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  /*! \file
      \brief Reference implementation for complex-valued GEMM in host-side code.
  */
  
  #pragma once
  
  #include "cutlass/coord.h"
  #include "cutlass/complex.h"
  #include "cutlass/numeric_types.h"
  #include "cutlass/functional.h"
  #include "cutlass/numeric_conversion.h"
  
  #include "cutlass/matrix_traits.h"
  #include "cutlass/tensor_view.h"
  #include "cutlass/gemm/gemm.h"
  
  namespace cutlass {
  namespace reference {
  namespace host {
  
  ////////////////////////////////////////////////////////////////////////////////////////////////////
  
  /// Computes a general matrix product among matrices (tensors of rank=2) pointed to by TensorRef
  /// objects.
  ///
  /// Explicitly naming types needed by this template can be cumbersome, particularly for the
  /// accumulator type, so a function argument 'initial_accum' is exposed. Passing
  /// AccumulatorType(0) as the last function argument can be easier than naming all template
  /// arguments explicitly.
  template <
    typename ElementA,
    typename LayoutA,
    typename ElementB,
    typename LayoutB,
    typename ElementC,
    typename LayoutC,
    typename ScalarType,
    typename ComputeType,
    typename ConvertOp = NumericConverter<ElementC, ScalarType>,
    typename InnerProductOp = multiply_add<ComputeType>
  >
  void GemmComplex(
    gemm::GemmCoord problem_size,
    ScalarType alpha,
    TensorRef<ElementA, LayoutA> tensor_a,
    ComplexTransform transform_a,
    TensorRef<ElementB, LayoutB> tensor_b,
    ComplexTransform transform_b,
    ScalarType beta,
    TensorRef<ElementC, LayoutC> tensor_c,
    TensorRef<ElementC, LayoutC> tensor_d,
    ComputeType initial_accum) {
  
    static_assert(
      LayoutA::kRank == 2 &&
      LayoutB::kRank == 2 &&
      LayoutC::kRank == 2, "Tensors must be of rank 2");
  
    // Note: batch is ignored.
    int const M = problem_size.m();
    int const N = problem_size.n();
    int const K = problem_size.k();
  
    // Blocking necessary to speedup reference implementation
    int const Mblock = 16;
    int const Nblock = 16;
  
    ConvertOp convert_op;
    InnerProductOp inner_product_op;
  
    for (int row_block = 0; row_block < M; row_block += Mblock) {
      for (int col_block = 0; col_block < N; col_block += Nblock) {
  
        ComputeType accum[Mblock][Nblock];
  
        for (int j = 0; j < Nblock; j++) {
          for (int i = 0; i < Mblock; i++) {
            accum[i][j] = initial_accum;
          }
        }
  
        for (int k_block = 0; k_block < K; ++k_block) {
          for (int j = 0; j < Nblock; j++) {
            for (int i = 0; i < Mblock; i++) {
              int row = row_block + i;
              int col = col_block + j;
  
              if (row < M && col < N) {
                ElementA a = tensor_a.at(MatrixCoord(row, k_block));
                ElementB b = tensor_b.at(MatrixCoord(k_block, col));
  
                ComputeType a_ik = ComputeType(a);
                ComputeType b_kj = ComputeType(b);
  
                if (transform_a == ComplexTransform::kConjugate) {
                  a_ik = conj(a_ik);
                }
  
                if (transform_b == ComplexTransform::kConjugate) {
                  b_kj = conj(b_kj);
                }
  
                accum[i][j] = inner_product_op(a_ik, b_kj,  accum[i][j]);
              }
            }
          }
        }
  
        for (int j = 0; j < Nblock; j++) {
          for (int i = 0; i < Mblock; i++) {
            int row = row_block + i;
            int col = col_block + j;
  
            MatrixCoord coord = MatrixCoord(row, col);
  
            if (row < M && col < N) {
  
              tensor_d.at(coord) = convert_op(
                alpha * ScalarType(accum[i][j]) + 
                beta * ScalarType(tensor_c.at(coord)));
            }
          }
        }
      }
    }
  }
  
  ////////////////////////////////////////////////////////////////////////////////////////////////////
  
  /// Computes a general matrix product among matrices (tensors of rank=2) pointed to by TensorRef
  /// objects.
  ///
  /// This assumes the accumulator type is the same type as the scalars.
  template <
    typename ElementA,
    typename LayoutA,
    typename ElementB,
    typename LayoutB,
    typename ElementC,
    typename LayoutC,
    typename ScalarType
  >
  void GemmComplex(
    gemm::GemmCoord problem_size,
    ScalarType alpha,
    TensorRef<ElementA, LayoutA> tensor_a,
    ComplexTransform transform_a,
    TensorRef<ElementB, LayoutB> tensor_b,
    ComplexTransform transform_b,
    ScalarType beta,
    TensorRef<ElementC, LayoutC> tensor_c,
    TensorRef<ElementC, LayoutC> tensor_d) {
  
    GemmComplex(problem_size, alpha, tensor_a, transform_a, tensor_b, transform_b, beta, tensor_c, tensor_d, ScalarType(0));
  }
  
  ////////////////////////////////////////////////////////////////////////////////////////////////////
  
  } // namespace host
  } // namespace reference
  } // namespace cutlass
  