ConstantFolding.cpp revision 3bfbc4587a7e79f08f8c126a9e62c3475fb90f8b
15f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)//===-- ConstantFolding.cpp - Fold instructions into constants ------------===//
25f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)//
35f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)//                     The LLVM Compiler Infrastructure
45f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)//
55f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)// This file is distributed under the University of Illinois Open Source
66e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)// License. See LICENSE.TXT for details.
76e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)//
85f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)//===----------------------------------------------------------------------===//
96e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)//
106e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)// This file defines routines for folding instructions into constants.
115f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)//
126e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)// Also, to supplement the basic VMCore ConstantExpr simplifications,
136e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)// this file defines some additional folding routines that can make use of
145f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)// TargetData information. These functions cannot go in VMCore due to library
155f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)// dependency issues.
165f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)//
175f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)//===----------------------------------------------------------------------===//
185f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
195f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/Analysis/ConstantFolding.h"
205f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/Constants.h"
215f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/DerivedTypes.h"
225f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/Function.h"
235f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/GlobalVariable.h"
245f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/Instructions.h"
255f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/Intrinsics.h"
265f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/LLVMContext.h"
275f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/ADT/SmallVector.h"
285f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/ADT/StringMap.h"
295f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/Target/TargetData.h"
305f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/Support/ErrorHandling.h"
315f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/Support/GetElementPtrTypeIterator.h"
325f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include "llvm/Support/MathExtras.h"
335f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include <cerrno>
345f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)#include <cmath>
355f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)using namespace llvm;
365f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
375f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)//===----------------------------------------------------------------------===//
385f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)// Constant Folding internal helper functions
395f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)//===----------------------------------------------------------------------===//
405f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
415f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)/// IsConstantOffsetFromGlobal - If this constant is actually a constant offset
426e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)/// from a global, return the global and the constant.  Because of
435f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)/// constantexprs, this function is recursive.
445f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)static bool IsConstantOffsetFromGlobal(Constant *C, GlobalValue *&GV,
455f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)                                       int64_t &Offset, const TargetData &TD) {
465f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  // Trivial case, constant is the global.
475f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  if ((GV = dyn_cast<GlobalValue>(C))) {
485f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    Offset = 0;
495f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    return true;
505f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  }
515f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
525f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  // Otherwise, if this isn't a constant expr, bail out.
535f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  ConstantExpr *CE = dyn_cast<ConstantExpr>(C);
545f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  if (!CE) return false;
555f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
565f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  // Look through ptr->int and ptr->ptr casts.
576e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)  if (CE->getOpcode() == Instruction::PtrToInt ||
585f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)      CE->getOpcode() == Instruction::BitCast)
595f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    return IsConstantOffsetFromGlobal(CE->getOperand(0), GV, Offset, TD);
606e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)
615f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  // i32* getelementptr ([5 x i32]* @a, i32 0, i32 5)
625f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  if (CE->getOpcode() == Instruction::GetElementPtr) {
635f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    // Cannot compute this if the element type of the pointer is missing size
645f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    // info.
656e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)    if (!cast<PointerType>(CE->getOperand(0)->getType())
665f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)                 ->getElementType()->isSized())
675f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)      return false;
685f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
695f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    // If the base isn't a global+constant, we aren't either.
705f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    if (!IsConstantOffsetFromGlobal(CE->getOperand(0), GV, Offset, TD))
715f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)      return false;
725f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
735f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    // Otherwise, add any offset that our operands provide.
745f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    gep_type_iterator GTI = gep_type_begin(CE);
756e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)    for (User::const_op_iterator i = CE->op_begin() + 1, e = CE->op_end();
766e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)         i != e; ++i, ++GTI) {
776e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)      ConstantInt *CI = dyn_cast<ConstantInt>(*i);
786e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)      if (!CI) return false;  // Index isn't a simple constant?
796e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)      if (CI->getZExtValue() == 0) continue;  // Not adding anything.
805f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
815f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)      if (const StructType *ST = dyn_cast<StructType>(*GTI)) {
826e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)        // N = N + Offset
836e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)        Offset += TD.getStructLayout(ST)->getElementOffset(CI->getZExtValue());
845f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)      } else {
855f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)        const SequentialType *SQT = cast<SequentialType>(*GTI);
865f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)        Offset += TD.getTypeAllocSize(SQT->getElementType())*CI->getSExtValue();
875f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)      }
885f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    }
895f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    return true;
905f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  }
915f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
925f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  return false;
935f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)}
945f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
955f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
965f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)/// SymbolicallyEvaluateBinop - One of Op0/Op1 is a constant expression.
975f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)/// Attempt to symbolically evaluate the result of a binary operator merging
985f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)/// these together.  If target data info is available, it is provided as TD,
996e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)/// otherwise TD is null.
1005f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)static Constant *SymbolicallyEvaluateBinop(unsigned Opc, Constant *Op0,
1015f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)                                           Constant *Op1, const TargetData *TD,
1025f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)                                           LLVMContext &Context){
1035f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  // SROA
1045f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
1055f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  // Fold (and 0xffffffff00000000, (shl x, 32)) -> shl.
1065f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  // Fold (lshr (or X, Y), 32) -> (lshr [X/Y], 32) if one doesn't contribute
1075f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  // bits.
1085f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
1095f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)
1106e8cce623b6e4fe0c9e4af605d675dd9d0338c38Torne (Richard Coles)  // If the constant expr is something like &A[123] - &A[4].f, fold this into a
1115f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  // constant.  This happens frequently when iterating over a global array.
1125f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)  if (Opc == Instruction::Sub && TD) {
1135f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    GlobalValue *GV1, *GV2;
1145f1c94371a64b3196d4be9466099bb892df9b88eTorne (Richard Coles)    int64_t Offs1, Offs2;
115
116    if (IsConstantOffsetFromGlobal(Op0, GV1, Offs1, *TD))
117      if (IsConstantOffsetFromGlobal(Op1, GV2, Offs2, *TD) &&
118          GV1 == GV2) {
119        // (&GV+C1) - (&GV+C2) -> C1-C2, pointer arithmetic cannot overflow.
120        return ConstantInt::get(Op0->getType(), Offs1-Offs2);
121      }
122  }
123
124  return 0;
125}
126
127/// SymbolicallyEvaluateGEP - If we can symbolically evaluate the specified GEP
128/// constant expression, do so.
129static Constant *SymbolicallyEvaluateGEP(Constant* const* Ops, unsigned NumOps,
130                                         const Type *ResultTy,
131                                         LLVMContext &Context,
132                                         const TargetData *TD) {
133  Constant *Ptr = Ops[0];
134  if (!TD || !cast<PointerType>(Ptr->getType())->getElementType()->isSized())
135    return 0;
136
137  unsigned BitWidth = TD->getTypeSizeInBits(TD->getIntPtrType(Context));
138  APInt BasePtr(BitWidth, 0);
139  bool BaseIsInt = true;
140  if (!Ptr->isNullValue()) {
141    // If this is a inttoptr from a constant int, we can fold this as the base,
142    // otherwise we can't.
143    if (ConstantExpr *CE = dyn_cast<ConstantExpr>(Ptr))
144      if (CE->getOpcode() == Instruction::IntToPtr)
145        if (ConstantInt *Base = dyn_cast<ConstantInt>(CE->getOperand(0))) {
146          BasePtr = Base->getValue();
147          BasePtr.zextOrTrunc(BitWidth);
148        }
149
150    if (BasePtr == 0)
151      BaseIsInt = false;
152  }
153
154  // If this is a constant expr gep that is effectively computing an
155  // "offsetof", fold it into 'cast int Size to T*' instead of 'gep 0, 0, 12'
156  for (unsigned i = 1; i != NumOps; ++i)
157    if (!isa<ConstantInt>(Ops[i]))
158      return 0;
159
160  APInt Offset = APInt(BitWidth,
161                       TD->getIndexedOffset(Ptr->getType(),
162                                            (Value**)Ops+1, NumOps-1));
163  // If the base value for this address is a literal integer value, fold the
164  // getelementptr to the resulting integer value casted to the pointer type.
165  if (BaseIsInt) {
166    Constant *C = ConstantInt::get(Context, Offset+BasePtr);
167    return ConstantExpr::getIntToPtr(C, ResultTy);
168  }
169
170  // Otherwise form a regular getelementptr. Recompute the indices so that
171  // we eliminate over-indexing of the notional static type array bounds.
172  // This makes it easy to determine if the getelementptr is "inbounds".
173  // Also, this helps GlobalOpt do SROA on GlobalVariables.
174  const Type *Ty = Ptr->getType();
175  SmallVector<Constant*, 32> NewIdxs;
176  do {
177    if (const SequentialType *ATy = dyn_cast<SequentialType>(Ty)) {
178      // The only pointer indexing we'll do is on the first index of the GEP.
179      if (isa<PointerType>(ATy) && !NewIdxs.empty())
180        break;
181      // Determine which element of the array the offset points into.
182      APInt ElemSize(BitWidth, TD->getTypeAllocSize(ATy->getElementType()));
183      if (ElemSize == 0)
184        return 0;
185      APInt NewIdx = Offset.udiv(ElemSize);
186      Offset -= NewIdx * ElemSize;
187      NewIdxs.push_back(ConstantInt::get(TD->getIntPtrType(Context), NewIdx));
188      Ty = ATy->getElementType();
189    } else if (const StructType *STy = dyn_cast<StructType>(Ty)) {
190      // Determine which field of the struct the offset points into. The
191      // getZExtValue is at least as safe as the StructLayout API because we
192      // know the offset is within the struct at this point.
193      const StructLayout &SL = *TD->getStructLayout(STy);
194      unsigned ElIdx = SL.getElementContainingOffset(Offset.getZExtValue());
195      NewIdxs.push_back(ConstantInt::get(Type::getInt32Ty(Context), ElIdx));
196      Offset -= APInt(BitWidth, SL.getElementOffset(ElIdx));
197      Ty = STy->getTypeAtIndex(ElIdx);
198    } else {
199      // We've reached some non-indexable type.
200      break;
201    }
202  } while (Ty != cast<PointerType>(ResultTy)->getElementType());
203
204  // If we haven't used up the entire offset by descending the static
205  // type, then the offset is pointing into the middle of an indivisible
206  // member, so we can't simplify it.
207  if (Offset != 0)
208    return 0;
209
210  // Create a GEP.
211  Constant *C =
212    ConstantExpr::getGetElementPtr(Ptr, &NewIdxs[0], NewIdxs.size());
213  assert(cast<PointerType>(C->getType())->getElementType() == Ty &&
214         "Computed GetElementPtr has unexpected type!");
215
216  // If we ended up indexing a member with a type that doesn't match
217  // the type of what the original indices indexed, add a cast.
218  if (Ty != cast<PointerType>(ResultTy)->getElementType())
219    C = ConstantExpr::getBitCast(C, ResultTy);
220
221  return C;
222}
223
224/// FoldBitCast - Constant fold bitcast, symbolically evaluating it with
225/// targetdata.  Return 0 if unfoldable.
226static Constant *FoldBitCast(Constant *C, const Type *DestTy,
227                             const TargetData &TD, LLVMContext &Context) {
228  // If this is a bitcast from constant vector -> vector, fold it.
229  if (ConstantVector *CV = dyn_cast<ConstantVector>(C)) {
230    if (const VectorType *DestVTy = dyn_cast<VectorType>(DestTy)) {
231      // If the element types match, VMCore can fold it.
232      unsigned NumDstElt = DestVTy->getNumElements();
233      unsigned NumSrcElt = CV->getNumOperands();
234      if (NumDstElt == NumSrcElt)
235        return 0;
236
237      const Type *SrcEltTy = CV->getType()->getElementType();
238      const Type *DstEltTy = DestVTy->getElementType();
239
240      // Otherwise, we're changing the number of elements in a vector, which
241      // requires endianness information to do the right thing.  For example,
242      //    bitcast (<2 x i64> <i64 0, i64 1> to <4 x i32>)
243      // folds to (little endian):
244      //    <4 x i32> <i32 0, i32 0, i32 1, i32 0>
245      // and to (big endian):
246      //    <4 x i32> <i32 0, i32 0, i32 0, i32 1>
247
248      // First thing is first.  We only want to think about integer here, so if
249      // we have something in FP form, recast it as integer.
250      if (DstEltTy->isFloatingPoint()) {
251        // Fold to an vector of integers with same size as our FP type.
252        unsigned FPWidth = DstEltTy->getPrimitiveSizeInBits();
253        const Type *DestIVTy = VectorType::get(
254                                 IntegerType::get(Context, FPWidth), NumDstElt);
255        // Recursively handle this integer conversion, if possible.
256        C = FoldBitCast(C, DestIVTy, TD, Context);
257        if (!C) return 0;
258
259        // Finally, VMCore can handle this now that #elts line up.
260        return ConstantExpr::getBitCast(C, DestTy);
261      }
262
263      // Okay, we know the destination is integer, if the input is FP, convert
264      // it to integer first.
265      if (SrcEltTy->isFloatingPoint()) {
266        unsigned FPWidth = SrcEltTy->getPrimitiveSizeInBits();
267        const Type *SrcIVTy = VectorType::get(
268                                 IntegerType::get(Context, FPWidth), NumSrcElt);
269        // Ask VMCore to do the conversion now that #elts line up.
270        C = ConstantExpr::getBitCast(C, SrcIVTy);
271        CV = dyn_cast<ConstantVector>(C);
272        if (!CV) return 0;  // If VMCore wasn't able to fold it, bail out.
273      }
274
275      // Now we know that the input and output vectors are both integer vectors
276      // of the same size, and that their #elements is not the same.  Do the
277      // conversion here, which depends on whether the input or output has
278      // more elements.
279      bool isLittleEndian = TD.isLittleEndian();
280
281      SmallVector<Constant*, 32> Result;
282      if (NumDstElt < NumSrcElt) {
283        // Handle: bitcast (<4 x i32> <i32 0, i32 1, i32 2, i32 3> to <2 x i64>)
284        Constant *Zero = Constant::getNullValue(DstEltTy);
285        unsigned Ratio = NumSrcElt/NumDstElt;
286        unsigned SrcBitSize = SrcEltTy->getPrimitiveSizeInBits();
287        unsigned SrcElt = 0;
288        for (unsigned i = 0; i != NumDstElt; ++i) {
289          // Build each element of the result.
290          Constant *Elt = Zero;
291          unsigned ShiftAmt = isLittleEndian ? 0 : SrcBitSize*(Ratio-1);
292          for (unsigned j = 0; j != Ratio; ++j) {
293            Constant *Src = dyn_cast<ConstantInt>(CV->getOperand(SrcElt++));
294            if (!Src) return 0;  // Reject constantexpr elements.
295
296            // Zero extend the element to the right size.
297            Src = ConstantExpr::getZExt(Src, Elt->getType());
298
299            // Shift it to the right place, depending on endianness.
300            Src = ConstantExpr::getShl(Src,
301                             ConstantInt::get(Src->getType(), ShiftAmt));
302            ShiftAmt += isLittleEndian ? SrcBitSize : -SrcBitSize;
303
304            // Mix it in.
305            Elt = ConstantExpr::getOr(Elt, Src);
306          }
307          Result.push_back(Elt);
308        }
309      } else {
310        // Handle: bitcast (<2 x i64> <i64 0, i64 1> to <4 x i32>)
311        unsigned Ratio = NumDstElt/NumSrcElt;
312        unsigned DstBitSize = DstEltTy->getPrimitiveSizeInBits();
313
314        // Loop over each source value, expanding into multiple results.
315        for (unsigned i = 0; i != NumSrcElt; ++i) {
316          Constant *Src = dyn_cast<ConstantInt>(CV->getOperand(i));
317          if (!Src) return 0;  // Reject constantexpr elements.
318
319          unsigned ShiftAmt = isLittleEndian ? 0 : DstBitSize*(Ratio-1);
320          for (unsigned j = 0; j != Ratio; ++j) {
321            // Shift the piece of the value into the right place, depending on
322            // endianness.
323            Constant *Elt = ConstantExpr::getLShr(Src,
324                            ConstantInt::get(Src->getType(), ShiftAmt));
325            ShiftAmt += isLittleEndian ? DstBitSize : -DstBitSize;
326
327            // Truncate and remember this piece.
328            Result.push_back(ConstantExpr::getTrunc(Elt, DstEltTy));
329          }
330        }
331      }
332
333      return ConstantVector::get(Result.data(), Result.size());
334    }
335  }
336
337  return 0;
338}
339
340
341//===----------------------------------------------------------------------===//
342// Constant Folding public APIs
343//===----------------------------------------------------------------------===//
344
345
346/// ConstantFoldInstruction - Attempt to constant fold the specified
347/// instruction.  If successful, the constant result is returned, if not, null
348/// is returned.  Note that this function can only fail when attempting to fold
349/// instructions like loads and stores, which have no constant expression form.
350///
351Constant *llvm::ConstantFoldInstruction(Instruction *I, LLVMContext &Context,
352                                        const TargetData *TD) {
353  if (PHINode *PN = dyn_cast<PHINode>(I)) {
354    if (PN->getNumIncomingValues() == 0)
355      return UndefValue::get(PN->getType());
356
357    Constant *Result = dyn_cast<Constant>(PN->getIncomingValue(0));
358    if (Result == 0) return 0;
359
360    // Handle PHI nodes specially here...
361    for (unsigned i = 1, e = PN->getNumIncomingValues(); i != e; ++i)
362      if (PN->getIncomingValue(i) != Result && PN->getIncomingValue(i) != PN)
363        return 0;   // Not all the same incoming constants...
364
365    // If we reach here, all incoming values are the same constant.
366    return Result;
367  }
368
369  // Scan the operand list, checking to see if they are all constants, if so,
370  // hand off to ConstantFoldInstOperands.
371  SmallVector<Constant*, 8> Ops;
372  for (User::op_iterator i = I->op_begin(), e = I->op_end(); i != e; ++i)
373    if (Constant *Op = dyn_cast<Constant>(*i))
374      Ops.push_back(Op);
375    else
376      return 0;  // All operands not constant!
377
378  if (const CmpInst *CI = dyn_cast<CmpInst>(I))
379    return ConstantFoldCompareInstOperands(CI->getPredicate(),
380                                           Ops.data(), Ops.size(),
381                                           Context, TD);
382  else
383    return ConstantFoldInstOperands(I->getOpcode(), I->getType(),
384                                    Ops.data(), Ops.size(), Context, TD);
385}
386
387/// ConstantFoldConstantExpression - Attempt to fold the constant expression
388/// using the specified TargetData.  If successful, the constant result is
389/// result is returned, if not, null is returned.
390Constant *llvm::ConstantFoldConstantExpression(ConstantExpr *CE,
391                                               LLVMContext &Context,
392                                               const TargetData *TD) {
393  SmallVector<Constant*, 8> Ops;
394  for (User::op_iterator i = CE->op_begin(), e = CE->op_end(); i != e; ++i)
395    Ops.push_back(cast<Constant>(*i));
396
397  if (CE->isCompare())
398    return ConstantFoldCompareInstOperands(CE->getPredicate(),
399                                           Ops.data(), Ops.size(),
400                                           Context, TD);
401  else
402    return ConstantFoldInstOperands(CE->getOpcode(), CE->getType(),
403                                    Ops.data(), Ops.size(), Context, TD);
404}
405
406/// ConstantFoldInstOperands - Attempt to constant fold an instruction with the
407/// specified opcode and operands.  If successful, the constant result is
408/// returned, if not, null is returned.  Note that this function can fail when
409/// attempting to fold instructions like loads and stores, which have no
410/// constant expression form.
411///
412Constant *llvm::ConstantFoldInstOperands(unsigned Opcode, const Type *DestTy,
413                                         Constant* const* Ops, unsigned NumOps,
414                                         LLVMContext &Context,
415                                         const TargetData *TD) {
416  // Handle easy binops first.
417  if (Instruction::isBinaryOp(Opcode)) {
418    if (isa<ConstantExpr>(Ops[0]) || isa<ConstantExpr>(Ops[1]))
419      if (Constant *C = SymbolicallyEvaluateBinop(Opcode, Ops[0], Ops[1], TD,
420                                                  Context))
421        return C;
422
423    return ConstantExpr::get(Opcode, Ops[0], Ops[1]);
424  }
425
426  switch (Opcode) {
427  default: return 0;
428  case Instruction::Call:
429    if (Function *F = dyn_cast<Function>(Ops[0]))
430      if (canConstantFoldCallTo(F))
431        return ConstantFoldCall(F, Ops+1, NumOps-1);
432    return 0;
433  case Instruction::ICmp:
434  case Instruction::FCmp:
435    llvm_unreachable("This function is invalid for compares: no predicate specified");
436  case Instruction::PtrToInt:
437    // If the input is a inttoptr, eliminate the pair.  This requires knowing
438    // the width of a pointer, so it can't be done in ConstantExpr::getCast.
439    if (ConstantExpr *CE = dyn_cast<ConstantExpr>(Ops[0])) {
440      if (TD && CE->getOpcode() == Instruction::IntToPtr) {
441        Constant *Input = CE->getOperand(0);
442        unsigned InWidth = Input->getType()->getScalarSizeInBits();
443        if (TD->getPointerSizeInBits() < InWidth) {
444          Constant *Mask =
445            ConstantInt::get(Context, APInt::getLowBitsSet(InWidth,
446                                                  TD->getPointerSizeInBits()));
447          Input = ConstantExpr::getAnd(Input, Mask);
448        }
449        // Do a zext or trunc to get to the dest size.
450        return ConstantExpr::getIntegerCast(Input, DestTy, false);
451      }
452    }
453    return ConstantExpr::getCast(Opcode, Ops[0], DestTy);
454  case Instruction::IntToPtr:
455    // If the input is a ptrtoint, turn the pair into a ptr to ptr bitcast if
456    // the int size is >= the ptr size.  This requires knowing the width of a
457    // pointer, so it can't be done in ConstantExpr::getCast.
458    if (ConstantExpr *CE = dyn_cast<ConstantExpr>(Ops[0])) {
459      if (TD &&
460          TD->getPointerSizeInBits() <=
461          CE->getType()->getScalarSizeInBits()) {
462        if (CE->getOpcode() == Instruction::PtrToInt) {
463          Constant *Input = CE->getOperand(0);
464          Constant *C = FoldBitCast(Input, DestTy, *TD, Context);
465          return C ? C : ConstantExpr::getBitCast(Input, DestTy);
466        }
467        // If there's a constant offset added to the integer value before
468        // it is casted back to a pointer, see if the expression can be
469        // converted into a GEP.
470        if (CE->getOpcode() == Instruction::Add)
471          if (ConstantInt *L = dyn_cast<ConstantInt>(CE->getOperand(0)))
472            if (ConstantExpr *R = dyn_cast<ConstantExpr>(CE->getOperand(1)))
473              if (R->getOpcode() == Instruction::PtrToInt)
474                if (GlobalVariable *GV =
475                      dyn_cast<GlobalVariable>(R->getOperand(0))) {
476                  const PointerType *GVTy = cast<PointerType>(GV->getType());
477                  if (const ArrayType *AT =
478                        dyn_cast<ArrayType>(GVTy->getElementType())) {
479                    const Type *ElTy = AT->getElementType();
480                    uint64_t AllocSize = TD->getTypeAllocSize(ElTy);
481                    APInt PSA(L->getValue().getBitWidth(), AllocSize);
482                    if (ElTy == cast<PointerType>(DestTy)->getElementType() &&
483                        L->getValue().urem(PSA) == 0) {
484                      APInt ElemIdx = L->getValue().udiv(PSA);
485                      if (ElemIdx.ult(APInt(ElemIdx.getBitWidth(),
486                                            AT->getNumElements()))) {
487                        Constant *Index[] = {
488                          Constant::getNullValue(CE->getType()),
489                          ConstantInt::get(Context, ElemIdx)
490                        };
491                        return
492                        ConstantExpr::getGetElementPtr(GV, &Index[0], 2);
493                      }
494                    }
495                  }
496                }
497      }
498    }
499    return ConstantExpr::getCast(Opcode, Ops[0], DestTy);
500  case Instruction::Trunc:
501  case Instruction::ZExt:
502  case Instruction::SExt:
503  case Instruction::FPTrunc:
504  case Instruction::FPExt:
505  case Instruction::UIToFP:
506  case Instruction::SIToFP:
507  case Instruction::FPToUI:
508  case Instruction::FPToSI:
509      return ConstantExpr::getCast(Opcode, Ops[0], DestTy);
510  case Instruction::BitCast:
511    if (TD)
512      if (Constant *C = FoldBitCast(Ops[0], DestTy, *TD, Context))
513        return C;
514    return ConstantExpr::getBitCast(Ops[0], DestTy);
515  case Instruction::Select:
516    return ConstantExpr::getSelect(Ops[0], Ops[1], Ops[2]);
517  case Instruction::ExtractElement:
518    return ConstantExpr::getExtractElement(Ops[0], Ops[1]);
519  case Instruction::InsertElement:
520    return ConstantExpr::getInsertElement(Ops[0], Ops[1], Ops[2]);
521  case Instruction::ShuffleVector:
522    return ConstantExpr::getShuffleVector(Ops[0], Ops[1], Ops[2]);
523  case Instruction::GetElementPtr:
524    if (Constant *C = SymbolicallyEvaluateGEP(Ops, NumOps, DestTy, Context, TD))
525      return C;
526
527    return ConstantExpr::getGetElementPtr(Ops[0], Ops+1, NumOps-1);
528  }
529}
530
531/// ConstantFoldCompareInstOperands - Attempt to constant fold a compare
532/// instruction (icmp/fcmp) with the specified operands.  If it fails, it
533/// returns a constant expression of the specified operands.
534///
535Constant *llvm::ConstantFoldCompareInstOperands(unsigned Predicate,
536                                                Constant*const * Ops,
537                                                unsigned NumOps,
538                                                LLVMContext &Context,
539                                                const TargetData *TD) {
540  // fold: icmp (inttoptr x), null         -> icmp x, 0
541  // fold: icmp (ptrtoint x), 0            -> icmp x, null
542  // fold: icmp (inttoptr x), (inttoptr y) -> icmp trunc/zext x, trunc/zext y
543  // fold: icmp (ptrtoint x), (ptrtoint y) -> icmp x, y
544  //
545  // ConstantExpr::getCompare cannot do this, because it doesn't have TD
546  // around to know if bit truncation is happening.
547  if (ConstantExpr *CE0 = dyn_cast<ConstantExpr>(Ops[0])) {
548    if (TD && Ops[1]->isNullValue()) {
549      const Type *IntPtrTy = TD->getIntPtrType(Context);
550      if (CE0->getOpcode() == Instruction::IntToPtr) {
551        // Convert the integer value to the right size to ensure we get the
552        // proper extension or truncation.
553        Constant *C = ConstantExpr::getIntegerCast(CE0->getOperand(0),
554                                                   IntPtrTy, false);
555        Constant *NewOps[] = { C, Constant::getNullValue(C->getType()) };
556        return ConstantFoldCompareInstOperands(Predicate, NewOps, 2,
557                                               Context, TD);
558      }
559
560      // Only do this transformation if the int is intptrty in size, otherwise
561      // there is a truncation or extension that we aren't modeling.
562      if (CE0->getOpcode() == Instruction::PtrToInt &&
563          CE0->getType() == IntPtrTy) {
564        Constant *C = CE0->getOperand(0);
565        Constant *NewOps[] = { C, Constant::getNullValue(C->getType()) };
566        // FIXME!
567        return ConstantFoldCompareInstOperands(Predicate, NewOps, 2,
568                                               Context, TD);
569      }
570    }
571
572    if (ConstantExpr *CE1 = dyn_cast<ConstantExpr>(Ops[1])) {
573      if (TD && CE0->getOpcode() == CE1->getOpcode()) {
574        const Type *IntPtrTy = TD->getIntPtrType(Context);
575
576        if (CE0->getOpcode() == Instruction::IntToPtr) {
577          // Convert the integer value to the right size to ensure we get the
578          // proper extension or truncation.
579          Constant *C0 = ConstantExpr::getIntegerCast(CE0->getOperand(0),
580                                                      IntPtrTy, false);
581          Constant *C1 = ConstantExpr::getIntegerCast(CE1->getOperand(0),
582                                                      IntPtrTy, false);
583          Constant *NewOps[] = { C0, C1 };
584          return ConstantFoldCompareInstOperands(Predicate, NewOps, 2,
585                                                 Context, TD);
586        }
587
588        // Only do this transformation if the int is intptrty in size, otherwise
589        // there is a truncation or extension that we aren't modeling.
590        if ((CE0->getOpcode() == Instruction::PtrToInt &&
591             CE0->getType() == IntPtrTy &&
592             CE0->getOperand(0)->getType() == CE1->getOperand(0)->getType())) {
593          Constant *NewOps[] = {
594            CE0->getOperand(0), CE1->getOperand(0)
595          };
596          return ConstantFoldCompareInstOperands(Predicate, NewOps, 2,
597                                                 Context, TD);
598        }
599      }
600    }
601  }
602  return ConstantExpr::getCompare(Predicate, Ops[0], Ops[1]);
603}
604
605
606/// ConstantFoldLoadThroughGEPConstantExpr - Given a constant and a
607/// getelementptr constantexpr, return the constant value being addressed by the
608/// constant expression, or null if something is funny and we can't decide.
609Constant *llvm::ConstantFoldLoadThroughGEPConstantExpr(Constant *C,
610                                                       ConstantExpr *CE,
611                                                       LLVMContext &Context) {
612  if (CE->getOperand(1) != Constant::getNullValue(CE->getOperand(1)->getType()))
613    return 0;  // Do not allow stepping over the value!
614
615  // Loop over all of the operands, tracking down which value we are
616  // addressing...
617  gep_type_iterator I = gep_type_begin(CE), E = gep_type_end(CE);
618  for (++I; I != E; ++I)
619    if (const StructType *STy = dyn_cast<StructType>(*I)) {
620      ConstantInt *CU = cast<ConstantInt>(I.getOperand());
621      assert(CU->getZExtValue() < STy->getNumElements() &&
622             "Struct index out of range!");
623      unsigned El = (unsigned)CU->getZExtValue();
624      if (ConstantStruct *CS = dyn_cast<ConstantStruct>(C)) {
625        C = CS->getOperand(El);
626      } else if (isa<ConstantAggregateZero>(C)) {
627        C = Constant::getNullValue(STy->getElementType(El));
628      } else if (isa<UndefValue>(C)) {
629        C = UndefValue::get(STy->getElementType(El));
630      } else {
631        return 0;
632      }
633    } else if (ConstantInt *CI = dyn_cast<ConstantInt>(I.getOperand())) {
634      if (const ArrayType *ATy = dyn_cast<ArrayType>(*I)) {
635        if (CI->getZExtValue() >= ATy->getNumElements())
636         return 0;
637        if (ConstantArray *CA = dyn_cast<ConstantArray>(C))
638          C = CA->getOperand(CI->getZExtValue());
639        else if (isa<ConstantAggregateZero>(C))
640          C = Constant::getNullValue(ATy->getElementType());
641        else if (isa<UndefValue>(C))
642          C = UndefValue::get(ATy->getElementType());
643        else
644          return 0;
645      } else if (const VectorType *PTy = dyn_cast<VectorType>(*I)) {
646        if (CI->getZExtValue() >= PTy->getNumElements())
647          return 0;
648        if (ConstantVector *CP = dyn_cast<ConstantVector>(C))
649          C = CP->getOperand(CI->getZExtValue());
650        else if (isa<ConstantAggregateZero>(C))
651          C = Constant::getNullValue(PTy->getElementType());
652        else if (isa<UndefValue>(C))
653          C = UndefValue::get(PTy->getElementType());
654        else
655          return 0;
656      } else {
657        return 0;
658      }
659    } else {
660      return 0;
661    }
662  return C;
663}
664
665
666//===----------------------------------------------------------------------===//
667//  Constant Folding for Calls
668//
669
670/// canConstantFoldCallTo - Return true if its even possible to fold a call to
671/// the specified function.
672bool
673llvm::canConstantFoldCallTo(const Function *F) {
674  switch (F->getIntrinsicID()) {
675  case Intrinsic::sqrt:
676  case Intrinsic::powi:
677  case Intrinsic::bswap:
678  case Intrinsic::ctpop:
679  case Intrinsic::ctlz:
680  case Intrinsic::cttz:
681    return true;
682  default: break;
683  }
684
685  if (!F->hasName()) return false;
686  StringRef Name = F->getName();
687
688  // In these cases, the check of the length is required.  We don't want to
689  // return true for a name like "cos\0blah" which strcmp would return equal to
690  // "cos", but has length 8.
691  switch (Name[0]) {
692  default: return false;
693  case 'a':
694    return Name == "acos" || Name == "asin" ||
695      Name == "atan" || Name == "atan2";
696  case 'c':
697    return Name == "cos" || Name == "ceil" || Name == "cosf" || Name == "cosh";
698  case 'e':
699    return Name == "exp";
700  case 'f':
701    return Name == "fabs" || Name == "fmod" || Name == "floor";
702  case 'l':
703    return Name == "log" || Name == "log10";
704  case 'p':
705    return Name == "pow";
706  case 's':
707    return Name == "sin" || Name == "sinh" || Name == "sqrt" ||
708      Name == "sinf" || Name == "sqrtf";
709  case 't':
710    return Name == "tan" || Name == "tanh";
711  }
712}
713
714static Constant *ConstantFoldFP(double (*NativeFP)(double), double V,
715                                const Type *Ty, LLVMContext &Context) {
716  errno = 0;
717  V = NativeFP(V);
718  if (errno != 0) {
719    errno = 0;
720    return 0;
721  }
722
723  if (Ty == Type::getFloatTy(Context))
724    return ConstantFP::get(Context, APFloat((float)V));
725  if (Ty == Type::getDoubleTy(Context))
726    return ConstantFP::get(Context, APFloat(V));
727  llvm_unreachable("Can only constant fold float/double");
728  return 0; // dummy return to suppress warning
729}
730
731static Constant *ConstantFoldBinaryFP(double (*NativeFP)(double, double),
732                                      double V, double W,
733                                      const Type *Ty,
734                                      LLVMContext &Context) {
735  errno = 0;
736  V = NativeFP(V, W);
737  if (errno != 0) {
738    errno = 0;
739    return 0;
740  }
741
742  if (Ty == Type::getFloatTy(Context))
743    return ConstantFP::get(Context, APFloat((float)V));
744  if (Ty == Type::getDoubleTy(Context))
745    return ConstantFP::get(Context, APFloat(V));
746  llvm_unreachable("Can only constant fold float/double");
747  return 0; // dummy return to suppress warning
748}
749
750/// ConstantFoldCall - Attempt to constant fold a call to the specified function
751/// with the specified arguments, returning null if unsuccessful.
752
753Constant *
754llvm::ConstantFoldCall(Function *F,
755                       Constant* const* Operands, unsigned NumOperands) {
756  if (!F->hasName()) return 0;
757  LLVMContext &Context = F->getContext();
758  StringRef Name = F->getName();
759
760  const Type *Ty = F->getReturnType();
761  if (NumOperands == 1) {
762    if (ConstantFP *Op = dyn_cast<ConstantFP>(Operands[0])) {
763      if (Ty!=Type::getFloatTy(F->getContext()) &&
764          Ty!=Type::getDoubleTy(Context))
765        return 0;
766      /// Currently APFloat versions of these functions do not exist, so we use
767      /// the host native double versions.  Float versions are not called
768      /// directly but for all these it is true (float)(f((double)arg)) ==
769      /// f(arg).  Long double not supported yet.
770      double V = Ty==Type::getFloatTy(F->getContext()) ?
771                                     (double)Op->getValueAPF().convertToFloat():
772                                     Op->getValueAPF().convertToDouble();
773      switch (Name[0]) {
774      case 'a':
775        if (Name == "acos")
776          return ConstantFoldFP(acos, V, Ty, Context);
777        else if (Name == "asin")
778          return ConstantFoldFP(asin, V, Ty, Context);
779        else if (Name == "atan")
780          return ConstantFoldFP(atan, V, Ty, Context);
781        break;
782      case 'c':
783        if (Name == "ceil")
784          return ConstantFoldFP(ceil, V, Ty, Context);
785        else if (Name == "cos")
786          return ConstantFoldFP(cos, V, Ty, Context);
787        else if (Name == "cosh")
788          return ConstantFoldFP(cosh, V, Ty, Context);
789        else if (Name == "cosf")
790          return ConstantFoldFP(cos, V, Ty, Context);
791        break;
792      case 'e':
793        if (Name == "exp")
794          return ConstantFoldFP(exp, V, Ty, Context);
795        break;
796      case 'f':
797        if (Name == "fabs")
798          return ConstantFoldFP(fabs, V, Ty, Context);
799        else if (Name == "floor")
800          return ConstantFoldFP(floor, V, Ty, Context);
801        break;
802      case 'l':
803        if (Name == "log" && V > 0)
804          return ConstantFoldFP(log, V, Ty, Context);
805        else if (Name == "log10" && V > 0)
806          return ConstantFoldFP(log10, V, Ty, Context);
807        else if (Name == "llvm.sqrt.f32" ||
808                 Name == "llvm.sqrt.f64") {
809          if (V >= -0.0)
810            return ConstantFoldFP(sqrt, V, Ty, Context);
811          else // Undefined
812            return Constant::getNullValue(Ty);
813        }
814        break;
815      case 's':
816        if (Name == "sin")
817          return ConstantFoldFP(sin, V, Ty, Context);
818        else if (Name == "sinh")
819          return ConstantFoldFP(sinh, V, Ty, Context);
820        else if (Name == "sqrt" && V >= 0)
821          return ConstantFoldFP(sqrt, V, Ty, Context);
822        else if (Name == "sqrtf" && V >= 0)
823          return ConstantFoldFP(sqrt, V, Ty, Context);
824        else if (Name == "sinf")
825          return ConstantFoldFP(sin, V, Ty, Context);
826        break;
827      case 't':
828        if (Name == "tan")
829          return ConstantFoldFP(tan, V, Ty, Context);
830        else if (Name == "tanh")
831          return ConstantFoldFP(tanh, V, Ty, Context);
832        break;
833      default:
834        break;
835      }
836    } else if (ConstantInt *Op = dyn_cast<ConstantInt>(Operands[0])) {
837      if (Name.startswith("llvm.bswap"))
838        return ConstantInt::get(Context, Op->getValue().byteSwap());
839      else if (Name.startswith("llvm.ctpop"))
840        return ConstantInt::get(Ty, Op->getValue().countPopulation());
841      else if (Name.startswith("llvm.cttz"))
842        return ConstantInt::get(Ty, Op->getValue().countTrailingZeros());
843      else if (Name.startswith("llvm.ctlz"))
844        return ConstantInt::get(Ty, Op->getValue().countLeadingZeros());
845    }
846  } else if (NumOperands == 2) {
847    if (ConstantFP *Op1 = dyn_cast<ConstantFP>(Operands[0])) {
848      if (Ty!=Type::getFloatTy(F->getContext()) &&
849          Ty!=Type::getDoubleTy(Context))
850        return 0;
851      double Op1V = Ty==Type::getFloatTy(F->getContext()) ?
852                      (double)Op1->getValueAPF().convertToFloat():
853                      Op1->getValueAPF().convertToDouble();
854      if (ConstantFP *Op2 = dyn_cast<ConstantFP>(Operands[1])) {
855        double Op2V = Ty==Type::getFloatTy(F->getContext()) ?
856                      (double)Op2->getValueAPF().convertToFloat():
857                      Op2->getValueAPF().convertToDouble();
858
859        if (Name == "pow") {
860          return ConstantFoldBinaryFP(pow, Op1V, Op2V, Ty, Context);
861        } else if (Name == "fmod") {
862          return ConstantFoldBinaryFP(fmod, Op1V, Op2V, Ty, Context);
863        } else if (Name == "atan2") {
864          return ConstantFoldBinaryFP(atan2, Op1V, Op2V, Ty, Context);
865        }
866      } else if (ConstantInt *Op2C = dyn_cast<ConstantInt>(Operands[1])) {
867        if (Name == "llvm.powi.f32") {
868          return ConstantFP::get(Context, APFloat((float)std::pow((float)Op1V,
869                                                 (int)Op2C->getZExtValue())));
870        } else if (Name == "llvm.powi.f64") {
871          return ConstantFP::get(Context, APFloat((double)std::pow((double)Op1V,
872                                                 (int)Op2C->getZExtValue())));
873        }
874      }
875    }
876  }
877  return 0;
878}
879
880