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/IntrinsicInst.h"
19#include "llvm/LLVMContext.h"
20#include "llvm/Support/Debug.h"
21#include "llvm/Target/TargetData.h"
22#include "llvm/ADT/STLExtras.h"
23
24using namespace llvm;
25
26/// ReuseOrCreateCast - Arrange for there to be a cast of V to Ty at IP,
27/// reusing an existing cast if a suitable one exists, moving an existing
28/// cast if a suitable one exists but isn't in the right place, or
29/// creating a new one.
30Value *SCEVExpander::ReuseOrCreateCast(Value *V, Type *Ty,
31                                       Instruction::CastOps Op,
32                                       BasicBlock::iterator IP) {
33  // Check to see if there is already a cast!
34  for (Value::use_iterator UI = V->use_begin(), E = V->use_end();
35       UI != E; ++UI) {
36    User *U = *UI;
37    if (U->getType() == Ty)
38      if (CastInst *CI = dyn_cast<CastInst>(U))
39        if (CI->getOpcode() == Op) {
40          // If the cast isn't where we want it, fix it.
41          if (BasicBlock::iterator(CI) != IP) {
42            // Create a new cast, and leave the old cast in place in case
43            // it is being used as an insert point. Clear its operand
44            // so that it doesn't hold anything live.
45            Instruction *NewCI = CastInst::Create(Op, V, Ty, "", IP);
46            NewCI->takeName(CI);
47            CI->replaceAllUsesWith(NewCI);
48            CI->setOperand(0, UndefValue::get(V->getType()));
49            rememberInstruction(NewCI);
50            return NewCI;
51          }
52          rememberInstruction(CI);
53          return CI;
54        }
55  }
56
57  // Create a new cast.
58  Instruction *I = CastInst::Create(Op, V, Ty, V->getName(), IP);
59  rememberInstruction(I);
60  return I;
61}
62
63/// InsertNoopCastOfTo - Insert a cast of V to the specified type,
64/// which must be possible with a noop cast, doing what we can to share
65/// the casts.
66Value *SCEVExpander::InsertNoopCastOfTo(Value *V, Type *Ty) {
67  Instruction::CastOps Op = CastInst::getCastOpcode(V, false, Ty, false);
68  assert((Op == Instruction::BitCast ||
69          Op == Instruction::PtrToInt ||
70          Op == Instruction::IntToPtr) &&
71         "InsertNoopCastOfTo cannot perform non-noop casts!");
72  assert(SE.getTypeSizeInBits(V->getType()) == SE.getTypeSizeInBits(Ty) &&
73         "InsertNoopCastOfTo cannot change sizes!");
74
75  // Short-circuit unnecessary bitcasts.
76  if (Op == Instruction::BitCast && V->getType() == Ty)
77    return V;
78
79  // Short-circuit unnecessary inttoptr<->ptrtoint casts.
80  if ((Op == Instruction::PtrToInt || Op == Instruction::IntToPtr) &&
81      SE.getTypeSizeInBits(Ty) == SE.getTypeSizeInBits(V->getType())) {
82    if (CastInst *CI = dyn_cast<CastInst>(V))
83      if ((CI->getOpcode() == Instruction::PtrToInt ||
84           CI->getOpcode() == Instruction::IntToPtr) &&
85          SE.getTypeSizeInBits(CI->getType()) ==
86          SE.getTypeSizeInBits(CI->getOperand(0)->getType()))
87        return CI->getOperand(0);
88    if (ConstantExpr *CE = dyn_cast<ConstantExpr>(V))
89      if ((CE->getOpcode() == Instruction::PtrToInt ||
90           CE->getOpcode() == Instruction::IntToPtr) &&
91          SE.getTypeSizeInBits(CE->getType()) ==
92          SE.getTypeSizeInBits(CE->getOperand(0)->getType()))
93        return CE->getOperand(0);
94  }
95
96  // Fold a cast of a constant.
97  if (Constant *C = dyn_cast<Constant>(V))
98    return ConstantExpr::getCast(Op, C, Ty);
99
100  // Cast the argument at the beginning of the entry block, after
101  // any bitcasts of other arguments.
102  if (Argument *A = dyn_cast<Argument>(V)) {
103    BasicBlock::iterator IP = A->getParent()->getEntryBlock().begin();
104    while ((isa<BitCastInst>(IP) &&
105            isa<Argument>(cast<BitCastInst>(IP)->getOperand(0)) &&
106            cast<BitCastInst>(IP)->getOperand(0) != A) ||
107           isa<DbgInfoIntrinsic>(IP) ||
108           isa<LandingPadInst>(IP))
109      ++IP;
110    return ReuseOrCreateCast(A, Ty, Op, IP);
111  }
112
113  // Cast the instruction immediately after the instruction.
114  Instruction *I = cast<Instruction>(V);
115  BasicBlock::iterator IP = I; ++IP;
116  if (InvokeInst *II = dyn_cast<InvokeInst>(I))
117    IP = II->getNormalDest()->begin();
118  while (isa<PHINode>(IP) || isa<DbgInfoIntrinsic>(IP) ||
119         isa<LandingPadInst>(IP))
120    ++IP;
121  return ReuseOrCreateCast(I, Ty, Op, IP);
122}
123
124/// InsertBinop - Insert the specified binary operator, doing a small amount
125/// of work to avoid inserting an obviously redundant operation.
126Value *SCEVExpander::InsertBinop(Instruction::BinaryOps Opcode,
127                                 Value *LHS, Value *RHS) {
128  // Fold a binop with constant operands.
129  if (Constant *CLHS = dyn_cast<Constant>(LHS))
130    if (Constant *CRHS = dyn_cast<Constant>(RHS))
131      return ConstantExpr::get(Opcode, CLHS, CRHS);
132
133  // Do a quick scan to see if we have this binop nearby.  If so, reuse it.
134  unsigned ScanLimit = 6;
135  BasicBlock::iterator BlockBegin = Builder.GetInsertBlock()->begin();
136  // Scanning starts from the last instruction before the insertion point.
137  BasicBlock::iterator IP = Builder.GetInsertPoint();
138  if (IP != BlockBegin) {
139    --IP;
140    for (; ScanLimit; --IP, --ScanLimit) {
141      // Don't count dbg.value against the ScanLimit, to avoid perturbing the
142      // generated code.
143      if (isa<DbgInfoIntrinsic>(IP))
144        ScanLimit++;
145      if (IP->getOpcode() == (unsigned)Opcode && IP->getOperand(0) == LHS &&
146          IP->getOperand(1) == RHS)
147        return IP;
148      if (IP == BlockBegin) break;
149    }
150  }
151
152  // Save the original insertion point so we can restore it when we're done.
153  BasicBlock *SaveInsertBB = Builder.GetInsertBlock();
154  BasicBlock::iterator SaveInsertPt = Builder.GetInsertPoint();
155
156  // Move the insertion point out of as many loops as we can.
157  while (const Loop *L = SE.LI->getLoopFor(Builder.GetInsertBlock())) {
158    if (!L->isLoopInvariant(LHS) || !L->isLoopInvariant(RHS)) break;
159    BasicBlock *Preheader = L->getLoopPreheader();
160    if (!Preheader) break;
161
162    // Ok, move up a level.
163    Builder.SetInsertPoint(Preheader, Preheader->getTerminator());
164  }
165
166  // If we haven't found this binop, insert it.
167  Instruction *BO = cast<Instruction>(Builder.CreateBinOp(Opcode, LHS, RHS));
168  BO->setDebugLoc(SaveInsertPt->getDebugLoc());
169  rememberInstruction(BO);
170
171  // Restore the original insert point.
172  if (SaveInsertBB)
173    restoreInsertPoint(SaveInsertBB, SaveInsertPt);
174
175  return BO;
176}
177
178/// FactorOutConstant - Test if S is divisible by Factor, using signed
179/// division. If so, update S with Factor divided out and return true.
180/// S need not be evenly divisible if a reasonable remainder can be
181/// computed.
182/// TODO: When ScalarEvolution gets a SCEVSDivExpr, this can be made
183/// unnecessary; in its place, just signed-divide Ops[i] by the scale and
184/// check to see if the divide was folded.
185static bool FactorOutConstant(const SCEV *&S,
186                              const SCEV *&Remainder,
187                              const SCEV *Factor,
188                              ScalarEvolution &SE,
189                              const TargetData *TD) {
190  // Everything is divisible by one.
191  if (Factor->isOne())
192    return true;
193
194  // x/x == 1.
195  if (S == Factor) {
196    S = SE.getConstant(S->getType(), 1);
197    return true;
198  }
199
200  // For a Constant, check for a multiple of the given factor.
201  if (const SCEVConstant *C = dyn_cast<SCEVConstant>(S)) {
202    // 0/x == 0.
203    if (C->isZero())
204      return true;
205    // Check for divisibility.
206    if (const SCEVConstant *FC = dyn_cast<SCEVConstant>(Factor)) {
207      ConstantInt *CI =
208        ConstantInt::get(SE.getContext(),
209                         C->getValue()->getValue().sdiv(
210                                                   FC->getValue()->getValue()));
211      // If the quotient is zero and the remainder is non-zero, reject
212      // the value at this scale. It will be considered for subsequent
213      // smaller scales.
214      if (!CI->isZero()) {
215        const SCEV *Div = SE.getConstant(CI);
216        S = Div;
217        Remainder =
218          SE.getAddExpr(Remainder,
219                        SE.getConstant(C->getValue()->getValue().srem(
220                                                  FC->getValue()->getValue())));
221        return true;
222      }
223    }
224  }
225
226  // In a Mul, check if there is a constant operand which is a multiple
227  // of the given factor.
228  if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(S)) {
229    if (TD) {
230      // With TargetData, the size is known. Check if there is a constant
231      // operand which is a multiple of the given factor. If so, we can
232      // factor it.
233      const SCEVConstant *FC = cast<SCEVConstant>(Factor);
234      if (const SCEVConstant *C = dyn_cast<SCEVConstant>(M->getOperand(0)))
235        if (!C->getValue()->getValue().srem(FC->getValue()->getValue())) {
236          SmallVector<const SCEV *, 4> NewMulOps(M->op_begin(), M->op_end());
237          NewMulOps[0] =
238            SE.getConstant(C->getValue()->getValue().sdiv(
239                                                   FC->getValue()->getValue()));
240          S = SE.getMulExpr(NewMulOps);
241          return true;
242        }
243    } else {
244      // Without TargetData, check if Factor can be factored out of any of the
245      // Mul's operands. If so, we can just remove it.
246      for (unsigned i = 0, e = M->getNumOperands(); i != e; ++i) {
247        const SCEV *SOp = M->getOperand(i);
248        const SCEV *Remainder = SE.getConstant(SOp->getType(), 0);
249        if (FactorOutConstant(SOp, Remainder, Factor, SE, TD) &&
250            Remainder->isZero()) {
251          SmallVector<const SCEV *, 4> NewMulOps(M->op_begin(), M->op_end());
252          NewMulOps[i] = SOp;
253          S = SE.getMulExpr(NewMulOps);
254          return true;
255        }
256      }
257    }
258  }
259
260  // In an AddRec, check if both start and step are divisible.
261  if (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(S)) {
262    const SCEV *Step = A->getStepRecurrence(SE);
263    const SCEV *StepRem = SE.getConstant(Step->getType(), 0);
264    if (!FactorOutConstant(Step, StepRem, Factor, SE, TD))
265      return false;
266    if (!StepRem->isZero())
267      return false;
268    const SCEV *Start = A->getStart();
269    if (!FactorOutConstant(Start, Remainder, Factor, SE, TD))
270      return false;
271    // FIXME: can use A->getNoWrapFlags(FlagNW)
272    S = SE.getAddRecExpr(Start, Step, A->getLoop(), SCEV::FlagAnyWrap);
273    return true;
274  }
275
276  return false;
277}
278
279/// SimplifyAddOperands - Sort and simplify a list of add operands. NumAddRecs
280/// is the number of SCEVAddRecExprs present, which are kept at the end of
281/// the list.
282///
283static void SimplifyAddOperands(SmallVectorImpl<const SCEV *> &Ops,
284                                Type *Ty,
285                                ScalarEvolution &SE) {
286  unsigned NumAddRecs = 0;
287  for (unsigned i = Ops.size(); i > 0 && isa<SCEVAddRecExpr>(Ops[i-1]); --i)
288    ++NumAddRecs;
289  // Group Ops into non-addrecs and addrecs.
290  SmallVector<const SCEV *, 8> NoAddRecs(Ops.begin(), Ops.end() - NumAddRecs);
291  SmallVector<const SCEV *, 8> AddRecs(Ops.end() - NumAddRecs, Ops.end());
292  // Let ScalarEvolution sort and simplify the non-addrecs list.
293  const SCEV *Sum = NoAddRecs.empty() ?
294                    SE.getConstant(Ty, 0) :
295                    SE.getAddExpr(NoAddRecs);
296  // If it returned an add, use the operands. Otherwise it simplified
297  // the sum into a single value, so just use that.
298  Ops.clear();
299  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Sum))
300    Ops.append(Add->op_begin(), Add->op_end());
301  else if (!Sum->isZero())
302    Ops.push_back(Sum);
303  // Then append the addrecs.
304  Ops.append(AddRecs.begin(), AddRecs.end());
305}
306
307/// SplitAddRecs - Flatten a list of add operands, moving addrec start values
308/// out to the top level. For example, convert {a + b,+,c} to a, b, {0,+,d}.
309/// This helps expose more opportunities for folding parts of the expressions
310/// into GEP indices.
311///
312static void SplitAddRecs(SmallVectorImpl<const SCEV *> &Ops,
313                         Type *Ty,
314                         ScalarEvolution &SE) {
315  // Find the addrecs.
316  SmallVector<const SCEV *, 8> AddRecs;
317  for (unsigned i = 0, e = Ops.size(); i != e; ++i)
318    while (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(Ops[i])) {
319      const SCEV *Start = A->getStart();
320      if (Start->isZero()) break;
321      const SCEV *Zero = SE.getConstant(Ty, 0);
322      AddRecs.push_back(SE.getAddRecExpr(Zero,
323                                         A->getStepRecurrence(SE),
324                                         A->getLoop(),
325                                         // FIXME: A->getNoWrapFlags(FlagNW)
326                                         SCEV::FlagAnyWrap));
327      if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(Start)) {
328        Ops[i] = Zero;
329        Ops.append(Add->op_begin(), Add->op_end());
330        e += Add->getNumOperands();
331      } else {
332        Ops[i] = Start;
333      }
334    }
335  if (!AddRecs.empty()) {
336    // Add the addrecs onto the end of the list.
337    Ops.append(AddRecs.begin(), AddRecs.end());
338    // Resort the operand list, moving any constants to the front.
339    SimplifyAddOperands(Ops, Ty, SE);
340  }
341}
342
343/// expandAddToGEP - Expand an addition expression with a pointer type into
344/// a GEP instead of using ptrtoint+arithmetic+inttoptr. This helps
345/// BasicAliasAnalysis and other passes analyze the result. See the rules
346/// for getelementptr vs. inttoptr in
347/// http://llvm.org/docs/LangRef.html#pointeraliasing
348/// for details.
349///
350/// Design note: The correctness of using getelementptr here depends on
351/// ScalarEvolution not recognizing inttoptr and ptrtoint operators, as
352/// they may introduce pointer arithmetic which may not be safely converted
353/// into getelementptr.
354///
355/// Design note: It might seem desirable for this function to be more
356/// loop-aware. If some of the indices are loop-invariant while others
357/// aren't, it might seem desirable to emit multiple GEPs, keeping the
358/// loop-invariant portions of the overall computation outside the loop.
359/// However, there are a few reasons this is not done here. Hoisting simple
360/// arithmetic is a low-level optimization that often isn't very
361/// important until late in the optimization process. In fact, passes
362/// like InstructionCombining will combine GEPs, even if it means
363/// pushing loop-invariant computation down into loops, so even if the
364/// GEPs were split here, the work would quickly be undone. The
365/// LoopStrengthReduction pass, which is usually run quite late (and
366/// after the last InstructionCombining pass), takes care of hoisting
367/// loop-invariant portions of expressions, after considering what
368/// can be folded using target addressing modes.
369///
370Value *SCEVExpander::expandAddToGEP(const SCEV *const *op_begin,
371                                    const SCEV *const *op_end,
372                                    PointerType *PTy,
373                                    Type *Ty,
374                                    Value *V) {
375  Type *ElTy = PTy->getElementType();
376  SmallVector<Value *, 4> GepIndices;
377  SmallVector<const SCEV *, 8> Ops(op_begin, op_end);
378  bool AnyNonZeroIndices = false;
379
380  // Split AddRecs up into parts as either of the parts may be usable
381  // without the other.
382  SplitAddRecs(Ops, Ty, SE);
383
384  // Descend down the pointer's type and attempt to convert the other
385  // operands into GEP indices, at each level. The first index in a GEP
386  // indexes into the array implied by the pointer operand; the rest of
387  // the indices index into the element or field type selected by the
388  // preceding index.
389  for (;;) {
390    // If the scale size is not 0, attempt to factor out a scale for
391    // array indexing.
392    SmallVector<const SCEV *, 8> ScaledOps;
393    if (ElTy->isSized()) {
394      const SCEV *ElSize = SE.getSizeOfExpr(ElTy);
395      if (!ElSize->isZero()) {
396        SmallVector<const SCEV *, 8> NewOps;
397        for (unsigned i = 0, e = Ops.size(); i != e; ++i) {
398          const SCEV *Op = Ops[i];
399          const SCEV *Remainder = SE.getConstant(Ty, 0);
400          if (FactorOutConstant(Op, Remainder, ElSize, SE, SE.TD)) {
401            // Op now has ElSize factored out.
402            ScaledOps.push_back(Op);
403            if (!Remainder->isZero())
404              NewOps.push_back(Remainder);
405            AnyNonZeroIndices = true;
406          } else {
407            // The operand was not divisible, so add it to the list of operands
408            // we'll scan next iteration.
409            NewOps.push_back(Ops[i]);
410          }
411        }
412        // If we made any changes, update Ops.
413        if (!ScaledOps.empty()) {
414          Ops = NewOps;
415          SimplifyAddOperands(Ops, Ty, SE);
416        }
417      }
418    }
419
420    // Record the scaled array index for this level of the type. If
421    // we didn't find any operands that could be factored, tentatively
422    // assume that element zero was selected (since the zero offset
423    // would obviously be folded away).
424    Value *Scaled = ScaledOps.empty() ?
425                    Constant::getNullValue(Ty) :
426                    expandCodeFor(SE.getAddExpr(ScaledOps), Ty);
427    GepIndices.push_back(Scaled);
428
429    // Collect struct field index operands.
430    while (StructType *STy = dyn_cast<StructType>(ElTy)) {
431      bool FoundFieldNo = false;
432      // An empty struct has no fields.
433      if (STy->getNumElements() == 0) break;
434      if (SE.TD) {
435        // With TargetData, field offsets are known. See if a constant offset
436        // falls within any of the struct fields.
437        if (Ops.empty()) break;
438        if (const SCEVConstant *C = dyn_cast<SCEVConstant>(Ops[0]))
439          if (SE.getTypeSizeInBits(C->getType()) <= 64) {
440            const StructLayout &SL = *SE.TD->getStructLayout(STy);
441            uint64_t FullOffset = C->getValue()->getZExtValue();
442            if (FullOffset < SL.getSizeInBytes()) {
443              unsigned ElIdx = SL.getElementContainingOffset(FullOffset);
444              GepIndices.push_back(
445                  ConstantInt::get(Type::getInt32Ty(Ty->getContext()), ElIdx));
446              ElTy = STy->getTypeAtIndex(ElIdx);
447              Ops[0] =
448                SE.getConstant(Ty, FullOffset - SL.getElementOffset(ElIdx));
449              AnyNonZeroIndices = true;
450              FoundFieldNo = true;
451            }
452          }
453      } else {
454        // Without TargetData, just check for an offsetof expression of the
455        // appropriate struct type.
456        for (unsigned i = 0, e = Ops.size(); i != e; ++i)
457          if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(Ops[i])) {
458            Type *CTy;
459            Constant *FieldNo;
460            if (U->isOffsetOf(CTy, FieldNo) && CTy == STy) {
461              GepIndices.push_back(FieldNo);
462              ElTy =
463                STy->getTypeAtIndex(cast<ConstantInt>(FieldNo)->getZExtValue());
464              Ops[i] = SE.getConstant(Ty, 0);
465              AnyNonZeroIndices = true;
466              FoundFieldNo = true;
467              break;
468            }
469          }
470      }
471      // If no struct field offsets were found, tentatively assume that
472      // field zero was selected (since the zero offset would obviously
473      // be folded away).
474      if (!FoundFieldNo) {
475        ElTy = STy->getTypeAtIndex(0u);
476        GepIndices.push_back(
477          Constant::getNullValue(Type::getInt32Ty(Ty->getContext())));
478      }
479    }
480
481    if (ArrayType *ATy = dyn_cast<ArrayType>(ElTy))
482      ElTy = ATy->getElementType();
483    else
484      break;
485  }
486
487  // If none of the operands were convertible to proper GEP indices, cast
488  // the base to i8* and do an ugly getelementptr with that. It's still
489  // better than ptrtoint+arithmetic+inttoptr at least.
490  if (!AnyNonZeroIndices) {
491    // Cast the base to i8*.
492    V = InsertNoopCastOfTo(V,
493       Type::getInt8PtrTy(Ty->getContext(), PTy->getAddressSpace()));
494
495    // Expand the operands for a plain byte offset.
496    Value *Idx = expandCodeFor(SE.getAddExpr(Ops), Ty);
497
498    // Fold a GEP with constant operands.
499    if (Constant *CLHS = dyn_cast<Constant>(V))
500      if (Constant *CRHS = dyn_cast<Constant>(Idx))
501        return ConstantExpr::getGetElementPtr(CLHS, CRHS);
502
503    // Do a quick scan to see if we have this GEP nearby.  If so, reuse it.
504    unsigned ScanLimit = 6;
505    BasicBlock::iterator BlockBegin = Builder.GetInsertBlock()->begin();
506    // Scanning starts from the last instruction before the insertion point.
507    BasicBlock::iterator IP = Builder.GetInsertPoint();
508    if (IP != BlockBegin) {
509      --IP;
510      for (; ScanLimit; --IP, --ScanLimit) {
511        // Don't count dbg.value against the ScanLimit, to avoid perturbing the
512        // generated code.
513        if (isa<DbgInfoIntrinsic>(IP))
514          ScanLimit++;
515        if (IP->getOpcode() == Instruction::GetElementPtr &&
516            IP->getOperand(0) == V && IP->getOperand(1) == Idx)
517          return IP;
518        if (IP == BlockBegin) break;
519      }
520    }
521
522    // Save the original insertion point so we can restore it when we're done.
523    BasicBlock *SaveInsertBB = Builder.GetInsertBlock();
524    BasicBlock::iterator SaveInsertPt = Builder.GetInsertPoint();
525
526    // Move the insertion point out of as many loops as we can.
527    while (const Loop *L = SE.LI->getLoopFor(Builder.GetInsertBlock())) {
528      if (!L->isLoopInvariant(V) || !L->isLoopInvariant(Idx)) break;
529      BasicBlock *Preheader = L->getLoopPreheader();
530      if (!Preheader) break;
531
532      // Ok, move up a level.
533      Builder.SetInsertPoint(Preheader, Preheader->getTerminator());
534    }
535
536    // Emit a GEP.
537    Value *GEP = Builder.CreateGEP(V, Idx, "uglygep");
538    rememberInstruction(GEP);
539
540    // Restore the original insert point.
541    if (SaveInsertBB)
542      restoreInsertPoint(SaveInsertBB, SaveInsertPt);
543
544    return GEP;
545  }
546
547  // Save the original insertion point so we can restore it when we're done.
548  BasicBlock *SaveInsertBB = Builder.GetInsertBlock();
549  BasicBlock::iterator SaveInsertPt = Builder.GetInsertPoint();
550
551  // Move the insertion point out of as many loops as we can.
552  while (const Loop *L = SE.LI->getLoopFor(Builder.GetInsertBlock())) {
553    if (!L->isLoopInvariant(V)) break;
554
555    bool AnyIndexNotLoopInvariant = false;
556    for (SmallVectorImpl<Value *>::const_iterator I = GepIndices.begin(),
557         E = GepIndices.end(); I != E; ++I)
558      if (!L->isLoopInvariant(*I)) {
559        AnyIndexNotLoopInvariant = true;
560        break;
561      }
562    if (AnyIndexNotLoopInvariant)
563      break;
564
565    BasicBlock *Preheader = L->getLoopPreheader();
566    if (!Preheader) break;
567
568    // Ok, move up a level.
569    Builder.SetInsertPoint(Preheader, Preheader->getTerminator());
570  }
571
572  // Insert a pretty getelementptr. Note that this GEP is not marked inbounds,
573  // because ScalarEvolution may have changed the address arithmetic to
574  // compute a value which is beyond the end of the allocated object.
575  Value *Casted = V;
576  if (V->getType() != PTy)
577    Casted = InsertNoopCastOfTo(Casted, PTy);
578  Value *GEP = Builder.CreateGEP(Casted,
579                                 GepIndices,
580                                 "scevgep");
581  Ops.push_back(SE.getUnknown(GEP));
582  rememberInstruction(GEP);
583
584  // Restore the original insert point.
585  if (SaveInsertBB)
586    restoreInsertPoint(SaveInsertBB, SaveInsertPt);
587
588  return expand(SE.getAddExpr(Ops));
589}
590
591/// isNonConstantNegative - Return true if the specified scev is negated, but
592/// not a constant.
593static bool isNonConstantNegative(const SCEV *F) {
594  const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(F);
595  if (!Mul) return false;
596
597  // If there is a constant factor, it will be first.
598  const SCEVConstant *SC = dyn_cast<SCEVConstant>(Mul->getOperand(0));
599  if (!SC) return false;
600
601  // Return true if the value is negative, this matches things like (-42 * V).
602  return SC->getValue()->getValue().isNegative();
603}
604
605/// PickMostRelevantLoop - Given two loops pick the one that's most relevant for
606/// SCEV expansion. If they are nested, this is the most nested. If they are
607/// neighboring, pick the later.
608static const Loop *PickMostRelevantLoop(const Loop *A, const Loop *B,
609                                        DominatorTree &DT) {
610  if (!A) return B;
611  if (!B) return A;
612  if (A->contains(B)) return B;
613  if (B->contains(A)) return A;
614  if (DT.dominates(A->getHeader(), B->getHeader())) return B;
615  if (DT.dominates(B->getHeader(), A->getHeader())) return A;
616  return A; // Arbitrarily break the tie.
617}
618
619/// getRelevantLoop - Get the most relevant loop associated with the given
620/// expression, according to PickMostRelevantLoop.
621const Loop *SCEVExpander::getRelevantLoop(const SCEV *S) {
622  // Test whether we've already computed the most relevant loop for this SCEV.
623  std::pair<DenseMap<const SCEV *, const Loop *>::iterator, bool> Pair =
624    RelevantLoops.insert(std::make_pair(S, static_cast<const Loop *>(0)));
625  if (!Pair.second)
626    return Pair.first->second;
627
628  if (isa<SCEVConstant>(S))
629    // A constant has no relevant loops.
630    return 0;
631  if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
632    if (const Instruction *I = dyn_cast<Instruction>(U->getValue()))
633      return Pair.first->second = SE.LI->getLoopFor(I->getParent());
634    // A non-instruction has no relevant loops.
635    return 0;
636  }
637  if (const SCEVNAryExpr *N = dyn_cast<SCEVNAryExpr>(S)) {
638    const Loop *L = 0;
639    if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
640      L = AR->getLoop();
641    for (SCEVNAryExpr::op_iterator I = N->op_begin(), E = N->op_end();
642         I != E; ++I)
643      L = PickMostRelevantLoop(L, getRelevantLoop(*I), *SE.DT);
644    return RelevantLoops[N] = L;
645  }
646  if (const SCEVCastExpr *C = dyn_cast<SCEVCastExpr>(S)) {
647    const Loop *Result = getRelevantLoop(C->getOperand());
648    return RelevantLoops[C] = Result;
649  }
650  if (const SCEVUDivExpr *D = dyn_cast<SCEVUDivExpr>(S)) {
651    const Loop *Result =
652      PickMostRelevantLoop(getRelevantLoop(D->getLHS()),
653                           getRelevantLoop(D->getRHS()),
654                           *SE.DT);
655    return RelevantLoops[D] = Result;
656  }
657  llvm_unreachable("Unexpected SCEV type!");
658  return 0;
659}
660
661namespace {
662
663/// LoopCompare - Compare loops by PickMostRelevantLoop.
664class LoopCompare {
665  DominatorTree &DT;
666public:
667  explicit LoopCompare(DominatorTree &dt) : DT(dt) {}
668
669  bool operator()(std::pair<const Loop *, const SCEV *> LHS,
670                  std::pair<const Loop *, const SCEV *> RHS) const {
671    // Keep pointer operands sorted at the end.
672    if (LHS.second->getType()->isPointerTy() !=
673        RHS.second->getType()->isPointerTy())
674      return LHS.second->getType()->isPointerTy();
675
676    // Compare loops with PickMostRelevantLoop.
677    if (LHS.first != RHS.first)
678      return PickMostRelevantLoop(LHS.first, RHS.first, DT) != LHS.first;
679
680    // If one operand is a non-constant negative and the other is not,
681    // put the non-constant negative on the right so that a sub can
682    // be used instead of a negate and add.
683    if (isNonConstantNegative(LHS.second)) {
684      if (!isNonConstantNegative(RHS.second))
685        return false;
686    } else if (isNonConstantNegative(RHS.second))
687      return true;
688
689    // Otherwise they are equivalent according to this comparison.
690    return false;
691  }
692};
693
694}
695
696Value *SCEVExpander::visitAddExpr(const SCEVAddExpr *S) {
697  Type *Ty = SE.getEffectiveSCEVType(S->getType());
698
699  // Collect all the add operands in a loop, along with their associated loops.
700  // Iterate in reverse so that constants are emitted last, all else equal, and
701  // so that pointer operands are inserted first, which the code below relies on
702  // to form more involved GEPs.
703  SmallVector<std::pair<const Loop *, const SCEV *>, 8> OpsAndLoops;
704  for (std::reverse_iterator<SCEVAddExpr::op_iterator> I(S->op_end()),
705       E(S->op_begin()); I != E; ++I)
706    OpsAndLoops.push_back(std::make_pair(getRelevantLoop(*I), *I));
707
708  // Sort by loop. Use a stable sort so that constants follow non-constants and
709  // pointer operands precede non-pointer operands.
710  std::stable_sort(OpsAndLoops.begin(), OpsAndLoops.end(), LoopCompare(*SE.DT));
711
712  // Emit instructions to add all the operands. Hoist as much as possible
713  // out of loops, and form meaningful getelementptrs where possible.
714  Value *Sum = 0;
715  for (SmallVectorImpl<std::pair<const Loop *, const SCEV *> >::iterator
716       I = OpsAndLoops.begin(), E = OpsAndLoops.end(); I != E; ) {
717    const Loop *CurLoop = I->first;
718    const SCEV *Op = I->second;
719    if (!Sum) {
720      // This is the first operand. Just expand it.
721      Sum = expand(Op);
722      ++I;
723    } else if (PointerType *PTy = dyn_cast<PointerType>(Sum->getType())) {
724      // The running sum expression is a pointer. Try to form a getelementptr
725      // at this level with that as the base.
726      SmallVector<const SCEV *, 4> NewOps;
727      for (; I != E && I->first == CurLoop; ++I) {
728        // If the operand is SCEVUnknown and not instructions, peek through
729        // it, to enable more of it to be folded into the GEP.
730        const SCEV *X = I->second;
731        if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(X))
732          if (!isa<Instruction>(U->getValue()))
733            X = SE.getSCEV(U->getValue());
734        NewOps.push_back(X);
735      }
736      Sum = expandAddToGEP(NewOps.begin(), NewOps.end(), PTy, Ty, Sum);
737    } else if (PointerType *PTy = dyn_cast<PointerType>(Op->getType())) {
738      // The running sum is an integer, and there's a pointer at this level.
739      // Try to form a getelementptr. If the running sum is instructions,
740      // use a SCEVUnknown to avoid re-analyzing them.
741      SmallVector<const SCEV *, 4> NewOps;
742      NewOps.push_back(isa<Instruction>(Sum) ? SE.getUnknown(Sum) :
743                                               SE.getSCEV(Sum));
744      for (++I; I != E && I->first == CurLoop; ++I)
745        NewOps.push_back(I->second);
746      Sum = expandAddToGEP(NewOps.begin(), NewOps.end(), PTy, Ty, expand(Op));
747    } else if (isNonConstantNegative(Op)) {
748      // Instead of doing a negate and add, just do a subtract.
749      Value *W = expandCodeFor(SE.getNegativeSCEV(Op), Ty);
750      Sum = InsertNoopCastOfTo(Sum, Ty);
751      Sum = InsertBinop(Instruction::Sub, Sum, W);
752      ++I;
753    } else {
754      // A simple add.
755      Value *W = expandCodeFor(Op, Ty);
756      Sum = InsertNoopCastOfTo(Sum, Ty);
757      // Canonicalize a constant to the RHS.
758      if (isa<Constant>(Sum)) std::swap(Sum, W);
759      Sum = InsertBinop(Instruction::Add, Sum, W);
760      ++I;
761    }
762  }
763
764  return Sum;
765}
766
767Value *SCEVExpander::visitMulExpr(const SCEVMulExpr *S) {
768  Type *Ty = SE.getEffectiveSCEVType(S->getType());
769
770  // Collect all the mul operands in a loop, along with their associated loops.
771  // Iterate in reverse so that constants are emitted last, all else equal.
772  SmallVector<std::pair<const Loop *, const SCEV *>, 8> OpsAndLoops;
773  for (std::reverse_iterator<SCEVMulExpr::op_iterator> I(S->op_end()),
774       E(S->op_begin()); I != E; ++I)
775    OpsAndLoops.push_back(std::make_pair(getRelevantLoop(*I), *I));
776
777  // Sort by loop. Use a stable sort so that constants follow non-constants.
778  std::stable_sort(OpsAndLoops.begin(), OpsAndLoops.end(), LoopCompare(*SE.DT));
779
780  // Emit instructions to mul all the operands. Hoist as much as possible
781  // out of loops.
782  Value *Prod = 0;
783  for (SmallVectorImpl<std::pair<const Loop *, const SCEV *> >::iterator
784       I = OpsAndLoops.begin(), E = OpsAndLoops.end(); I != E; ) {
785    const SCEV *Op = I->second;
786    if (!Prod) {
787      // This is the first operand. Just expand it.
788      Prod = expand(Op);
789      ++I;
790    } else if (Op->isAllOnesValue()) {
791      // Instead of doing a multiply by negative one, just do a negate.
792      Prod = InsertNoopCastOfTo(Prod, Ty);
793      Prod = InsertBinop(Instruction::Sub, Constant::getNullValue(Ty), Prod);
794      ++I;
795    } else {
796      // A simple mul.
797      Value *W = expandCodeFor(Op, Ty);
798      Prod = InsertNoopCastOfTo(Prod, Ty);
799      // Canonicalize a constant to the RHS.
800      if (isa<Constant>(Prod)) std::swap(Prod, W);
801      Prod = InsertBinop(Instruction::Mul, Prod, W);
802      ++I;
803    }
804  }
805
806  return Prod;
807}
808
809Value *SCEVExpander::visitUDivExpr(const SCEVUDivExpr *S) {
810  Type *Ty = SE.getEffectiveSCEVType(S->getType());
811
812  Value *LHS = expandCodeFor(S->getLHS(), Ty);
813  if (const SCEVConstant *SC = dyn_cast<SCEVConstant>(S->getRHS())) {
814    const APInt &RHS = SC->getValue()->getValue();
815    if (RHS.isPowerOf2())
816      return InsertBinop(Instruction::LShr, LHS,
817                         ConstantInt::get(Ty, RHS.logBase2()));
818  }
819
820  Value *RHS = expandCodeFor(S->getRHS(), Ty);
821  return InsertBinop(Instruction::UDiv, LHS, RHS);
822}
823
824/// Move parts of Base into Rest to leave Base with the minimal
825/// expression that provides a pointer operand suitable for a
826/// GEP expansion.
827static void ExposePointerBase(const SCEV *&Base, const SCEV *&Rest,
828                              ScalarEvolution &SE) {
829  while (const SCEVAddRecExpr *A = dyn_cast<SCEVAddRecExpr>(Base)) {
830    Base = A->getStart();
831    Rest = SE.getAddExpr(Rest,
832                         SE.getAddRecExpr(SE.getConstant(A->getType(), 0),
833                                          A->getStepRecurrence(SE),
834                                          A->getLoop(),
835                                          // FIXME: A->getNoWrapFlags(FlagNW)
836                                          SCEV::FlagAnyWrap));
837  }
838  if (const SCEVAddExpr *A = dyn_cast<SCEVAddExpr>(Base)) {
839    Base = A->getOperand(A->getNumOperands()-1);
840    SmallVector<const SCEV *, 8> NewAddOps(A->op_begin(), A->op_end());
841    NewAddOps.back() = Rest;
842    Rest = SE.getAddExpr(NewAddOps);
843    ExposePointerBase(Base, Rest, SE);
844  }
845}
846
847/// Determine if this is a well-behaved chain of instructions leading back to
848/// the PHI. If so, it may be reused by expanded expressions.
849bool SCEVExpander::isNormalAddRecExprPHI(PHINode *PN, Instruction *IncV,
850                                         const Loop *L) {
851  if (IncV->getNumOperands() == 0 || isa<PHINode>(IncV) ||
852      (isa<CastInst>(IncV) && !isa<BitCastInst>(IncV)))
853    return false;
854  // If any of the operands don't dominate the insert position, bail.
855  // Addrec operands are always loop-invariant, so this can only happen
856  // if there are instructions which haven't been hoisted.
857  if (L == IVIncInsertLoop) {
858    for (User::op_iterator OI = IncV->op_begin()+1,
859           OE = IncV->op_end(); OI != OE; ++OI)
860      if (Instruction *OInst = dyn_cast<Instruction>(OI))
861        if (!SE.DT->dominates(OInst, IVIncInsertPos))
862          return false;
863  }
864  // Advance to the next instruction.
865  IncV = dyn_cast<Instruction>(IncV->getOperand(0));
866  if (!IncV)
867    return false;
868
869  if (IncV->mayHaveSideEffects())
870    return false;
871
872  if (IncV != PN)
873    return true;
874
875  return isNormalAddRecExprPHI(PN, IncV, L);
876}
877
878/// Determine if this cyclic phi is in a form that would have been generated by
879/// LSR. We don't care if the phi was actually expanded in this pass, as long
880/// as it is in a low-cost form, for example, no implied multiplication. This
881/// should match any patterns generated by getAddRecExprPHILiterally and
882/// expandAddtoGEP.
883bool SCEVExpander::isExpandedAddRecExprPHI(PHINode *PN, Instruction *IncV,
884                                           const Loop *L) {
885  switch (IncV->getOpcode()) {
886  // Check for a simple Add/Sub or GEP of a loop invariant step.
887  case Instruction::Add:
888  case Instruction::Sub:
889    return IncV->getOperand(0) == PN
890      && L->isLoopInvariant(IncV->getOperand(1));
891  case Instruction::BitCast:
892    IncV = dyn_cast<GetElementPtrInst>(IncV->getOperand(0));
893    if (!IncV)
894      return false;
895    // fall-thru to GEP handling
896  case Instruction::GetElementPtr: {
897    // This must be a pointer addition of constants (pretty) or some number of
898    // address-size elements (ugly).
899    for (Instruction::op_iterator I = IncV->op_begin()+1, E = IncV->op_end();
900         I != E; ++I) {
901      if (isa<Constant>(*I))
902        continue;
903      // ugly geps have 2 operands.
904      // i1* is used by the expander to represent an address-size element.
905      if (IncV->getNumOperands() != 2)
906        return false;
907      unsigned AS = cast<PointerType>(IncV->getType())->getAddressSpace();
908      if (IncV->getType() != Type::getInt1PtrTy(SE.getContext(), AS)
909          && IncV->getType() != Type::getInt8PtrTy(SE.getContext(), AS))
910        return false;
911      // Ensure the operands dominate the insertion point. I don't know of a
912      // case when this would not be true, so this is somewhat untested.
913      if (L == IVIncInsertLoop) {
914        for (User::op_iterator OI = IncV->op_begin()+1,
915               OE = IncV->op_end(); OI != OE; ++OI)
916          if (Instruction *OInst = dyn_cast<Instruction>(OI))
917            if (!SE.DT->dominates(OInst, IVIncInsertPos))
918              return false;
919      }
920      break;
921    }
922    IncV = dyn_cast<Instruction>(IncV->getOperand(0));
923    if (IncV && IncV->getOpcode() == Instruction::BitCast)
924      IncV = dyn_cast<Instruction>(IncV->getOperand(0));
925    return IncV == PN;
926  }
927  default:
928    return false;
929  }
930}
931
932/// getAddRecExprPHILiterally - Helper for expandAddRecExprLiterally. Expand
933/// the base addrec, which is the addrec without any non-loop-dominating
934/// values, and return the PHI.
935PHINode *
936SCEVExpander::getAddRecExprPHILiterally(const SCEVAddRecExpr *Normalized,
937                                        const Loop *L,
938                                        Type *ExpandTy,
939                                        Type *IntTy) {
940  assert((!IVIncInsertLoop||IVIncInsertPos) && "Uninitialized insert position");
941
942  // Reuse a previously-inserted PHI, if present.
943  BasicBlock *LatchBlock = L->getLoopLatch();
944  if (LatchBlock) {
945    for (BasicBlock::iterator I = L->getHeader()->begin();
946         PHINode *PN = dyn_cast<PHINode>(I); ++I) {
947      if (!SE.isSCEVable(PN->getType()) ||
948          (SE.getEffectiveSCEVType(PN->getType()) !=
949           SE.getEffectiveSCEVType(Normalized->getType())) ||
950          SE.getSCEV(PN) != Normalized)
951        continue;
952
953      Instruction *IncV =
954        cast<Instruction>(PN->getIncomingValueForBlock(LatchBlock));
955
956      if (LSRMode) {
957        if (!isExpandedAddRecExprPHI(PN, IncV, L))
958          continue;
959      }
960      else {
961        if (!isNormalAddRecExprPHI(PN, IncV, L))
962          continue;
963      }
964      // Ok, the add recurrence looks usable.
965      // Remember this PHI, even in post-inc mode.
966      InsertedValues.insert(PN);
967      // Remember the increment.
968      rememberInstruction(IncV);
969      if (L == IVIncInsertLoop)
970        do {
971          if (SE.DT->dominates(IncV, IVIncInsertPos))
972            break;
973          // Make sure the increment is where we want it. But don't move it
974          // down past a potential existing post-inc user.
975          IncV->moveBefore(IVIncInsertPos);
976          IVIncInsertPos = IncV;
977          IncV = cast<Instruction>(IncV->getOperand(0));
978        } while (IncV != PN);
979      return PN;
980    }
981  }
982
983  // Save the original insertion point so we can restore it when we're done.
984  BasicBlock *SaveInsertBB = Builder.GetInsertBlock();
985  BasicBlock::iterator SaveInsertPt = Builder.GetInsertPoint();
986
987  // Expand code for the start value.
988  Value *StartV = expandCodeFor(Normalized->getStart(), ExpandTy,
989                                L->getHeader()->begin());
990
991  // StartV must be hoisted into L's preheader to dominate the new phi.
992  assert(!isa<Instruction>(StartV) ||
993         SE.DT->properlyDominates(cast<Instruction>(StartV)->getParent(),
994                                  L->getHeader()));
995
996  // Expand code for the step value. Insert instructions right before the
997  // terminator corresponding to the back-edge. Do this before creating the PHI
998  // so that PHI reuse code doesn't see an incomplete PHI. If the stride is
999  // negative, insert a sub instead of an add for the increment (unless it's a
1000  // constant, because subtracts of constants are canonicalized to adds).
1001  const SCEV *Step = Normalized->getStepRecurrence(SE);
1002  bool isPointer = ExpandTy->isPointerTy();
1003  bool isNegative = !isPointer && isNonConstantNegative(Step);
1004  if (isNegative)
1005    Step = SE.getNegativeSCEV(Step);
1006  Value *StepV = expandCodeFor(Step, IntTy, L->getHeader()->begin());
1007
1008  // Create the PHI.
1009  BasicBlock *Header = L->getHeader();
1010  Builder.SetInsertPoint(Header, Header->begin());
1011  pred_iterator HPB = pred_begin(Header), HPE = pred_end(Header);
1012  PHINode *PN = Builder.CreatePHI(ExpandTy, std::distance(HPB, HPE),
1013                                  Twine(IVName) + ".iv");
1014  rememberInstruction(PN);
1015
1016  // Create the step instructions and populate the PHI.
1017  for (pred_iterator HPI = HPB; HPI != HPE; ++HPI) {
1018    BasicBlock *Pred = *HPI;
1019
1020    // Add a start value.
1021    if (!L->contains(Pred)) {
1022      PN->addIncoming(StartV, Pred);
1023      continue;
1024    }
1025
1026    // Create a step value and add it to the PHI. If IVIncInsertLoop is
1027    // non-null and equal to the addrec's loop, insert the instructions
1028    // at IVIncInsertPos.
1029    Instruction *InsertPos = L == IVIncInsertLoop ?
1030      IVIncInsertPos : Pred->getTerminator();
1031    Builder.SetInsertPoint(InsertPos);
1032    Value *IncV;
1033    // If the PHI is a pointer, use a GEP, otherwise use an add or sub.
1034    if (isPointer) {
1035      PointerType *GEPPtrTy = cast<PointerType>(ExpandTy);
1036      // If the step isn't constant, don't use an implicitly scaled GEP, because
1037      // that would require a multiply inside the loop.
1038      if (!isa<ConstantInt>(StepV))
1039        GEPPtrTy = PointerType::get(Type::getInt1Ty(SE.getContext()),
1040                                    GEPPtrTy->getAddressSpace());
1041      const SCEV *const StepArray[1] = { SE.getSCEV(StepV) };
1042      IncV = expandAddToGEP(StepArray, StepArray+1, GEPPtrTy, IntTy, PN);
1043      if (IncV->getType() != PN->getType()) {
1044        IncV = Builder.CreateBitCast(IncV, PN->getType());
1045        rememberInstruction(IncV);
1046      }
1047    } else {
1048      IncV = isNegative ?
1049        Builder.CreateSub(PN, StepV, Twine(IVName) + ".iv.next") :
1050        Builder.CreateAdd(PN, StepV, Twine(IVName) + ".iv.next");
1051      rememberInstruction(IncV);
1052    }
1053    PN->addIncoming(IncV, Pred);
1054  }
1055
1056  // Restore the original insert point.
1057  if (SaveInsertBB)
1058    restoreInsertPoint(SaveInsertBB, SaveInsertPt);
1059
1060  // Remember this PHI, even in post-inc mode.
1061  InsertedValues.insert(PN);
1062
1063  return PN;
1064}
1065
1066Value *SCEVExpander::expandAddRecExprLiterally(const SCEVAddRecExpr *S) {
1067  Type *STy = S->getType();
1068  Type *IntTy = SE.getEffectiveSCEVType(STy);
1069  const Loop *L = S->getLoop();
1070
1071  // Determine a normalized form of this expression, which is the expression
1072  // before any post-inc adjustment is made.
1073  const SCEVAddRecExpr *Normalized = S;
1074  if (PostIncLoops.count(L)) {
1075    PostIncLoopSet Loops;
1076    Loops.insert(L);
1077    Normalized =
1078      cast<SCEVAddRecExpr>(TransformForPostIncUse(Normalize, S, 0, 0,
1079                                                  Loops, SE, *SE.DT));
1080  }
1081
1082  // Strip off any non-loop-dominating component from the addrec start.
1083  const SCEV *Start = Normalized->getStart();
1084  const SCEV *PostLoopOffset = 0;
1085  if (!SE.properlyDominates(Start, L->getHeader())) {
1086    PostLoopOffset = Start;
1087    Start = SE.getConstant(Normalized->getType(), 0);
1088    Normalized = cast<SCEVAddRecExpr>(
1089      SE.getAddRecExpr(Start, Normalized->getStepRecurrence(SE),
1090                       Normalized->getLoop(),
1091                       // FIXME: Normalized->getNoWrapFlags(FlagNW)
1092                       SCEV::FlagAnyWrap));
1093  }
1094
1095  // Strip off any non-loop-dominating component from the addrec step.
1096  const SCEV *Step = Normalized->getStepRecurrence(SE);
1097  const SCEV *PostLoopScale = 0;
1098  if (!SE.dominates(Step, L->getHeader())) {
1099    PostLoopScale = Step;
1100    Step = SE.getConstant(Normalized->getType(), 1);
1101    Normalized =
1102      cast<SCEVAddRecExpr>(SE.getAddRecExpr(Start, Step,
1103                                            Normalized->getLoop(),
1104                                            // FIXME: Normalized
1105                                            // ->getNoWrapFlags(FlagNW)
1106                                            SCEV::FlagAnyWrap));
1107  }
1108
1109  // Expand the core addrec. If we need post-loop scaling, force it to
1110  // expand to an integer type to avoid the need for additional casting.
1111  Type *ExpandTy = PostLoopScale ? IntTy : STy;
1112  PHINode *PN = getAddRecExprPHILiterally(Normalized, L, ExpandTy, IntTy);
1113
1114  // Accommodate post-inc mode, if necessary.
1115  Value *Result;
1116  if (!PostIncLoops.count(L))
1117    Result = PN;
1118  else {
1119    // In PostInc mode, use the post-incremented value.
1120    BasicBlock *LatchBlock = L->getLoopLatch();
1121    assert(LatchBlock && "PostInc mode requires a unique loop latch!");
1122    Result = PN->getIncomingValueForBlock(LatchBlock);
1123
1124    // For an expansion to use the postinc form, the client must call
1125    // expandCodeFor with an InsertPoint that is either outside the PostIncLoop
1126    // or dominated by IVIncInsertPos.
1127    assert((!isa<Instruction>(Result) ||
1128            SE.DT->dominates(cast<Instruction>(Result),
1129                             Builder.GetInsertPoint())) &&
1130           "postinc expansion does not dominate use");
1131  }
1132
1133  // Re-apply any non-loop-dominating scale.
1134  if (PostLoopScale) {
1135    Result = InsertNoopCastOfTo(Result, IntTy);
1136    Result = Builder.CreateMul(Result,
1137                               expandCodeFor(PostLoopScale, IntTy));
1138    rememberInstruction(Result);
1139  }
1140
1141  // Re-apply any non-loop-dominating offset.
1142  if (PostLoopOffset) {
1143    if (PointerType *PTy = dyn_cast<PointerType>(ExpandTy)) {
1144      const SCEV *const OffsetArray[1] = { PostLoopOffset };
1145      Result = expandAddToGEP(OffsetArray, OffsetArray+1, PTy, IntTy, Result);
1146    } else {
1147      Result = InsertNoopCastOfTo(Result, IntTy);
1148      Result = Builder.CreateAdd(Result,
1149                                 expandCodeFor(PostLoopOffset, IntTy));
1150      rememberInstruction(Result);
1151    }
1152  }
1153
1154  return Result;
1155}
1156
1157Value *SCEVExpander::visitAddRecExpr(const SCEVAddRecExpr *S) {
1158  if (!CanonicalMode) return expandAddRecExprLiterally(S);
1159
1160  Type *Ty = SE.getEffectiveSCEVType(S->getType());
1161  const Loop *L = S->getLoop();
1162
1163  // First check for an existing canonical IV in a suitable type.
1164  PHINode *CanonicalIV = 0;
1165  if (PHINode *PN = L->getCanonicalInductionVariable())
1166    if (SE.getTypeSizeInBits(PN->getType()) >= SE.getTypeSizeInBits(Ty))
1167      CanonicalIV = PN;
1168
1169  // Rewrite an AddRec in terms of the canonical induction variable, if
1170  // its type is more narrow.
1171  if (CanonicalIV &&
1172      SE.getTypeSizeInBits(CanonicalIV->getType()) >
1173      SE.getTypeSizeInBits(Ty)) {
1174    SmallVector<const SCEV *, 4> NewOps(S->getNumOperands());
1175    for (unsigned i = 0, e = S->getNumOperands(); i != e; ++i)
1176      NewOps[i] = SE.getAnyExtendExpr(S->op_begin()[i], CanonicalIV->getType());
1177    Value *V = expand(SE.getAddRecExpr(NewOps, S->getLoop(),
1178                                       // FIXME: S->getNoWrapFlags(FlagNW)
1179                                       SCEV::FlagAnyWrap));
1180    BasicBlock *SaveInsertBB = Builder.GetInsertBlock();
1181    BasicBlock::iterator SaveInsertPt = Builder.GetInsertPoint();
1182    BasicBlock::iterator NewInsertPt =
1183      llvm::next(BasicBlock::iterator(cast<Instruction>(V)));
1184    while (isa<PHINode>(NewInsertPt) || isa<DbgInfoIntrinsic>(NewInsertPt) ||
1185           isa<LandingPadInst>(NewInsertPt))
1186      ++NewInsertPt;
1187    V = expandCodeFor(SE.getTruncateExpr(SE.getUnknown(V), Ty), 0,
1188                      NewInsertPt);
1189    restoreInsertPoint(SaveInsertBB, SaveInsertPt);
1190    return V;
1191  }
1192
1193  // {X,+,F} --> X + {0,+,F}
1194  if (!S->getStart()->isZero()) {
1195    SmallVector<const SCEV *, 4> NewOps(S->op_begin(), S->op_end());
1196    NewOps[0] = SE.getConstant(Ty, 0);
1197    // FIXME: can use S->getNoWrapFlags()
1198    const SCEV *Rest = SE.getAddRecExpr(NewOps, L, SCEV::FlagAnyWrap);
1199
1200    // Turn things like ptrtoint+arithmetic+inttoptr into GEP. See the
1201    // comments on expandAddToGEP for details.
1202    const SCEV *Base = S->getStart();
1203    const SCEV *RestArray[1] = { Rest };
1204    // Dig into the expression to find the pointer base for a GEP.
1205    ExposePointerBase(Base, RestArray[0], SE);
1206    // If we found a pointer, expand the AddRec with a GEP.
1207    if (PointerType *PTy = dyn_cast<PointerType>(Base->getType())) {
1208      // Make sure the Base isn't something exotic, such as a multiplied
1209      // or divided pointer value. In those cases, the result type isn't
1210      // actually a pointer type.
1211      if (!isa<SCEVMulExpr>(Base) && !isa<SCEVUDivExpr>(Base)) {
1212        Value *StartV = expand(Base);
1213        assert(StartV->getType() == PTy && "Pointer type mismatch for GEP!");
1214        return expandAddToGEP(RestArray, RestArray+1, PTy, Ty, StartV);
1215      }
1216    }
1217
1218    // Just do a normal add. Pre-expand the operands to suppress folding.
1219    return expand(SE.getAddExpr(SE.getUnknown(expand(S->getStart())),
1220                                SE.getUnknown(expand(Rest))));
1221  }
1222
1223  // If we don't yet have a canonical IV, create one.
1224  if (!CanonicalIV) {
1225    // Create and insert the PHI node for the induction variable in the
1226    // specified loop.
1227    BasicBlock *Header = L->getHeader();
1228    pred_iterator HPB = pred_begin(Header), HPE = pred_end(Header);
1229    CanonicalIV = PHINode::Create(Ty, std::distance(HPB, HPE), "indvar",
1230                                  Header->begin());
1231    rememberInstruction(CanonicalIV);
1232
1233    Constant *One = ConstantInt::get(Ty, 1);
1234    for (pred_iterator HPI = HPB; HPI != HPE; ++HPI) {
1235      BasicBlock *HP = *HPI;
1236      if (L->contains(HP)) {
1237        // Insert a unit add instruction right before the terminator
1238        // corresponding to the back-edge.
1239        Instruction *Add = BinaryOperator::CreateAdd(CanonicalIV, One,
1240                                                     "indvar.next",
1241                                                     HP->getTerminator());
1242        Add->setDebugLoc(HP->getTerminator()->getDebugLoc());
1243        rememberInstruction(Add);
1244        CanonicalIV->addIncoming(Add, HP);
1245      } else {
1246        CanonicalIV->addIncoming(Constant::getNullValue(Ty), HP);
1247      }
1248    }
1249  }
1250
1251  // {0,+,1} --> Insert a canonical induction variable into the loop!
1252  if (S->isAffine() && S->getOperand(1)->isOne()) {
1253    assert(Ty == SE.getEffectiveSCEVType(CanonicalIV->getType()) &&
1254           "IVs with types different from the canonical IV should "
1255           "already have been handled!");
1256    return CanonicalIV;
1257  }
1258
1259  // {0,+,F} --> {0,+,1} * F
1260
1261  // If this is a simple linear addrec, emit it now as a special case.
1262  if (S->isAffine())    // {0,+,F} --> i*F
1263    return
1264      expand(SE.getTruncateOrNoop(
1265        SE.getMulExpr(SE.getUnknown(CanonicalIV),
1266                      SE.getNoopOrAnyExtend(S->getOperand(1),
1267                                            CanonicalIV->getType())),
1268        Ty));
1269
1270  // If this is a chain of recurrences, turn it into a closed form, using the
1271  // folders, then expandCodeFor the closed form.  This allows the folders to
1272  // simplify the expression without having to build a bunch of special code
1273  // into this folder.
1274  const SCEV *IH = SE.getUnknown(CanonicalIV);   // Get I as a "symbolic" SCEV.
1275
1276  // Promote S up to the canonical IV type, if the cast is foldable.
1277  const SCEV *NewS = S;
1278  const SCEV *Ext = SE.getNoopOrAnyExtend(S, CanonicalIV->getType());
1279  if (isa<SCEVAddRecExpr>(Ext))
1280    NewS = Ext;
1281
1282  const SCEV *V = cast<SCEVAddRecExpr>(NewS)->evaluateAtIteration(IH, SE);
1283  //cerr << "Evaluated: " << *this << "\n     to: " << *V << "\n";
1284
1285  // Truncate the result down to the original type, if needed.
1286  const SCEV *T = SE.getTruncateOrNoop(V, Ty);
1287  return expand(T);
1288}
1289
1290Value *SCEVExpander::visitTruncateExpr(const SCEVTruncateExpr *S) {
1291  Type *Ty = SE.getEffectiveSCEVType(S->getType());
1292  Value *V = expandCodeFor(S->getOperand(),
1293                           SE.getEffectiveSCEVType(S->getOperand()->getType()));
1294  Value *I = Builder.CreateTrunc(V, Ty);
1295  rememberInstruction(I);
1296  return I;
1297}
1298
1299Value *SCEVExpander::visitZeroExtendExpr(const SCEVZeroExtendExpr *S) {
1300  Type *Ty = SE.getEffectiveSCEVType(S->getType());
1301  Value *V = expandCodeFor(S->getOperand(),
1302                           SE.getEffectiveSCEVType(S->getOperand()->getType()));
1303  Value *I = Builder.CreateZExt(V, Ty);
1304  rememberInstruction(I);
1305  return I;
1306}
1307
1308Value *SCEVExpander::visitSignExtendExpr(const SCEVSignExtendExpr *S) {
1309  Type *Ty = SE.getEffectiveSCEVType(S->getType());
1310  Value *V = expandCodeFor(S->getOperand(),
1311                           SE.getEffectiveSCEVType(S->getOperand()->getType()));
1312  Value *I = Builder.CreateSExt(V, Ty);
1313  rememberInstruction(I);
1314  return I;
1315}
1316
1317Value *SCEVExpander::visitSMaxExpr(const SCEVSMaxExpr *S) {
1318  Value *LHS = expand(S->getOperand(S->getNumOperands()-1));
1319  Type *Ty = LHS->getType();
1320  for (int i = S->getNumOperands()-2; i >= 0; --i) {
1321    // In the case of mixed integer and pointer types, do the
1322    // rest of the comparisons as integer.
1323    if (S->getOperand(i)->getType() != Ty) {
1324      Ty = SE.getEffectiveSCEVType(Ty);
1325      LHS = InsertNoopCastOfTo(LHS, Ty);
1326    }
1327    Value *RHS = expandCodeFor(S->getOperand(i), Ty);
1328    Value *ICmp = Builder.CreateICmpSGT(LHS, RHS);
1329    rememberInstruction(ICmp);
1330    Value *Sel = Builder.CreateSelect(ICmp, LHS, RHS, "smax");
1331    rememberInstruction(Sel);
1332    LHS = Sel;
1333  }
1334  // In the case of mixed integer and pointer types, cast the
1335  // final result back to the pointer type.
1336  if (LHS->getType() != S->getType())
1337    LHS = InsertNoopCastOfTo(LHS, S->getType());
1338  return LHS;
1339}
1340
1341Value *SCEVExpander::visitUMaxExpr(const SCEVUMaxExpr *S) {
1342  Value *LHS = expand(S->getOperand(S->getNumOperands()-1));
1343  Type *Ty = LHS->getType();
1344  for (int i = S->getNumOperands()-2; i >= 0; --i) {
1345    // In the case of mixed integer and pointer types, do the
1346    // rest of the comparisons as integer.
1347    if (S->getOperand(i)->getType() != Ty) {
1348      Ty = SE.getEffectiveSCEVType(Ty);
1349      LHS = InsertNoopCastOfTo(LHS, Ty);
1350    }
1351    Value *RHS = expandCodeFor(S->getOperand(i), Ty);
1352    Value *ICmp = Builder.CreateICmpUGT(LHS, RHS);
1353    rememberInstruction(ICmp);
1354    Value *Sel = Builder.CreateSelect(ICmp, LHS, RHS, "umax");
1355    rememberInstruction(Sel);
1356    LHS = Sel;
1357  }
1358  // In the case of mixed integer and pointer types, cast the
1359  // final result back to the pointer type.
1360  if (LHS->getType() != S->getType())
1361    LHS = InsertNoopCastOfTo(LHS, S->getType());
1362  return LHS;
1363}
1364
1365Value *SCEVExpander::expandCodeFor(const SCEV *SH, Type *Ty,
1366                                   Instruction *I) {
1367  BasicBlock::iterator IP = I;
1368  while (isInsertedInstruction(IP) || isa<DbgInfoIntrinsic>(IP))
1369    ++IP;
1370  Builder.SetInsertPoint(IP->getParent(), IP);
1371  return expandCodeFor(SH, Ty);
1372}
1373
1374Value *SCEVExpander::expandCodeFor(const SCEV *SH, Type *Ty) {
1375  // Expand the code for this SCEV.
1376  Value *V = expand(SH);
1377  if (Ty) {
1378    assert(SE.getTypeSizeInBits(Ty) == SE.getTypeSizeInBits(SH->getType()) &&
1379           "non-trivial casts should be done with the SCEVs directly!");
1380    V = InsertNoopCastOfTo(V, Ty);
1381  }
1382  return V;
1383}
1384
1385Value *SCEVExpander::expand(const SCEV *S) {
1386  // Compute an insertion point for this SCEV object. Hoist the instructions
1387  // as far out in the loop nest as possible.
1388  Instruction *InsertPt = Builder.GetInsertPoint();
1389  for (Loop *L = SE.LI->getLoopFor(Builder.GetInsertBlock()); ;
1390       L = L->getParentLoop())
1391    if (SE.isLoopInvariant(S, L)) {
1392      if (!L) break;
1393      if (BasicBlock *Preheader = L->getLoopPreheader())
1394        InsertPt = Preheader->getTerminator();
1395    } else {
1396      // If the SCEV is computable at this level, insert it into the header
1397      // after the PHIs (and after any other instructions that we've inserted
1398      // there) so that it is guaranteed to dominate any user inside the loop.
1399      if (L && SE.hasComputableLoopEvolution(S, L) && !PostIncLoops.count(L))
1400        InsertPt = L->getHeader()->getFirstInsertionPt();
1401      while (isInsertedInstruction(InsertPt) || isa<DbgInfoIntrinsic>(InsertPt))
1402        InsertPt = llvm::next(BasicBlock::iterator(InsertPt));
1403      break;
1404    }
1405
1406  // Check to see if we already expanded this here.
1407  std::map<std::pair<const SCEV *, Instruction *>,
1408           AssertingVH<Value> >::iterator I =
1409    InsertedExpressions.find(std::make_pair(S, InsertPt));
1410  if (I != InsertedExpressions.end())
1411    return I->second;
1412
1413  BasicBlock *SaveInsertBB = Builder.GetInsertBlock();
1414  BasicBlock::iterator SaveInsertPt = Builder.GetInsertPoint();
1415  Builder.SetInsertPoint(InsertPt->getParent(), InsertPt);
1416
1417  // Expand the expression into instructions.
1418  Value *V = visit(S);
1419
1420  // Remember the expanded value for this SCEV at this location.
1421  //
1422  // This is independent of PostIncLoops. The mapped value simply materializes
1423  // the expression at this insertion point. If the mapped value happened to be
1424  // a postinc expansion, it could be reused by a non postinc user, but only if
1425  // its insertion point was already at the head of the loop.
1426  InsertedExpressions[std::make_pair(S, InsertPt)] = V;
1427
1428  restoreInsertPoint(SaveInsertBB, SaveInsertPt);
1429  return V;
1430}
1431
1432void SCEVExpander::rememberInstruction(Value *I) {
1433  if (!PostIncLoops.empty())
1434    InsertedPostIncValues.insert(I);
1435  else
1436    InsertedValues.insert(I);
1437
1438  // If we just claimed an existing instruction and that instruction had
1439  // been the insert point, adjust the insert point forward so that
1440  // subsequently inserted code will be dominated.
1441  if (Builder.GetInsertPoint() == I) {
1442    BasicBlock::iterator It = cast<Instruction>(I);
1443    do { ++It; } while (isInsertedInstruction(It) ||
1444                        isa<DbgInfoIntrinsic>(It));
1445    Builder.SetInsertPoint(Builder.GetInsertBlock(), It);
1446  }
1447}
1448
1449void SCEVExpander::restoreInsertPoint(BasicBlock *BB, BasicBlock::iterator I) {
1450  // If we acquired more instructions since the old insert point was saved,
1451  // advance past them.
1452  while (isInsertedInstruction(I) || isa<DbgInfoIntrinsic>(I)) ++I;
1453
1454  Builder.SetInsertPoint(BB, I);
1455}
1456
1457/// getOrInsertCanonicalInductionVariable - This method returns the
1458/// canonical induction variable of the specified type for the specified
1459/// loop (inserting one if there is none).  A canonical induction variable
1460/// starts at zero and steps by one on each iteration.
1461PHINode *
1462SCEVExpander::getOrInsertCanonicalInductionVariable(const Loop *L,
1463                                                    Type *Ty) {
1464  assert(Ty->isIntegerTy() && "Can only insert integer induction variables!");
1465
1466  // Build a SCEV for {0,+,1}<L>.
1467  // Conservatively use FlagAnyWrap for now.
1468  const SCEV *H = SE.getAddRecExpr(SE.getConstant(Ty, 0),
1469                                   SE.getConstant(Ty, 1), L, SCEV::FlagAnyWrap);
1470
1471  // Emit code for it.
1472  BasicBlock *SaveInsertBB = Builder.GetInsertBlock();
1473  BasicBlock::iterator SaveInsertPt = Builder.GetInsertPoint();
1474  PHINode *V = cast<PHINode>(expandCodeFor(H, 0, L->getHeader()->begin()));
1475  if (SaveInsertBB)
1476    restoreInsertPoint(SaveInsertBB, SaveInsertPt);
1477
1478  return V;
1479}
1480
1481/// hoistStep - Attempt to hoist an IV increment above a potential use.
1482///
1483/// To successfully hoist, two criteria must be met:
1484/// - IncV operands dominate InsertPos and
1485/// - InsertPos dominates IncV
1486///
1487/// Meeting the second condition means that we don't need to check all of IncV's
1488/// existing uses (it's moving up in the domtree).
1489///
1490/// This does not yet recursively hoist the operands, although that would
1491/// not be difficult.
1492///
1493/// This does not require a SCEVExpander instance and could be replaced by a
1494/// general code-insertion helper.
1495bool SCEVExpander::hoistStep(Instruction *IncV, Instruction *InsertPos,
1496                             const DominatorTree *DT) {
1497  if (DT->dominates(IncV, InsertPos))
1498    return true;
1499
1500  if (!DT->dominates(InsertPos->getParent(), IncV->getParent()))
1501    return false;
1502
1503  if (IncV->mayHaveSideEffects())
1504    return false;
1505
1506  // Attempt to hoist IncV
1507  for (User::op_iterator OI = IncV->op_begin(), OE = IncV->op_end();
1508       OI != OE; ++OI) {
1509    Instruction *OInst = dyn_cast<Instruction>(OI);
1510    if (OInst && !DT->dominates(OInst, InsertPos))
1511      return false;
1512  }
1513  IncV->moveBefore(InsertPos);
1514  return true;
1515}
1516
1517/// replaceCongruentIVs - Check for congruent phis in this loop header and
1518/// replace them with their most canonical representative. Return the number of
1519/// phis eliminated.
1520///
1521/// This does not depend on any SCEVExpander state but should be used in
1522/// the same context that SCEVExpander is used.
1523unsigned SCEVExpander::replaceCongruentIVs(Loop *L, const DominatorTree *DT,
1524                                           SmallVectorImpl<WeakVH> &DeadInsts) {
1525  unsigned NumElim = 0;
1526  DenseMap<const SCEV *, PHINode *> ExprToIVMap;
1527  for (BasicBlock::iterator I = L->getHeader()->begin(); isa<PHINode>(I); ++I) {
1528    PHINode *Phi = cast<PHINode>(I);
1529    if (!SE.isSCEVable(Phi->getType()))
1530      continue;
1531
1532    PHINode *&OrigPhiRef = ExprToIVMap[SE.getSCEV(Phi)];
1533    if (!OrigPhiRef) {
1534      OrigPhiRef = Phi;
1535      continue;
1536    }
1537
1538    // If one phi derives from the other via GEPs, types may differ.
1539    // We could consider adding a bitcast here to handle it.
1540    if (OrigPhiRef->getType() != Phi->getType())
1541      continue;
1542
1543    if (BasicBlock *LatchBlock = L->getLoopLatch()) {
1544      Instruction *OrigInc =
1545        cast<Instruction>(OrigPhiRef->getIncomingValueForBlock(LatchBlock));
1546      Instruction *IsomorphicInc =
1547        cast<Instruction>(Phi->getIncomingValueForBlock(LatchBlock));
1548
1549      // If this phi is more canonical, swap it with the original.
1550      if (!isExpandedAddRecExprPHI(OrigPhiRef, OrigInc, L)
1551          && isExpandedAddRecExprPHI(Phi, IsomorphicInc, L)) {
1552        std::swap(OrigPhiRef, Phi);
1553        std::swap(OrigInc, IsomorphicInc);
1554      }
1555      // Replacing the congruent phi is sufficient because acyclic redundancy
1556      // elimination, CSE/GVN, should handle the rest. However, once SCEV proves
1557      // that a phi is congruent, it's often the head of an IV user cycle that
1558      // is isomorphic with the original phi. So it's worth eagerly cleaning up
1559      // the common case of a single IV increment.
1560      if (OrigInc != IsomorphicInc &&
1561          OrigInc->getType() == IsomorphicInc->getType() &&
1562          SE.getSCEV(OrigInc) == SE.getSCEV(IsomorphicInc) &&
1563          hoistStep(OrigInc, IsomorphicInc, DT)) {
1564        DEBUG_WITH_TYPE(DebugType, dbgs()
1565                        << "INDVARS: Eliminated congruent iv.inc: "
1566                        << *IsomorphicInc << '\n');
1567        IsomorphicInc->replaceAllUsesWith(OrigInc);
1568        DeadInsts.push_back(IsomorphicInc);
1569      }
1570    }
1571    DEBUG_WITH_TYPE(DebugType, dbgs()
1572                    << "INDVARS: Eliminated congruent iv: " << *Phi << '\n');
1573    ++NumElim;
1574    Phi->replaceAllUsesWith(OrigPhiRef);
1575    DeadInsts.push_back(Phi);
1576  }
1577  return NumElim;
1578}
1579