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 //===---- Delinearization.h - MultiDimensional Index Delinearization ------===//
 //
 // Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
 // See https://llvm.org/LICENSE.txt for license information.
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
 //
 // 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.
 //
 //===----------------------------------------------------------------------===//
 
 #ifndef LLVM_ANALYSIS_DELINEARIZATION_H
 #define LLVM_ANALYSIS_DELINEARIZATION_H
 
 #include "llvm/IR/PassManager.h"
 
 namespace llvm {
 class raw_ostream;
 template <typename T> class SmallVectorImpl;
 class GetElementPtrInst;
 class Instruction;
 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 different 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);
 
 /// Gathers the individual index expressions from a GEP instruction.
 ///
 /// This function optimistically assumes the GEP references into a fixed size
 /// array. If this is actually true, this function returns a list of array
 /// subscript expressions in \p Subscripts and a list of integers describing
 /// the size of the individual array dimensions in \p Sizes. Both lists have
 /// either equal length or the size list is one element shorter in case there
 /// is no known size available for the outermost array dimension. Returns true
 /// if successful and false otherwise.
 bool getIndexExpressionsFromGEP(ScalarEvolution &SE,
                                 const GetElementPtrInst *GEP,
                                 SmallVectorImpl<const SCEV *> &Subscripts,
                                 SmallVectorImpl<int> &Sizes);
 
 /// Implementation of fixed size array delinearization. Try to delinearize
 /// access function for a fixed size multi-dimensional array, by deriving
 /// subscripts from GEP instructions. Returns true upon success and false
 /// otherwise. \p Inst is the load/store instruction whose pointer operand is
 /// the one we want to delinearize. \p AccessFn is its corresponding SCEV
 /// expression w.r.t. the surrounding loop.
 bool tryDelinearizeFixedSizeImpl(ScalarEvolution *SE, Instruction *Inst,
                                  const SCEV *AccessFn,
                                  SmallVectorImpl<const SCEV *> &Subscripts,
                                  SmallVectorImpl<int> &Sizes);
 
 struct DelinearizationPrinterPass
     : public PassInfoMixin<DelinearizationPrinterPass> {
   explicit DelinearizationPrinterPass(raw_ostream &OS);
   PreservedAnalyses run(Function &F, FunctionAnalysisManager &AM);
   static bool isRequired() { return true; }
 
 private:
   raw_ostream &OS;
 };
 } // namespace llvm
 
 #endif // LLVM_ANALYSIS_DELINEARIZATION_H

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