delinearization of arrays

git-svn-id: https://llvm.org/svn/llvm-project/llvm/trunk@194527 91177308-0d34-0410-b5e6-96231b3b80d8

include/llvm/Analysis/DependenceAnalysis.h

@@ -908,6 +908,10 @@ namespace llvm {
     /// based on the current constraint.
     void updateDirection(Dependence::DVEntry &Level,
                          const Constraint &CurConstraint) const;
+
+    bool tryDelinearize(const SCEV *SrcSCEV, const SCEV *DstSCEV,
+                        SmallVectorImpl<Subscript> &Pair) const;
+
   public:
     static char ID; // Class identification, replacement for typeinfo
     DependenceAnalysis() : FunctionPass(ID) {

include/llvm/Analysis/Passes.h

@@ -134,6 +134,13 @@ namespace llvm {
   //
   FunctionPass *createCostModelAnalysisPass();
 
+  //===--------------------------------------------------------------------===//
+  //
+  // createDelinearizationPass - This pass implements attempts to restore
+  // multidimensional array indices from linearized expressions.
+  //
+  FunctionPass *createDelinearizationPass();
+
   //===--------------------------------------------------------------------===//
   //
   // Minor pass prototypes, allowing us to expose them through bugpoint and

include/llvm/Analysis/ScalarEvolutionExpressions.h

@@ -351,8 +351,14 @@ namespace llvm {
     static inline bool classof(const SCEV *S) {
       return S->getSCEVType() == scAddRecExpr;
     }
-  };
 
+    /// Splits the SCEV into two vectors of SCEVs representing the subscripts
+    /// and sizes of an array access. Returns the remainder of the
+    /// delinearization that is the offset start of the array.
+    const SCEV *delinearize(ScalarEvolution &SE,
+                            SmallVectorImpl<const SCEV *> &Subscripts,
+                            SmallVectorImpl<const SCEV *> &Sizes) const;
+  };
 
   //===--------------------------------------------------------------------===//
   /// SCEVSMaxExpr - This class represents a signed maximum selection.

include/llvm/InitializePasses.h

@@ -102,6 +102,7 @@ void initializeDSEPass(PassRegistry&);
 void initializeDebugIRPass(PassRegistry&);
 void initializeDeadInstEliminationPass(PassRegistry&);
 void initializeDeadMachineInstructionElimPass(PassRegistry&);
+void initializeDelinearizationPass(PassRegistry &);
 void initializeDependenceAnalysisPass(PassRegistry&);
 void initializeDomOnlyPrinterPass(PassRegistry&);
 void initializeDomOnlyViewerPass(PassRegistry&);

lib/Analysis/Analysis.cpp

@@ -34,6 +34,7 @@ void llvm::initializeAnalysis(PassRegistry &Registry) {
   initializeCFGOnlyViewerPass(Registry);
   initializeCFGOnlyPrinterPass(Registry);
   initializeDependenceAnalysisPass(Registry);
+  initializeDelinearizationPass(Registry);
   initializeDominanceFrontierPass(Registry);
   initializeDomViewerPass(Registry);
   initializeDomPrinterPass(Registry);

lib/Analysis/CMakeLists.txt

@@ -14,6 +14,7 @@ add_llvm_library(LLVMAnalysis
   CostModel.cpp
   CodeMetrics.cpp
   ConstantFolding.cpp
+  Delinearization.cpp
   DependenceAnalysis.cpp
   DomPrinter.cpp
   DominanceFrontier.cpp

lib/Analysis/Delinearization.cpp

@@ -0,0 +1,125 @@
+//===---- Delinearization.cpp - MultiDimensional Index Delinearization ----===//
+//
+//                     The LLVM Compiler Infrastructure
+//
+// This file is distributed under the University of Illinois Open Source
+// License. See LICENSE.TXT for details.
+//
+//===----------------------------------------------------------------------===//
+//
+// This implements an analysis pass that tries to delinearize all GEP
+// instructions in all loops using the SCEV analysis functionality. This pass is
+// only used for testing purposes: if your pass needs delinearization, please
+// use the on-demand SCEVAddRecExpr::delinearize() function.
+//
+//===----------------------------------------------------------------------===//
+
+#define DL_NAME "delinearize"
+#define DEBUG_TYPE DL_NAME
+#include "llvm/IR/Constants.h"
+#include "llvm/IR/DerivedTypes.h"
+#include "llvm/IR/Function.h"
+#include "llvm/IR/Instructions.h"
+#include "llvm/IR/LLVMContext.h"
+#include "llvm/Pass.h"
+#include "llvm/IR/Type.h"
+#include "llvm/Analysis/LoopInfo.h"
+#include "llvm/Analysis/Passes.h"
+#include "llvm/Analysis/ScalarEvolution.h"
+#include "llvm/Analysis/ScalarEvolutionExpressions.h"
+#include "llvm/Support/CommandLine.h"
+#include "llvm/Support/Debug.h"
+#include "llvm/Support/InstIterator.h"
+#include "llvm/Support/raw_ostream.h"
+
+using namespace llvm;
+
+class Delinearization : public FunctionPass {
+  Delinearization(const Delinearization &); // do not implement
+protected:
+  Function *F;
+  LoopInfo *LI;
+  ScalarEvolution *SE;
+
+public:
+  static char ID; // Pass identification, replacement for typeid
+
+  Delinearization() : FunctionPass(ID) {
+    initializeDelinearizationPass(*PassRegistry::getPassRegistry());
+  }
+  virtual bool runOnFunction(Function &F);
+  virtual void getAnalysisUsage(AnalysisUsage &AU) const;
+  virtual void print(raw_ostream &O, const Module *M = 0) const;
+};
+
+void Delinearization::getAnalysisUsage(AnalysisUsage &AU) const {
+  AU.setPreservesAll();
+  AU.addRequired<LoopInfo>();
+  AU.addRequired<ScalarEvolution>();
+}
+
+bool Delinearization::runOnFunction(Function &F) {
+  this->F = &F;
+  SE = &getAnalysis<ScalarEvolution>();
+  LI = &getAnalysis<LoopInfo>();
+  return false;
+}
+
+static Value *getPointerOperand(Instruction &Inst) {
+  if (LoadInst *Load = dyn_cast<LoadInst>(&Inst))
+    return Load->getPointerOperand();
+  else if (StoreInst *Store = dyn_cast<StoreInst>(&Inst))
+    return Store->getPointerOperand();
+  else if (GetElementPtrInst *Gep = dyn_cast<GetElementPtrInst>(&Inst))
+    return Gep->getPointerOperand();
+  return NULL;
+}
+
+void Delinearization::print(raw_ostream &O, const Module *) const {
+  O << "Delinearization on function " << F->getName() << ":\n";
+  for (inst_iterator I = inst_begin(F), E = inst_end(F); I != E; ++I) {
+    Instruction *Inst = &(*I);
+    if (!isa<StoreInst>(Inst) && !isa<LoadInst>(Inst) &&
+        !isa<GetElementPtrInst>(Inst))
+      continue;
+
+    const BasicBlock *BB = Inst->getParent();
+    // Delinearize the memory access as analyzed in all the surrounding loops.
+    // Do not analyze memory accesses outside loops.
+    for (Loop *L = LI->getLoopFor(BB); L != NULL; L = L->getParentLoop()) {
+      const SCEV *AccessFn = SE->getSCEVAtScope(getPointerOperand(*Inst), L);
+      const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(AccessFn);
+      if (!AR)
+        break;
+
+      O << "AddRec: " << *AR << "\n";
+
+      SmallVector<const SCEV *, 3> Subscripts, Sizes;
+      const SCEV *Res = AR->delinearize(*SE, Subscripts, Sizes);
+      int Size = Subscripts.size();
+      if (Res == AR || Size == 0) {
+        O << "failed to delinearize\n";
+        continue;
+      }
+      O << "Base offset: " << *Res << "\n";
+      O << "ArrayDecl[UnknownSize]";
+      for (int i = 0; i < Size - 1; i++)
+        O << "[" << *Sizes[i] << "]";
+      O << " with elements of " << *Sizes[Size - 1] << " bytes.\n";
+
+      O << "ArrayRef";
+      for (int i = 0; i < Size; i++)
+        O << "[" << *Subscripts[i] << "]";
+      O << "\n";
+    }
+  }
+}
+
+char Delinearization::ID = 0;
+static const char delinearization_name[] = "Delinearization";
+INITIALIZE_PASS_BEGIN(Delinearization, DL_NAME, delinearization_name, true,
+                      true)
+INITIALIZE_PASS_DEPENDENCY(LoopInfo)
+INITIALIZE_PASS_END(Delinearization, DL_NAME, delinearization_name, true, true)
+
+FunctionPass *llvm::createDelinearizationPass() { return new Delinearization; }

lib/Analysis/DependenceAnalysis.cpp

@@ -61,6 +61,7 @@
 #include "llvm/Analysis/ScalarEvolutionExpressions.h"
 #include "llvm/Analysis/ValueTracking.h"
 #include "llvm/IR/Operator.h"
+#include "llvm/Support/CommandLine.h"
 #include "llvm/Support/Debug.h"
 #include "llvm/Support/ErrorHandling.h"
 #include "llvm/Support/InstIterator.h"
@@ -104,6 +105,10 @@ STATISTIC(BanerjeeApplications, "Banerjee applications");
 STATISTIC(BanerjeeIndependence, "Banerjee independence");
 STATISTIC(BanerjeeSuccesses, "Banerjee successes");
 
+static cl::opt<bool>
+Delinearize("da-delinearize", cl::init(false), cl::Hidden, cl::ZeroOrMore,
+            cl::desc("Try to delinearize array references."));
+
 //===----------------------------------------------------------------------===//
 // basics
 
@@ -3171,6 +3176,44 @@ void DependenceAnalysis::updateDirection(Dependence::DVEntry &Level,
     llvm_unreachable("constraint has unexpected kind");
 }
 
+/// Check if we can delinearize the subscripts. If the SCEVs representing the
+/// source and destination array references are recurrences on a nested loop,
+/// this function flattens the nested recurrences into seperate recurrences
+/// for each loop level.
+bool
+DependenceAnalysis::tryDelinearize(const SCEV *SrcSCEV, const SCEV *DstSCEV,
+                                   SmallVectorImpl<Subscript> &Pair) const {
+  const SCEVAddRecExpr *SrcAR = dyn_cast<SCEVAddRecExpr>(SrcSCEV);
+  const SCEVAddRecExpr *DstAR = dyn_cast<SCEVAddRecExpr>(DstSCEV);
+  if (!SrcAR || !DstAR || !SrcAR->isAffine() || !DstAR->isAffine())
+    return false;
+
+  SmallVector<const SCEV *, 4> SrcSubscripts, DstSubscripts, SrcSizes, DstSizes;
+  SrcAR->delinearize(*SE, SrcSubscripts, SrcSizes);
+  DstAR->delinearize(*SE, DstSubscripts, DstSizes);
+
+  int size = SrcSubscripts.size();
+  int dstSize = DstSubscripts.size();
+  if (size != dstSize || size < 2)
+    return false;
+
+#ifndef NDEBUG
+  DEBUG(errs() << "\nSrcSubscripts: ");
+  for (int i = 0; i < size; i++)
+    DEBUG(errs() << *SrcSubscripts[i]);
+  DEBUG(errs() << "\nDstSubscripts: ");
+  for (int i = 0; i < size; i++)
+    DEBUG(errs() << *DstSubscripts[i]);
+#endif
+
+  Pair.resize(size);
+  for (int i = 0; i < size; ++i) {
+    Pair[i].Src = SrcSubscripts[i];
+    Pair[i].Dst = DstSubscripts[i];
+  }
+
+  return true;
+}
 
 //===----------------------------------------------------------------------===//
 
@@ -3280,6 +3323,12 @@ Dependence *DependenceAnalysis::depends(Instruction *Src,
     Pair[0].Dst = DstSCEV;
   }
 
+  if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
+      tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair)) {
+    DEBUG(dbgs() << "    delinerized GEP\n");
+    Pairs = Pair.size();
+  }
+
   for (unsigned P = 0; P < Pairs; ++P) {
     Pair[P].Loops.resize(MaxLevels + 1);
     Pair[P].GroupLoops.resize(MaxLevels + 1);
@@ -3698,6 +3747,12 @@ const  SCEV *DependenceAnalysis::getSplitIteration(const Dependence *Dep,
     Pair[0].Dst = DstSCEV;
   }
 
+  if (Delinearize && Pairs == 1 && CommonLevels > 1 &&
+      tryDelinearize(Pair[0].Src, Pair[0].Dst, Pair)) {
+    DEBUG(dbgs() << "    delinerized GEP\n");
+    Pairs = Pair.size();
+  }
+
   for (unsigned P = 0; P < Pairs; ++P) {
     Pair[P].Loops.resize(MaxLevels + 1);
     Pair[P].GroupLoops.resize(MaxLevels + 1);

lib/Analysis/ScalarEvolution.cpp

@@ -6677,7 +6677,478 @@ const SCEV *SCEVAddRecExpr::getNumIterationsInRange(ConstantRange Range,
   return SE.getCouldNotCompute();
 }
 
+static const APInt gcd(const SCEVConstant *C1, const SCEVConstant *C2) {
+  APInt A = C1->getValue()->getValue().abs();
+  APInt B = C2->getValue()->getValue().abs();
+  uint32_t ABW = A.getBitWidth();
+  uint32_t BBW = B.getBitWidth();
 
+  if (ABW > BBW)
+    B.zext(ABW);
+  else if (ABW < BBW)
+    A.zext(BBW);
+
+  return APIntOps::GreatestCommonDivisor(A, B);
+}
+
+static const APInt srem(const SCEVConstant *C1, const SCEVConstant *C2) {
+  APInt A = C1->getValue()->getValue();
+  APInt B = C2->getValue()->getValue();
+  uint32_t ABW = A.getBitWidth();
+  uint32_t BBW = B.getBitWidth();
+
+  if (ABW > BBW)
+    B.sext(ABW);
+  else if (ABW < BBW)
+    A.sext(BBW);
+
+  return APIntOps::srem(A, B);
+}
+
+static const APInt sdiv(const SCEVConstant *C1, const SCEVConstant *C2) {
+  APInt A = C1->getValue()->getValue();
+  APInt B = C2->getValue()->getValue();
+  uint32_t ABW = A.getBitWidth();
+  uint32_t BBW = B.getBitWidth();
+
+  if (ABW > BBW)
+    B.sext(ABW);
+  else if (ABW < BBW)
+    A.sext(BBW);
+
+  return APIntOps::sdiv(A, B);
+}
+
+namespace {
+struct SCEVGCD : public SCEVVisitor<SCEVGCD, const SCEV *> {
+public:
+  // Pattern match Step into Start. When Step is a multiply expression, find
+  // the largest subexpression of Step that appears in Start. When Start is an
+  // add expression, try to match Step in the subexpressions of Start, non
+  // matching subexpressions are returned under Remainder.
+  static const SCEV *findGCD(ScalarEvolution &SE, const SCEV *Start,
+                             const SCEV *Step, const SCEV **Remainder) {
+    assert(Remainder && "Remainder should not be NULL");
+    SCEVGCD R(SE, Step, SE.getConstant(Step->getType(), 0));
+    const SCEV *Res = R.visit(Start);
+    *Remainder = R.Remainder;
+    return Res;
+  }
+
+  SCEVGCD(ScalarEvolution &S, const SCEV *G, const SCEV *R)
+      : SE(S), GCD(G), Remainder(R) {
+    Zero = SE.getConstant(GCD->getType(), 0);
+    One = SE.getConstant(GCD->getType(), 1);
+  }
+
+  const SCEV *visitConstant(const SCEVConstant *Constant) {
+    if (GCD == Constant || Constant == Zero)
+      return GCD;
+
+    if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD)) {
+      const SCEV *Res = SE.getConstant(gcd(Constant, CGCD));
+      if (Res != One)
+        return Res;
+
+      Remainder = SE.getConstant(srem(Constant, CGCD));
+      Constant = cast<SCEVConstant>(SE.getMinusSCEV(Constant, Remainder));
+      Res = SE.getConstant(gcd(Constant, CGCD));
+      return Res;
+    }
+
+    // When GCD is not a constant, it could be that the GCD is an Add, Mul,
+    // AddRec, etc., in which case we want to find out how many times the
+    // Constant divides the GCD: we then return that as the new GCD.
+    const SCEV *Rem = Zero;
+    const SCEV *Res = findGCD(SE, GCD, Constant, &Rem);
+
+    if (Res == One || Rem != Zero) {
+      Remainder = Constant;
+      return One;
+    }
+
+    assert(isa<SCEVConstant>(Res) && "Res should be a constant");
+    Remainder = SE.getConstant(srem(Constant, cast<SCEVConstant>(Res)));
+    return Res;
+  }
+
+  const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
+    if (GCD != Expr)
+      Remainder = Expr;
+    return GCD;
+  }
+
+  const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
+    if (GCD != Expr)
+      Remainder = Expr;
+    return GCD;
+  }
+
+  const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
+    if (GCD != Expr)
+      Remainder = Expr;
+    return GCD;
+  }
+
+  const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
+    if (GCD == Expr)
+      return GCD;
+
+    for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
+      const SCEV *Rem = Zero;
+      const SCEV *Res = findGCD(SE, Expr->getOperand(e - 1 - i), GCD, &Rem);
+
+      // FIXME: There may be ambiguous situations: for instance,
+      // GCD(-4 + (3 * %m), 2 * %m) where 2 divides -4 and %m divides (3 * %m).
+      // The order in which the AddExpr is traversed computes a different GCD
+      // and Remainder.
+      if (Res != One)
+        GCD = Res;
+      if (Rem != Zero)
+        Remainder = SE.getAddExpr(Remainder, Rem);
+    }
+
+    return GCD;
+  }
+
+  const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
+    if (GCD == Expr)
+      return GCD;
+
+    for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
+      if (Expr->getOperand(i) == GCD)
+        return GCD;
+    }
+
+    // If we have not returned yet, it means that GCD is not part of Expr.
+    const SCEV *PartialGCD = One;
+    for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
+      const SCEV *Rem = Zero;
+      const SCEV *Res = findGCD(SE, Expr->getOperand(i), GCD, &Rem);
+      if (Rem != Zero)
+        // GCD does not divide Expr->getOperand(i).
+        continue;
+
+      if (Res == GCD)
+        return GCD;
+      PartialGCD = SE.getMulExpr(PartialGCD, Res);
+      if (PartialGCD == GCD)
+        return GCD;
+    }
+
+    if (PartialGCD != One)
+      return PartialGCD;
+
+    Remainder = Expr;
+    const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(GCD);
+    if (!Mul)
+      return PartialGCD;
+
+    // When the GCD is a multiply expression, try to decompose it:
+    // this occurs when Step does not divide the Start expression
+    // as in: {(-4 + (3 * %m)),+,(2 * %m)}
+    for (int i = 0, e = Mul->getNumOperands(); i < e; ++i) {
+      const SCEV *Rem = Zero;
+      const SCEV *Res = findGCD(SE, Expr, Mul->getOperand(i), &Rem);
+      if (Rem == Zero) {
+        Remainder = Rem;
+        return Res;
+      }
+    }
+
+    return PartialGCD;
+  }
+
+  const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
+    if (GCD != Expr)
+      Remainder = Expr;
+    return GCD;
+  }
+
+  const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
+    if (GCD == Expr)
+      return GCD;
+
+    if (!Expr->isAffine()) {
+      Remainder = Expr;
+      return GCD;
+    }
+
+    const SCEV *Rem = Zero;
+    const SCEV *Res = findGCD(SE, Expr->getOperand(0), GCD, &Rem);
+    if (Rem != Zero)
+      Remainder = SE.getAddExpr(Remainder, Rem);
+
+    Rem = Zero;
+    Res = findGCD(SE, Expr->getOperand(1), Res, &Rem);
+    if (Rem != Zero) {
+      Remainder = Expr;
+      return GCD;
+    }
+
+    return Res;
+  }
+
+  const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
+    if (GCD != Expr)
+      Remainder = Expr;
+    return GCD;
+  }
+
+  const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
+    if (GCD != Expr)
+      Remainder = Expr;
+    return GCD;
+  }
+
+  const SCEV *visitUnknown(const SCEVUnknown *Expr) {
+    if (GCD != Expr)
+      Remainder = Expr;
+    return GCD;
+  }
+
+  const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
+    return One;
+  }
+
+private:
+  ScalarEvolution &SE;
+  const SCEV *GCD, *Remainder, *Zero, *One;
+};
+
+struct SCEVDivision : public SCEVVisitor<SCEVDivision, const SCEV *> {
+public:
+  // Remove from Start all multiples of Step.
+  static const SCEV *divide(ScalarEvolution &SE, const SCEV *Start,
+                            const SCEV *Step) {
+    SCEVDivision D(SE, Step);
+    const SCEV *Rem = D.Zero;
+    (void)Rem;
+    // The division is guaranteed to succeed: Step should divide Start with no
+    // remainder.
+    assert(Step == SCEVGCD::findGCD(SE, Start, Step, &Rem) && Rem == D.Zero &&
+           "Step should divide Start with no remainder.");
+    return D.visit(Start);
+  }
+
+  SCEVDivision(ScalarEvolution &S, const SCEV *G) : SE(S), GCD(G) {
+    Zero = SE.getConstant(GCD->getType(), 0);
+    One = SE.getConstant(GCD->getType(), 1);
+  }
+
+  const SCEV *visitConstant(const SCEVConstant *Constant) {
+    if (GCD == Constant)
+      return One;
+
+    if (const SCEVConstant *CGCD = dyn_cast<SCEVConstant>(GCD))
+      return SE.getConstant(sdiv(Constant, CGCD));
+    return Constant;
+  }
+
+  const SCEV *visitTruncateExpr(const SCEVTruncateExpr *Expr) {
+    if (GCD == Expr)
+      return One;
+    return Expr;
+  }
+
+  const SCEV *visitZeroExtendExpr(const SCEVZeroExtendExpr *Expr) {
+    if (GCD == Expr)
+      return One;
+    return Expr;
+  }
+
+  const SCEV *visitSignExtendExpr(const SCEVSignExtendExpr *Expr) {
+    if (GCD == Expr)
+      return One;
+    return Expr;
+  }
+
+  const SCEV *visitAddExpr(const SCEVAddExpr *Expr) {
+    if (GCD == Expr)
+      return One;
+
+    SmallVector<const SCEV *, 2> Operands;
+    for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
+      Operands.push_back(divide(SE, Expr->getOperand(i), GCD));
+
+    if (Operands.size() == 1)
+      return Operands[0];
+    return SE.getAddExpr(Operands);
+  }
+
+  const SCEV *visitMulExpr(const SCEVMulExpr *Expr) {
+    if (GCD == Expr)
+      return One;
+
+    bool FoundGCDTerm = false;
+    for (int i = 0, e = Expr->getNumOperands(); i < e; ++i)
+      if (Expr->getOperand(i) == GCD)
+        FoundGCDTerm = true;
+
+    SmallVector<const SCEV *, 2> Operands;
+    if (FoundGCDTerm) {
+      FoundGCDTerm = false;
+      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
+        if (FoundGCDTerm)
+          Operands.push_back(Expr->getOperand(i));
+        else if (Expr->getOperand(i) == GCD)
+          FoundGCDTerm = true;
+        else
+          Operands.push_back(Expr->getOperand(i));
+      }
+    } else {
+      FoundGCDTerm = false;
+      const SCEV *PartialGCD = One;
+      for (int i = 0, e = Expr->getNumOperands(); i < e; ++i) {
+        if (PartialGCD == GCD) {
+          Operands.push_back(Expr->getOperand(i));
+          continue;
+        }
+
+        const SCEV *Rem = Zero;
+        const SCEV *Res = SCEVGCD::findGCD(SE, Expr->getOperand(i), GCD, &Rem);
+        if (Rem == Zero) {
+          PartialGCD = SE.getMulExpr(PartialGCD, Res);
+          Operands.push_back(divide(SE, Expr->getOperand(i), GCD));
+        } else {
+          Operands.push_back(Expr->getOperand(i));
+        }
+      }
+    }
+
+    if (Operands.size() == 1)
+      return Operands[0];
+    return SE.getMulExpr(Operands);
+  }
+
+  const SCEV *visitUDivExpr(const SCEVUDivExpr *Expr) {
+    if (GCD == Expr)
+      return One;
+    return Expr;
+  }
+
+  const SCEV *visitAddRecExpr(const SCEVAddRecExpr *Expr) {
+    if (GCD == Expr)
+      return One;
+
+    assert(Expr->isAffine() && "Expr should be affine");
+
+    const SCEV *Start = divide(SE, Expr->getStart(), GCD);
+    const SCEV *Step = divide(SE, Expr->getStepRecurrence(SE), GCD);
+
+    return SE.getAddRecExpr(Start, Step, Expr->getLoop(),
+                            Expr->getNoWrapFlags());
+  }
+
+  const SCEV *visitSMaxExpr(const SCEVSMaxExpr *Expr) {
+    if (GCD == Expr)
+      return One;
+    return Expr;
+  }
+
+  const SCEV *visitUMaxExpr(const SCEVUMaxExpr *Expr) {
+    if (GCD == Expr)
+      return One;
+    return Expr;
+  }
+
+  const SCEV *visitUnknown(const SCEVUnknown *Expr) {
+    if (GCD == Expr)
+      return One;
+    return Expr;
+  }
+
+  const SCEV *visitCouldNotCompute(const SCEVCouldNotCompute *Expr) {
+    return Expr;
+  }
+
+private:
+  ScalarEvolution &SE;
+  const SCEV *GCD, *Zero, *One;
+};
+}
+
+/// Splits the SCEV into two vectors of SCEVs representing the subscripts and
+/// sizes of an array access. Returns the remainder of the delinearization that
+/// is the offset start of the array. For example
+/// delinearize ({(((-4 + (3 * %m)))),+,(%m)}<%for.i>) {
+///   IV: {0,+,1}<%for.i>
+///   Start: -4 + (3 * %m)
+///   Step: %m
+///   SCEVUDiv (Start, Step) = 3 remainder -4
+///   rem = delinearize (3) = 3
+///   Subscripts.push_back(IV + rem)
+///   Sizes.push_back(Step)
+///   return remainder -4
+/// }
+/// When delinearize fails, it returns the SCEV unchanged.
+const SCEV *
+SCEVAddRecExpr::delinearize(ScalarEvolution &SE,
+                            SmallVectorImpl<const SCEV *> &Subscripts,
+                            SmallVectorImpl<const SCEV *> &Sizes) const {
+  if (!this->isAffine())
+    return this;
+
+  const SCEV *Start = this->getStart();
+  const SCEV *Step = this->getStepRecurrence(SE);
+  const SCEV *Zero = SE.getConstant(this->getType(), 0);
+  const SCEV *One = SE.getConstant(this->getType(), 1);
+  const SCEV *IV =
+      SE.getAddRecExpr(Zero, One, this->getLoop(), this->getNoWrapFlags());
+
+  DEBUG(dbgs() << "(delinearize: " << *this << "\n");
+
+  if (Step == One) {
+    DEBUG(dbgs() << "failed to delinearize " << *this << "\n)\n");
+    return this;
+  }
+
+  const SCEV *Remainder = NULL;
+  const SCEV *GCD = SCEVGCD::findGCD(SE, Start, Step, &Remainder);
+
+  DEBUG(dbgs() << "GCD: " << *GCD << "\n");
+  DEBUG(dbgs() << "Remainder: " << *Remainder << "\n");
+
+  if (GCD == One) {
+    DEBUG(dbgs() << "failed to delinearize " << *this << "\n)\n");
+    return this;
+  }
+
+  const SCEV *Quotient =
+      SCEVDivision::divide(SE, SE.getMinusSCEV(Start, Remainder), GCD);
+  DEBUG(dbgs() << "Quotient: " << *Quotient << "\n");
+
+  const SCEV *Rem;
+  if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(Quotient))
+    Rem = AR->delinearize(SE, Subscripts, Sizes);
+  else
+    Rem = Quotient;
+
+  if (Step != GCD) {
+    Step = SCEVDivision::divide(SE, Step, GCD);
+    IV = SE.getMulExpr(IV, Step);
+  }
+  const SCEV *Index = SE.getAddExpr(IV, Rem);
+
+  Subscripts.push_back(Index);
+  Sizes.push_back(GCD);
+
+#ifndef NDEBUG
+  int Size = Sizes.size();
+  DEBUG(dbgs() << "succeeded to delinearize " << *this << "\n");
+  DEBUG(dbgs() << "ArrayDecl[UnknownSize]");
+  for (int i = 0; i < Size - 1; i++)
+    DEBUG(dbgs() << "[" << *Sizes[i] << "]");
+  DEBUG(dbgs() << " with elements of " << *Sizes[Size - 1] << " bytes.\n");
+
+  DEBUG(dbgs() << "ArrayRef");
+  for (int i = 0; i < Size; i++)
+    DEBUG(dbgs() << "[" << *Subscripts[i] << "]");
+  DEBUG(dbgs() << "\n)\n");
+#endif
+
+  return Remainder;
+}
 
 //===----------------------------------------------------------------------===//
 //                   SCEVCallbackVH Class Implementation

test/Analysis/Delinearization/a.ll

@@ -0,0 +1,74 @@
+; RUN: opt < %s -analyze -delinearize | FileCheck %s
+;
+; void foo(long n, long m, long o, int A[n][m][o]) {
+;   for (long i = 0; i < n; i++)
+;     for (long j = 0; j < m; j++)
+;       for (long k = 0; k < o; k++)
+;         A[2*i+3][3*j-4][5*k+7] = 1;
+; }
+
+; AddRec: {{{(28 + (4 * (-4 + (3 * %m)) * %o) + %A),+,(8 * %m * %o)}<%for.i>,+,(12 * %o)}<%for.j>,+,20}<%for.k>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(i32) bytes.
+; CHECK: ArrayRef[{3,+,2}<%for.i>][{-4,+,3}<%for.j>][{7,+,5}<%for.k>]
+
+; AddRec: {{(8 + ((4 + (12 * %m)) * %o) + %A),+,(8 * %m * %o)}<%for.i>,+,(12 * %o)}<%for.j>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][%o] with elements of sizeof(i32) bytes.
+; CHECK: ArrayRef[{(1 + (3 * %m)),+,(2 * %m)}<%for.i>][{2,+,(3 * %o)}<%for.j>]
+
+; AddRec: {(8 + ((-8 + (24 * %m)) * %o) + %A),+,(8 * %m * %o)}<%for.i>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize] with elements of 2 bytes.
+; CHECK: ArrayRef[{((1 + ((-1 + (3 * %m)) * %o)) * sizeof(i32)),+,(%m * %o * sizeof(i32))}<%for.i>]
+
+; Function Attrs: nounwind uwtable
+define void @foo(i64 %n, i64 %m, i64 %o, i32* nocapture %A) #0 {
+entry:
+  %cmp32 = icmp sgt i64 %n, 0
+  br i1 %cmp32, label %for.cond1.preheader.lr.ph, label %for.end17
+
+for.cond1.preheader.lr.ph:                        ; preds = %entry
+  %cmp230 = icmp sgt i64 %m, 0
+  %cmp528 = icmp sgt i64 %o, 0
+  br i1 %cmp230, label %for.i, label %for.end17
+
+for.inc15.us:                                     ; preds = %for.inc12.us.us, %for.i
+  %inc16.us = add nsw i64 %i.033.us, 1
+  %exitcond55 = icmp eq i64 %inc16.us, %n
+  br i1 %exitcond55, label %for.end17, label %for.i
+
+for.i:                     ; preds = %for.cond1.preheader.lr.ph, %for.inc15.us
+  %i.033.us = phi i64 [ %inc16.us, %for.inc15.us ], [ 0, %for.cond1.preheader.lr.ph ]
+  %mul8.us = shl i64 %i.033.us, 1
+  %add9.us = add nsw i64 %mul8.us, 3
+  %0 = mul i64 %add9.us, %m
+  %sub.us = add i64 %0, -4
+  br i1 %cmp528, label %for.j, label %for.inc15.us
+
+for.inc12.us.us:                                  ; preds = %for.k
+  %inc13.us.us = add nsw i64 %j.031.us.us, 1
+  %exitcond54 = icmp eq i64 %inc13.us.us, %m
+  br i1 %exitcond54, label %for.inc15.us, label %for.j
+
+for.j:                            ; preds = %for.i, %for.inc12.us.us
+  %j.031.us.us = phi i64 [ %inc13.us.us, %for.inc12.us.us ], [ 0, %for.i ]
+  %mul7.us.us = mul nsw i64 %j.031.us.us, 3
+  %tmp.us.us = add i64 %sub.us, %mul7.us.us
+  %tmp27.us.us = mul i64 %tmp.us.us, %o
+  br label %for.k
+
+for.k:                                  ; preds = %for.k, %for.j
+  %k.029.us.us = phi i64 [ 0, %for.j ], [ %inc.us.us, %for.k ]
+  %mul.us.us = mul nsw i64 %k.029.us.us, 5
+  %arrayidx.sum.us.us = add i64 %mul.us.us, 7
+  %arrayidx10.sum.us.us = add i64 %arrayidx.sum.us.us, %tmp27.us.us
+  %arrayidx11.us.us = getelementptr inbounds i32* %A, i64 %arrayidx10.sum.us.us
+  store i32 1, i32* %arrayidx11.us.us, align 4
+  %inc.us.us = add nsw i64 %k.029.us.us, 1
+  %exitcond = icmp eq i64 %inc.us.us, %o
+  br i1 %exitcond, label %for.inc12.us.us, label %for.k
+
+for.end17:                                        ; preds = %for.inc15.us, %for.cond1.preheader.lr.ph, %entry
+  ret void
+}

test/Analysis/Delinearization/himeno_1.ll

@@ -0,0 +1,102 @@
+; RUN: opt < %s -analyze -delinearize | FileCheck %s
+
+; #define MR(mt,n,r,c,d)  mt->m[(n) * mt->mrows * mt->mcols * mt->mdeps + (r) * mt->mcols* mt->mdeps + (c) * mt->mdeps + (d)]
+;
+; struct Mat {
+;   float* m;
+;   int mnums;
+;   int mrows;
+;   int mcols;
+;   int mdeps;
+; };
+;
+; typedef struct Mat Matrix;
+;
+; void jacobi(int nn, Matrix* a, Matrix* p)
+; {
+;   long i, j, k, max,jmax,kmax;
+;
+;   p_rows_sub = p->mrows - 1;
+;   p_cols_sub = p->mcols - 1;
+;   p_deps_sub = p->mdeps - 1;
+;
+;     for(i = 1; i < p_rows_sub; i++)
+;       for(j = 1; j < p_cols_sub; j++)
+;         for(k = 1; k < p_deps_sub; k++)
+;           MR(a,0,i,j,k) = i + j + k;
+; }
+
+; AddRec: {{{(4 + (4 * (sext i32 %a.deps to i64) * (1 + (sext i32 %a.cols to i64))) + %a.base),+,(4 * (sext i32 %a.deps to i64) * (sext i32 %a.cols to i64))}<%for.i>,+,(4 * (sext i32 %a.deps to i64))}<%for.j>,+,4}<%for.k>
+; CHECK: Base offset: %a.base
+; CHECK: ArrayDecl[UnknownSize][(sext i32 %a.cols to i64)][(sext i32 %a.deps to i64)] with elements of sizeof(float) bytes.
+; CHECK: ArrayRef[{1,+,1}<nuw><nsw><%for.i>][{1,+,1}<nuw><nsw><%for.j>][{1,+,1}<nuw><nsw><%for.k>]
+
+; AddRec: {{(-4 + (4 * (sext i32 (-1 + %p.deps) to i64)) + (4 * (sext i32 %a.deps to i64) * (1 + (sext i32 %a.cols to i64))) + %a.base),+,(4 * (sext i32 %a.deps to i64) * (sext i32 %a.cols to i64))}<%for.i>,+,(4 * (sext i32 %a.deps to i64))}<%for.j>
+; CHECK: Base offset: %a.base
+; CHECK: ArrayDecl[UnknownSize][(sext i32 %a.deps to i64)] with elements of sizeof(float) bytes.
+; CHECK: ArrayRef[{(1 + (sext i32 %a.cols to i64)),+,(sext i32 %a.cols to i64)}<%for.i>][{(-1 + (sext i32 (-1 + %p.deps) to i64)),+,(sext i32 %a.deps to i64)}<%for.j>]
+
+; AddRec: {(-4 + (4 * (sext i32 (-1 + %p.deps) to i64)) + ((sext i32 %a.deps to i64) * (-4 + (4 * (sext i32 (-1 + %p.cols) to i64)) + (4 * (sext i32 %a.cols to i64)))) + %a.base),+,(4 * (sext i32 %a.deps to i64) * (sext i32 %a.cols to i64))}<%for.i>
+; CHECK: Base offset: %a.base
+; CHECK: ArrayDecl[UnknownSize] with elements of sizeof(float) bytes.
+; CHECK: ArrayRef[{(-1 + (sext i32 (-1 + %p.deps) to i64) + ((sext i32 %a.deps to i64) * (-1 + (sext i32 (-1 + %p.cols) to i64) + (sext i32 %a.cols to i64)))),+,((sext i32 %a.deps to i64) * (sext i32 %a.cols to i64))}<%for.i>]
+
+%struct.Mat = type { float*, i32, i32, i32, i32 }
+
+define void @jacobi(i32 %nn, %struct.Mat* nocapture %a, %struct.Mat* nocapture %p) nounwind uwtable {
+entry:
+  %p.rows.ptr = getelementptr inbounds %struct.Mat* %p, i64 0, i32 2
+  %p.rows = load i32* %p.rows.ptr
+  %p.rows.sub = add i32 %p.rows, -1
+  %p.rows.sext = sext i32 %p.rows.sub to i64
+  %p.cols.ptr = getelementptr inbounds %struct.Mat* %p, i64 0, i32 3
+  %p.cols = load i32* %p.cols.ptr
+  %p.cols.sub = add i32 %p.cols, -1
+  %p.cols.sext = sext i32 %p.cols.sub to i64
+  %p.deps.ptr = getelementptr inbounds %struct.Mat* %p, i64 0, i32 4
+  %p.deps = load i32* %p.deps.ptr
+  %p.deps.sub = add i32 %p.deps, -1
+  %p.deps.sext = sext i32 %p.deps.sub to i64
+  %a.cols.ptr = getelementptr inbounds %struct.Mat* %a, i64 0, i32 3
+  %a.cols = load i32* %a.cols.ptr
+  %a.deps.ptr = getelementptr inbounds %struct.Mat* %a, i64 0, i32 4
+  %a.deps = load i32* %a.deps.ptr
+  %a.base.ptr = getelementptr inbounds %struct.Mat* %a, i64 0, i32 0
+  %a.base = load float** %a.base.ptr, align 8
+  br label %for.i
+
+for.i:                                            ; preds = %for.i.inc, %entry
+  %i = phi i64 [ %i.inc, %for.i.inc ], [ 1, %entry ]
+  br label %for.j
+
+for.j:                                            ; preds = %for.j.inc, %for.i
+  %j = phi i64 [ %j.inc, %for.j.inc ], [ 1, %for.i ]
+  %a.cols.sext = sext i32 %a.cols to i64
+  %a.deps.sext = sext i32 %a.deps to i64
+  br label %for.k
+
+for.k:                                            ; preds = %for.k, %for.j
+  %k = phi i64 [ 1, %for.j ], [ %k.inc, %for.k ]
+  %tmp1 = mul nsw i64 %a.cols.sext, %i
+  %tmp2 = add i64 %tmp1, %j
+  %tmp3 = mul i64 %tmp2, %a.deps.sext
+  %tmp4 = add nsw i64 %k, %tmp3
+  %arrayidx = getelementptr inbounds float* %a.base, i64 %tmp4
+  store float 1.000000e+00, float* %arrayidx
+  %k.inc = add nsw i64 %k, 1
+  %k.exitcond = icmp eq i64 %k.inc, %p.deps.sext
+  br i1 %k.exitcond, label %for.j.inc, label %for.k
+
+for.j.inc:                                        ; preds = %for.k
+  %j.inc = add nsw i64 %j, 1
+  %j.exitcond = icmp eq i64 %j.inc, %p.cols.sext
+  br i1 %j.exitcond, label %for.i.inc, label %for.j
+
+for.i.inc:                                        ; preds = %for.j.inc
+  %i.inc = add nsw i64 %i, 1
+  %i.exitcond = icmp eq i64 %i.inc, %p.rows.sext
+  br i1 %i.exitcond, label %end, label %for.i
+
+end:                                              ; preds = %for.i.inc
+  ret void
+}

test/Analysis/Delinearization/himeno_2.ll

@@ -0,0 +1,102 @@
+; RUN: opt < %s -analyze -delinearize | FileCheck %s
+
+; #define MR(mt,n,r,c,d)  mt->m[(n) * mt->mrows * mt->mcols * mt->mdeps + (r) * mt->mcols* mt->mdeps + (c) * mt->mdeps + (d)]
+;
+; struct Mat {
+;   float* m;
+;   int mnums;
+;   int mrows;
+;   int mcols;
+;   int mdeps;
+; };
+;
+; typedef struct Mat Matrix;
+;
+; void jacobi(int nn, Matrix* a, Matrix* p)
+; {
+;   long i, j, k, max,jmax,kmax;
+;
+;   p_rows_sub = p->mrows - 1;
+;   p_cols_sub = p->mcols - 1;
+;   p_deps_sub = p->mdeps - 1;
+;
+;     for(i = 1; i < p_rows_sub; i++)
+;       for(j = 1; j < p_cols_sub; j++)
+;         for(k = 1; k < p_deps_sub; k++)
+;           MR(a,0,i,j,k) = i + j + k;
+; }
+
+; AddRec: {{{(4 + (4 * (sext i32 %a.deps to i64) * (1 + (sext i32 %a.cols to i64))) + %a.base),+,(4 * (sext i32 %a.deps to i64) * (sext i32 %a.cols to i64))}<%for.i>,+,(4 * (sext i32 %a.deps to i64))}<%for.j>,+,4}<%for.k>
+; CHECK: Base offset: %a.base
+; CHECK: ArrayDecl[UnknownSize][(sext i32 %a.cols to i64)][(sext i32 %a.deps to i64)] with elements of sizeof(float) bytes.
+; CHECK: ArrayRef[{1,+,1}<nuw><nsw><%for.i>][{1,+,1}<nuw><nsw><%for.j>][{1,+,1}<nuw><nsw><%for.k>]
+
+; AddRec: {{(-4 + (4 * (sext i32 (-1 + %p.deps) to i64)) + (4 * (sext i32 %a.deps to i64) * (1 + (sext i32 %a.cols to i64))) + %a.base),+,(4 * (sext i32 %a.deps to i64) * (sext i32 %a.cols to i64))}<%for.i>,+,(4 * (sext i32 %a.deps to i64))}<%for.j>
+; CHECK: Base offset: %a.base
+; CHECK: ArrayDecl[UnknownSize][(sext i32 %a.deps to i64)] with elements of sizeof(float) bytes.
+; CHECK: ArrayRef[{(1 + (sext i32 %a.cols to i64)),+,(sext i32 %a.cols to i64)}<%for.i>][{(-1 + (sext i32 (-1 + %p.deps) to i64)),+,(sext i32 %a.deps to i64)}<%for.j>]
+
+; AddRec: {(-4 + (4 * (sext i32 (-1 + %p.deps) to i64)) + ((sext i32 %a.deps to i64) * (-4 + (4 * (sext i32 (-1 + %p.cols) to i64)) + (4 * (sext i32 %a.cols to i64)))) + %a.base),+,(4 * (sext i32 %a.deps to i64) * (sext i32 %a.cols to i64))}<%for.i>
+; CHECK: Base offset: %a.base
+; CHECK: ArrayDecl[UnknownSize] with elements of sizeof(float) bytes.
+; CHECK: ArrayRef[{(-1 + (sext i32 (-1 + %p.deps) to i64) + ((sext i32 %a.deps to i64) * (-1 + (sext i32 (-1 + %p.cols) to i64) + (sext i32 %a.cols to i64)))),+,((sext i32 %a.deps to i64) * (sext i32 %a.cols to i64))}<%for.i>]
+
+%struct.Mat = type { float*, i32, i32, i32, i32 }
+
+define void @jacobi(i32 %nn, %struct.Mat* nocapture %a, %struct.Mat* nocapture %p) nounwind uwtable {
+entry:
+  %p.rows.ptr = getelementptr inbounds %struct.Mat* %p, i64 0, i32 2
+  %p.rows = load i32* %p.rows.ptr
+  %p.rows.sub = add i32 %p.rows, -1
+  %p.rows.sext = sext i32 %p.rows.sub to i64
+  %p.cols.ptr = getelementptr inbounds %struct.Mat* %p, i64 0, i32 3
+  %p.cols = load i32* %p.cols.ptr
+  %p.cols.sub = add i32 %p.cols, -1
+  %p.cols.sext = sext i32 %p.cols.sub to i64
+  %p.deps.ptr = getelementptr inbounds %struct.Mat* %p, i64 0, i32 4
+  %p.deps = load i32* %p.deps.ptr
+  %p.deps.sub = add i32 %p.deps, -1
+  %p.deps.sext = sext i32 %p.deps.sub to i64
+  %a.cols.ptr = getelementptr inbounds %struct.Mat* %a, i64 0, i32 3
+  %a.cols = load i32* %a.cols.ptr
+  %a.cols.sext = sext i32 %a.cols to i64
+  %a.deps.ptr = getelementptr inbounds %struct.Mat* %a, i64 0, i32 4
+  %a.deps = load i32* %a.deps.ptr
+  %a.deps.sext = sext i32 %a.deps to i64
+  %a.base.ptr = getelementptr inbounds %struct.Mat* %a, i64 0, i32 0
+  %a.base = load float** %a.base.ptr, align 8
+  br label %for.i
+
+for.i:                                            ; preds = %for.i.inc, %entry
+  %i = phi i64 [ %i.inc, %for.i.inc ], [ 1, %entry ]
+  br label %for.j
+
+for.j:                                            ; preds = %for.j.inc, %for.i
+  %j = phi i64 [ %j.inc, %for.j.inc ], [ 1, %for.i ]
+  br label %for.k
+
+for.k:                                            ; preds = %for.k, %for.j
+  %k = phi i64 [ 1, %for.j ], [ %k.inc, %for.k ]
+  %tmp1 = mul nsw i64 %a.cols.sext, %i
+  %tmp2 = add i64 %tmp1, %j
+  %tmp3 = mul i64 %tmp2, %a.deps.sext
+  %tmp4 = add nsw i64 %k, %tmp3
+  %arrayidx = getelementptr inbounds float* %a.base, i64 %tmp4
+  store float 1.000000e+00, float* %arrayidx
+  %k.inc = add nsw i64 %k, 1
+  %k.exitcond = icmp eq i64 %k.inc, %p.deps.sext
+  br i1 %k.exitcond, label %for.j.inc, label %for.k
+
+for.j.inc:                                        ; preds = %for.k
+  %j.inc = add nsw i64 %j, 1
+  %j.exitcond = icmp eq i64 %j.inc, %p.cols.sext
+  br i1 %j.exitcond, label %for.i.inc, label %for.j
+
+for.i.inc:                                        ; preds = %for.j.inc
+  %i.inc = add nsw i64 %i, 1
+  %i.exitcond = icmp eq i64 %i.inc, %p.rows.sext
+  br i1 %i.exitcond, label %end, label %for.i
+
+end:                                              ; preds = %for.i.inc
+  ret void
+}

test/Analysis/Delinearization/lit.local.cfg

@@ -0,0 +1 @@
+config.suffixes = ['.ll', '.c', '.cpp']

test/Analysis/Delinearization/multidim_ivs_and_integer_offsets_3d.ll

@@ -0,0 +1,68 @@
+; RUN: opt < %s -analyze -delinearize  | FileCheck %s
+
+; void foo(long n, long m, long o, double A[n][m][o]) {
+;
+;   for (long i = 0; i < n; i++)
+;     for (long j = 0; j < m; j++)
+;       for (long k = 0; k < o; k++)
+;         A[i+3][j-4][k+7] = 1.0;
+; }
+
+; AddRec: {{{(56 + (8 * (-4 + (3 * %m)) * %o) + %A),+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{3,+,1}<nw><%for.i>][{-4,+,1}<nw><%for.j>][{7,+,1}<nw><%for.k>]
+
+; AddRec: {{(48 + ((-24 + (24 * %m)) * %o) + %A),+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][%o] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{(-3 + (3 * %m)),+,%m}<%for.i>][{6,+,%o}<%for.j>]
+
+; AddRec: {(48 + ((-32 + (32 * %m)) * %o) + %A),+,(8 * %m * %o)}<%for.i>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{(6 + ((-4 + (4 * %m)) * %o)),+,(%m * %o)}<%for.i>]
+
+define void @foo(i64 %n, i64 %m, i64 %o, double* %A) {
+entry:
+  br label %for.i
+
+for.i:
+  %i = phi i64 [ 0, %entry ], [ %i.inc, %for.i.inc ]
+  br label %for.j
+
+for.j:
+  %j = phi i64 [ 0, %for.i ], [ %j.inc, %for.j.inc ]
+  br label %for.k
+
+for.k:
+  %k = phi i64 [ 0, %for.j ], [ %k.inc, %for.k.inc ]
+  %offset0 = add nsw i64 %i, 3
+  %subscript0 = mul i64 %offset0, %m
+  %offset1 = add nsw i64 %j, -4
+  %subscript1 = add i64 %offset1, %subscript0
+  %subscript2 = mul i64 %subscript1, %o
+  %offset2 = add nsw i64 %k, 7
+  %subscript = add i64 %subscript2, %offset2
+  %idx = getelementptr inbounds double* %A, i64 %subscript
+  store double 1.0, double* %idx
+  br label %for.k.inc
+
+for.k.inc:
+  %k.inc = add nsw i64 %k, 1
+  %k.exitcond = icmp eq i64 %k.inc, %o
+  br i1 %k.exitcond, label %for.j.inc, label %for.k
+
+for.j.inc:
+  %j.inc = add nsw i64 %j, 1
+  %j.exitcond = icmp eq i64 %j.inc, %m
+  br i1 %j.exitcond, label %for.i.inc, label %for.j
+
+for.i.inc:
+  %i.inc = add nsw i64 %i, 1
+  %i.exitcond = icmp eq i64 %i.inc, %n
+  br i1 %i.exitcond, label %end, label %for.i
+
+end:
+  ret void
+}

test/Analysis/Delinearization/multidim_ivs_and_integer_offsets_nts_3d.ll

@@ -0,0 +1,72 @@
+; RUN: opt < %s -analyze -delinearize | FileCheck %s
+
+; void foo(long n, long m, long o, long p, double A[n][m][o+p]) {
+;
+;   for (long i = 0; i < n; i++)
+;     for (long j = 0; j < m; j++)
+;       for (long k = 0; k < o; k++)
+;         A[i+3][j-4][k+7] = 1.0;
+; }
+
+; AddRec: {{{(56 + (8 * (-4 + (3 * %m)) * (%o + %p)) + %A),+,(8 * (%o + %p) * %m)}<%for.cond4.preheader.lr.ph.us>,+,(8 * (%o + %p))}<%for.body6.lr.ph.us.us>,+,8}<%for.body6.us.us>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][%m][(%o + %p)] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{3,+,1}<nw><%for.cond4.preheader.lr.ph.us>][{-4,+,1}<nw><%for.body6.lr.ph.us.us>][{7,+,1}<nw><%for.body6.us.us>]
+
+; AddRec: {{(48 + (8 * %o) + (8 * (-4 + (3 * %m)) * (%o + %p)) + %A),+,(8 * (%o + %p) * %m)}<%for.cond4.preheader.lr.ph.us>,+,(8 * (%o + %p))}<%for.body6.lr.ph.us.us>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][(%o + %p)] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{(-4 + (3 * %m)),+,%m}<%for.cond4.preheader.lr.ph.us>][{(6 + %o),+,(%o + %p)}<%for.body6.lr.ph.us.us>]
+
+; AddRec: {(48 + (8 * %o) + ((-40 + (32 * %m)) * (%o + %p)) + %A),+,(8 * (%o + %p) * %m)}<%for.cond4.preheader.lr.ph.us>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{(6 + ((-5 + (4 * %m)) * (%o + %p)) + %o),+,((%o + %p) * %m)}<%for.cond4.preheader.lr.ph.us>]
+
+define void @foo(i64 %n, i64 %m, i64 %o, i64 %p, double* nocapture %A) nounwind uwtable {
+entry:
+  %add = add nsw i64 %p, %o
+  %cmp22 = icmp sgt i64 %n, 0
+  br i1 %cmp22, label %for.cond1.preheader.lr.ph, label %for.end16
+
+for.cond1.preheader.lr.ph:                        ; preds = %entry
+  %cmp220 = icmp sgt i64 %m, 0
+  %cmp518 = icmp sgt i64 %o, 0
+  br i1 %cmp220, label %for.cond4.preheader.lr.ph.us, label %for.end16
+
+for.inc14.us:                                     ; preds = %for.cond4.preheader.lr.ph.us, %for.inc11.us.us
+  %inc15.us = add nsw i64 %i.023.us, 1
+  %exitcond43 = icmp eq i64 %inc15.us, %n
+  br i1 %exitcond43, label %for.end16, label %for.cond4.preheader.lr.ph.us
+
+for.cond4.preheader.lr.ph.us:                     ; preds = %for.inc14.us, %for.cond1.preheader.lr.ph
+  %i.023.us = phi i64 [ %inc15.us, %for.inc14.us ], [ 0, %for.cond1.preheader.lr.ph ]
+  %add8.us = add nsw i64 %i.023.us, 3
+  %0 = mul i64 %add8.us, %m
+  %sub.us = add i64 %0, -4
+  br i1 %cmp518, label %for.body6.lr.ph.us.us, label %for.inc14.us
+
+for.inc11.us.us:                                  ; preds = %for.body6.us.us
+  %inc12.us.us = add nsw i64 %j.021.us.us, 1
+  %exitcond42 = icmp eq i64 %inc12.us.us, %m
+  br i1 %exitcond42, label %for.inc14.us, label %for.body6.lr.ph.us.us
+
+for.body6.lr.ph.us.us:                            ; preds = %for.cond4.preheader.lr.ph.us, %for.inc11.us.us
+  %j.021.us.us = phi i64 [ %inc12.us.us, %for.inc11.us.us ], [ 0, %for.cond4.preheader.lr.ph.us ]
+  %tmp.us.us = add i64 %sub.us, %j.021.us.us
+  %tmp17.us.us = mul i64 %tmp.us.us, %add
+  br label %for.body6.us.us
+
+for.body6.us.us:                                  ; preds = %for.body6.us.us, %for.body6.lr.ph.us.us
+  %k.019.us.us = phi i64 [ 0, %for.body6.lr.ph.us.us ], [ %inc.us.us, %for.body6.us.us ]
+  %arrayidx.sum.us.us = add i64 %k.019.us.us, 7
+  %arrayidx9.sum.us.us = add i64 %arrayidx.sum.us.us, %tmp17.us.us
+  %arrayidx10.us.us = getelementptr inbounds double* %A, i64 %arrayidx9.sum.us.us
+  store double 1.000000e+00, double* %arrayidx10.us.us, align 8
+  %inc.us.us = add nsw i64 %k.019.us.us, 1
+  %exitcond = icmp eq i64 %inc.us.us, %o
+  br i1 %exitcond, label %for.inc11.us.us, label %for.body6.us.us
+
+for.end16:                                        ; preds = %for.cond1.preheader.lr.ph, %for.inc14.us, %entry
+  ret void
+}

test/Analysis/Delinearization/multidim_ivs_and_parameteric_offsets_3d.ll

@@ -0,0 +1,68 @@
+; RUN: opt < %s -analyze -delinearize | FileCheck %s
+
+; void foo(long n, long m, long o, double A[n][m][o], long p, long q, long r) {
+;
+;   for (long i = 0; i < n; i++)
+;     for (long j = 0; j < m; j++)
+;       for (long k = 0; k < o; k++)
+;         A[i+p][j+q][k+r] = 1.0;
+; }
+
+; AddRec: {{{((8 * ((((%m * %p) + %q) * %o) + %r)) + %A),+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{%p,+,1}<nw><%for.i>][{%q,+,1}<nw><%for.j>][{%r,+,1}<nw><%for.k>]
+
+; AddRec: {{(-8 + (8 * ((((%m * %p) + %q) * %o) + %r)) + (8 * %o) + %A),+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][%o] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{(1 + (%m * %p) + %q),+,%m}<%for.i>][{(-1 + %r),+,%o}<%for.j>]
+
+; AddRec: {(-8 + (8 * ((((%m * %p) + %q) * %o) + %r)) + (8 * %m * %o) + %A),+,(8 * %m * %o)}<%for.i>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{(-1 + ((((1 + %p) * %m) + %q) * %o) + %r),+,(%m * %o)}<%for.i>]
+
+define void @foo(i64 %n, i64 %m, i64 %o, double* %A, i64 %p, i64 %q, i64 %r) {
+entry:
+  br label %for.i
+
+for.i:
+  %i = phi i64 [ 0, %entry ], [ %i.inc, %for.i.inc ]
+  br label %for.j
+
+for.j:
+  %j = phi i64 [ 0, %for.i ], [ %j.inc, %for.j.inc ]
+  br label %for.k
+
+for.k:
+  %k = phi i64 [ 0, %for.j ], [ %k.inc, %for.k.inc ]
+  %offset0 = add nsw i64 %i, %p
+  %subscript0 = mul i64 %offset0, %m
+  %offset1 = add nsw i64 %j, %q
+  %subscript1 = add i64 %offset1, %subscript0
+  %subscript2 = mul i64 %subscript1, %o
+  %offset2 = add nsw i64 %k, %r
+  %subscript = add i64 %subscript2, %offset2
+  %idx = getelementptr inbounds double* %A, i64 %subscript
+  store double 1.0, double* %idx
+  br label %for.k.inc
+
+for.k.inc:
+  %k.inc = add nsw i64 %k, 1
+  %k.exitcond = icmp eq i64 %k.inc, %o
+  br i1 %k.exitcond, label %for.j.inc, label %for.k
+
+for.j.inc:
+  %j.inc = add nsw i64 %j, 1
+  %j.exitcond = icmp eq i64 %j.inc, %m
+  br i1 %j.exitcond, label %for.i.inc, label %for.j
+
+for.i.inc:
+  %i.inc = add nsw i64 %i, 1
+  %i.exitcond = icmp eq i64 %i.inc, %n
+  br i1 %i.exitcond, label %end, label %for.i
+
+end:
+  ret void
+}

test/Analysis/Delinearization/multidim_only_ivs_2d.ll

@@ -0,0 +1,46 @@
+; RUN: opt < %s -analyze -delinearize | FileCheck %s
+
+; Derived from the following code:
+;
+; void foo(long n, long m, double A[n][m]) {
+;   for (long i = 0; i < n; i++)
+;     for (long j = 0; j < m; j++)
+;       A[i][j] = 1.0;
+; }
+
+; AddRec: {{%A,+,(8 * %m)}<%for.i>,+,8}<%for.j>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][%m] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{0,+,1}<nuw><nsw><%for.i>][{0,+,1}<nuw><nsw><%for.j>]
+
+; AddRec: {(-8 + (8 * %m) + %A),+,(8 * %m)}<%for.i>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{(-1 + %m),+,%m}<%for.i>]
+
+define void @foo(i64 %n, i64 %m, double* %A) {
+entry:
+  br label %for.i
+
+for.i:
+  %i = phi i64 [ 0, %entry ], [ %i.inc, %for.i.inc ]
+  %tmp = mul nsw i64 %i, %m
+  br label %for.j
+
+for.j:
+  %j = phi i64 [ 0, %for.i ], [ %j.inc, %for.j ]
+  %vlaarrayidx.sum = add i64 %j, %tmp
+  %arrayidx = getelementptr inbounds double* %A, i64 %vlaarrayidx.sum
+  store double 1.0, double* %arrayidx
+  %j.inc = add nsw i64 %j, 1
+  %j.exitcond = icmp eq i64 %j.inc, %m
+  br i1 %j.exitcond, label %for.i.inc, label %for.j
+
+for.i.inc:
+  %i.inc = add nsw i64 %i, 1
+  %i.exitcond = icmp eq i64 %i.inc, %n
+  br i1 %i.exitcond, label %end, label %for.i
+
+end:
+  ret void
+}

test/Analysis/Delinearization/multidim_only_ivs_2d_nested.ll

@@ -0,0 +1,78 @@
+; RUN: opt < %s -analyze -delinearize | FileCheck %s
+
+; extern void bar(long n, long m, double A[n][m]);
+;
+; void foo(long a, long b) {
+;   for (long n = 1; n < a; ++n)
+;   for (long m = 1; m < b; ++m) {
+;     double A[n][m];
+;     for (long i = 0; i < n; i++)
+;       for (long j = 0; j < m; j++)
+;         A[i][j] = 1.0;
+;     bar(n, m, A);
+;   }
+; }
+
+; AddRec: {{%vla.us,+,{8,+,8}<%for.cond7.preheader.lr.ph.split.us.us>}<%for.body9.lr.ph.us.us>,+,8}<%for.body9.us.us>
+; CHECK: Base offset: %vla.us
+; CHECK: ArrayDecl[UnknownSize][{1,+,1}<%for.cond7.preheader.lr.ph.split.us.us>] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{0,+,1}<nuw><nsw><%for.body9.lr.ph.us.us>][{0,+,1}<nuw><nsw><%for.body9.us.us>]
+
+define void @foo(i64 %a, i64 %b) nounwind uwtable {
+entry:
+  %cmp43 = icmp sgt i64 %a, 1
+  br i1 %cmp43, label %for.cond1.preheader.lr.ph, label %for.end19
+
+for.cond1.preheader.lr.ph:                        ; preds = %entry
+  %cmp224 = icmp sgt i64 %b, 1
+  br label %for.cond1.preheader
+
+for.cond1.preheader:                              ; preds = %for.inc17, %for.cond1.preheader.lr.ph
+  %indvars.iv51 = phi i64 [ 1, %for.cond1.preheader.lr.ph ], [ %indvars.iv.next52, %for.inc17 ]
+  br i1 %cmp224, label %for.cond7.preheader.lr.ph.split.us.us, label %for.inc17
+
+for.end13.us:                                     ; preds = %for.inc11.us.us
+  call void @bar(i64 %indvars.iv51, i64 %indvars.iv48, double* %vla.us) nounwind
+  call void @llvm.stackrestore(i8* %1)
+  %indvars.iv.next49 = add i64 %indvars.iv48, 1
+  %exitcond54 = icmp eq i64 %indvars.iv.next49, %b
+  br i1 %exitcond54, label %for.inc17, label %for.cond7.preheader.lr.ph.split.us.us
+
+for.inc11.us.us:                                  ; preds = %for.body9.us.us
+  %inc12.us.us = add nsw i64 %i.023.us.us, 1
+  %exitcond53 = icmp eq i64 %inc12.us.us, %indvars.iv51
+  br i1 %exitcond53, label %for.end13.us, label %for.body9.lr.ph.us.us
+
+for.body9.lr.ph.us.us:                            ; preds = %for.cond7.preheader.lr.ph.split.us.us, %for.inc11.us.us
+  %i.023.us.us = phi i64 [ 0, %for.cond7.preheader.lr.ph.split.us.us ], [ %inc12.us.us, %for.inc11.us.us ]
+  %0 = mul nsw i64 %i.023.us.us, %indvars.iv48
+  br label %for.body9.us.us
+
+for.body9.us.us:                                  ; preds = %for.body9.us.us, %for.body9.lr.ph.us.us
+  %j.021.us.us = phi i64 [ 0, %for.body9.lr.ph.us.us ], [ %inc.us.us, %for.body9.us.us ]
+  %arrayidx.sum.us.us = add i64 %j.021.us.us, %0
+  %arrayidx10.us.us = getelementptr inbounds double* %vla.us, i64 %arrayidx.sum.us.us
+  store double 1.000000e+00, double* %arrayidx10.us.us, align 8
+  %inc.us.us = add nsw i64 %j.021.us.us, 1
+  %exitcond50 = icmp eq i64 %inc.us.us, %indvars.iv48
+  br i1 %exitcond50, label %for.inc11.us.us, label %for.body9.us.us
+
+for.cond7.preheader.lr.ph.split.us.us:            ; preds = %for.cond1.preheader, %for.end13.us
+  %indvars.iv48 = phi i64 [ %indvars.iv.next49, %for.end13.us ], [ 1, %for.cond1.preheader ]
+  %1 = call i8* @llvm.stacksave()
+  %2 = mul nuw i64 %indvars.iv48, %indvars.iv51
+  %vla.us = alloca double, i64 %2, align 16
+  br label %for.body9.lr.ph.us.us
+
+for.inc17:                                        ; preds = %for.end13.us, %for.cond1.preheader
+  %indvars.iv.next52 = add i64 %indvars.iv51, 1
+  %exitcond55 = icmp eq i64 %indvars.iv.next52, %a
+  br i1 %exitcond55, label %for.end19, label %for.cond1.preheader
+
+for.end19:                                        ; preds = %for.inc17, %entry
+  ret void
+}
+
+declare i8* @llvm.stacksave() nounwind
+declare void @bar(i64, i64, double*)
+declare void @llvm.stackrestore(i8*) nounwind

test/Analysis/Delinearization/multidim_only_ivs_3d.ll

@@ -0,0 +1,65 @@
+; RUN: opt < %s -analyze -delinearize | FileCheck %s
+
+; void foo(long n, long m, long o, double A[n][m][o]) {
+;
+;   for (long i = 0; i < n; i++)
+;     for (long j = 0; j < m; j++)
+;       for (long k = 0; k < o; k++)
+;         A[i][j][k] = 1.0;
+; }
+
+; AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{0,+,1}<nuw><nsw><%for.i>][{0,+,1}<nuw><nsw><%for.j>][{0,+,1}<nuw><nsw><%for.k>]
+
+; AddRec: {{(-8 + (8 * %o) + %A),+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][(%m * %o)] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{0,+,1}<nuw><nsw><%for.i>][{(-1 + %o),+,%o}<%for.j>]
+
+; AddRec: {(-8 + (8 * %m * %o) + %A),+,(8 * %m * %o)}<%for.i>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize] with elements of sizeof(double) bytes.
+; CHECK: ArrayRef[{(-1 + (%m * %o)),+,(%m * %o)}<%for.i>]
+
+define void @foo(i64 %n, i64 %m, i64 %o, double* %A) {
+entry:
+  br label %for.i
+
+for.i:
+  %i = phi i64 [ 0, %entry ], [ %i.inc, %for.i.inc ]
+  br label %for.j
+
+for.j:
+  %j = phi i64 [ 0, %for.i ], [ %j.inc, %for.j.inc ]
+  br label %for.k
+
+for.k:
+  %k = phi i64 [ 0, %for.j ], [ %k.inc, %for.k.inc ]
+  %subscript0 = mul i64 %i, %m
+  %subscript1 = add i64 %j, %subscript0
+  %subscript2 = mul i64 %subscript1, %o
+  %subscript = add i64 %subscript2, %k
+  %idx = getelementptr inbounds double* %A, i64 %subscript
+  store double 1.0, double* %idx
+  br label %for.k.inc
+
+for.k.inc:
+  %k.inc = add nsw i64 %k, 1
+  %k.exitcond = icmp eq i64 %k.inc, %o
+  br i1 %k.exitcond, label %for.j.inc, label %for.k
+
+for.j.inc:
+  %j.inc = add nsw i64 %j, 1
+  %j.exitcond = icmp eq i64 %j.inc, %m
+  br i1 %j.exitcond, label %for.i.inc, label %for.j
+
+for.i.inc:
+  %i.inc = add nsw i64 %i, 1
+  %i.exitcond = icmp eq i64 %i.inc, %n
+  br i1 %i.exitcond, label %end, label %for.i
+
+end:
+  ret void
+}

test/Analysis/Delinearization/multidim_only_ivs_3d_cast.ll

@@ -0,0 +1,75 @@
+; RUN: opt < %s -analyze -delinearize | FileCheck %s
+; void foo(int n, int m, int o, double A[n][m][o]) {
+;
+;   for (int i = 0; i < n; i++)
+;     for (int j = 0; j < m; j++)
+;       for (int k = 0; k < o; k++)
+;         A[i][j][k] = 1.0;
+; }
+
+; AddRec: {{{%A,+,(8 * (zext i32 %m to i64) * (zext i32 %o to i64))}<%for.i>,+,(8 * (zext i32 %o to i64))}<%for.j>,+,8}<%for.k>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][(zext i32 %m to i64)][(zext i32 %o to i64)] with elements of 8 bytes.
+; CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
+
+; AddRec: {{((8 * (zext i32 (-1 + %o) to i64)) + %A),+,(8 * (zext i32 %m to i64) * (zext i32 %o to i64))}<%for.i>,+,(8 * (zext i32 %o to i64))}<%for.j>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize][((zext i32 %m to i64) * (zext i32 %o to i64))] with elements of 8 bytes.
+; CHECK: ArrayRef[{0,+,1}<%for.i>][{(zext i32 (-1 + %o) to i64),+,(zext i32 %o to i64)}<%for.j>]
+
+; AddRec: {((8 * (zext i32 (-1 + %o) to i64)) + (8 * (zext i32 (-1 + %m) to i64) * (zext i32 %o to i64)) + %A),+,(8 * (zext i32 %m to i64) * (zext i32 %o to i64))}<%for.i>
+; CHECK: Base offset: %A
+; CHECK: ArrayDecl[UnknownSize] with elements of 8 bytes.
+; CHECK: ArrayRef[{((zext i32 (-1 + %o) to i64) + ((zext i32 (-1 + %m) to i64) * (zext i32 %o to i64))),+,((zext i32 %m to i64) * (zext i32 %o to i64))}<%for.i>]
+
+target datalayout = "e-p:64:64:64-i1:8:8-i8:8:8-i16:16:16-i32:32:32-i64:64:64-f32:32:32-f64:64:64-v64:64:64-v128:128:128-a0:0:64-s0:64:64-f80:128:128-n8:16:32:64-S128"
+target triple = "x86_64-unknown-linux-gnu"
+
+define void @foo(i32 %n, i32 %m, i32 %o, double* %A) {
+entry:
+  %m_zext = zext i32 %m to i64
+  %n_zext = zext i32 %o to i64
+  br label %for.i
+
+for.i:
+  %i = phi i64 [ %i.inc, %for.i.inc ], [ 0, %entry ]
+  br label %for.j
+
+for.j:
+  %j = phi i64 [ %j.inc, %for.j.inc ], [ 0, %for.i ]
+  br label %for.k
+
+for.k:
+  %k = phi i64 [ %k.inc, %for.k.inc ], [ 0, %for.j ]
+  %tmp = mul i64 %i, %m_zext
+  %tmp1 = trunc i64 %j to i32
+  %tmp2 = trunc i64 %i to i32
+  %mul.us.us = mul nsw i32 %tmp1, %tmp2
+  %tmp.us.us = add i64 %j, %tmp
+  %tmp17.us.us = mul i64 %tmp.us.us, %n_zext
+  %subscript = add i64 %tmp17.us.us, %k
+  %idx = getelementptr inbounds double* %A, i64 %subscript
+  store double 1.0, double* %idx
+  br label %for.k.inc
+
+for.k.inc:
+  %k.inc = add i64 %k, 1
+  %k.inc.trunc = trunc i64 %k.inc to i32
+  %k.exitcond = icmp eq i32 %k.inc.trunc, %o
+  br i1 %k.exitcond, label %for.j.inc, label %for.k
+
+for.j.inc:
+  %j.inc = add i64 %j, 1
+  %j.inc.trunc = trunc i64 %j.inc to i32
+  %j.exitcond = icmp eq i32 %j.inc.trunc, %m
+  br i1 %j.exitcond, label %for.i.inc, label %for.j
+
+for.i.inc:
+  %i.inc = add i64 %i, 1
+  %i.inc.trunc = trunc i64 %i.inc to i32
+  %i.exitcond = icmp eq i32 %i.inc.trunc, %n
+  br i1 %i.exitcond, label %end, label %for.i
+
+end:
+  ret void
+}