// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2014-2015 Benoit Steiner <benoit.steiner.goog@gmail.com>
// Copyright (C) 2015 Navdeep Jaitly <ndjaitly@google.com>
// Copyright (C) 2014 Eric Martin <eric@ericmart.in>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#ifndef EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_GPU_H
#define EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_GPU_H

#if defined(EIGEN_USE_GPU) && defined(EIGEN_GPUCC)

// IWYU pragma: private
#include "./InternalHeaderCheck.h"

namespace Eigen {

template <typename Scalar, typename Index, typename LhsMapper, typename RhsMapper, typename OutputMapper,
          bool needs_edge_check>
__device__ EIGEN_STRONG_INLINE void EigenContractionKernelInternal(const LhsMapper lhs, const RhsMapper rhs,
                                                                   const OutputMapper output, Scalar* lhs_shmem,
                                                                   Scalar* rhs_shmem, const Index m_size,
                                                                   const Index n_size, const Index k_size) {
  const Index m_block_idx = blockIdx.x;
  const Index n_block_idx = blockIdx.y;

  const Index base_m = 64 * m_block_idx;
  const Index base_n = 64 * n_block_idx;

  // declare and initialize 64 registers for output 8x8 block

  // prefetch registers
  Scalar lhs_pf0;
  Scalar lhs_pf1;
  Scalar lhs_pf2;
  Scalar lhs_pf3;
  Scalar lhs_pf4;
  Scalar lhs_pf5;
  Scalar lhs_pf6;
  Scalar lhs_pf7;

  Scalar rhs_pf0;
  Scalar rhs_pf1;
  Scalar rhs_pf2;
  Scalar rhs_pf3;
  Scalar rhs_pf4;
  Scalar rhs_pf5;
  Scalar rhs_pf6;
  Scalar rhs_pf7;

  // shared memory is formatted
  // (contract idx in block, nocontract idx in block, block idx)
  // where block idx is column major. This transposition limits the number of
  // bank conflicts when reading the LHS. The core idea is that since the contracting
  // index is shared by both sides, then the contracting index should be in threadIdx.x.

  // On the LHS, we pad each row inside of each block with an extra element. This makes
  // each block 8 rows of 9 elements, which is 72 elements. This gives no bank conflicts
  // on writes and very few 2-way conflicts on reads. There is an 8x8 grid of these blocks.

  // On the RHS we just add 8 padding elements to the end of each block. This gives no bank
  // conflicts on writes and also none on reads.

  // storage indices
  const Index lhs_store_idx_base = threadIdx.y * 72 + threadIdx.x * 9 + threadIdx.z;
  const Index rhs_store_idx_base = threadIdx.y * 72 + threadIdx.z * 8 + threadIdx.x;

  const Index lhs_store_idx_0 = lhs_store_idx_base + 576 * 0;
  const Index lhs_store_idx_1 = lhs_store_idx_base + 576 * 1;
  const Index lhs_store_idx_2 = lhs_store_idx_base + 576 * 2;
  const Index lhs_store_idx_3 = lhs_store_idx_base + 576 * 3;
  const Index lhs_store_idx_4 = lhs_store_idx_base + 576 * 4;
  const Index lhs_store_idx_5 = lhs_store_idx_base + 576 * 5;
  const Index lhs_store_idx_6 = lhs_store_idx_base + 576 * 6;
  const Index lhs_store_idx_7 = lhs_store_idx_base + 576 * 7;

  const Index rhs_store_idx_0 = rhs_store_idx_base + 576 * 0;
  const Index rhs_store_idx_1 = rhs_store_idx_base + 576 * 1;
  const Index rhs_store_idx_2 = rhs_store_idx_base + 576 * 2;
  const Index rhs_store_idx_3 = rhs_store_idx_base + 576 * 3;
  const Index rhs_store_idx_4 = rhs_store_idx_base + 576 * 4;
  const Index rhs_store_idx_5 = rhs_store_idx_base + 576 * 5;
  const Index rhs_store_idx_6 = rhs_store_idx_base + 576 * 6;
  const Index rhs_store_idx_7 = rhs_store_idx_base + 576 * 7;

  // in the loading code, the following variables are important:
  // threadIdx.x: the vertical position in an 8x8 block
  // threadIdx.y: the vertical index of the 8x8 block in the grid
  // threadIdx.z: the horizontal position in an 8x8 block
  // k: the horizontal index of the 8x8 block in the grid
  //
  // The k parameter is implicit (it was the loop counter for a loop that went
  // from 0 to <8, but now that loop is unrolled in the below code.

  const Index load_idx_vert = threadIdx.x + 8 * threadIdx.y;
  const Index lhs_vert = base_m + load_idx_vert;

#define prefetchIntoRegisters(base_k)                         \
  {                                                           \
    lhs_pf0 = conv(0);                                        \
    lhs_pf1 = conv(0);                                        \
    lhs_pf2 = conv(0);                                        \
    lhs_pf3 = conv(0);                                        \
    lhs_pf4 = conv(0);                                        \
    lhs_pf5 = conv(0);                                        \
    lhs_pf6 = conv(0);                                        \
    lhs_pf7 = conv(0);                                        \
                                                              \
    rhs_pf0 = conv(0);                                        \
    rhs_pf1 = conv(0);                                        \
    rhs_pf2 = conv(0);                                        \
    rhs_pf3 = conv(0);                                        \
    rhs_pf4 = conv(0);                                        \
    rhs_pf5 = conv(0);                                        \
    rhs_pf6 = conv(0);                                        \
    rhs_pf7 = conv(0);                                        \
                                                              \
    if (!needs_edge_check || lhs_vert < m_size) {             \
      const Index lhs_horiz_0 = base_k + threadIdx.z + 0 * 8; \
      const Index lhs_horiz_1 = base_k + threadIdx.z + 1 * 8; \
      const Index lhs_horiz_2 = base_k + threadIdx.z + 2 * 8; \
      const Index lhs_horiz_3 = base_k + threadIdx.z + 3 * 8; \
      const Index lhs_horiz_4 = base_k + threadIdx.z + 4 * 8; \
      const Index lhs_horiz_5 = base_k + threadIdx.z + 5 * 8; \
      const Index lhs_horiz_6 = base_k + threadIdx.z + 6 * 8; \
      const Index lhs_horiz_7 = base_k + threadIdx.z + 7 * 8; \
                                                              \
      if (!needs_edge_check || lhs_horiz_7 < k_size) {        \
        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                 \
        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                 \
        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                 \
        lhs_pf3 = lhs(lhs_vert, lhs_horiz_3);                 \
        lhs_pf4 = lhs(lhs_vert, lhs_horiz_4);                 \
        lhs_pf5 = lhs(lhs_vert, lhs_horiz_5);                 \
        lhs_pf6 = lhs(lhs_vert, lhs_horiz_6);                 \
        lhs_pf7 = lhs(lhs_vert, lhs_horiz_7);                 \
      } else if (lhs_horiz_6 < k_size) {                      \
        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                 \
        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                 \
        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                 \
        lhs_pf3 = lhs(lhs_vert, lhs_horiz_3);                 \
        lhs_pf4 = lhs(lhs_vert, lhs_horiz_4);                 \
        lhs_pf5 = lhs(lhs_vert, lhs_horiz_5);                 \
        lhs_pf6 = lhs(lhs_vert, lhs_horiz_6);                 \
      } else if (lhs_horiz_5 < k_size) {                      \
        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                 \
        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                 \
        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                 \
        lhs_pf3 = lhs(lhs_vert, lhs_horiz_3);                 \
        lhs_pf4 = lhs(lhs_vert, lhs_horiz_4);                 \
        lhs_pf5 = lhs(lhs_vert, lhs_horiz_5);                 \
      } else if (lhs_horiz_4 < k_size) {                      \
        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                 \
        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                 \
        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                 \
        lhs_pf3 = lhs(lhs_vert, lhs_horiz_3);                 \
        lhs_pf4 = lhs(lhs_vert, lhs_horiz_4);                 \
      } else if (lhs_horiz_3 < k_size) {                      \
        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                 \
        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                 \
        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                 \
        lhs_pf3 = lhs(lhs_vert, lhs_horiz_3);                 \
      } else if (lhs_horiz_2 < k_size) {                      \
        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                 \
        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                 \
        lhs_pf2 = lhs(lhs_vert, lhs_horiz_2);                 \
      } else if (lhs_horiz_1 < k_size) {                      \
        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                 \
        lhs_pf1 = lhs(lhs_vert, lhs_horiz_1);                 \
      } else if (lhs_horiz_0 < k_size) {                      \
        lhs_pf0 = lhs(lhs_vert, lhs_horiz_0);                 \
      }                                                       \
    }                                                         \
                                                              \
    const Index rhs_vert = base_k + load_idx_vert;            \
    if (!needs_edge_check || rhs_vert < k_size) {             \
      const Index rhs_horiz_0 = base_n + threadIdx.z + 0 * 8; \
      const Index rhs_horiz_1 = base_n + threadIdx.z + 1 * 8; \
      const Index rhs_horiz_2 = base_n + threadIdx.z + 2 * 8; \
      const Index rhs_horiz_3 = base_n + threadIdx.z + 3 * 8; \
      const Index rhs_horiz_4 = base_n + threadIdx.z + 4 * 8; \
      const Index rhs_horiz_5 = base_n + threadIdx.z + 5 * 8; \
      const Index rhs_horiz_6 = base_n + threadIdx.z + 6 * 8; \
      const Index rhs_horiz_7 = base_n + threadIdx.z + 7 * 8; \
                                                              \
      if (rhs_horiz_7 < n_size) {                             \
        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                 \
        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                 \
        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                 \
        rhs_pf3 = rhs(rhs_vert, rhs_horiz_3);                 \
        rhs_pf4 = rhs(rhs_vert, rhs_horiz_4);                 \
        rhs_pf5 = rhs(rhs_vert, rhs_horiz_5);                 \
        rhs_pf6 = rhs(rhs_vert, rhs_horiz_6);                 \
        rhs_pf7 = rhs(rhs_vert, rhs_horiz_7);                 \
      } else if (rhs_horiz_6 < n_size) {                      \
        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                 \
        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                 \
        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                 \
        rhs_pf3 = rhs(rhs_vert, rhs_horiz_3);                 \
        rhs_pf4 = rhs(rhs_vert, rhs_horiz_4);                 \
        rhs_pf5 = rhs(rhs_vert, rhs_horiz_5);                 \
        rhs_pf6 = rhs(rhs_vert, rhs_horiz_6);                 \
      } else if (rhs_horiz_5 < n_size) {                      \
        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                 \
        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                 \
        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                 \
        rhs_pf3 = rhs(rhs_vert, rhs_horiz_3);                 \
        rhs_pf4 = rhs(rhs_vert, rhs_horiz_4);                 \
        rhs_pf5 = rhs(rhs_vert, rhs_horiz_5);                 \
      } else if (rhs_horiz_4 < n_size) {                      \
        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                 \
        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                 \
        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                 \
        rhs_pf3 = rhs(rhs_vert, rhs_horiz_3);                 \
        rhs_pf4 = rhs(rhs_vert, rhs_horiz_4);                 \
      } else if (rhs_horiz_3 < n_size) {                      \
        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                 \
        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                 \
        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                 \
        rhs_pf3 = rhs(rhs_vert, rhs_horiz_3);                 \
      } else if (rhs_horiz_2 < n_size) {                      \
        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                 \
        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                 \
        rhs_pf2 = rhs(rhs_vert, rhs_horiz_2);                 \
      } else if (rhs_horiz_1 < n_size) {                      \
        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                 \
        rhs_pf1 = rhs(rhs_vert, rhs_horiz_1);                 \
      } else if (rhs_horiz_0 < n_size) {                      \
        rhs_pf0 = rhs(rhs_vert, rhs_horiz_0);                 \
      }                                                       \
    }                                                         \
  }

#define writeRegToShmem()               \
  lhs_shmem[lhs_store_idx_0] = lhs_pf0; \
  rhs_shmem[rhs_store_idx_0] = rhs_pf0; \
                                        \
  lhs_shmem[lhs_store_idx_1] = lhs_pf1; \
  rhs_shmem[rhs_store_idx_1] = rhs_pf1; \
                                        \
  lhs_shmem[lhs_store_idx_2] = lhs_pf2; \
  rhs_shmem[rhs_store_idx_2] = rhs_pf2; \
                                        \
  lhs_shmem[lhs_store_idx_3] = lhs_pf3; \
  rhs_shmem[rhs_store_idx_3] = rhs_pf3; \
                                        \
  lhs_shmem[lhs_store_idx_4] = lhs_pf4; \
  rhs_shmem[rhs_store_idx_4] = rhs_pf4; \
                                        \
  lhs_shmem[lhs_store_idx_5] = lhs_pf5; \
  rhs_shmem[rhs_store_idx_5] = rhs_pf5; \
                                        \
  lhs_shmem[lhs_store_idx_6] = lhs_pf6; \
  rhs_shmem[rhs_store_idx_6] = rhs_pf6; \
                                        \
  lhs_shmem[lhs_store_idx_7] = lhs_pf7; \
  rhs_shmem[rhs_store_idx_7] = rhs_pf7;

  // declare and initialize result array
#define res(i, j) _res_##i##j
#define initResultRow(i)      \
  Scalar res(i, 0) = conv(0); \
  Scalar res(i, 1) = conv(0); \
  Scalar res(i, 2) = conv(0); \
  Scalar res(i, 3) = conv(0); \
  Scalar res(i, 4) = conv(0); \
  Scalar res(i, 5) = conv(0); \
  Scalar res(i, 6) = conv(0); \
  Scalar res(i, 7) = conv(0);

  internal::scalar_cast_op<int, Scalar> conv;
  initResultRow(0);
  initResultRow(1);
  initResultRow(2);
  initResultRow(3);
  initResultRow(4);
  initResultRow(5);
  initResultRow(6);
  initResultRow(7);
#undef initResultRow

  for (Index base_k = 0; base_k < k_size; base_k += 64) {
    // wait for previous iteration to finish with shmem. Despite common sense,
    // the code is a bit faster with this here then at bottom of loop
    __syncthreads();

    prefetchIntoRegisters(base_k);
    writeRegToShmem();

#undef prefetchIntoRegisters
#undef writeRegToShmem

    // wait for shared mem packing to be done before starting computation
    __syncthreads();

    // compute 8x8 matrix product by outer product. This involves packing one column
    // of LHS and one row of RHS into registers (takes 16 registers).

#define lcol(i) _lcol##i
    Scalar lcol(0);
    Scalar lcol(1);
    Scalar lcol(2);
    Scalar lcol(3);
    Scalar lcol(4);
    Scalar lcol(5);
    Scalar lcol(6);
    Scalar lcol(7);

#define rrow(j) _rrow##j
    Scalar rrow(0);
    Scalar rrow(1);
    Scalar rrow(2);
    Scalar rrow(3);
    Scalar rrow(4);
    Scalar rrow(5);
    Scalar rrow(6);
    Scalar rrow(7);

    // Now x corresponds to k, y to m, and z to n
    const Scalar* lhs_block = &lhs_shmem[threadIdx.x + 9 * threadIdx.y];
    const Scalar* rhs_block = &rhs_shmem[threadIdx.x + 8 * threadIdx.z];

#define lhs_element(i, j) lhs_block[72 * ((i) + 8 * (j))]
#define rhs_element(i, j) rhs_block[72 * ((i) + 8 * (j))]

#define loadData(i, j)         \
  lcol(0) = lhs_element(0, j); \
  rrow(0) = rhs_element(i, 0); \
  lcol(1) = lhs_element(1, j); \
  rrow(1) = rhs_element(i, 1); \
  lcol(2) = lhs_element(2, j); \
  rrow(2) = rhs_element(i, 2); \
  lcol(3) = lhs_element(3, j); \
  rrow(3) = rhs_element(i, 3); \
  lcol(4) = lhs_element(4, j); \
  rrow(4) = rhs_element(i, 4); \
  lcol(5) = lhs_element(5, j); \
  rrow(5) = rhs_element(i, 5); \
  lcol(6) = lhs_element(6, j); \
  rrow(6) = rhs_element(i, 6); \
  lcol(7) = lhs_element(7, j); \
  rrow(7) = rhs_element(i, 7);

#define computeCol(j)             \
  res(0, j) += lcol(0) * rrow(j); \
  res(1, j) += lcol(1) * rrow(j); \
  res(2, j) += lcol(2) * rrow(j); \
  res(3, j) += lcol(3) * rrow(j); \
  res(4, j) += lcol(4) * rrow(j); \
  res(5, j) += lcol(5) * rrow(j); \
  res(6, j) += lcol(6) * rrow(j); \
  res(7, j) += lcol(7) * rrow(j);

#define computePass(i) \
  loadData(i, i);      \
                       \
  computeCol(0);       \
  computeCol(1);       \
  computeCol(2);       \
  computeCol(3);       \
  computeCol(4);       \
  computeCol(5);       \
  computeCol(6);       \
  computeCol(7);

    computePass(0);
    computePass(1);
    computePass(2);
    computePass(3);
    computePass(4);
    computePass(5);
    computePass(6);
    computePass(7);

#undef lcol
#undef rrow
#undef lhs_element
#undef rhs_element
#undef loadData
#undef computeCol
#undef computePass
  }  // end loop over k

  // we've now iterated over all of the large (ie width 64) k blocks and
  // accumulated results in registers. At this point thread (x, y, z) contains
  // the sum across all big k blocks of the product of little k block of index (x, y)
  // with block of index (y, z). To compute the final output, we need to reduce
  // the 8 threads over y by summation.
#if defined(EIGEN_HIPCC) || (defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000)
#define shuffleInc(i, j, mask) res(i, j) += __shfl_xor(res(i, j), mask)
#else
#define shuffleInc(i, j, mask) res(i, j) += __shfl_xor_sync(0xFFFFFFFF, res(i, j), mask)
#endif

#define reduceRow(i, mask) \
  shuffleInc(i, 0, mask);  \
  shuffleInc(i, 1, mask);  \
  shuffleInc(i, 2, mask);  \
  shuffleInc(i, 3, mask);  \
  shuffleInc(i, 4, mask);  \
  shuffleInc(i, 5, mask);  \
  shuffleInc(i, 6, mask);  \
  shuffleInc(i, 7, mask);

#define reduceMatrix(mask) \
  reduceRow(0, mask);      \
  reduceRow(1, mask);      \
  reduceRow(2, mask);      \
  reduceRow(3, mask);      \
  reduceRow(4, mask);      \
  reduceRow(5, mask);      \
  reduceRow(6, mask);      \
  reduceRow(7, mask);

  // actually perform the reduction, now each thread of index (_, y, z)
  // contains the correct values in its registers that belong in the output
  // block
  reduceMatrix(1);
  reduceMatrix(2);
  reduceMatrix(4);

#undef shuffleInc
#undef reduceRow
#undef reduceMatrix

  // now we need to copy the 64 values into main memory. We can't split work
  // among threads because all variables are in registers. There's 2 ways
  // to do this:
  // (1) have 1 thread do 64 writes from registers into global memory
  // (2) have 1 thread do 64 writes into shared memory, and then 8 threads
  //     each do 8 writes into global memory. We can just overwrite the shared
  //     memory from the problem we just solved.
  // (2) is slightly faster than (1) due to less branching and more ILP

  // TODO: won't yield much gain, but could just use currently unused shared mem
  //       and then we won't have to sync
  // wait for shared mem to be out of use
  __syncthreads();

#define writeResultShmem(i, j) lhs_shmem[i + 8 * threadIdx.y + 64 * threadIdx.z + 512 * j] = res(i, j);

#define writeRow(i)       \
  writeResultShmem(i, 0); \
  writeResultShmem(i, 1); \
  writeResultShmem(i, 2); \
  writeResultShmem(i, 3); \
  writeResultShmem(i, 4); \
  writeResultShmem(i, 5); \
  writeResultShmem(i, 6); \
  writeResultShmem(i, 7);

  if (threadIdx.x == 0) {
    writeRow(0);
    writeRow(1);
    writeRow(2);
    writeRow(3);
    writeRow(4);
    writeRow(5);
    writeRow(6);
    writeRow(7);
  }
#undef writeResultShmem
#undef writeRow

  const int max_i_write = numext::mini((int)((m_size - base_m - threadIdx.y + 7) / 8), 8);
  const int max_j_write = numext::mini((int)((n_size - base_n - threadIdx.z + 7) / 8), 8);

  if (threadIdx.x < max_i_write) {
    if (max_j_write == 8) {
      // TODO: can i trade bank conflicts for coalesced writes?
      Scalar val0 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 0];
      Scalar val1 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 1];
      Scalar val2 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 2];
      Scalar val3 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 3];
      Scalar val4 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 4];
      Scalar val5 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 5];
      Scalar val6 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 6];
      Scalar val7 = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * 7];

      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 0) = val0;
      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 1) = val1;
      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 2) = val2;
      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 3) = val3;
      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 4) = val4;
      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 5) = val5;
      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 6) = val6;
      output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * 7) = val7;
    } else {
#pragma unroll 7
      for (int j = 0; j < max_j_write; j++) {
        Scalar val = lhs_shmem[threadIdx.x + 8 * threadIdx.y + 64 * threadIdx.z + 512 * j];
        output(base_m + threadIdx.y + 8 * threadIdx.x, base_n + threadIdx.z + 8 * j) = val;
      }
    }
  }
#undef res
}

template <typename Scalar, typename Index, typename LhsMapper, typename RhsMapper, typename OutputMapper>
__global__ void
#if defined(EIGEN_HIPCC)
__launch_bounds__(512, 1)
#else
__launch_bounds__(512)
#endif
    EigenContractionKernel(const LhsMapper lhs, const RhsMapper rhs, const OutputMapper output, const Index m_size,
                           const Index n_size, const Index k_size) {
  __shared__ Scalar lhs_shmem[72 * 64];
  __shared__ Scalar rhs_shmem[72 * 64];

  const Index m_block_idx = blockIdx.x;
  const Index n_block_idx = blockIdx.y;

  const Index base_m = 64 * m_block_idx;
  const Index base_n = 64 * n_block_idx;

  if (base_m + 63 < m_size && base_n + 63 < n_size) {
    EigenContractionKernelInternal<Scalar, Index, LhsMapper, RhsMapper, OutputMapper, false>(
        lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size);
  } else {
    EigenContractionKernelInternal<Scalar, Index, LhsMapper, RhsMapper, OutputMapper, true>(
        lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size);
  }
}

template <typename Index, typename LhsMapper, typename RhsMapper, typename OutputMapper, bool CHECK_LHS_BOUNDARY,
          bool CHECK_RHS_BOUNDARY>
__device__ __forceinline__ void EigenFloatContractionKernelInternal16x16(const LhsMapper lhs, const RhsMapper rhs,
                                                                         const OutputMapper output,
                                                                         float2 lhs_shmem2[][16],
                                                                         float2 rhs_shmem2[][8], const Index m_size,
                                                                         const Index n_size, const Index k_size,
                                                                         const Index base_m, const Index base_n) {
  // prefetch registers
  float4 lhs_pf0, rhs_pf0;

  float4 results[4];
  for (int i = 0; i < 4; i++) {
    results[i].x = results[i].y = results[i].z = results[i].w = 0;
  }

#define prefetch_lhs(reg, row, col)                                 \
  if (!CHECK_LHS_BOUNDARY) {                                        \
    if (col < k_size) {                                             \
      reg = lhs.template loadPacket<float4, Unaligned>(row, col);   \
    }                                                               \
  } else {                                                          \
    if (col < k_size) {                                             \
      if (row + 3 < m_size) {                                       \
        reg = lhs.template loadPacket<float4, Unaligned>(row, col); \
      } else if (row + 2 < m_size) {                                \
        reg.x = lhs(row + 0, col);                                  \
        reg.y = lhs(row + 1, col);                                  \
        reg.z = lhs(row + 2, col);                                  \
      } else if (row + 1 < m_size) {                                \
        reg.x = lhs(row + 0, col);                                  \
        reg.y = lhs(row + 1, col);                                  \
      } else if (row < m_size) {                                    \
        reg.x = lhs(row + 0, col);                                  \
      }                                                             \
    }                                                               \
  }

  Index lhs_vert = base_m + threadIdx.x * 4;

  for (Index k = 0; k < k_size; k += 16) {
    lhs_pf0 = internal::pset1<float4>(0);
    rhs_pf0 = internal::pset1<float4>(0);

    Index lhs_horiz = threadIdx.y + k;
    prefetch_lhs(lhs_pf0, lhs_vert, lhs_horiz)

        Index rhs_vert = k + (threadIdx.x % 4) * 4;
    Index rhs_horiz0 = (threadIdx.x >> 2) + threadIdx.y * 4 + base_n;

    if (!CHECK_RHS_BOUNDARY) {
      if ((rhs_vert + 3) < k_size) {
        // just CHECK_RHS_BOUNDARY
        rhs_pf0 = rhs.template loadPacket<float4, Unaligned>(rhs_vert, rhs_horiz0);
      } else if (rhs_vert + 2 < k_size) {
        // just CHECK_RHS_BOUNDARY
        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
        rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
        rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);
      } else if (rhs_vert + 1 < k_size) {
        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
        rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
      } else if (rhs_vert < k_size) {
        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
      }
    } else {
      if (rhs_horiz0 < n_size) {
        if ((rhs_vert + 3) < k_size) {
          rhs_pf0 = rhs.template loadPacket<float4, Unaligned>(rhs_vert, rhs_horiz0);
        } else if ((rhs_vert + 2) < k_size) {
          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
          rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);
        } else if ((rhs_vert + 1) < k_size) {
          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
        } else if (rhs_vert < k_size) {
          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
        }
      }
    }
    float x1, x2;
    // the following can be a bitwise operation..... some day.
    if ((threadIdx.x % 8) < 4) {
      x1 = rhs_pf0.y;
      x2 = rhs_pf0.w;
    } else {
      x1 = rhs_pf0.x;
      x2 = rhs_pf0.z;
    }
#if defined(EIGEN_HIPCC) || (defined(EIGEN_CUDA_SDK_VER) && EIGEN_CUDA_SDK_VER < 90000)
    x1 = __shfl_xor(x1, 4);
    x2 = __shfl_xor(x2, 4);
#else
    x1 = __shfl_xor_sync(0xFFFFFFFF, x1, 4);
    x2 = __shfl_xor_sync(0xFFFFFFFF, x2, 4);
#endif
    if ((threadIdx.x % 8) < 4) {
      rhs_pf0.y = x1;
      rhs_pf0.w = x2;
    } else {
      rhs_pf0.x = x1;
      rhs_pf0.z = x2;
    }

    // We have 64 features.
    // Row 0 -> times (0, 4, 8, 12, 1, 5, 9, 13) for features 0, 1.
    // Row 1 -> times (0, 4, 8, 12, 1, 5, 9, 13) for features 2, 3.
    // ...
    // Row 31 -> times (0, 4, 8, 12, 1, 5, 9, 13) for features 62, 63
    // Row 32 -> times (2, 6, 10, 14, 3, 7, 11, 15) for features 0, 1
    // ...
    rhs_shmem2[(threadIdx.x >> 3) + threadIdx.y * 2][threadIdx.x % 8] = make_float2(rhs_pf0.x, rhs_pf0.y);
    rhs_shmem2[(threadIdx.x >> 3) + threadIdx.y * 2 + 32][threadIdx.x % 8] = make_float2(rhs_pf0.z, rhs_pf0.w);

    // Row 0 (time 0) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), ..  (60, 61)
    // Row 1 (time 1) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), ..  (60, 61)
    // ...
    // Row 15 (time 15) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), ..  (60, 61)
    // Row 16 (time 0) -> features (2, 3), (6, 7), .. (30, 31), (34, 35), ..  (62, 63)
    // ...

    lhs_shmem2[threadIdx.y][threadIdx.x] = make_float2(lhs_pf0.x, lhs_pf0.y);
    lhs_shmem2[threadIdx.y + 16][threadIdx.x] = make_float2(lhs_pf0.z, lhs_pf0.w);

#define add_vals(fl1, fl2, fr1, fr2) \
  results[0].x += fl1.x * fr1.x;     \
  results[0].y += fl1.y * fr1.x;     \
  results[0].z += fl2.x * fr1.x;     \
  results[0].w += fl2.y * fr1.x;     \
                                     \
  results[1].x += fl1.x * fr1.y;     \
  results[1].y += fl1.y * fr1.y;     \
  results[1].z += fl2.x * fr1.y;     \
  results[1].w += fl2.y * fr1.y;     \
                                     \
  results[2].x += fl1.x * fr2.x;     \
  results[2].y += fl1.y * fr2.x;     \
  results[2].z += fl2.x * fr2.x;     \
  results[2].w += fl2.y * fr2.x;     \
                                     \
  results[3].x += fl1.x * fr2.y;     \
  results[3].y += fl1.y * fr2.y;     \
  results[3].z += fl2.x * fr2.y;     \
  results[3].w += fl2.y * fr2.y;

    __syncthreads();

// Do the multiplies.
#pragma unroll
    for (int koff = 0; koff < 16; koff++) {
      // 32 x threads.
      float2 fl1 = lhs_shmem2[koff][threadIdx.x];
      float2 fl2 = lhs_shmem2[koff + 16][threadIdx.x];

      int start_feature = threadIdx.y * 4;
      float2 fr1 = rhs_shmem2[(start_feature >> 1) + 32 * ((koff % 4) / 2)][koff / 4 + (koff % 2) * 4];
      float2 fr2 = rhs_shmem2[(start_feature >> 1) + 1 + 32 * ((koff % 4) / 2)][koff / 4 + (koff % 2) * 4];

      add_vals(fl1, fl2, fr1, fr2)
    }
    __syncthreads();
  }

#undef prefetch_lhs
#undef add_vals

  Index horiz_base = threadIdx.y * 4 + base_n;
  if (!CHECK_LHS_BOUNDARY && !CHECK_RHS_BOUNDARY) {
    for (int i = 0; i < 4; i++) {
      output(lhs_vert, horiz_base + i) = results[i].x;
      output(lhs_vert + 1, horiz_base + i) = results[i].y;
      output(lhs_vert + 2, horiz_base + i) = results[i].z;
      output(lhs_vert + 3, horiz_base + i) = results[i].w;
    }
  } else if (!CHECK_RHS_BOUNDARY) {
    // CHECK LHS
    if (lhs_vert + 3 < m_size) {
      for (int i = 0; i < 4; i++) {
        output(lhs_vert, horiz_base + i) = results[i].x;
        output(lhs_vert + 1, horiz_base + i) = results[i].y;
        output(lhs_vert + 2, horiz_base + i) = results[i].z;
        output(lhs_vert + 3, horiz_base + i) = results[i].w;
      }
    } else if (lhs_vert + 2 < m_size) {
      for (int i = 0; i < 4; i++) {
        output(lhs_vert, horiz_base + i) = results[i].x;
        output(lhs_vert + 1, horiz_base + i) = results[i].y;
        output(lhs_vert + 2, horiz_base + i) = results[i].z;
      }
    } else if (lhs_vert + 1 < m_size) {
      for (int i = 0; i < 4; i++) {
        output(lhs_vert, horiz_base + i) = results[i].x;
        output(lhs_vert + 1, horiz_base + i) = results[i].y;
      }
    } else if (lhs_vert < m_size) {
      for (int i = 0; i < 4; i++) {
        output(lhs_vert, horiz_base + i) = results[i].x;
      }
    }
  } else if (!CHECK_LHS_BOUNDARY) {
    // CHECK RHS
    /*
    int ncols_rem = fminf(n_size- horiz_base, 4);
    for (int i = 0; i < ncols_rem; i++) {
      output(lhs_vert, horiz_base + i) = results[i].x;
      output(lhs_vert + 1, horiz_base + i) = results[i].y;
      output(lhs_vert + 2, horiz_base + i) = results[i].z;
      output(lhs_vert + 3, horiz_base + i) = results[i].w;
    }*/
    for (int i = 0; i < 4; i++) {
      if (horiz_base + i < n_size) {
        output(lhs_vert, horiz_base + i) = results[i].x;
        output(lhs_vert + 1, horiz_base + i) = results[i].y;
        output(lhs_vert + 2, horiz_base + i) = results[i].z;
        output(lhs_vert + 3, horiz_base + i) = results[i].w;
      }
    }
  } else {
    // CHECK both boundaries.
    for (int i = 0; i < 4; i++) {
      if (horiz_base + i < n_size) {
        if (lhs_vert < m_size) output(lhs_vert, horiz_base + i) = results[i].x;
        if (lhs_vert + 1 < m_size) output(lhs_vert + 1, horiz_base + i) = results[i].y;
        if (lhs_vert + 2 < m_size) output(lhs_vert + 2, horiz_base + i) = results[i].z;
        if (lhs_vert + 3 < m_size) output(lhs_vert + 3, horiz_base + i) = results[i].w;
      }
    }
  }
}

template <typename Index, typename LhsMapper, typename RhsMapper, typename OutputMapper, bool CHECK_LHS_BOUNDARY,
          bool CHECK_RHS_BOUNDARY>
__device__ __forceinline__ void EigenFloatContractionKernelInternal(const LhsMapper lhs, const RhsMapper rhs,
                                                                    const OutputMapper output, float2 lhs_shmem2[][32],
                                                                    float2 rhs_shmem2[][8], const Index m_size,
                                                                    const Index n_size, const Index k_size,
                                                                    const Index base_m, const Index base_n) {
  // prefetch registers
  float4 lhs_pf0, lhs_pf1, lhs_pf2, lhs_pf3;
  float4 rhs_pf0, rhs_pf1;

  float4 results[8];
  for (int i = 0; i < 8; i++) {
    results[i].x = results[i].y = results[i].z = results[i].w = 0;
  }

  Index lhs_vert = base_m + threadIdx.x * 4 + (threadIdx.y % 4) * 32;
  for (Index k = 0; k < k_size; k += 32) {
    lhs_pf0 = internal::pset1<float4>(0);
    lhs_pf1 = internal::pset1<float4>(0);
    lhs_pf2 = internal::pset1<float4>(0);
    lhs_pf3 = internal::pset1<float4>(0);

    rhs_pf0 = internal::pset1<float4>(0);
    rhs_pf1 = internal::pset1<float4>(0);

    if (!CHECK_LHS_BOUNDARY) {
      if ((threadIdx.y / 4 + k + 24) < k_size) {
        lhs_pf0 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k));
        lhs_pf1 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 8));
        lhs_pf2 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 16));
        lhs_pf3 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 24));
      } else if ((threadIdx.y / 4 + k + 16) < k_size) {
        lhs_pf0 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k));
        lhs_pf1 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 8));
        lhs_pf2 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 16));
      } else if ((threadIdx.y / 4 + k + 8) < k_size) {
        lhs_pf0 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k));
        lhs_pf1 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 8));
      } else if ((threadIdx.y / 4 + k) < k_size) {
        lhs_pf0 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k));
      }
    } else {
      // just CHECK_LHS_BOUNDARY
      if (lhs_vert + 3 < m_size) {
        if ((threadIdx.y / 4 + k + 24) < k_size) {
          lhs_pf0 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k));
          lhs_pf1 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 8));
          lhs_pf2 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 16));
          lhs_pf3 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 24));
        } else if ((threadIdx.y / 4 + k + 16) < k_size) {
          lhs_pf0 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k));
          lhs_pf1 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 8));
          lhs_pf2 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 16));
        } else if ((threadIdx.y / 4 + k + 8) < k_size) {
          lhs_pf0 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k));
          lhs_pf1 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k + 8));
        } else if ((threadIdx.y / 4 + k) < k_size) {
          lhs_pf0 = lhs.template loadPacket<float4, Unaligned>(lhs_vert, (threadIdx.y / 4 + k));
        }
      } else if (lhs_vert + 2 < m_size) {
        if ((threadIdx.y / 4 + k + 24) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
          lhs_pf0.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k));
          lhs_pf0.z = lhs(lhs_vert + 2, (threadIdx.y / 4 + k));
          lhs_pf1.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 8));
          lhs_pf1.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 8));
          lhs_pf1.z = lhs(lhs_vert + 2, (threadIdx.y / 4 + k + 8));
          lhs_pf2.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 16));
          lhs_pf2.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 16));
          lhs_pf2.z = lhs(lhs_vert + 2, (threadIdx.y / 4 + k + 16));
          lhs_pf3.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 24));
          lhs_pf3.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 24));
          lhs_pf3.z = lhs(lhs_vert + 2, (threadIdx.y / 4 + k + 24));
        } else if ((threadIdx.y / 4 + k + 16) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
          lhs_pf0.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k));
          lhs_pf0.z = lhs(lhs_vert + 2, (threadIdx.y / 4 + k));
          lhs_pf1.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 8));
          lhs_pf1.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 8));
          lhs_pf1.z = lhs(lhs_vert + 2, (threadIdx.y / 4 + k + 8));
          lhs_pf2.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 16));
          lhs_pf2.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 16));
          lhs_pf2.z = lhs(lhs_vert + 2, (threadIdx.y / 4 + k + 16));
        } else if ((threadIdx.y / 4 + k + 8) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
          lhs_pf0.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k));
          lhs_pf0.z = lhs(lhs_vert + 2, (threadIdx.y / 4 + k));
          lhs_pf1.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 8));
          lhs_pf1.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 8));
          lhs_pf1.z = lhs(lhs_vert + 2, (threadIdx.y / 4 + k + 8));
        } else if ((threadIdx.y / 4 + k) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
          lhs_pf0.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k));
          lhs_pf0.z = lhs(lhs_vert + 2, (threadIdx.y / 4 + k));
        }
      } else if (lhs_vert + 1 < m_size) {
        if ((threadIdx.y / 4 + k + 24) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
          lhs_pf0.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k));
          lhs_pf1.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 8));
          lhs_pf1.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 8));
          lhs_pf2.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 16));
          lhs_pf2.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 16));
          lhs_pf3.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 24));
          lhs_pf3.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 24));
        } else if ((threadIdx.y / 4 + k + 16) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
          lhs_pf0.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k));
          lhs_pf1.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 8));
          lhs_pf1.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 8));
          lhs_pf2.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 16));
          lhs_pf2.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 16));
        } else if ((threadIdx.y / 4 + k + 8) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
          lhs_pf0.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k));
          lhs_pf1.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 8));
          lhs_pf1.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k + 8));
        } else if ((threadIdx.y / 4 + k) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
          lhs_pf0.y = lhs(lhs_vert + 1, (threadIdx.y / 4 + k));
        }
      } else if (lhs_vert < m_size) {
        if ((threadIdx.y / 4 + k + 24) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
          lhs_pf1.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 8));
          lhs_pf2.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 16));
          lhs_pf3.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 24));
        } else if ((threadIdx.y / 4 + k + 16) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
          lhs_pf1.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 8));
          lhs_pf2.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 16));
        } else if ((threadIdx.y / 4 + k + 8) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
          lhs_pf1.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k + 8));
        } else if ((threadIdx.y / 4 + k) < k_size) {
          lhs_pf0.x = lhs(lhs_vert + 0, (threadIdx.y / 4 + k));
        }
      }
    }
    __syncthreads();
    Index rhs_vert = k + threadIdx.x * 4;
    Index rhs_horiz0 = threadIdx.y * 2 + base_n;
    Index rhs_horiz1 = threadIdx.y * 2 + 1 + base_n;
    if (!CHECK_RHS_BOUNDARY) {
      if ((rhs_vert + 3) < k_size) {
        // just CHECK_RHS_BOUNDARY
        rhs_pf0 = rhs.template loadPacket<float4, Unaligned>(rhs_vert, rhs_horiz0);
        rhs_pf1 = rhs.template loadPacket<float4, Unaligned>(rhs_vert, rhs_horiz1);
      } else if (rhs_vert + 2 < k_size) {
        // just CHECK_RHS_BOUNDARY
        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
        rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
        rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);
        rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
        rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);
        rhs_pf1.z = rhs(rhs_vert + 2, rhs_horiz1);
      } else if (rhs_vert + 1 < k_size) {
        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
        rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
        rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
        rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);
      } else if (rhs_vert < k_size) {
        rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
        rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
      }
    } else {
      if (rhs_horiz1 < n_size) {
        if ((rhs_vert + 3) < k_size) {
          // just CHECK_RHS_BOUNDARY
          rhs_pf0 = rhs.template loadPacket<float4, Unaligned>(rhs_vert, rhs_horiz0);
          rhs_pf1 = rhs.template loadPacket<float4, Unaligned>(rhs_vert, rhs_horiz1);
        } else if (rhs_vert + 2 < k_size) {
          // just CHECK_RHS_BOUNDARY
          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
          rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);
          rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
          rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);
          rhs_pf1.z = rhs(rhs_vert + 2, rhs_horiz1);
        } else if (k + threadIdx.x * 4 + 1 < k_size) {
          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
          rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
          rhs_pf1.y = rhs(rhs_vert + 1, rhs_horiz1);
        } else if (k + threadIdx.x * 4 < k_size) {
          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
          rhs_pf1.x = rhs(rhs_vert, rhs_horiz1);
        }
      } else if (rhs_horiz0 < n_size) {
        if ((rhs_vert + 3) < k_size) {
          // just CHECK_RHS_BOUNDARY
          rhs_pf0 = rhs.template loadPacket<float4, Unaligned>(rhs_vert, rhs_horiz0);
        } else if ((rhs_vert + 2) < k_size) {
          // just CHECK_RHS_BOUNDARY
          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
          rhs_pf0.z = rhs(rhs_vert + 2, rhs_horiz0);
        } else if ((rhs_vert + 1) < k_size) {
          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
          rhs_pf0.y = rhs(rhs_vert + 1, rhs_horiz0);
        } else if (rhs_vert < k_size) {
          rhs_pf0.x = rhs(rhs_vert, rhs_horiz0);
        }
      }
    }
    __syncthreads();
    // Loaded. Do computation
    // Row 0 -> times (0, 4, 8, .. 28) for features 0, 1.
    // Row 1 -> times (0, 4, 8, .. 28) for features 2, 3.
    // ..
    // Row 31 -> times (0, 4, 8, .. 28) for features 62, 63
    rhs_shmem2[threadIdx.y][threadIdx.x] = make_float2(rhs_pf0.x, rhs_pf1.x);
    // Row 32 -> times (1, 5, 9, .. 29) for features 0, 1.
    // Row 33 -> times (1, 5, 9, .. 29) for features 2, 3.
    // ..
    rhs_shmem2[threadIdx.y + 32][threadIdx.x] = make_float2(rhs_pf0.y, rhs_pf1.y);
    // Row 64 -> times (2, 6, 10, .. 30) for features 0, 1.
    // Row 65 -> times (2, 6, 10, .. 30) for features 2, 3.
    rhs_shmem2[threadIdx.y + 64][threadIdx.x] = make_float2(rhs_pf0.z, rhs_pf1.z);
    // Row 96 -> times (3, 7, 11, .. 31) for features 0, 1.
    // Row 97 -> times (3, 7, 11, .. 31) for features 2, 3.
    rhs_shmem2[threadIdx.y + 96][threadIdx.x] = make_float2(rhs_pf0.w, rhs_pf1.w);

    // LHS.
    // Row 0 (time 0) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), ..  (60, 61) .. (124, 125)
    // Row 1 (time 1) -> features (0, 1), (4, 5), .. (28, 29), (32, 33), ..  (60, 61) .. (124, 125)
    // ...
    // Row 8 (time 0) -> features (2, 3), (6, 7), .. (30, 31), (34, 35), ..  (62, 63) .. (126, 127)
    // Row 15 (time 7) -> features (2, 3), (6, 7), .. (30, 31), (34, 35), ..  (62, 63) .. (126, 127)

#define add_vals(a_feat1, a_feat2, f1, f2, f3, f4) \
  results[0].x += a_feat1.x * f1.x;                \
  results[1].x += a_feat1.x * f1.y;                \
  results[2].x += a_feat1.x * f2.x;                \
  results[3].x += a_feat1.x * f2.y;                \
  results[4].x += a_feat1.x * f3.x;                \
  results[5].x += a_feat1.x * f3.y;                \
  results[6].x += a_feat1.x * f4.x;                \
  results[7].x += a_feat1.x * f4.y;                \
                                                   \
  results[0].y += a_feat1.y * f1.x;                \
  results[1].y += a_feat1.y * f1.y;                \
  results[2].y += a_feat1.y * f2.x;                \
  results[3].y += a_feat1.y * f2.y;                \
  results[4].y += a_feat1.y * f3.x;                \
  results[5].y += a_feat1.y * f3.y;                \
  results[6].y += a_feat1.y * f4.x;                \
  results[7].y += a_feat1.y * f4.y;                \
                                                   \
  results[0].z += a_feat2.x * f1.x;                \
  results[1].z += a_feat2.x * f1.y;                \
  results[2].z += a_feat2.x * f2.x;                \
  results[3].z += a_feat2.x * f2.y;                \
  results[4].z += a_feat2.x * f3.x;                \
  results[5].z += a_feat2.x * f3.y;                \
  results[6].z += a_feat2.x * f4.x;                \
  results[7].z += a_feat2.x * f4.y;                \
                                                   \
  results[0].w += a_feat2.y * f1.x;                \
  results[1].w += a_feat2.y * f1.y;                \
  results[2].w += a_feat2.y * f2.x;                \
  results[3].w += a_feat2.y * f2.y;                \
  results[4].w += a_feat2.y * f3.x;                \
  results[5].w += a_feat2.y * f3.y;                \
  results[6].w += a_feat2.y * f4.x;                \
  results[7].w += a_feat2.y * f4.y;

    lhs_shmem2[threadIdx.y / 4][threadIdx.x + (threadIdx.y % 4) * 8] = make_float2(lhs_pf0.x, lhs_pf0.y);
    lhs_shmem2[threadIdx.y / 4 + 8][threadIdx.x + (threadIdx.y % 4) * 8] = make_float2(lhs_pf1.x, lhs_pf1.y);
    lhs_shmem2[threadIdx.y / 4 + 16][threadIdx.x + (threadIdx.y % 4) * 8] = make_float2(lhs_pf2.x, lhs_pf2.y);
    lhs_shmem2[threadIdx.y / 4 + 24][threadIdx.x + (threadIdx.y % 4) * 8] = make_float2(lhs_pf3.x, lhs_pf3.y);

    lhs_shmem2[threadIdx.y / 4 + 32][threadIdx.x + (threadIdx.y % 4) * 8] = make_float2(lhs_pf0.z, lhs_pf0.w);
    lhs_shmem2[threadIdx.y / 4 + 40][threadIdx.x + (threadIdx.y % 4) * 8] = make_float2(lhs_pf1.z, lhs_pf1.w);
    lhs_shmem2[threadIdx.y / 4 + 48][threadIdx.x + (threadIdx.y % 4) * 8] = make_float2(lhs_pf2.z, lhs_pf2.w);
    lhs_shmem2[threadIdx.y / 4 + 56][threadIdx.x + (threadIdx.y % 4) * 8] = make_float2(lhs_pf3.z, lhs_pf3.w);

    __syncthreads();

// Do the multiplies.
#pragma unroll
    for (int koff = 0; koff < 32; koff++) {
      float2 a3 = lhs_shmem2[koff][threadIdx.x + (threadIdx.y % 4) * 8];
      float2 a4 = lhs_shmem2[koff + 32][threadIdx.x + (threadIdx.y % 4) * 8];

      // first feature is at (threadIdx.y/4) * 8 last is at start + 8.
      int start_feature = (threadIdx.y / 4) * 8;

      float2 br1 = rhs_shmem2[start_feature / 2 + (koff % 4) * 32][koff / 4];
      float2 br2 = rhs_shmem2[start_feature / 2 + 1 + (koff % 4) * 32][koff / 4];
      float2 br3 = rhs_shmem2[start_feature / 2 + 2 + (koff % 4) * 32][koff / 4];
      float2 br4 = rhs_shmem2[start_feature / 2 + 3 + (koff % 4) * 32][koff / 4];

      add_vals(a3, a4, br1, br2, br3, br4)
    }
    __syncthreads();
  }  // end loop over k

#undef add_vals

  __syncthreads();
  Index horiz_base = (threadIdx.y / 4) * 8 + base_n;
  if (!CHECK_LHS_BOUNDARY && !CHECK_RHS_BOUNDARY) {
    for (int i = 0; i < 8; i++) {
      output(lhs_vert, horiz_base + i) = results[i].x;
      output(lhs_vert + 1, horiz_base + i) = results[i].y;
      output(lhs_vert + 2, horiz_base + i) = results[i].z;
      output(lhs_vert + 3, horiz_base + i) = results[i].w;
    }
  } else if (!CHECK_RHS_BOUNDARY) {
    if (lhs_vert + 3 < m_size) {
      for (int i = 0; i < 8; i++) {
        output(lhs_vert, horiz_base + i) = results[i].x;
        output(lhs_vert + 1, horiz_base + i) = results[i].y;
        output(lhs_vert + 2, horiz_base + i) = results[i].z;
        output(lhs_vert + 3, horiz_base + i) = results[i].w;
      }
    } else if (lhs_vert + 2 < m_size) {
      for (int i = 0; i < 8; i++) {
        output(lhs_vert, horiz_base + i) = results[i].x;
        output(lhs_vert + 1, horiz_base + i) = results[i].y;
        output(lhs_vert + 2, horiz_base + i) = results[i].z;
      }
    } else if (lhs_vert + 1 < m_size) {
      for (int i = 0; i < 8; i++) {
        output(lhs_vert, horiz_base + i) = results[i].x;
        output(lhs_vert + 1, horiz_base + i) = results[i].y;
      }
    } else if (lhs_vert < m_size) {
      for (int i = 0; i < 8; i++) {
        output(lhs_vert, horiz_base + i) = results[i].x;
      }
    }
  } else if (!CHECK_LHS_BOUNDARY) {
    // CHECK BOUNDARY_B
    for (int i = 0; i < 8; i++) {
      if (horiz_base + i < n_size) {
        output(lhs_vert, horiz_base + i) = results[i].x;
        output(lhs_vert + 1, horiz_base + i) = results[i].y;
        output(lhs_vert + 2, horiz_base + i) = results[i].z;
        output(lhs_vert + 3, horiz_base + i) = results[i].w;
      }
    }
  } else {
    // CHECK both boundaries.
    for (int i = 0; i < 8; i++) {
      if (horiz_base + i < n_size) {
        if (lhs_vert < m_size) output(lhs_vert, horiz_base + i) = results[i].x;
        if (lhs_vert + 1 < m_size) output(lhs_vert + 1, horiz_base + i) = results[i].y;
        if (lhs_vert + 2 < m_size) output(lhs_vert + 2, horiz_base + i) = results[i].z;
        if (lhs_vert + 3 < m_size) output(lhs_vert + 3, horiz_base + i) = results[i].w;
      }
    }
  }
}

template <typename Index, typename LhsMapper, typename RhsMapper, typename OutputMapper>
__global__ void
#if defined(EIGEN_HIPCC)
__launch_bounds__(256, 1)
#else
__launch_bounds__(256)
#endif
    EigenFloatContractionKernel(const LhsMapper lhs, const RhsMapper rhs, const OutputMapper output, const Index m_size,
                                const Index n_size, const Index k_size) {
  __shared__ float2 lhs_shmem[64 * 32];
  __shared__ float2 rhs_shmem[128 * 8];

  typedef float2 LHS_MEM[64][32];
  typedef float2 RHS_MEM[128][8];

  const Index m_block_idx = blockIdx.x;
  const Index n_block_idx = blockIdx.y;

  const Index base_m = 128 * m_block_idx;
  const Index base_n = 64 * n_block_idx;

  bool check_rhs = (base_n + 63) >= n_size;
  bool check_lhs128 = (base_m + 127) >= m_size;

  if (!check_rhs) {
    if (!check_lhs128) {
      // >= 128 rows left
      EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, false, false>(
          lhs, rhs, output, *((LHS_MEM*)lhs_shmem), *((RHS_MEM*)rhs_shmem), m_size, n_size, k_size, base_m, base_n);
    } else {
      EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, true, false>(
          lhs, rhs, output, *((LHS_MEM*)lhs_shmem), *((RHS_MEM*)rhs_shmem), m_size, n_size, k_size, base_m, base_n);
    }
  } else {
    if (!check_lhs128) {
      // >= 128 rows left
      EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, false, true>(
          lhs, rhs, output, *((LHS_MEM*)lhs_shmem), *((RHS_MEM*)rhs_shmem), m_size, n_size, k_size, base_m, base_n);
    } else {
      EigenFloatContractionKernelInternal<Index, LhsMapper, RhsMapper, OutputMapper, true, true>(
          lhs, rhs, output, *((LHS_MEM*)lhs_shmem), *((RHS_MEM*)rhs_shmem), m_size, n_size, k_size, base_m, base_n);
    }
  }
}

template <typename Index, typename LhsMapper, typename RhsMapper, typename OutputMapper>
__global__ void
#if defined(EIGEN_HIPCC)
__launch_bounds__(256, 1)
#else
__launch_bounds__(256)
#endif
    EigenFloatContractionKernel16x16(const LhsMapper lhs, const RhsMapper rhs, const OutputMapper output,
                                     const Index m_size, const Index n_size, const Index k_size) {
  __shared__ float2 lhs_shmem[32][16];
  __shared__ float2 rhs_shmem[64][8];

  const Index m_block_idx = blockIdx.x;
  const Index n_block_idx = blockIdx.y;

  const Index base_m = 64 * m_block_idx;
  const Index base_n = 64 * n_block_idx;

  if (base_m + 63 < m_size) {
    if (base_n + 63 < n_size) {
      EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, false, false>(
          lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);
    } else {
      EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, false, true>(
          lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);
    }
  } else {
    if (base_n + 63 < n_size) {
      EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, true, false>(
          lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);
    } else {
      EigenFloatContractionKernelInternal16x16<Index, LhsMapper, RhsMapper, OutputMapper, true, true>(
          lhs, rhs, output, lhs_shmem, rhs_shmem, m_size, n_size, k_size, base_m, base_n);
    }
  }
}

template <typename Indices, typename LeftArgType, typename RightArgType, typename OutputKernelType>
struct TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, GpuDevice>
    : public TensorContractionEvaluatorBase<TensorEvaluator<
          const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, GpuDevice> > {
  typedef GpuDevice Device;

  typedef TensorEvaluator<const TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType>, Device> Self;
  typedef TensorContractionEvaluatorBase<Self> Base;

  typedef TensorContractionOp<Indices, LeftArgType, RightArgType, OutputKernelType> XprType;
  typedef std::remove_const_t<typename XprType::Scalar> Scalar;
  typedef typename XprType::Index Index;
  typedef typename XprType::CoeffReturnType CoeffReturnType;
  typedef typename PacketType<CoeffReturnType, GpuDevice>::type PacketReturnType;

  static constexpr int Layout = TensorEvaluator<LeftArgType, Device>::Layout;

  // Most of the code is assuming that both input tensors are ColMajor. If the
  // inputs are RowMajor, we will "cheat" by swapping the LHS and RHS:
  // If we want to compute A * B = C, where A is LHS and B is RHS, the code
  // will pretend B is LHS and A is RHS.
  typedef std::conditional_t<Layout == static_cast<int>(ColMajor), LeftArgType, RightArgType> EvalLeftArgType;
  typedef std::conditional_t<Layout == static_cast<int>(ColMajor), RightArgType, LeftArgType> EvalRightArgType;

  static constexpr int LDims =
      internal::array_size<typename TensorEvaluator<EvalLeftArgType, Device>::Dimensions>::value;
  static constexpr int RDims =
      internal::array_size<typename TensorEvaluator<EvalRightArgType, Device>::Dimensions>::value;
  static constexpr int ContractDims = internal::array_size<Indices>::value;

  typedef array<Index, LDims> left_dim_mapper_t;
  typedef array<Index, RDims> right_dim_mapper_t;

  typedef array<Index, ContractDims> contract_t;
  typedef array<Index, LDims - ContractDims> left_nocontract_t;
  typedef array<Index, RDims - ContractDims> right_nocontract_t;

  static constexpr int NumDims = LDims + RDims - 2 * ContractDims;

  typedef DSizes<Index, NumDims> Dimensions;

  // typedefs needed in evalTo
  typedef std::remove_const_t<typename EvalLeftArgType::Scalar> LhsScalar;
  typedef std::remove_const_t<typename EvalRightArgType::Scalar> RhsScalar;

  typedef TensorEvaluator<EvalLeftArgType, Device> LeftEvaluator;
  typedef TensorEvaluator<EvalRightArgType, Device> RightEvaluator;

  typedef typename LeftEvaluator::Dimensions LeftDimensions;
  typedef typename RightEvaluator::Dimensions RightDimensions;

  TensorEvaluator(const XprType& op, const Device& device) : Base(op, device) {
    EIGEN_STATIC_ASSERT((internal::is_same<OutputKernelType, const NoOpOutputKernel>::value),
                        GPU_TENSOR_CONTRACTION_DOES_NOT_SUPPORT_OUTPUT_KERNELS);
  }

  // We need to redefine this method to make nvcc happy
  EIGEN_STRONG_INLINE bool evalSubExprsIfNeeded(Scalar* data) {
    this->m_leftImpl.evalSubExprsIfNeeded(NULL);
    this->m_rightImpl.evalSubExprsIfNeeded(NULL);
    if (data) {
      evalTo(data);
      return false;
    } else {
      this->m_result = static_cast<Scalar*>(this->m_device.allocate(this->dimensions().TotalSize() * sizeof(Scalar)));
      evalTo(this->m_result);
      return true;
    }
  }

  void evalTo(Scalar* buffer) const {
    if (this->m_lhs_inner_dim_contiguous) {
      if (this->m_rhs_inner_dim_contiguous) {
        if (this->m_rhs_inner_dim_reordered) {
          evalTyped<true, true, true, Unaligned>(buffer);
        } else {
          evalTyped<true, true, false, Unaligned>(buffer);
        }
      } else {
        if (this->m_rhs_inner_dim_reordered) {
          evalTyped<true, false, true, Unaligned>(buffer);
        } else {
          evalTyped<true, false, false, Unaligned>(buffer);
        }
      }
    } else {
      if (this->m_rhs_inner_dim_contiguous) {
        if (this->m_rhs_inner_dim_reordered) {
          evalTyped<false, true, true, Unaligned>(buffer);
        } else {
          evalTyped<false, true, false, Unaligned>(buffer);
        }
      } else {
        if (this->m_rhs_inner_dim_reordered) {
          evalTyped<false, false, true, Unaligned>(buffer);
        } else {
          evalTyped<false, false, false, Unaligned>(buffer);
        }
      }
    }
  }

  template <typename LhsScalar, typename RhsScalar, typename Index, typename LhsMapper, typename RhsMapper,
            typename OutputMapper>
  struct LaunchKernels {
    static void Run(const LhsMapper& lhs, const RhsMapper& rhs, const OutputMapper& output, Index m, Index n, Index k,
                    const GpuDevice& device) {
      const Index m_blocks = (m + 63) / 64;
      const Index n_blocks = (n + 63) / 64;
      const dim3 num_blocks(m_blocks, n_blocks, 1);
      const dim3 block_size(8, 8, 8);
      LAUNCH_GPU_KERNEL((EigenContractionKernel<Scalar, Index, LhsMapper, RhsMapper, OutputMapper>), num_blocks,
                        block_size, 0, device, lhs, rhs, output, m, n, k);
    }
  };

  template <typename Index, typename LhsMapper, typename RhsMapper, typename OutputMapper>
  struct LaunchKernels<float, float, Index, LhsMapper, RhsMapper, OutputMapper> {
    static void Run(const LhsMapper& lhs, const RhsMapper& rhs, const OutputMapper& output, Index m, Index n, Index k,
                    const GpuDevice& device) {
      if (m < 768 || n < 768) {
        const Index m_blocks = (m + 63) / 64;
        const Index n_blocks = (n + 63) / 64;
        const dim3 num_blocks(m_blocks, n_blocks, 1);
        const dim3 block_size(16, 16, 1);
        LAUNCH_GPU_KERNEL((EigenFloatContractionKernel16x16<Index, LhsMapper, RhsMapper, OutputMapper>), num_blocks,
                          block_size, 0, device, lhs, rhs, output, m, n, k);
      } else {
        const Index m_blocks = (m + 127) / 128;
        const Index n_blocks = (n + 63) / 64;
        const dim3 num_blocks(m_blocks, n_blocks, 1);
        const dim3 block_size(8, 32, 1);
        LAUNCH_GPU_KERNEL((EigenFloatContractionKernel<Index, LhsMapper, RhsMapper, OutputMapper>), num_blocks,
                          block_size, 0, device, lhs, rhs, output, m, n, k);
      }
    }
  };

  template <bool lhs_inner_dim_contiguous, bool rhs_inner_dim_contiguous, bool rhs_inner_dim_reordered, int Alignment>
  void evalTyped(Scalar* buffer) const {
    // columns in left side, rows in right side
    const Index k = this->m_k_size;
    EIGEN_UNUSED_VARIABLE(k)

    // rows in left side
    const Index m = this->m_i_size;

    // columns in right side
    const Index n = this->m_j_size;

    // zero out the result buffer (which must be of size at least m * n * sizeof(Scalar))
    this->m_device.fill(buffer, buffer + m * n, Scalar(0));

    typedef internal::TensorContractionInputMapper<LhsScalar, Index, internal::Lhs, LeftEvaluator, left_nocontract_t,
                                                   contract_t, 4, lhs_inner_dim_contiguous, false, Unaligned>
        LhsMapper;

    typedef internal::TensorContractionInputMapper<RhsScalar, Index, internal::Rhs, RightEvaluator, right_nocontract_t,
                                                   contract_t, 4, rhs_inner_dim_contiguous, rhs_inner_dim_reordered,
                                                   Unaligned>
        RhsMapper;

    typedef internal::blas_data_mapper<Scalar, Index, ColMajor> OutputMapper;

    // initialize data mappers
    LhsMapper lhs(this->m_leftImpl, this->m_left_nocontract_strides, this->m_i_strides,
                  this->m_left_contracting_strides, this->m_k_strides);

    RhsMapper rhs(this->m_rightImpl, this->m_right_nocontract_strides, this->m_j_strides,
                  this->m_right_contracting_strides, this->m_k_strides);

    OutputMapper output(buffer, m);

#if defined(EIGEN_USE_HIP)
    setGpuSharedMemConfig(hipSharedMemBankSizeEightByte);
#else
    setGpuSharedMemConfig(cudaSharedMemBankSizeEightByte);
#endif

    LaunchKernels<LhsScalar, RhsScalar, Index, LhsMapper, RhsMapper, OutputMapper>::Run(lhs, rhs, output, m, n, k,
                                                                                        this->m_device);
  }
};

}  // end namespace Eigen

#endif  // EIGEN_USE_GPU and EIGEN_GPUCC
#endif  // EIGEN_CXX11_TENSOR_TENSOR_CONTRACTION_GPU_H