[llvm] 585c594 - Move delinearization logic out of SCEV [NFC]

Michael Kruse via llvm-commits llvm-commits at lists.llvm.org
Wed Sep 8 13:05:45 PDT 2021


You left getIndexExpressionsFromGEP inside ScalarEvolution. Don't you
consider it part of Delinearization? getElementSize is also only used
in delinearization use cases/was introduced for it.

Michael

Am Mi., 8. Sept. 2021 um 14:28 Uhr schrieb Philip Reames via
llvm-commits <llvm-commits at lists.llvm.org>:
>
>
> Author: Philip Reames
> Date: 2021-09-08T12:28:35-07:00
> New Revision: 585c594d749a2a88150b63804587af85abdabeaa
>
> URL: https://github.com/llvm/llvm-project/commit/585c594d749a2a88150b63804587af85abdabeaa
> DIFF: https://github.com/llvm/llvm-project/commit/585c594d749a2a88150b63804587af85abdabeaa.diff
>
> LOG: Move delinearization logic out of SCEV [NFC]
>
> None of this logic has anything to do with SCEV's internals, it just uses the existing public APIs.  As a result, we can move the code from ScalarEvolution.cpp/hpp to Delinearization.cpp/hpp with only minor changes.
>
> This was discussed in advance on today's loop opt call.  It turned out to be easy as hoped.
>
> Added:
>
>
> Modified:
>     llvm/include/llvm/Analysis/Delinearization.h
>     llvm/include/llvm/Analysis/ScalarEvolution.h
>     llvm/lib/Analysis/Delinearization.cpp
>     llvm/lib/Analysis/DependenceAnalysis.cpp
>     llvm/lib/Analysis/LoopCacheAnalysis.cpp
>     llvm/lib/Analysis/ScalarEvolution.cpp
>
> Removed:
>
>
>
> ################################################################################
> diff  --git a/llvm/include/llvm/Analysis/Delinearization.h b/llvm/include/llvm/Analysis/Delinearization.h
> index 2658b6bbc80c0..dec3fd9b08a9f 100644
> --- a/llvm/include/llvm/Analysis/Delinearization.h
> +++ b/llvm/include/llvm/Analysis/Delinearization.h
> @@ -16,10 +16,100 @@
>  #ifndef LLVM_ANALYSIS_DELINEARIZATION_H
>  #define LLVM_ANALYSIS_DELINEARIZATION_H
>
> +#include "llvm/ADT/SmallVector.h"
>  #include "llvm/IR/PassManager.h"
>  #include "llvm/Support/raw_ostream.h"
>
>  namespace llvm {
> +class ScalarEvolution;
> +class SCEV;
> +
> +/// Compute the array dimensions Sizes from the set of Terms extracted from
> +/// the memory access function of this SCEVAddRecExpr (second step of
> +/// delinearization).
> +void findArrayDimensions(ScalarEvolution &SE,
> +                         SmallVectorImpl<const SCEV *> &Terms,
> +                         SmallVectorImpl<const SCEV *> &Sizes,
> +                         const SCEV *ElementSize);
> +
> +/// Collect parametric terms occurring in step expressions (first step of
> +/// delinearization).
> +void collectParametricTerms(ScalarEvolution &SE, const SCEV *Expr,
> +                            SmallVectorImpl<const SCEV *> &Terms);
> +
> +/// Return in Subscripts the access functions for each dimension in Sizes
> +/// (third step of delinearization).
> +void computeAccessFunctions(ScalarEvolution &SE, const SCEV *Expr,
> +                            SmallVectorImpl<const SCEV *> &Subscripts,
> +                            SmallVectorImpl<const SCEV *> &Sizes);
> +/// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
> +/// subscripts and sizes of an array access.
> +///
> +/// The delinearization is a 3 step process: the first two steps compute the
> +/// sizes of each subscript and the third step computes the access functions
> +/// for the delinearized array:
> +///
> +/// 1. Find the terms in the step functions
> +/// 2. Compute the array size
> +/// 3. Compute the access function: divide the SCEV by the array size
> +///    starting with the innermost dimensions found in step 2. The Quotient
> +///    is the SCEV to be divided in the next step of the recursion. The
> +///    Remainder is the subscript of the innermost dimension. Loop over all
> +///    array dimensions computed in step 2.
> +///
> +/// To compute a uniform array size for several memory accesses to the same
> +/// object, one can collect in step 1 all the step terms for all the memory
> +/// accesses, and compute in step 2 a unique array shape. This guarantees
> +/// that the array shape will be the same across all memory accesses.
> +///
> +/// FIXME: We could derive the result of steps 1 and 2 from a description of
> +/// the array shape given in metadata.
> +///
> +/// Example:
> +///
> +/// A[][n][m]
> +///
> +/// for i
> +///   for j
> +///     for k
> +///       A[j+k][2i][5i] =
> +///
> +/// The initial SCEV:
> +///
> +/// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
> +///
> +/// 1. Find the
> diff erent terms in the step functions:
> +/// -> [2*m, 5, n*m, n*m]
> +///
> +/// 2. Compute the array size: sort and unique them
> +/// -> [n*m, 2*m, 5]
> +/// find the GCD of all the terms = 1
> +/// divide by the GCD and erase constant terms
> +/// -> [n*m, 2*m]
> +/// GCD = m
> +/// divide by GCD -> [n, 2]
> +/// remove constant terms
> +/// -> [n]
> +/// size of the array is A[unknown][n][m]
> +///
> +/// 3. Compute the access function
> +/// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
> +/// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
> +/// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
> +/// The remainder is the subscript of the innermost array dimension: [5i].
> +///
> +/// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
> +/// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
> +/// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
> +/// The Remainder is the subscript of the next array dimension: [2i].
> +///
> +/// The subscript of the outermost dimension is the Quotient: [j+k].
> +///
> +/// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
> +void delinearize(ScalarEvolution &SE, const SCEV *Expr,
> +                 SmallVectorImpl<const SCEV *> &Subscripts,
> +                 SmallVectorImpl<const SCEV *> &Sizes, const SCEV *ElementSize);
> +
>  struct DelinearizationPrinterPass
>      : public PassInfoMixin<DelinearizationPrinterPass> {
>    explicit DelinearizationPrinterPass(raw_ostream &OS);
>
> diff  --git a/llvm/include/llvm/Analysis/ScalarEvolution.h b/llvm/include/llvm/Analysis/ScalarEvolution.h
> index 6ae865e011cf0..445a925c70e83 100644
> --- a/llvm/include/llvm/Analysis/ScalarEvolution.h
> +++ b/llvm/include/llvm/Analysis/ScalarEvolution.h
> @@ -1099,29 +1099,11 @@ class ScalarEvolution {
>    /// Return the size of an element read or written by Inst.
>    const SCEV *getElementSize(Instruction *Inst);
>
> -  /// Compute the array dimensions Sizes from the set of Terms extracted from
> -  /// the memory access function of this SCEVAddRecExpr (second step of
> -  /// delinearization).
> -  void findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
> -                           SmallVectorImpl<const SCEV *> &Sizes,
> -                           const SCEV *ElementSize);
> -
>    void print(raw_ostream &OS) const;
>    void verify() const;
>    bool invalidate(Function &F, const PreservedAnalyses &PA,
>                    FunctionAnalysisManager::Invalidator &Inv);
>
> -  /// Collect parametric terms occurring in step expressions (first step of
> -  /// delinearization).
> -  void collectParametricTerms(const SCEV *Expr,
> -                              SmallVectorImpl<const SCEV *> &Terms);
> -
> -  /// Return in Subscripts the access functions for each dimension in Sizes
> -  /// (third step of delinearization).
> -  void computeAccessFunctions(const SCEV *Expr,
> -                              SmallVectorImpl<const SCEV *> &Subscripts,
> -                              SmallVectorImpl<const SCEV *> &Sizes);
> -
>    /// Gathers the individual index expressions from a GEP instruction.
>    ///
>    /// This function optimistically assumes the GEP references into a fixed size
> @@ -1135,74 +1117,6 @@ class ScalarEvolution {
>                                    SmallVectorImpl<const SCEV *> &Subscripts,
>                                    SmallVectorImpl<int> &Sizes);
>
> -  /// Split this SCEVAddRecExpr into two vectors of SCEVs representing the
> -  /// subscripts and sizes of an array access.
> -  ///
> -  /// The delinearization is a 3 step process: the first two steps compute the
> -  /// sizes of each subscript and the third step computes the access functions
> -  /// for the delinearized array:
> -  ///
> -  /// 1. Find the terms in the step functions
> -  /// 2. Compute the array size
> -  /// 3. Compute the access function: divide the SCEV by the array size
> -  ///    starting with the innermost dimensions found in step 2. The Quotient
> -  ///    is the SCEV to be divided in the next step of the recursion. The
> -  ///    Remainder is the subscript of the innermost dimension. Loop over all
> -  ///    array dimensions computed in step 2.
> -  ///
> -  /// To compute a uniform array size for several memory accesses to the same
> -  /// object, one can collect in step 1 all the step terms for all the memory
> -  /// accesses, and compute in step 2 a unique array shape. This guarantees
> -  /// that the array shape will be the same across all memory accesses.
> -  ///
> -  /// FIXME: We could derive the result of steps 1 and 2 from a description of
> -  /// the array shape given in metadata.
> -  ///
> -  /// Example:
> -  ///
> -  /// A[][n][m]
> -  ///
> -  /// for i
> -  ///   for j
> -  ///     for k
> -  ///       A[j+k][2i][5i] =
> -  ///
> -  /// The initial SCEV:
> -  ///
> -  /// A[{{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k]
> -  ///
> -  /// 1. Find the
> diff erent terms in the step functions:
> -  /// -> [2*m, 5, n*m, n*m]
> -  ///
> -  /// 2. Compute the array size: sort and unique them
> -  /// -> [n*m, 2*m, 5]
> -  /// find the GCD of all the terms = 1
> -  /// divide by the GCD and erase constant terms
> -  /// -> [n*m, 2*m]
> -  /// GCD = m
> -  /// divide by GCD -> [n, 2]
> -  /// remove constant terms
> -  /// -> [n]
> -  /// size of the array is A[unknown][n][m]
> -  ///
> -  /// 3. Compute the access function
> -  /// a. Divide {{{0,+,2*m+5}_i, +, n*m}_j, +, n*m}_k by the innermost size m
> -  /// Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k
> -  /// Remainder: {{{0,+,5}_i, +, 0}_j, +, 0}_k
> -  /// The remainder is the subscript of the innermost array dimension: [5i].
> -  ///
> -  /// b. Divide Quotient: {{{0,+,2}_i, +, n}_j, +, n}_k by next outer size n
> -  /// Quotient: {{{0,+,0}_i, +, 1}_j, +, 1}_k
> -  /// Remainder: {{{0,+,2}_i, +, 0}_j, +, 0}_k
> -  /// The Remainder is the subscript of the next array dimension: [2i].
> -  ///
> -  /// The subscript of the outermost dimension is the Quotient: [j+k].
> -  ///
> -  /// Overall, we have: A[][n][m], and the access function: A[j+k][2i][5i].
> -  void delinearize(const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
> -                   SmallVectorImpl<const SCEV *> &Sizes,
> -                   const SCEV *ElementSize);
> -
>    /// Return the DataLayout associated with the module this SCEV instance is
>    /// operating on.
>    const DataLayout &getDataLayout() const {
>
> diff  --git a/llvm/lib/Analysis/Delinearization.cpp b/llvm/lib/Analysis/Delinearization.cpp
> index 448e970e9bcc9..8219d59b8f40e 100644
> --- a/llvm/lib/Analysis/Delinearization.cpp
> +++ b/llvm/lib/Analysis/Delinearization.cpp
> @@ -17,6 +17,7 @@
>  #include "llvm/Analysis/LoopInfo.h"
>  #include "llvm/Analysis/Passes.h"
>  #include "llvm/Analysis/ScalarEvolution.h"
> +#include "llvm/Analysis/ScalarEvolutionDivision.h"
>  #include "llvm/Analysis/ScalarEvolutionExpressions.h"
>  #include "llvm/IR/Constants.h"
>  #include "llvm/IR/DerivedTypes.h"
> @@ -36,6 +37,454 @@ using namespace llvm;
>  #define DL_NAME "delinearize"
>  #define DEBUG_TYPE DL_NAME
>
> +// Return true when S contains at least an undef value.
> +static inline bool containsUndefs(const SCEV *S) {
> +  return SCEVExprContains(S, [](const SCEV *S) {
> +    if (const auto *SU = dyn_cast<SCEVUnknown>(S))
> +      return isa<UndefValue>(SU->getValue());
> +    return false;
> +  });
> +}
> +
> +namespace {
> +
> +// Collect all steps of SCEV expressions.
> +struct SCEVCollectStrides {
> +  ScalarEvolution &SE;
> +  SmallVectorImpl<const SCEV *> &Strides;
> +
> +  SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
> +      : SE(SE), Strides(S) {}
> +
> +  bool follow(const SCEV *S) {
> +    if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
> +      Strides.push_back(AR->getStepRecurrence(SE));
> +    return true;
> +  }
> +
> +  bool isDone() const { return false; }
> +};
> +
> +// Collect all SCEVUnknown and SCEVMulExpr expressions.
> +struct SCEVCollectTerms {
> +  SmallVectorImpl<const SCEV *> &Terms;
> +
> +  SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T) : Terms(T) {}
> +
> +  bool follow(const SCEV *S) {
> +    if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) ||
> +        isa<SCEVSignExtendExpr>(S)) {
> +      if (!containsUndefs(S))
> +        Terms.push_back(S);
> +
> +      // Stop recursion: once we collected a term, do not walk its operands.
> +      return false;
> +    }
> +
> +    // Keep looking.
> +    return true;
> +  }
> +
> +  bool isDone() const { return false; }
> +};
> +
> +// Check if a SCEV contains an AddRecExpr.
> +struct SCEVHasAddRec {
> +  bool &ContainsAddRec;
> +
> +  SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
> +    ContainsAddRec = false;
> +  }
> +
> +  bool follow(const SCEV *S) {
> +    if (isa<SCEVAddRecExpr>(S)) {
> +      ContainsAddRec = true;
> +
> +      // Stop recursion: once we collected a term, do not walk its operands.
> +      return false;
> +    }
> +
> +    // Keep looking.
> +    return true;
> +  }
> +
> +  bool isDone() const { return false; }
> +};
> +
> +// Find factors that are multiplied with an expression that (possibly as a
> +// subexpression) contains an AddRecExpr. In the expression:
> +//
> +//  8 * (100 +  %p * %q * (%a + {0, +, 1}_loop))
> +//
> +// "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
> +// that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
> +// parameters as they form a product with an induction variable.
> +//
> +// This collector expects all array size parameters to be in the same MulExpr.
> +// It might be necessary to later add support for collecting parameters that are
> +// spread over
> diff erent nested MulExpr.
> +struct SCEVCollectAddRecMultiplies {
> +  SmallVectorImpl<const SCEV *> &Terms;
> +  ScalarEvolution &SE;
> +
> +  SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T,
> +                              ScalarEvolution &SE)
> +      : Terms(T), SE(SE) {}
> +
> +  bool follow(const SCEV *S) {
> +    if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
> +      bool HasAddRec = false;
> +      SmallVector<const SCEV *, 0> Operands;
> +      for (auto Op : Mul->operands()) {
> +        const SCEVUnknown *Unknown = dyn_cast<SCEVUnknown>(Op);
> +        if (Unknown && !isa<CallInst>(Unknown->getValue())) {
> +          Operands.push_back(Op);
> +        } else if (Unknown) {
> +          HasAddRec = true;
> +        } else {
> +          bool ContainsAddRec = false;
> +          SCEVHasAddRec ContiansAddRec(ContainsAddRec);
> +          visitAll(Op, ContiansAddRec);
> +          HasAddRec |= ContainsAddRec;
> +        }
> +      }
> +      if (Operands.size() == 0)
> +        return true;
> +
> +      if (!HasAddRec)
> +        return false;
> +
> +      Terms.push_back(SE.getMulExpr(Operands));
> +      // Stop recursion: once we collected a term, do not walk its operands.
> +      return false;
> +    }
> +
> +    // Keep looking.
> +    return true;
> +  }
> +
> +  bool isDone() const { return false; }
> +};
> +
> +} // end anonymous namespace
> +
> +/// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
> +/// two places:
> +///   1) The strides of AddRec expressions.
> +///   2) Unknowns that are multiplied with AddRec expressions.
> +void llvm::collectParametricTerms(ScalarEvolution &SE, const SCEV *Expr,
> +                                  SmallVectorImpl<const SCEV *> &Terms) {
> +  SmallVector<const SCEV *, 4> Strides;
> +  SCEVCollectStrides StrideCollector(SE, Strides);
> +  visitAll(Expr, StrideCollector);
> +
> +  LLVM_DEBUG({
> +    dbgs() << "Strides:\n";
> +    for (const SCEV *S : Strides)
> +      dbgs() << *S << "\n";
> +  });
> +
> +  for (const SCEV *S : Strides) {
> +    SCEVCollectTerms TermCollector(Terms);
> +    visitAll(S, TermCollector);
> +  }
> +
> +  LLVM_DEBUG({
> +    dbgs() << "Terms:\n";
> +    for (const SCEV *T : Terms)
> +      dbgs() << *T << "\n";
> +  });
> +
> +  SCEVCollectAddRecMultiplies MulCollector(Terms, SE);
> +  visitAll(Expr, MulCollector);
> +}
> +
> +static bool findArrayDimensionsRec(ScalarEvolution &SE,
> +                                   SmallVectorImpl<const SCEV *> &Terms,
> +                                   SmallVectorImpl<const SCEV *> &Sizes) {
> +  int Last = Terms.size() - 1;
> +  const SCEV *Step = Terms[Last];
> +
> +  // End of recursion.
> +  if (Last == 0) {
> +    if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
> +      SmallVector<const SCEV *, 2> Qs;
> +      for (const SCEV *Op : M->operands())
> +        if (!isa<SCEVConstant>(Op))
> +          Qs.push_back(Op);
> +
> +      Step = SE.getMulExpr(Qs);
> +    }
> +
> +    Sizes.push_back(Step);
> +    return true;
> +  }
> +
> +  for (const SCEV *&Term : Terms) {
> +    // Normalize the terms before the next call to findArrayDimensionsRec.
> +    const SCEV *Q, *R;
> +    SCEVDivision::divide(SE, Term, Step, &Q, &R);
> +
> +    // Bail out when GCD does not evenly divide one of the terms.
> +    if (!R->isZero())
> +      return false;
> +
> +    Term = Q;
> +  }
> +
> +  // Remove all SCEVConstants.
> +  erase_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); });
> +
> +  if (Terms.size() > 0)
> +    if (!findArrayDimensionsRec(SE, Terms, Sizes))
> +      return false;
> +
> +  Sizes.push_back(Step);
> +  return true;
> +}
> +
> +// Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
> +static inline bool containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
> +  for (const SCEV *T : Terms)
> +    if (SCEVExprContains(T, [](const SCEV *S) { return isa<SCEVUnknown>(S); }))
> +      return true;
> +
> +  return false;
> +}
> +
> +// Return the number of product terms in S.
> +static inline int numberOfTerms(const SCEV *S) {
> +  if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
> +    return Expr->getNumOperands();
> +  return 1;
> +}
> +
> +static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
> +  if (isa<SCEVConstant>(T))
> +    return nullptr;
> +
> +  if (isa<SCEVUnknown>(T))
> +    return T;
> +
> +  if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
> +    SmallVector<const SCEV *, 2> Factors;
> +    for (const SCEV *Op : M->operands())
> +      if (!isa<SCEVConstant>(Op))
> +        Factors.push_back(Op);
> +
> +    return SE.getMulExpr(Factors);
> +  }
> +
> +  return T;
> +}
> +
> +void llvm::findArrayDimensions(ScalarEvolution &SE,
> +                               SmallVectorImpl<const SCEV *> &Terms,
> +                               SmallVectorImpl<const SCEV *> &Sizes,
> +                               const SCEV *ElementSize) {
> +  if (Terms.size() < 1 || !ElementSize)
> +    return;
> +
> +  // Early return when Terms do not contain parameters: we do not delinearize
> +  // non parametric SCEVs.
> +  if (!containsParameters(Terms))
> +    return;
> +
> +  LLVM_DEBUG({
> +    dbgs() << "Terms:\n";
> +    for (const SCEV *T : Terms)
> +      dbgs() << *T << "\n";
> +  });
> +
> +  // Remove duplicates.
> +  array_pod_sort(Terms.begin(), Terms.end());
> +  Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
> +
> +  // Put larger terms first.
> +  llvm::sort(Terms, [](const SCEV *LHS, const SCEV *RHS) {
> +    return numberOfTerms(LHS) > numberOfTerms(RHS);
> +  });
> +
> +  // Try to divide all terms by the element size. If term is not divisible by
> +  // element size, proceed with the original term.
> +  for (const SCEV *&Term : Terms) {
> +    const SCEV *Q, *R;
> +    SCEVDivision::divide(SE, Term, ElementSize, &Q, &R);
> +    if (!Q->isZero())
> +      Term = Q;
> +  }
> +
> +  SmallVector<const SCEV *, 4> NewTerms;
> +
> +  // Remove constant factors.
> +  for (const SCEV *T : Terms)
> +    if (const SCEV *NewT = removeConstantFactors(SE, T))
> +      NewTerms.push_back(NewT);
> +
> +  LLVM_DEBUG({
> +    dbgs() << "Terms after sorting:\n";
> +    for (const SCEV *T : NewTerms)
> +      dbgs() << *T << "\n";
> +  });
> +
> +  if (NewTerms.empty() || !findArrayDimensionsRec(SE, NewTerms, Sizes)) {
> +    Sizes.clear();
> +    return;
> +  }
> +
> +  // The last element to be pushed into Sizes is the size of an element.
> +  Sizes.push_back(ElementSize);
> +
> +  LLVM_DEBUG({
> +    dbgs() << "Sizes:\n";
> +    for (const SCEV *S : Sizes)
> +      dbgs() << *S << "\n";
> +  });
> +}
> +
> +void llvm::computeAccessFunctions(ScalarEvolution &SE, const SCEV *Expr,
> +                                  SmallVectorImpl<const SCEV *> &Subscripts,
> +                                  SmallVectorImpl<const SCEV *> &Sizes) {
> +  // Early exit in case this SCEV is not an affine multivariate function.
> +  if (Sizes.empty())
> +    return;
> +
> +  if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
> +    if (!AR->isAffine())
> +      return;
> +
> +  const SCEV *Res = Expr;
> +  int Last = Sizes.size() - 1;
> +  for (int i = Last; i >= 0; i--) {
> +    const SCEV *Q, *R;
> +    SCEVDivision::divide(SE, Res, Sizes[i], &Q, &R);
> +
> +    LLVM_DEBUG({
> +      dbgs() << "Res: " << *Res << "\n";
> +      dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
> +      dbgs() << "Res divided by Sizes[i]:\n";
> +      dbgs() << "Quotient: " << *Q << "\n";
> +      dbgs() << "Remainder: " << *R << "\n";
> +    });
> +
> +    Res = Q;
> +
> +    // Do not record the last subscript corresponding to the size of elements in
> +    // the array.
> +    if (i == Last) {
> +
> +      // Bail out if the remainder is too complex.
> +      if (isa<SCEVAddRecExpr>(R)) {
> +        Subscripts.clear();
> +        Sizes.clear();
> +        return;
> +      }
> +
> +      continue;
> +    }
> +
> +    // Record the access function for the current subscript.
> +    Subscripts.push_back(R);
> +  }
> +
> +  // Also push in last position the remainder of the last division: it will be
> +  // the access function of the innermost dimension.
> +  Subscripts.push_back(Res);
> +
> +  std::reverse(Subscripts.begin(), Subscripts.end());
> +
> +  LLVM_DEBUG({
> +    dbgs() << "Subscripts:\n";
> +    for (const SCEV *S : Subscripts)
> +      dbgs() << *S << "\n";
> +  });
> +}
> +
> +/// 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.  The SCEV->delinearize algorithm computes
> +/// the multiples of SCEV coefficients: that is a pattern matching of sub
> +/// expressions in the stride and base of a SCEV corresponding to the
> +/// computation of a GCD (greatest common divisor) of base and stride.  When
> +/// SCEV->delinearize fails, it returns the SCEV unchanged.
> +///
> +/// For example: when analyzing the memory access A[i][j][k] in this loop nest
> +///
> +///  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;
> +///  }
> +///
> +/// the delinearization input is the following AddRec SCEV:
> +///
> +///  AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
> +///
> +/// From this SCEV, we are able to say that the base offset of the access is %A
> +/// because it appears as an offset that does not divide any of the strides in
> +/// the loops:
> +///
> +///  CHECK: Base offset: %A
> +///
> +/// and then SCEV->delinearize determines the size of some of the dimensions of
> +/// the array as these are the multiples by which the strides are happening:
> +///
> +///  CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double)
> +///  bytes.
> +///
> +/// Note that the outermost dimension remains of UnknownSize because there are
> +/// no strides that would help identifying the size of the last dimension: when
> +/// the array has been statically allocated, one could compute the size of that
> +/// dimension by dividing the overall size of the array by the size of the known
> +/// dimensions: %m * %o * 8.
> +///
> +/// Finally delinearize provides the access functions for the array reference
> +/// that does correspond to A[i][j][k] of the above C testcase:
> +///
> +///  CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
> +///
> +/// The testcases are checking the output of a function pass:
> +/// DelinearizationPass that walks through all loads and stores of a function
> +/// asking for the SCEV of the memory access with respect to all enclosing
> +/// loops, calling SCEV->delinearize on that and printing the results.
> +void llvm::delinearize(ScalarEvolution &SE, const SCEV *Expr,
> +                       SmallVectorImpl<const SCEV *> &Subscripts,
> +                       SmallVectorImpl<const SCEV *> &Sizes,
> +                       const SCEV *ElementSize) {
> +  // First step: collect parametric terms.
> +  SmallVector<const SCEV *, 4> Terms;
> +  collectParametricTerms(SE, Expr, Terms);
> +
> +  if (Terms.empty())
> +    return;
> +
> +  // Second step: find subscript sizes.
> +  findArrayDimensions(SE, Terms, Sizes, ElementSize);
> +
> +  if (Sizes.empty())
> +    return;
> +
> +  // Third step: compute the access functions for each subscript.
> +  computeAccessFunctions(SE, Expr, Subscripts, Sizes);
> +
> +  if (Subscripts.empty())
> +    return;
> +
> +  LLVM_DEBUG({
> +    dbgs() << "succeeded to delinearize " << *Expr << "\n";
> +    dbgs() << "ArrayDecl[UnknownSize]";
> +    for (const SCEV *S : Sizes)
> +      dbgs() << "[" << *S << "]";
> +
> +    dbgs() << "\nArrayRef";
> +    for (const SCEV *S : Subscripts)
> +      dbgs() << "[" << *S << "]";
> +    dbgs() << "\n";
> +  });
> +}
> +
>  namespace {
>
>  class Delinearization : public FunctionPass {
> @@ -84,7 +533,7 @@ void printDelinearization(raw_ostream &O, Function *F, LoopInfo *LI,
>        O << "AccessFunction: " << *AccessFn << "\n";
>
>        SmallVector<const SCEV *, 3> Subscripts, Sizes;
> -      SE->delinearize(AccessFn, Subscripts, Sizes, SE->getElementSize(&Inst));
> +      delinearize(*SE, AccessFn, Subscripts, Sizes, SE->getElementSize(&Inst));
>        if (Subscripts.size() == 0 || Sizes.size() == 0 ||
>            Subscripts.size() != Sizes.size()) {
>          O << "failed to delinearize\n";
>
> diff  --git a/llvm/lib/Analysis/DependenceAnalysis.cpp b/llvm/lib/Analysis/DependenceAnalysis.cpp
> index 9c09894f3a451..fa9c672119455 100644
> --- a/llvm/lib/Analysis/DependenceAnalysis.cpp
> +++ b/llvm/lib/Analysis/DependenceAnalysis.cpp
> @@ -53,6 +53,7 @@
>  #include "llvm/ADT/STLExtras.h"
>  #include "llvm/ADT/Statistic.h"
>  #include "llvm/Analysis/AliasAnalysis.h"
> +#include "llvm/Analysis/Delinearization.h"
>  #include "llvm/Analysis/LoopInfo.h"
>  #include "llvm/Analysis/ScalarEvolution.h"
>  #include "llvm/Analysis/ScalarEvolutionExpressions.h"
> @@ -3439,16 +3440,16 @@ bool DependenceInfo::tryDelinearizeParametricSize(
>
>    // First step: collect parametric terms in both array references.
>    SmallVector<const SCEV *, 4> Terms;
> -  SE->collectParametricTerms(SrcAR, Terms);
> -  SE->collectParametricTerms(DstAR, Terms);
> +  collectParametricTerms(*SE, SrcAR, Terms);
> +  collectParametricTerms(*SE, DstAR, Terms);
>
>    // Second step: find subscript sizes.
>    SmallVector<const SCEV *, 4> Sizes;
> -  SE->findArrayDimensions(Terms, Sizes, ElementSize);
> +  findArrayDimensions(*SE, Terms, Sizes, ElementSize);
>
>    // Third step: compute the access functions for each subscript.
> -  SE->computeAccessFunctions(SrcAR, SrcSubscripts, Sizes);
> -  SE->computeAccessFunctions(DstAR, DstSubscripts, Sizes);
> +  computeAccessFunctions(*SE, SrcAR, SrcSubscripts, Sizes);
> +  computeAccessFunctions(*SE, DstAR, DstSubscripts, Sizes);
>
>    // Fail when there is only a subscript: that's a linearized access function.
>    if (SrcSubscripts.size() < 2 || DstSubscripts.size() < 2 ||
>
> diff  --git a/llvm/lib/Analysis/LoopCacheAnalysis.cpp b/llvm/lib/Analysis/LoopCacheAnalysis.cpp
> index 772e4eb239a9c..75bb8b02286c1 100644
> --- a/llvm/lib/Analysis/LoopCacheAnalysis.cpp
> +++ b/llvm/lib/Analysis/LoopCacheAnalysis.cpp
> @@ -30,6 +30,7 @@
>  #include "llvm/ADT/Sequence.h"
>  #include "llvm/ADT/SmallVector.h"
>  #include "llvm/Analysis/AliasAnalysis.h"
> +#include "llvm/Analysis/Delinearization.h"
>  #include "llvm/Analysis/DependenceAnalysis.h"
>  #include "llvm/Analysis/LoopInfo.h"
>  #include "llvm/Analysis/ScalarEvolutionExpressions.h"
> @@ -344,8 +345,8 @@ bool IndexedReference::delinearize(const LoopInfo &LI) {
>      LLVM_DEBUG(dbgs().indent(2) << "In Loop '" << L->getName()
>                                  << "', AccessFn: " << *AccessFn << "\n");
>
> -    SE.delinearize(AccessFn, Subscripts, Sizes,
> -                   SE.getElementSize(&StoreOrLoadInst));
> +    llvm::delinearize(SE, AccessFn, Subscripts, Sizes,
> +                      SE.getElementSize(&StoreOrLoadInst));
>
>      if (Subscripts.empty() || Sizes.empty() ||
>          Subscripts.size() != Sizes.size()) {
>
> diff  --git a/llvm/lib/Analysis/ScalarEvolution.cpp b/llvm/lib/Analysis/ScalarEvolution.cpp
> index 50901f3524d1b..151883ab67367 100644
> --- a/llvm/lib/Analysis/ScalarEvolution.cpp
> +++ b/llvm/lib/Analysis/ScalarEvolution.cpp
> @@ -12187,237 +12187,6 @@ static inline bool containsUndefs(const SCEV *S) {
>    });
>  }
>
> -namespace {
> -
> -// Collect all steps of SCEV expressions.
> -struct SCEVCollectStrides {
> -  ScalarEvolution &SE;
> -  SmallVectorImpl<const SCEV *> &Strides;
> -
> -  SCEVCollectStrides(ScalarEvolution &SE, SmallVectorImpl<const SCEV *> &S)
> -      : SE(SE), Strides(S) {}
> -
> -  bool follow(const SCEV *S) {
> -    if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S))
> -      Strides.push_back(AR->getStepRecurrence(SE));
> -    return true;
> -  }
> -
> -  bool isDone() const { return false; }
> -};
> -
> -// Collect all SCEVUnknown and SCEVMulExpr expressions.
> -struct SCEVCollectTerms {
> -  SmallVectorImpl<const SCEV *> &Terms;
> -
> -  SCEVCollectTerms(SmallVectorImpl<const SCEV *> &T) : Terms(T) {}
> -
> -  bool follow(const SCEV *S) {
> -    if (isa<SCEVUnknown>(S) || isa<SCEVMulExpr>(S) ||
> -        isa<SCEVSignExtendExpr>(S)) {
> -      if (!containsUndefs(S))
> -        Terms.push_back(S);
> -
> -      // Stop recursion: once we collected a term, do not walk its operands.
> -      return false;
> -    }
> -
> -    // Keep looking.
> -    return true;
> -  }
> -
> -  bool isDone() const { return false; }
> -};
> -
> -// Check if a SCEV contains an AddRecExpr.
> -struct SCEVHasAddRec {
> -  bool &ContainsAddRec;
> -
> -  SCEVHasAddRec(bool &ContainsAddRec) : ContainsAddRec(ContainsAddRec) {
> -    ContainsAddRec = false;
> -  }
> -
> -  bool follow(const SCEV *S) {
> -    if (isa<SCEVAddRecExpr>(S)) {
> -      ContainsAddRec = true;
> -
> -      // Stop recursion: once we collected a term, do not walk its operands.
> -      return false;
> -    }
> -
> -    // Keep looking.
> -    return true;
> -  }
> -
> -  bool isDone() const { return false; }
> -};
> -
> -// Find factors that are multiplied with an expression that (possibly as a
> -// subexpression) contains an AddRecExpr. In the expression:
> -//
> -//  8 * (100 +  %p * %q * (%a + {0, +, 1}_loop))
> -//
> -// "%p * %q" are factors multiplied by the expression "(%a + {0, +, 1}_loop)"
> -// that contains the AddRec {0, +, 1}_loop. %p * %q are likely to be array size
> -// parameters as they form a product with an induction variable.
> -//
> -// This collector expects all array size parameters to be in the same MulExpr.
> -// It might be necessary to later add support for collecting parameters that are
> -// spread over
> diff erent nested MulExpr.
> -struct SCEVCollectAddRecMultiplies {
> -  SmallVectorImpl<const SCEV *> &Terms;
> -  ScalarEvolution &SE;
> -
> -  SCEVCollectAddRecMultiplies(SmallVectorImpl<const SCEV *> &T, ScalarEvolution &SE)
> -      : Terms(T), SE(SE) {}
> -
> -  bool follow(const SCEV *S) {
> -    if (auto *Mul = dyn_cast<SCEVMulExpr>(S)) {
> -      bool HasAddRec = false;
> -      SmallVector<const SCEV *, 0> Operands;
> -      for (auto Op : Mul->operands()) {
> -        const SCEVUnknown *Unknown = dyn_cast<SCEVUnknown>(Op);
> -        if (Unknown && !isa<CallInst>(Unknown->getValue())) {
> -          Operands.push_back(Op);
> -        } else if (Unknown) {
> -          HasAddRec = true;
> -        } else {
> -          bool ContainsAddRec = false;
> -          SCEVHasAddRec ContiansAddRec(ContainsAddRec);
> -          visitAll(Op, ContiansAddRec);
> -          HasAddRec |= ContainsAddRec;
> -        }
> -      }
> -      if (Operands.size() == 0)
> -        return true;
> -
> -      if (!HasAddRec)
> -        return false;
> -
> -      Terms.push_back(SE.getMulExpr(Operands));
> -      // Stop recursion: once we collected a term, do not walk its operands.
> -      return false;
> -    }
> -
> -    // Keep looking.
> -    return true;
> -  }
> -
> -  bool isDone() const { return false; }
> -};
> -
> -} // end anonymous namespace
> -
> -/// Find parametric terms in this SCEVAddRecExpr. We first for parameters in
> -/// two places:
> -///   1) The strides of AddRec expressions.
> -///   2) Unknowns that are multiplied with AddRec expressions.
> -void ScalarEvolution::collectParametricTerms(const SCEV *Expr,
> -    SmallVectorImpl<const SCEV *> &Terms) {
> -  SmallVector<const SCEV *, 4> Strides;
> -  SCEVCollectStrides StrideCollector(*this, Strides);
> -  visitAll(Expr, StrideCollector);
> -
> -  LLVM_DEBUG({
> -    dbgs() << "Strides:\n";
> -    for (const SCEV *S : Strides)
> -      dbgs() << *S << "\n";
> -  });
> -
> -  for (const SCEV *S : Strides) {
> -    SCEVCollectTerms TermCollector(Terms);
> -    visitAll(S, TermCollector);
> -  }
> -
> -  LLVM_DEBUG({
> -    dbgs() << "Terms:\n";
> -    for (const SCEV *T : Terms)
> -      dbgs() << *T << "\n";
> -  });
> -
> -  SCEVCollectAddRecMultiplies MulCollector(Terms, *this);
> -  visitAll(Expr, MulCollector);
> -}
> -
> -static bool findArrayDimensionsRec(ScalarEvolution &SE,
> -                                   SmallVectorImpl<const SCEV *> &Terms,
> -                                   SmallVectorImpl<const SCEV *> &Sizes) {
> -  int Last = Terms.size() - 1;
> -  const SCEV *Step = Terms[Last];
> -
> -  // End of recursion.
> -  if (Last == 0) {
> -    if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(Step)) {
> -      SmallVector<const SCEV *, 2> Qs;
> -      for (const SCEV *Op : M->operands())
> -        if (!isa<SCEVConstant>(Op))
> -          Qs.push_back(Op);
> -
> -      Step = SE.getMulExpr(Qs);
> -    }
> -
> -    Sizes.push_back(Step);
> -    return true;
> -  }
> -
> -  for (const SCEV *&Term : Terms) {
> -    // Normalize the terms before the next call to findArrayDimensionsRec.
> -    const SCEV *Q, *R;
> -    SCEVDivision::divide(SE, Term, Step, &Q, &R);
> -
> -    // Bail out when GCD does not evenly divide one of the terms.
> -    if (!R->isZero())
> -      return false;
> -
> -    Term = Q;
> -  }
> -
> -  // Remove all SCEVConstants.
> -  erase_if(Terms, [](const SCEV *E) { return isa<SCEVConstant>(E); });
> -
> -  if (Terms.size() > 0)
> -    if (!findArrayDimensionsRec(SE, Terms, Sizes))
> -      return false;
> -
> -  Sizes.push_back(Step);
> -  return true;
> -}
> -
> -// Returns true when one of the SCEVs of Terms contains a SCEVUnknown parameter.
> -static inline bool containsParameters(SmallVectorImpl<const SCEV *> &Terms) {
> -  for (const SCEV *T : Terms)
> -    if (SCEVExprContains(T, [](const SCEV *S) { return isa<SCEVUnknown>(S); }))
> -      return true;
> -
> -  return false;
> -}
> -
> -// Return the number of product terms in S.
> -static inline int numberOfTerms(const SCEV *S) {
> -  if (const SCEVMulExpr *Expr = dyn_cast<SCEVMulExpr>(S))
> -    return Expr->getNumOperands();
> -  return 1;
> -}
> -
> -static const SCEV *removeConstantFactors(ScalarEvolution &SE, const SCEV *T) {
> -  if (isa<SCEVConstant>(T))
> -    return nullptr;
> -
> -  if (isa<SCEVUnknown>(T))
> -    return T;
> -
> -  if (const SCEVMulExpr *M = dyn_cast<SCEVMulExpr>(T)) {
> -    SmallVector<const SCEV *, 2> Factors;
> -    for (const SCEV *Op : M->operands())
> -      if (!isa<SCEVConstant>(Op))
> -        Factors.push_back(Op);
> -
> -    return SE.getMulExpr(Factors);
> -  }
> -
> -  return T;
> -}
> -
>  /// Return the size of an element read or written by Inst.
>  const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
>    Type *Ty;
> @@ -12432,211 +12201,6 @@ const SCEV *ScalarEvolution::getElementSize(Instruction *Inst) {
>    return getSizeOfExpr(ETy, Ty);
>  }
>
> -void ScalarEvolution::findArrayDimensions(SmallVectorImpl<const SCEV *> &Terms,
> -                                          SmallVectorImpl<const SCEV *> &Sizes,
> -                                          const SCEV *ElementSize) {
> -  if (Terms.size() < 1 || !ElementSize)
> -    return;
> -
> -  // Early return when Terms do not contain parameters: we do not delinearize
> -  // non parametric SCEVs.
> -  if (!containsParameters(Terms))
> -    return;
> -
> -  LLVM_DEBUG({
> -    dbgs() << "Terms:\n";
> -    for (const SCEV *T : Terms)
> -      dbgs() << *T << "\n";
> -  });
> -
> -  // Remove duplicates.
> -  array_pod_sort(Terms.begin(), Terms.end());
> -  Terms.erase(std::unique(Terms.begin(), Terms.end()), Terms.end());
> -
> -  // Put larger terms first.
> -  llvm::sort(Terms, [](const SCEV *LHS, const SCEV *RHS) {
> -    return numberOfTerms(LHS) > numberOfTerms(RHS);
> -  });
> -
> -  // Try to divide all terms by the element size. If term is not divisible by
> -  // element size, proceed with the original term.
> -  for (const SCEV *&Term : Terms) {
> -    const SCEV *Q, *R;
> -    SCEVDivision::divide(*this, Term, ElementSize, &Q, &R);
> -    if (!Q->isZero())
> -      Term = Q;
> -  }
> -
> -  SmallVector<const SCEV *, 4> NewTerms;
> -
> -  // Remove constant factors.
> -  for (const SCEV *T : Terms)
> -    if (const SCEV *NewT = removeConstantFactors(*this, T))
> -      NewTerms.push_back(NewT);
> -
> -  LLVM_DEBUG({
> -    dbgs() << "Terms after sorting:\n";
> -    for (const SCEV *T : NewTerms)
> -      dbgs() << *T << "\n";
> -  });
> -
> -  if (NewTerms.empty() || !findArrayDimensionsRec(*this, NewTerms, Sizes)) {
> -    Sizes.clear();
> -    return;
> -  }
> -
> -  // The last element to be pushed into Sizes is the size of an element.
> -  Sizes.push_back(ElementSize);
> -
> -  LLVM_DEBUG({
> -    dbgs() << "Sizes:\n";
> -    for (const SCEV *S : Sizes)
> -      dbgs() << *S << "\n";
> -  });
> -}
> -
> -void ScalarEvolution::computeAccessFunctions(
> -    const SCEV *Expr, SmallVectorImpl<const SCEV *> &Subscripts,
> -    SmallVectorImpl<const SCEV *> &Sizes) {
> -  // Early exit in case this SCEV is not an affine multivariate function.
> -  if (Sizes.empty())
> -    return;
> -
> -  if (auto *AR = dyn_cast<SCEVAddRecExpr>(Expr))
> -    if (!AR->isAffine())
> -      return;
> -
> -  const SCEV *Res = Expr;
> -  int Last = Sizes.size() - 1;
> -  for (int i = Last; i >= 0; i--) {
> -    const SCEV *Q, *R;
> -    SCEVDivision::divide(*this, Res, Sizes[i], &Q, &R);
> -
> -    LLVM_DEBUG({
> -      dbgs() << "Res: " << *Res << "\n";
> -      dbgs() << "Sizes[i]: " << *Sizes[i] << "\n";
> -      dbgs() << "Res divided by Sizes[i]:\n";
> -      dbgs() << "Quotient: " << *Q << "\n";
> -      dbgs() << "Remainder: " << *R << "\n";
> -    });
> -
> -    Res = Q;
> -
> -    // Do not record the last subscript corresponding to the size of elements in
> -    // the array.
> -    if (i == Last) {
> -
> -      // Bail out if the remainder is too complex.
> -      if (isa<SCEVAddRecExpr>(R)) {
> -        Subscripts.clear();
> -        Sizes.clear();
> -        return;
> -      }
> -
> -      continue;
> -    }
> -
> -    // Record the access function for the current subscript.
> -    Subscripts.push_back(R);
> -  }
> -
> -  // Also push in last position the remainder of the last division: it will be
> -  // the access function of the innermost dimension.
> -  Subscripts.push_back(Res);
> -
> -  std::reverse(Subscripts.begin(), Subscripts.end());
> -
> -  LLVM_DEBUG({
> -    dbgs() << "Subscripts:\n";
> -    for (const SCEV *S : Subscripts)
> -      dbgs() << *S << "\n";
> -  });
> -}
> -
> -/// 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.  The SCEV->delinearize algorithm computes
> -/// the multiples of SCEV coefficients: that is a pattern matching of sub
> -/// expressions in the stride and base of a SCEV corresponding to the
> -/// computation of a GCD (greatest common divisor) of base and stride.  When
> -/// SCEV->delinearize fails, it returns the SCEV unchanged.
> -///
> -/// For example: when analyzing the memory access A[i][j][k] in this loop nest
> -///
> -///  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;
> -///  }
> -///
> -/// the delinearization input is the following AddRec SCEV:
> -///
> -///  AddRec: {{{%A,+,(8 * %m * %o)}<%for.i>,+,(8 * %o)}<%for.j>,+,8}<%for.k>
> -///
> -/// From this SCEV, we are able to say that the base offset of the access is %A
> -/// because it appears as an offset that does not divide any of the strides in
> -/// the loops:
> -///
> -///  CHECK: Base offset: %A
> -///
> -/// and then SCEV->delinearize determines the size of some of the dimensions of
> -/// the array as these are the multiples by which the strides are happening:
> -///
> -///  CHECK: ArrayDecl[UnknownSize][%m][%o] with elements of sizeof(double) bytes.
> -///
> -/// Note that the outermost dimension remains of UnknownSize because there are
> -/// no strides that would help identifying the size of the last dimension: when
> -/// the array has been statically allocated, one could compute the size of that
> -/// dimension by dividing the overall size of the array by the size of the known
> -/// dimensions: %m * %o * 8.
> -///
> -/// Finally delinearize provides the access functions for the array reference
> -/// that does correspond to A[i][j][k] of the above C testcase:
> -///
> -///  CHECK: ArrayRef[{0,+,1}<%for.i>][{0,+,1}<%for.j>][{0,+,1}<%for.k>]
> -///
> -/// The testcases are checking the output of a function pass:
> -/// DelinearizationPass that walks through all loads and stores of a function
> -/// asking for the SCEV of the memory access with respect to all enclosing
> -/// loops, calling SCEV->delinearize on that and printing the results.
> -void ScalarEvolution::delinearize(const SCEV *Expr,
> -                                 SmallVectorImpl<const SCEV *> &Subscripts,
> -                                 SmallVectorImpl<const SCEV *> &Sizes,
> -                                 const SCEV *ElementSize) {
> -  // First step: collect parametric terms.
> -  SmallVector<const SCEV *, 4> Terms;
> -  collectParametricTerms(Expr, Terms);
> -
> -  if (Terms.empty())
> -    return;
> -
> -  // Second step: find subscript sizes.
> -  findArrayDimensions(Terms, Sizes, ElementSize);
> -
> -  if (Sizes.empty())
> -    return;
> -
> -  // Third step: compute the access functions for each subscript.
> -  computeAccessFunctions(Expr, Subscripts, Sizes);
> -
> -  if (Subscripts.empty())
> -    return;
> -
> -  LLVM_DEBUG({
> -    dbgs() << "succeeded to delinearize " << *Expr << "\n";
> -    dbgs() << "ArrayDecl[UnknownSize]";
> -    for (const SCEV *S : Sizes)
> -      dbgs() << "[" << *S << "]";
> -
> -    dbgs() << "\nArrayRef";
> -    for (const SCEV *S : Subscripts)
> -      dbgs() << "[" << *S << "]";
> -    dbgs() << "\n";
> -  });
> -}
> -
>  bool ScalarEvolution::getIndexExpressionsFromGEP(
>      const GetElementPtrInst *GEP, SmallVectorImpl<const SCEV *> &Subscripts,
>      SmallVectorImpl<int> &Sizes) {
>
>
>
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