren't, it might seem desirable to emit multiple GEPs, keeping the
 227 /// loop-invariant portions of the overall computation outside the loop.
 228 /// However, there are a few reasons this is not done here. Hoisting simple
 229 /// arithmetic is a low-level optimization that often isn't very
 230 /// important until late in the optimization process. In fact, passes
 231 /// like InstructionCombining will combine GEPs, even if it means
 232 /// pushing loop-invariant computation down into loops, so even if the
 233 /// GEPs were split here, the work would quickly be undone. The
 234 /// LoopStrengthReduction pass, which is usually run quite late (and
 235 /// after the last InstructionCombining pass), takes care of hoisting
 236 /// loop-invariant portions of expressions, after considering what
 237 /// can be folded using target addressing modes.
 238 ///
 239 Value *SCEVExpander::expandAddToGEP(const SCEV *const *op_begin,
 240                                     const SCEV *const *op_end,
 241                                     const PointerType *PTy,
 242                                     const Type *Ty,
 243                                     Value *V) {
 244   const Type *ElTy = PTy->getElementType();
 245   SmallVector<Value *, 4> GepIndices;
 246   SmallVector<const SCEV *, 8> Ops(op_begin, op_end);
 247   bool AnyNonZeroIndices = false;
 248
 249   // Decend down the pointer's type and attempt to convert the other
 250   // operands into GEP indices, at each level. The first index in a GEP
 251   // indexes into the array implied by the pointer operand; the rest of
 252   // the indices index into the element or field type selected by the
 253   // preceding index.
 254   for (;;) {
 255     APInt ElSize = APInt(SE.getTypeSizeInBits(Ty),
 256                          ElTy->isSized() ?  SE.TD->getTypeAllocSize(ElTy) : 0);
 257     SmallVector<const SCEV *, 8> NewOps;
 258     SmallVector<const SCEV *, 8> ScaledOps;
 259     for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
 260       // Split AddRecs up into parts as either of the parts may be usable
 261       // without the other.
 262       if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(Ops[i]))
 263         if (!A->getStart()->isZero()) {
 264           const SCEV *Start = A->getStart();
 265           Ops.push_back(SE.getAddRecExpr(SE.getIntegerSCEV(0, A->getType()),
 266                                          A->getStepRecurrence(SE),
 267                                          A->getLoop()));
 268           Ops[i] = Start;
 269           ++e;
 270         }
 271       // If the scale size is not 0, attempt to factor out a scale.
 272       if (ElSize != 0) {
 273         const SCEV *Op = Ops[i];
 274         const SCEV *Remainder = SE.getIntegerSCEV(0, Op->getType());
 275         if (FactorOutConstant(Op, Remainder, ElSize, SE)) {
 276           ScaledOps.push_back(Op); // Op now has ElSize factored out.
 277           NewOps.push_back(Remainder);
 278           continue;
 279         }
 280       }
 281       // If the operand was not divisible, add it to the list of operands
 282       // we'll scan next iteration.
 283       NewOps.push_back(Ops[i]);
 284     }
 285     Ops = NewOps;
 286     AnyNonZeroIndices |= !ScaledOps.empty();
 287     Value *Scaled = ScaledOps.empty() ?
 288                     getContext().getNullValue(Ty) :
 289                     expandCodeFor(SE.getAddExpr(ScaledOps), Ty);
 290     GepIndices.push_back(Scaled);
 291
 292     // Collect struct field index operands.
 293     if (!Ops.empty())
 294       while (const StructType *STy = dyn_cast<StructType>(ElTy)) {
 295         if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[0]))
 296           if (SE.getTypeSizeInBits(C->getType()) <= 64) {
 297             const StructLayout &SL = *SE.TD->getStructLayout(STy);
 298             uint64_t FullOffset = C->getValue()->getZExtValue();
 299             if (FullOffset < SL.getSizeInBytes()) {
 300               unsigned ElIdx = SL.getElementContainingOffset(FullOffset);
 301               GepIndices.push_back(ConstantInt::get(Type::Int32Ty, ElIdx));
 302               ElTy = STy->getTypeAtIndex(ElIdx);
 303               Ops[0] =
 304                 SE.getConstant(Ty, FullOffset - SL.getElementOffset(ElIdx));
 305               AnyNonZeroIndices = true;
 306               continue;
 307             }
 308           }
 309         break;
 310       }
 311
 312     if (const ArrayType *ATy = dyn_cast<ArrayType>(ElTy)) {
 313       ElTy = ATy->getElementType();
 314       continue;
 315     }
 316     break;
 317   }
 318
 319   // If none of the operands were convertable to proper GEP indices, cast
 320   // the base to i8* and do an ugly getelementptr with that. It's still
 321   // better than ptrtoint+arithmetic+inttoptr at least.
 322   if (!AnyNonZeroIndices) {
 323     V = InsertNoopCastOfTo(V,
 324                            Type::Int8Ty->getPointerTo(PTy->getAddressSpace()));
 325     Value *Idx = expandCodeFor(SE.getAddExpr(Ops), Ty);
 326
 327     // Fold a GEP with constant operands.
 328     if (Constant *CLHS = dyn_cast<Constant>(V))
 329       if (Constant *CRHS = dyn_cast<Constant>(Idx))
 330         return getContext().getConstantExprGetElementPtr(CLHS, &CRHS, 1);
 331
 332     // Do a quick scan to see if we have this GEP nearby.  If so, reuse it.
 333     unsigned ScanLimit = 6;
 334     BasicBlock::iterator BlockBegin = Builder.GetInsertBlock()->begin();
 335     // Scanning starts from the last instruction before the insertion point.
 336     BasicBlock::iterator IP = Builder.GetInsertPoint();
 337     if (IP != BlockBegin) {
 338       --IP;
 339       for (; ScanLimit; --IP, --ScanLimit) {
 340         if (IP->getOpcode() == Instruction::GetElementPtr &&
 341             IP->getOperand(0) == V && IP->getOperand(1) == Idx)
 342           return IP;
 343         if (IP == BlockBegin) break;
 344       }
 345     }
 346
 347     Value *GEP = Builder.CreateGEP(V, Idx, "scevgep");
 348     InsertedValues.insert(GEP);
 349     return GEP;
 350   }
 351
 352   // Insert a pretty getelementptr.
 353   Value *GEP = Builder.CreateGEP(V,
 354                                  GepIndices.begin(),
 355                                  GepIndices.end(),
 356                                  "scevgep");
 357   Ops.push_back(SE.getUnknown(GEP));
 358   InsertedValues.insert(GEP);
 359   return expand(SE.getAddExpr(Ops));
 360 }
 361
 362 Value *SCEVExpander::visitAddExpr(const SCEVAddExpr *S) {
 363   const Type *Ty = SE.getEffectiveSCEVType(S->getType());
 364   Value *V = expand(S->getOperand(S->getNumOperands()-1));
 365
 366   // Turn things like ptrtoint+arithmetic+inttoptr into GEP. See the
 367   // comments on expandAddToGEP for details.
 368   if (SE.TD)
 369     if (const PointerType *PTy = dyn_cast<PointerType>(V->getType())) {
 370       const SmallVectorImpl<const SCEV *> &Ops = S->getOperands();
 371       return expandAddToGEP(&Ops[0], &Ops[Ops.size() - 1], PTy, Ty, V);
 372     }
 373
 374   V = InsertNoopCastOfTo(V, Ty);
 375
 376   // Emit a bunch of add instructions
 377   for (int i = S->getNumOperands()-2; i >= 0; --i) {
 378     Value *W = expandCodeFor(S->getOperand(i), Ty);
 379     V = InsertBinop(Instruction::Add, V, W);
 380   }
 381   return V;
 382 }
 383
 384 Value *SCEVExpander::visitMulExpr(const SCEVMulExpr *S) {
 385   const Type *Ty = SE.getEffectiveSCEVType(S->getType());
 386   int FirstOp = 0;  // Set if we should emit a subtract.
 387   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(S->getOperand(0)))
 388     if (SC->getValue()->isAllOnesValue())
 389       FirstOp = 1;
 390
 391   int i = S->getNumOperands()-2;
 392   Value *V = expandCodeFor(S->getOperand(i+1), Ty);
 393
 394   // Emit a bunch of multiply instructions
 395   for (; i >= FirstOp; --i) {
 396     Value *W = expandCodeFor(S->getOperand(i), Ty);
 397     V = InsertBinop(Instruction::Mul, V, W);
 398   }
 399
 400   // -1 * ...  --->  0 - ...
 401   if (FirstOp == 1)
 402     V = InsertBinop(Instruction::Sub, getContext().getNullValue(Ty), V);
 403   return V;
 404 }
 405
 406 Value *SCEVExpander::visitUDivExpr(const SCEVUDivExpr *S) {
 407   const Type *Ty = SE.getEffectiveSCEVType(S->getType());
 408
 409   Value *LHS = expandCodeFor(S->getLHS(), Ty);
 410   if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(S->getRHS())) {
 411     const APInt &RHS = SC->getValue()->getValue();
 412     if (RHS.isPowerOf2())
 413       return InsertBinop(Instruction::LShr, LHS,
 414                          ConstantInt::get(Ty, RHS.logBase2()));
 415   }
 416
 417   Value *RHS = expandCodeFor(S->getRHS(), Ty);
 418   return InsertBinop(Instruction::UDiv, LHS, RHS);
 419 }
 420
 421 /// Move parts of Base into Rest to leave Base with the minimal
 422 /// expression that provides a pointer operand suitable for a
 423 /// GEP expansion.
 424 static void ExposePointerBase(const SCEV *&Base, const SCEV *&Rest,
 425                               ScalarEvolution &SE) {
 426   while (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(Base)) {
 427     Base = A->getStart();
 428     Rest = SE.getAddExpr(Rest,
 429                          SE.getAddRecExpr(SE.getIntegerSCEV(0, A->getType()),
 430                                           A->getStepRecurrence(SE),
 431                                           A->getLoop()));
 432   }
 433   if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(Base)) {
 434     Base = A->getOperand(A->getNumOperands()-1);
 435     SmallVector<const SCEV *, 8> NewAddOps(A->op_begin(), A->op_end());
 436     NewAddOps.back() = Rest;
 437     Rest = SE.getAddExpr(NewAddOps);
 438     ExposePointerBase(Base, Rest, SE);
 439   }
 440 }
 441
 442 Value *SCEVExpander::visitAddRecExpr(const SCEVAddRecExpr *S) {
 443   const Type *Ty = SE.getEffectiveSCEVType(S->getType());
 444   const Loop *L = S->getLoop();
 445
 446   // First check for an existing canonical IV in a suitable type.
 447   PHINode *CanonicalIV = 0;
 448   if (PHINode *PN = L->getCanonicalInductionVariable())
 449     if (SE.isSCEVable(PN->getType()) &&
 450         isa<IntegerType>(SE.getEffectiveSCEVType(PN->getType())) &&
 451         SE.getTypeSizeInBits(PN->getType()) >= SE.getTypeSizeInBits(Ty))
 452       CanonicalIV = PN;
 453
 454   // Rewrite an AddRec in terms of the canonical induction variable, if
 455   // its type is more narrow.
 456   if (CanonicalIV &&
 457       SE.getTypeSizeInBits(CanonicalIV->getType()) >
 458       SE.getTypeSizeInBits(Ty)) {
 459     const SCEV *Start = SE.getAnyExtendExpr(S->getStart(),
 460                                             CanonicalIV->getType());
 461     const SCEV *Step = SE.getAnyExtendExpr(S->getStepRecurrence(SE),
 462                                            CanonicalIV->getType());
 463     Value *V = expand(SE.getAddRecExpr(Start, Step, S->getLoop()));
 464     BasicBlock *SaveInsertBB = Builder.GetInsertBlock();
 465     BasicBlock::iterator SaveInsertPt = Builder.GetInsertPoint();
 466     BasicBlock::iterator NewInsertPt =
 467       next(BasicBlock::iterator(cast<Instruction>(V)));
 468     while (isa<PHINode>(NewInsertPt)) ++NewInsertPt;
 469     V = expandCodeFor(SE.getTruncateExpr(SE.getUnknown(V), Ty), 0,
 470                       NewInsertPt);
 471     Builder.SetInsertPoint(SaveInsertBB, SaveInsertPt);
 472     return V;
 473   }
 474
 475   // {X,+,F} --> X + {0,+,F}
 476   if (!S->getStart()->isZero()) {
 477     const SmallVectorImpl<const SCEV *> &SOperands = S->getOperands();
 478     SmallVector<const SCEV *, 4> NewOps(SOperands.begin(), SOperands.end());
 479     NewOps[0] = SE.getIntegerSCEV(0, Ty);
 480     const SCEV *Rest = SE.getAddRecExpr(NewOps, L);
 481
 482     // Turn things like ptrtoint+arithmetic+inttoptr into GEP. See the
 483     // comments on expandAddToGEP for details.
 484     if (SE.TD) {
 485       const SCEV *Base = S->getStart();
 486       const SCEV *RestArray[1] = { Rest };
 487       // Dig into the expression to find the pointer base for a GEP.
 488       ExposePointerBase(Base, RestArray[0], SE);
 489       // If we found a pointer, expand the AddRec with a GEP.
 490       if (const PointerType *PTy = dyn_cast<PointerType>(Base->getType())) {
 491         // Make sure the Base isn't something exotic, such as a multiplied
 492         // or divided pointer value. In those cases, the result type isn't
 493         // actually a pointer type.
 494         if (!isa<SCEVMulExpr>(Base) && !isa<SCEVUDivExpr>(Base)) {
 495           Value *StartV = expand(Base);
 496           assert(StartV->getType() == PTy && "Pointer type mismatch for GEP!");
 497           return expandAddToGEP(RestArray, RestArray+1, PTy, Ty, StartV);
 498         }
 499       }
 500     }
 501
 502     // Just do a normal add. Pre-expand the operands to suppress folding.
 503     return expand(SE.getAddExpr(SE.getUnknown(expand(S->getStart())),
 504                                 SE.getUnknown(expand(Rest))));
 505   }
 506
 507   // {0,+,1} --> Insert a canonical induction variable into the loop!
 508   if (S->isAffine() &&
 509       S->getOperand(1) == SE.getIntegerSCEV(1, Ty)) {
 510     // If there's a canonical IV, just use it.
 511     if (CanonicalIV) {
 512       assert(Ty == SE.getEffectiveSCEVType(CanonicalIV->getType()) &&
 513              "IVs with types different from the canonical IV should "
 514              "already have been handled!");
 515       return CanonicalIV;
 516     }
 517
 518     // Create and insert the PHI node for the induction variable in the
 519     // specified loop.
 520     BasicBlock *Header = L->getHeader();
 521     BasicBlock *Preheader = L->getLoopPreheader();
 522     PHINode *PN = PHINode::Create(Ty, "indvar", Header->begin());
 523     InsertedValues.insert(PN);
 524     PN->addIncoming(getContext().getNullValue(Ty), Preheader);
 525
 526     pred_iterator HPI = pred_begin(Header);
 527     assert(HPI != pred_end(Header) && "Loop with zero preds???");
 528     if (!L->contains(*HPI)) ++HPI;
 529     assert(HPI != pred_end(Header) && L->contains(*HPI) &&
 530            "No backedge in loop?");
 531
 532     // Insert a unit add instruction right before the terminator corresponding
 533     // to the back-edge.
 534     Constant *One = ConstantInt::get(Ty, 1);
 535     Instruction *Add = BinaryOperator::CreateAdd(PN, One, "indvar.next",
 536                                                  (*HPI)->getTerminator());
 537     InsertedValues.insert(Add);
 538
 539     pred_iterator PI = pred_begin(Header);
 540     if (*PI == Preheader)
 541       ++PI;
 542     PN->addIncoming(Add, *PI);
 543     return PN;
 544   }
 545
 546   // {0,+,F} --> {0,+,1} * F
 547   // Get the canonical induction variable I for this loop.
 548   Value *I = CanonicalIV ?
 549              CanonicalIV :
 550              getOrInsertCanonicalInductionVariable(L, Ty);
 551
 552   // If this is a simple linear addrec, emit it now as a special case.
 553   if (S->isAffine())    // {0,+,F} --> i*F
 554     return
 555       expand(SE.getTruncateOrNoop(
 556         SE.getMulExpr(SE.getUnknown(I),
 557                       SE.getNoopOrAnyExtend(S->getOperand(1),
 558                                             I->getType())),
 559         Ty));
 560
 561   // If this is a chain of recurrences, turn it into a closed form, using the
 562   // folders, then expandCodeFor the closed form.  This allows the folders to
 563   // simplify the expression without having to build a bunch of special code
 564   // into this folder.
 565   const SCEV *IH = SE.getUnknown(I);   // Get I as a "symbolic" SCEV.
 566
 567   // Promote S up to the canonical IV type, if the cast is foldable.
 568   const SCEV *NewS = S;
 569   const SCEV *Ext = SE.getNoopOrAnyExtend(S, I->getType());
 570   if (isa<SCEVAddRecExpr>(Ext))
 571     NewS = Ext;
 572
 573   const SCEV *V = cast<SCEVAddRecExpr>(NewS)->evaluateAtIteration(IH, SE);
 574   //cerr << "Evaluated: " << *this << "\n     to: " << *V << "\n";
 575
 576   // Truncate the result down to the original type, if needed.
 577   const SCEV *T = SE.getTruncateOrNoop(V, Ty);
 578   return expand(T);
 579 }
 580
 581 Value *SCEVExpander::visitTruncateExpr(const SCEVTruncateExpr *S) {
 582   const Type *Ty = SE.getEffectiveSCEVType(S->getType());
 583   Value *V = expandCodeFor(S->getOperand(),
 584                            SE.getEffectiveSCEVType(S->getOperand()->getType()));
 585   Value *I = Builder.CreateTrunc(V, Ty, "tmp");
 586   InsertedValues.insert(I);
 587   return I;
 588 }
 589
 590 Value *SCEVExpander::visitZeroExtendExpr(const SCEVZeroExtendExpr *S) {
 591   const Type *Ty = SE.getEffectiveSCEVType(S->getType());
 592   Value *V = expandCodeFor(S->getOperand(),
 593                            SE.getEffectiveSCEVType(S->getOperand()->getType()));
 594   Value *I = Builder.CreateZExt(V, Ty, "tmp");
 595   InsertedValues.insert(I);
 596   return I;
 597 }
 598
 599 Value *SCEVExpander::visitSignExtendExpr(const SCEVSignExtendExpr *S) {
 600   const Type *Ty = SE.getEffectiveSCEVType(S->getType());
 601   Value *V = expandCodeFor(S->getOperand(),
 602                            SE.getEffectiveSCEVType(S->getOperand()->getType()));
 603   Value *I = Builder.CreateSExt(V, Ty, "tmp");
 604   InsertedValues.insert(I);
 605   return I;
 606 }
 607
 608 Value *SCEVExpander::visitSMaxExpr(const SCEVSMaxExpr *S) {
 609   Value *LHS = expand(S->getOperand(S->getNumOperands()-1));
 610   const Type *Ty = LHS->getType();
 611   for (int i = S->getNumOperands()-2; i >= 0; --i) {
 612     // In the case of mixed integer and pointer types, do the
 613     // rest of the comparisons as integer.
 614     if (S->getOperand(i)->getType() != Ty) {
 615       Ty = SE.getEffectiveSCEVType(Ty);
 616       LHS = InsertNoopCastOfTo(LHS, Ty);
 617     }
 618     Value *RHS = expandCodeFor(S->getOperand(i), Ty);
 619     Value *ICmp = Builder.CreateICmpSGT(LHS, RHS, "tmp");
 620     InsertedValues.insert(ICmp);
 621     Value *Sel = Builder.CreateSelect(ICmp, LHS, RHS, "smax");
 622     InsertedValues.insert(Sel);
 623     LHS = Sel;
 624   }
 625   // In the case of mixed integer and pointer types, cast the
 626   // final result back to the pointer type.
 627   if (LHS->getType() != S->getType())
 628     LHS = InsertNoopCastOfTo(LHS, S->getType());
 629   return LHS;
 630 }
 631
 632 Value *SCEVExpander::visitUMaxExpr(const SCEVUMaxExpr *S) {
 633   Value *LHS = expand(S->getOperand(S->getNumOperands()-1));
 634   const Type *Ty = LHS->getType();
 635   for (int i = S->getNumOperands()-2; i >= 0; --i) {
 636     // In the case of mixed integer and pointer types, do the
 637     // rest of the comparisons as integer.
 638     if (S->getOperand(i)->getType() != Ty) {
 639       Ty = SE.getEffectiveSCEVType(Ty);
 640       LHS = InsertNoopCastOfTo(LHS, Ty);
 641     }
 642     Value *RHS = expandCodeFor(S->getOperand(i), Ty);
 643     Value *ICmp = Builder.CreateICmpUGT(LHS, RHS, "tmp");
 644     InsertedValues.insert(ICmp);
 645     Value *Sel = Builder.CreateSelect(ICmp, LHS, RHS, "umax");
 646     InsertedValues.insert(Sel);
 647     LHS = Sel;
 648   }
 649   // In the case of mixed integer and pointer types, cast the
 650   // final result back to the pointer type.
 651   if (LHS->getType() != S->getType())
 652     LHS = InsertNoopCastOfTo(LHS, S->getType());
 653   return LHS;
 654 }
 655
 656 Value *SCEVExpander::expandCodeFor(const SCEV *SH, const Type *Ty) {
 657   // Expand the code for this SCEV.
 658   Value *V = expand(SH);
 659   if (Ty) {
 660     assert(SE.getTypeSizeInBits(Ty) == SE.getTypeSizeInBits(SH->getType()) &&
 661            "non-trivial casts should be done with the SCEVs directly!");
 662     V = InsertNoopCastOfTo(V, Ty);
 663   }
 664   return V;
 665 }
 666
 667 Value *SCEVExpander::expand(const SCEV *S) {
 668   // Compute an insertion point for this SCEV object. Hoist the instructions
 669   // as far out in the loop nest as possible.
 670   Instruction *InsertPt = Builder.GetInsertPoint();
 671   for (Loop *L = SE.LI->getLoopFor(Builder.GetInsertBlock()); ;
 672        L = L->getParentLoop())
 673     if (S->isLoopInvariant(L)) {
 674       if (!L) break;
 675       if (BasicBlock *Preheader = L->getLoopPreheader())
 676         InsertPt = Preheader->getTerminator();
 677     } else {
 678       // If the SCEV is computable at this level, insert it into the header
 679       // after the PHIs (and after any other instructions that we've inserted
 680       // there) so that it is guaranteed to dominate any user inside the loop.
 681       if (L && S->hasComputableLoopEvolution(L))
 682         InsertPt = L->getHeader()->getFirstNonPHI();
 683       while (isInsertedInstruction(InsertPt))
 684         InsertPt = next(BasicBlock::iterator(InsertPt));
 685       break;
 686     }
 687
 688   // Check to see if we already expanded this here.
 689   std::map<std::pair<const SCEV *, Instruction *>,
 690            AssertingVH<Value> >::iterator I =
 691     InsertedExpressions.find(std::make_pair(S, InsertPt));
 692   if (I != InsertedExpressions.end())
 693     return I->second;
 694
 695   BasicBlock *SaveInsertBB = Builder.GetInsertBlock();
 696   BasicBlock::iterator SaveInsertPt = Builder.GetInsertPoint();
 697   Builder.SetInsertPoint(InsertPt->getParent(), InsertPt);
 698
 699   // Expand the expression into instructions.
 700   Value *V = visit(S);
 701
 702   // Remember the expanded value for this SCEV at this location.
 703   InsertedExpressions[std::make_pair(S, InsertPt)] = V;
 704
 705   Builder.SetInsertPoint(SaveInsertBB, SaveInsertPt);
 706   return V;
 707 }
 708
 709 /// getOrInsertCanonicalInductionVariable - This method returns the
 710 /// canonical induction variable of the specified type for the specified
 711 /// loop (inserting one if there is none).  A canonical induction variable
 712 /// starts at zero and steps by one on each iteration.
 713 Value *
 714 SCEVExpander::getOrInsertCanonicalInductionVariable(const Loop *L,
 715                                                     const Type *Ty) {
 716   assert(Ty->isInteger() && "Can only insert integer induction variables!");
 717   const SCEV *H = SE.getAddRecExpr(SE.getIntegerSCEV(0, Ty),
 718                                    SE.getIntegerSCEV(1, Ty), L);
 719   BasicBlock *SaveInsertBB = Builder.GetInsertBlock();
 720   BasicBlock::iterator SaveInsertPt = Builder.GetInsertPoint();
 721   Value *V = expandCodeFor(H, 0, L->getHeader()->begin());
 722   if (SaveInsertBB)
 723     Builder.SetInsertPoint(SaveInsertBB, SaveInsertPt);
 724   return V;
 725 }