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 * contributors may be used to endorse or promote products derived from
 * this software without specific prior written permission.
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 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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#pragma once

#include <cute/config.hpp>

#include <cute/util/type_traits.hpp>
#include <cute/algorithm/functional.hpp>

#include <cute/tensor.hpp>

#include <cute/atom/mma_atom.hpp>

/** The gemm algorithm takes four (or three) tensors and computes
 *   D = A * B + C
 * It dispatches based on the number of modes each tensor has:
 *
 * 1. `(V) x (V) => (V)`.
 *      The element-wise product of vectors. Dispatches to FMA or MMA.
 * 2. `(M) x (N) => (M,N)`.
 *      The outer product of vectors. Dispatches to [3] with new mode K=(1).
 * 3. `(M,K) x (N,K) => (M,N)`.
 *      The product of matrices. Dispatches to [5] with MMA vector-mode V.
 * 4. `(V,M) x (V,N) => (V,M,N)`.
 *      The batched outer product of vectors. Accounts for register reuse and dispatches to [1] for each (m,n).
 * 5. `(V,M,K) x (V,N,K) => (V,M,N)`.
 *      The batched product of matrices. Dispatches to [4] for each (k).
 */

namespace cute
{

//
// Three arguments to four
//

template <class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout>
CUTE_HOST_DEVICE
void
gemm(Tensor<TA, ALayout> const& A,
     Tensor<TB, BLayout> const& B,
     Tensor<TC, CLayout>      & C)
{
  return gemm(C, A, B, C);
}

template <class MMA,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout>
CUTE_HOST_DEVICE
void
gemm(MMA_Atom<MMA>       const& mma,
     Tensor<TA, ALayout> const& A,
     Tensor<TB, BLayout> const& B,
     Tensor<TC, CLayout>      & C)
{
  return gemm(mma, C, A, B, C);
}

//
// Accept mutable temporaries
//

template <class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout>
CUTE_HOST_DEVICE
void
gemm(Tensor<TA, ALayout> const& A,
     Tensor<TB, BLayout> const& B,
     Tensor<TC, CLayout>     && C)
{
  return gemm(C, A, B, C);
}

template <class TD, class DLayout,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout>
CUTE_HOST_DEVICE
void
gemm(Tensor<TD, DLayout>     && D,
     Tensor<TA, ALayout> const& A,
     Tensor<TB, BLayout> const& B,
     Tensor<TC, CLayout> const& C)
{
  return gemm(D, A, B, C);
}

template <class MMA,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout>
CUTE_HOST_DEVICE
void
gemm(MMA_Atom<MMA>       const& mma,
     Tensor<TA, ALayout> const& A,
     Tensor<TB, BLayout> const& B,
     Tensor<TC, CLayout>     && C)
{
  return gemm(mma, C, A, B, C);
}

template <class MMA,
          class TD, class DLayout,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout>
CUTE_HOST_DEVICE
void
gemm(MMA_Atom<MMA>       const& mma,
     Tensor<TD, DLayout>     && D,
     Tensor<TA, ALayout> const& A,
     Tensor<TB, BLayout> const& B,
     Tensor<TC, CLayout> const& C)
{
  return gemm(mma, D, A, B, C);
}

//
// Default MMA is UniversalFMA
//

template <class TD, class DLayout,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout>
CUTE_HOST_DEVICE
void
gemm(Tensor<TD, DLayout>      & D,
     Tensor<TA, ALayout> const& A,
     Tensor<TB, BLayout> const& B,
     Tensor<TC, CLayout> const& C)
{
  using MMA = MMA_Atom<UniversalFMA<typename Tensor<TD,DLayout>::value_type,
                                    typename Tensor<TA,ALayout>::value_type,
                                    typename Tensor<TB,BLayout>::value_type,
                                    typename Tensor<TC,CLayout>::value_type>>;

  return gemm(MMA{}, D, A, B, C);
}

//
// Thread-Local Register-Memory GEMMs
//

// Dispatch [1]: (V) x (V) => (V)
template <class MMA,
          class TD, class DLayout,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout,
          __CUTE_REQUIRES(DLayout::rank == 1 && is_rmem<TD>::value &&
                          ALayout::rank == 1 && is_rmem<TA>::value &&
                          BLayout::rank == 1 && is_rmem<TB>::value &&
                          CLayout::rank == 1 && is_rmem<TC>::value)>
CUTE_HOST_DEVICE
void
gemm(MMA_Atom<MMA>       const& mma,
     Tensor<TD, DLayout>      & D,  // (V) Logical data
     Tensor<TA, ALayout> const& A,  // (V) Logical data
     Tensor<TB, BLayout> const& B,  // (V) Logical data
     Tensor<TC, CLayout> const& C)  // (V) Logical data
{
  // No static assertions on (V), MMA checks compatibility
  mma.call(D, A, B, C);
}

// Dispatch [2]: (M) x (N) => (M,N)
template <class MMA,
          class TD, class DLayout,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout,
          __CUTE_REQUIRES(DLayout::rank == 2 && is_rmem<TD>::value &&
                          ALayout::rank == 1 && is_rmem<TA>::value &&
                          BLayout::rank == 1 && is_rmem<TB>::value &&
                          CLayout::rank == 2 && is_rmem<TC>::value)>
CUTE_HOST_DEVICE
void
gemm(MMA_Atom<MMA>       const& mma,
     Tensor<TD, DLayout>      & D,  // (M,N) Logical data
     Tensor<TA, ALayout> const& A,  // (M)   Logical data
     Tensor<TB, BLayout> const& B,  // (N)   Logical data
     Tensor<TC, CLayout> const& C)  // (M,N) Logical data
{
  CUTE_STATIC_ASSERT_V(size<0>(A) == size<0>(C));  // AM == CM
  CUTE_STATIC_ASSERT_V(size<0>(B) == size<1>(C));  // BN == CN
  CUTE_STATIC_ASSERT_V(size<0>(C) == size<0>(D) && size<1>(C) == size<1>(D));
  gemm(mma,
       D,                                                       // (M,N)
       make_tensor(A.data(), append<2>(A.layout())),            // (M,1)
       make_tensor(B.data(), append<2>(B.layout())),            // (N,1)
       C);                                                      // (M,N)
}

// Dispatch [3]: (M,K) x (N,K) => (M,N)
template <class MMA,
          class TD, class DLayout,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout,
          __CUTE_REQUIRES(DLayout::rank == 2 && is_rmem<TD>::value &&
                          ALayout::rank == 2 && is_rmem<TA>::value &&
                          BLayout::rank == 2 && is_rmem<TB>::value &&
                          CLayout::rank == 2 && is_rmem<TC>::value)>
CUTE_HOST_DEVICE
void
gemm(MMA_Atom<MMA>       const& mma,
     Tensor<TD, DLayout>      & D,  // (M,N) Logical data
     Tensor<TA, ALayout> const& A,  // (M,K) Logical data
     Tensor<TB, BLayout> const& B,  // (N,K) Logical data
     Tensor<TC, CLayout> const& C)  // (M,N) Logical data
{
  CUTE_STATIC_ASSERT_V(size<0>(A) == size<0>(C));  // AM == CM
  CUTE_STATIC_ASSERT_V(size<0>(B) == size<1>(C));  // BN == CN
  CUTE_STATIC_ASSERT_V(size<1>(A) == size<1>(B));  // AK == BK
  CUTE_STATIC_ASSERT_V(size<0>(C) == size<0>(D) && size<1>(C) == size<1>(D));

  // Assert this is a 1-value MMA
  CUTE_STATIC_ASSERT_V(size<1>(typename MMA_Atom<MMA>::LayoutC_TV{}) == Int<1>{});
  CUTE_STATIC_ASSERT_V(size<1>(typename MMA_Atom<MMA>::LayoutA_TV{}) == Int<1>{});
  CUTE_STATIC_ASSERT_V(size<1>(typename MMA_Atom<MMA>::LayoutB_TV{}) == Int<1>{});
  
  gemm(mma,
       make_tensor(D.data(), prepend<3>(D.layout())),      // (1,M,N)
       make_tensor(A.data(), prepend<3>(A.layout())),      // (1,M,K)
       make_tensor(B.data(), prepend<3>(B.layout())),      // (1,N,K)
       make_tensor(C.data(), prepend<3>(C.layout())));     // (1,M,N)
}

// Dispatch [4]: (V,M) x (V,N) => (V,M,N)
template <class MMA,
          class TD, class DLayout,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout,
          __CUTE_REQUIRES(DLayout::rank == 3 && is_rmem<TD>::value &&
                          ALayout::rank == 2 && is_rmem<TA>::value &&
                          BLayout::rank == 2 && is_rmem<TB>::value &&
                          CLayout::rank == 3 && is_rmem<TC>::value)>
CUTE_HOST_DEVICE
void
gemm(MMA_Atom<MMA>       const& mma,
     Tensor<TD, DLayout>      & D,  // (V,M,N) Logical data
     Tensor<TA, ALayout> const& A,  // (V,M)   Logical data
     Tensor<TB, BLayout> const& B,  // (V,N)   Logical data
     Tensor<TC, CLayout> const& C)  // (V,M,N) Logical data
{
  CUTE_STATIC_ASSERT_V(size<1>(A) == size<1>(C));  // AM == CM
  CUTE_STATIC_ASSERT_V(size<1>(B) == size<2>(C));  // BN == CN
  CUTE_STATIC_ASSERT_V(size<0>(C) == size<0>(D) && size<1>(C) == size<1>(D) && size<2>(C) == size<2>(D));
  auto M = size<1>(A);
  auto N = size<1>(B);
  // REGISTER .reuse OPTIMIZATIONS
  // 64-bit traversal specialization -- serpentine path
  if constexpr (decltype(size<0>(A))::value * sizeof(typename TA::value_type) == 8 &&
                decltype(size<0>(B))::value * sizeof(typename TB::value_type) == 8)
  {
#if 1 // NOTE: Row- vs Col- major could depend on the C-matrix order... (which we can test)
    // Row-major serpentine iteration
    CUTE_UNROLL
    for (int m = 0; m < M; ++m) {
      CUTE_UNROLL
      for (int n = 0; n < N; ++n) {
        int ns = (m & 1) ? N-1-n : n;  // Serpentine coordinate
        gemm(mma, D(_,m,ns), A(_,m), B(_,ns), C(_,m,ns));
      }
    }
#else
    // Col-major serpentine iteration
    CUTE_UNROLL
    for (int n = 0; n < N; ++n) {
      CUTE_UNROLL
      for (int m = 0; m < M; ++m) {
        int ms = (n & 1) ? M-1-m : m;  // Serpentine coordinate
        gemm(mma, D(_,ms,n), A(_,ms), B(_,n), C(_,ms,n));
      }
    }
#endif
  } else
  // 32-bit traversal specialization -- kinked serpentine path
  if constexpr (decltype(size<0>(A))::value * sizeof(typename TA::value_type) == 4 &&
                decltype(size<0>(B))::value * sizeof(typename TB::value_type) == 4)
  {
#if 1  // NOTE: Row- vs Col- major could depend on the C-matrix order... (which we can test)
    // Row-major kinked serpentine iteration
    CUTE_UNROLL
    for (int m = 0; m < M; m += 2) {
      CUTE_UNROLL
      for (int n = 0; n < N; ++n) {
        int ns = (m & 2) ? N-1-n : n;
        gemm(mma, D(_,m+0,ns), A(_,m+0), B(_,ns), C(_,m+0,ns));

        if (m+1 < M) {
          gemm(mma, D(_,m+1,ns), A(_,m+1), B(_,ns), C(_,m+1,ns));
        }
      }
    }
#else
    // Col-major kinked serpentine iteration
    CUTE_UNROLL
    for (int n = 0; n < N; n += 2) {
      CUTE_UNROLL
      for (int m = 0; m < M; ++m) {
        // Kinked serpentine traversal for maximum register reuse
        int ms = (n & 2) ? M-1-m : m;
        gemm(mma, D(_,ms,n+0), A(_,ms), B(_,n+0), C(_,ms,n+0));

        if (n+1 < N) {
          gemm(mma, D(_,ms,n+1), A(_,ms), B(_,n+1), C(_,ms,n+1));
        }
      }
    }
#endif
  } else
  // 64-bit + 32-bit traversal order -- keep A (64-bit) in the outer loop and serpentine B
  if constexpr (decltype(size<0>(A))::value * sizeof(typename TA::value_type) == 8 &&
                decltype(size<0>(B))::value * sizeof(typename TB::value_type) == 4) {
    // Row-major serpentine iteration
    CUTE_UNROLL
    for (int m = 0; m < M; ++m) {
      CUTE_UNROLL
      for (int n = 0; n < N; ++n) {
        int ns = (m & 1) ? N-1-n : n;  // Serpentine coordinate
        gemm(mma, D(_,m,ns), A(_,m), B(_,ns), C(_,m,ns));
      }
    }
  } else
  // 32-bit + 64-bit traversal order -- keep B (64-bit) in the outer loop and serpentine A
  if constexpr (decltype(size<0>(A))::value * sizeof(typename TA::value_type) == 4 &&
                decltype(size<0>(B))::value * sizeof(typename TB::value_type) == 8) {
    // Col-major serpentine iteration
    CUTE_UNROLL
    for (int n = 0; n < N; ++n) {
      CUTE_UNROLL
      for (int m = 0; m < M; ++m) {
        int ms = (n & 1) ? M-1-m : m;  // Serpentine coordinate
        gemm(mma, D(_,ms,n), A(_,ms), B(_,n), C(_,ms,n));
      }
    }
  } else
  // Fallback to serpentine loop
  {
    // Col-major serpentine iteration
    CUTE_UNROLL
    for (int n = 0; n < N; ++n) {
      CUTE_UNROLL
      for (int m = 0; m < M; ++m) {
        int ms = (n & 1) ? M-1-m : m;  // Serpentine coordinate
        gemm(mma, D(_,ms,n), A(_,ms), B(_,n), C(_,ms,n));
      }
    }
  }
}

// Dispatch [5]: (V,M,K) x (V,N,K) => (V,M,N)
template <class MMA,
          class TD, class DLayout,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout,
          __CUTE_REQUIRES(DLayout::rank == 3 && is_rmem<TD>::value &&
                          ALayout::rank == 3 && is_rmem<TA>::value &&
                          BLayout::rank == 3 && is_rmem<TB>::value &&
                          CLayout::rank == 3 && is_rmem<TC>::value)>
CUTE_HOST_DEVICE
void
gemm(MMA_Atom<MMA>       const& mma,
     Tensor<TD, DLayout>      & D,  // (V,M,N) Logical data
     Tensor<TA, ALayout> const& A,  // (V,M,K) Logical data
     Tensor<TB, BLayout> const& B,  // (V,N,K) Logical data
     Tensor<TC, CLayout> const& C)  // (V,M,N) Logical data
{
  CUTE_STATIC_ASSERT_V(size<1>(A) == size<1>(C));  // AM == CM
  CUTE_STATIC_ASSERT_V(size<1>(B) == size<2>(C));  // BN == CN
  CUTE_STATIC_ASSERT_V(size<2>(A) == size<2>(B));  // AK == BK
  CUTE_STATIC_ASSERT_V(size<0>(C) == size<0>(D) && size<1>(C) == size<1>(D) && size<2>(C) == size<2>(D));
  auto K = size<2>(A);

  CUTE_UNROLL
  for (int k = 0; k < K; ++k) {
    gemm(mma, D, A(_,_,k), B(_,_,k), C);
  }
}

//
// Thread-Local Shared-Memory GEMMs
//

// Dispatch [1]: (V) x (V) => (V)
// Dispatch [2]: (M) x (N) => (M,N)
// Dispatch [3]: (M,K) x (N,K) => (M,N)
// Dispatch [4]: (V,M) x (V,N) => (V,M,N)
// Dispatch [5]: (V,M,K) x (V,N,K) => (V,M,N)
// Dispatch [3]: (M,K) x (N,K) => (M,N)
template <class MMA,
          class TD, class DLayout,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout,
          __CUTE_REQUIRES(DLayout::rank == 2 && is_rmem<TD>::value &&
                          ALayout::rank == 2 && is_smem<TA>::value &&
                          BLayout::rank == 2 && is_smem<TB>::value &&
                          CLayout::rank == 2 && is_rmem<TC>::value)>
CUTE_HOST_DEVICE
void
gemm(MMA_Atom<MMA>       const& mma,
     Tensor<TD, DLayout>      & D,  // (M,N) Logical data
     Tensor<TA, ALayout> const& A,  // (M,K) Logical data
     Tensor<TB, BLayout> const& B,  // (N,K) Logical data
     Tensor<TC, CLayout> const& C)  // (M,N) Logical data
{
  CUTE_STATIC_ASSERT_V(size<0>(A) == size<0>(C));  // AM == CM
  CUTE_STATIC_ASSERT_V(size<0>(B) == size<1>(C));  // BN == CN
  CUTE_STATIC_ASSERT_V(size<1>(A) == size<1>(B));  // AK == BK
  CUTE_STATIC_ASSERT_V(size<0>(C) == size<0>(D) && size<1>(C) == size<1>(D));

  // Assert this is a 1-value MMA
  CUTE_STATIC_ASSERT_V(size<1>(typename MMA_Atom<MMA>::LayoutC_TV{}) == Int<1>{});
  CUTE_STATIC_ASSERT_V(size<1>(typename MMA_Atom<MMA>::LayoutA_TV{}) == Int<1>{});
  CUTE_STATIC_ASSERT_V(size<1>(typename MMA_Atom<MMA>::LayoutB_TV{}) == Int<1>{});
  gemm(mma,
       make_tensor(D.data(), prepend<3>(D.layout())),      // (1,M,N)
       make_tensor(A.data(), prepend<3>(A.layout())),      // (1,M,K)
       make_tensor(B.data(), prepend<3>(B.layout())),      // (1,N,K)
       make_tensor(C.data(), prepend<3>(C.layout())));     // (1,M,N)
}

// Dispatch [5]: (V,M,K) x (V,N,K) => (V,M,N)
template <class MMA,
          class TD, class DLayout,
          class TA, class ALayout,
          class TB, class BLayout,
          class TC, class CLayout,
          __CUTE_REQUIRES(DLayout::rank == 3 && is_rmem<TD>::value &&
                          ALayout::rank == 3 && is_smem<TA>::value &&
                          BLayout::rank == 3 && is_smem<TB>::value &&
                          CLayout::rank == 3 && is_rmem<TC>::value)>
CUTE_HOST_DEVICE
void
gemm(MMA_Atom<MMA>       const& mma,
     Tensor<TD, DLayout>      & D,  // (V,M,N) Logical data
     Tensor<TA, ALayout> const& A,  // (V,M,K) Logical data
     Tensor<TB, BLayout> const& B,  // (V,N,K) Logical data
     Tensor<TC, CLayout> const& C)  // (V,M,N) Logical data
{
  CUTE_STATIC_ASSERT_V(size<1>(A) == size<1>(C));  // AM == CM
  CUTE_STATIC_ASSERT_V(size<1>(B) == size<2>(C));  // BN == CN
  CUTE_STATIC_ASSERT_V(size<2>(A) == size<2>(B));  // AK == BK
  CUTE_STATIC_ASSERT_V(size<0>(C) == size<0>(D) && size<1>(C) == size<1>(D) && size<2>(C) == size<2>(D));

  auto rA = MMA_Atom<MMA>::make_fragment_A(A);
  auto rB = MMA_Atom<MMA>::make_fragment_B(B);

  auto K = size<2>(A);

  CUTE_UNROLL
  for (int k = 0; k < K; ++k)
  {
    copy(A(_,_,k), rA(_,_,k));
    copy(B(_,_,k), rB(_,_,k));
    // Thread-level register gemm for k
    gemm(mma, D, rA(_,_,k), rB(_,_,k), C);
  }
}

//
// Collective Shared-Memory GEMMs
//

template <class... Args,
          class Alpha, class TA, class ALayout, class TB, class BLayout,
          class Beta,  class TC, class CLayout,
          class ALoadTransformOp, class BLoadTransformOp,
          __CUTE_REQUIRES(ALayout::rank == 2 && is_smem<TA>::value &&
                          BLayout::rank == 2 && is_smem<TB>::value &&
                          CLayout::rank == 2 && is_smem<TC>::value)>
CUTE_HOST_DEVICE
void
gemm(ThrMMA<Args...> const& thr_mma,
     Alpha const& alpha,
     Tensor<TA, ALayout> sA,
     Tensor<TB, BLayout> sB,
     Beta  const& beta,
     Tensor<TC, CLayout> sC,
     ALoadTransformOp const& sA_load_op /* transforms A values before used in GEMM */,
     BLoadTransformOp const& sB_load_op /* transforms B values before used in GEMM */)
{
  CUTE_STATIC_ASSERT_V(size<0>(sA) == size<0>(sC));  // AM == CM
  CUTE_STATIC_ASSERT_V(size<0>(sB) == size<1>(sC));  // BN == CN
  CUTE_STATIC_ASSERT_V(size<1>(sA) == size<1>(sB));  // AK == BK

  using TypeA = typename TA::value_type;
  using TypeB = typename TB::value_type;
  using TypeC = typename TC::value_type;

  static_assert(is_same_v<decay_t<invoke_result_t<ALoadTransformOp, TypeA>>, TypeA>,
    "ALoadTransformOp functor must accept and return value of type TA::value_type");
  static_assert(is_same_v<decay_t<invoke_result_t<BLoadTransformOp, TypeB>>, TypeB>,
    "BLoadTransformOp functor must accept and return value of type TB::value_type");

  // Original, static size of the problem
  auto M = size<0>(sC);
  auto N = size<1>(sC);
  auto K = size<1>(sA);

  // Block size of the compute tile
  auto BLK_M = tile_size<0>(thr_mma);
  auto BLK_N = tile_size<1>(thr_mma);
  auto BLK_K = tile_size<2>(thr_mma);

  // Compute the "residues"
  auto m_residue = M - BLK_M * (ceil_div(M, BLK_M) - Int<1>{});  //  (0,BLK_M]
  auto n_residue = N - BLK_N * (ceil_div(N, BLK_N) - Int<1>{});  //  (0,BLK_N]
  auto k_residue = K - BLK_K * (ceil_div(K, BLK_K)           );  // (-BLK_K,0]

  // Shift the origin so k_residue is zeroth tile
  sA.data() = &sA(0,k_residue);
  sB.data() = &sB(0,k_residue);

#if 0
  if (thread0()) {
    printf("%d in BLK_M (%d)\n", int(m_residue), int(BLK_M));
    printf("%d in BLK_N (%d)\n", int(n_residue), int(BLK_N));
    printf("%d in BLK_K (%d)\n", int(k_residue), int(BLK_K));
  }
#endif

  //
  // MMA Partitioning
  //

  // Round the layout extents up to BLK_X
  Tensor rounded_sA = sA.compose(make_shape(ceil_div(M, BLK_M) * BLK_M, ceil_div(K, BLK_K) * BLK_K));
  Tensor rounded_sB = sB.compose(make_shape(ceil_div(N, BLK_N) * BLK_N, ceil_div(K, BLK_K) * BLK_K));
  Tensor rounded_sC = sC.compose(make_shape(ceil_div(M, BLK_M) * BLK_M, ceil_div(N, BLK_N) * BLK_N));

#if 0
  if (thread0()) {
    print(rounded_sA.layout()); print("\n");
    print(rounded_sB.layout()); print("\n");
    print(rounded_sC.layout()); print("\n");
  }
#endif

  // Partition the sA and sB tiles across the threads for the MMA
  Tensor tCsA = thr_mma.partition_A(rounded_sA);                    // (MMA,MMA_M,MMA_K)
  Tensor tCsB = thr_mma.partition_B(rounded_sB);                    // (MMA,MMA_N,MMA_K)
  Tensor tCsC = thr_mma.partition_C(rounded_sC);                    // (MMA,MMA_M,MMA_N)
  // Create register tensors for the MMA to operate on
  Tensor tCrA = thr_mma.make_fragment_A(tCsA);                      // (MMA,MMA_M,MMA_K)
  Tensor tCrB = thr_mma.make_fragment_B(tCsB);                      // (MMA,MMA_N,MMA_K)
  Tensor tCrC = thr_mma.make_fragment_C(tCsC);                      // (MMA,MMA_M,MMA_N)

#if 0
  if (thread0()) {
    print(tCsA.layout()); print("\n");
    print(tCsB.layout()); print("\n");
    print(tCsC.layout()); print("\n");
    print(tCrA.layout()); print("\n");
    print(tCrB.layout()); print("\n");
    print(tCrC.layout()); print("\n");
  }
#endif

  //
  // PREDICATION
  //

  // Allocate the preds for only the MMA-mode of tCsA and tCsB
  Tensor tCpA = make_tensor<bool>(size<0>(tCsA));
  Tensor tCpB = make_tensor<bool>(size<0>(tCsB));

  // Create coordinate tensors on a single compute block for predication
  Tensor cA = make_identity_tensor(make_shape(BLK_M, BLK_K));        // (BLK_M,BLK_K) -> (blk_m,blk_k)
  Tensor cB = make_identity_tensor(make_shape(BLK_N, BLK_K));        // (BLK_M,BLK_K) -> (blk_n,blk_k)

  // Repeat partitioning with thr_mma
  Tensor tCcA = thr_mma.partition_A(cA);                             // (MMA,1,1) -> (blk_m,blk_k)
  Tensor tCcB = thr_mma.partition_B(cB);                             // (MMA,1,1) -> (blk_n,blk_k)

  // Populate the m and n predicates
  CUTE_UNROLL
  for (int i = 0; i < size(tCpA); ++i) {
    tCpA(i) = elem_less(get<0>(tCcA(i)), m_residue);
  }
  CUTE_UNROLL
  for (int i = 0; i < size(tCpB); ++i) {
    tCpB(i) = elem_less(get<0>(tCcB(i)), n_residue);
  }

#if 0
  printf("Thr %d: A(%d,%d):%d  B(%d,%d):%d\n",
         threadIdx.x,
         int(get<0>(tCcA(0))), int(get<1>(tCcA(0))), int(tCpA(0)),
         int(get<0>(tCcB(0))), int(get<1>(tCcB(0))), int(tCpB(0)));
#endif

  //
  // PREFETCH k_block = 0 (with k-predication)
  //

  CUTE_UNROLL
  for (int i = 0; i < size<0>(tCsA); ++i) {                // Copy MMA_I
    if (k_residue == 0 || get<1>(tCcA(i)) >= -k_residue) { // k_block = 0, predicated on k
      CUTE_UNROLL
      for (int m = 0; m < size<1>(tCsA); ++m) {            // Copy MMA_M, predicated on m
        tCrA(i,m,0) = (m_residue == BLK_M || m < size<1>(tCsA)-1 || tCpA(i)) ? sA_load_op(tCsA(i,m,0)) : TypeA{};
      }
    }
  }

  CUTE_UNROLL
  for (int i = 0; i < size<0>(tCsB); ++i) {                // Copy MMA_I
    if (k_residue == 0 || get<1>(tCcB(i)) >= -k_residue) { // k_block = 0, predicated on k
      CUTE_UNROLL
      for (int n = 0; n < size<1>(tCsB); ++n) {            // Copy MMA_N, predicated on n
        tCrB(i,n,0) = (n_residue == BLK_N || n < size<1>(tCsB)-1 || tCpB(i)) ? sB_load_op(tCsB(i,n,0)) : TypeB{};
      }
    }
  }
  //
  // MAINLOOP
  //

  // Clear accumulators
  clear(tCrC);

  constexpr int K_BLOCK_MAX = size<2>(tCrA);

  CUTE_UNROLL
  for (int k_block = 0; k_block < K_BLOCK_MAX; ++k_block)
  {
    // static-if load the next k_block. No k-predication required on these loads.
    if (k_block < K_BLOCK_MAX-1)
    {
      // Load the next k_block
      int k_next = k_block + 1;

      CUTE_UNROLL
      for (int m = 0; m < size<1>(tCsA); ++m) {            // Copy MMA_M
        CUTE_UNROLL
        for (int i = 0; i < size<0>(tCsA); ++i) {          // Copy_if MMA_I predicated on m
          tCrA(i,m,k_next) = (m_residue == BLK_M || m < size<1>(tCsA)-1 || tCpA(i)) ? sA_load_op(tCsA(i,m,k_next)) : TypeA{};
        }
      }

      CUTE_UNROLL
      for (int n = 0; n < size<1>(tCsB); ++n) {            // Copy MMA_N
        CUTE_UNROLL
        for (int i = 0; i < size<0>(tCsB); ++i) {          // Copy MMA_I predicated on n
          tCrB(i,n,k_next) = (n_residue == BLK_N || n < size<1>(tCsB)-1 || tCpB(i)) ? sB_load_op(tCsB(i,n,k_next)) : TypeB{};
        }
      }
    }

    // GEMM on k_block in registers
    gemm(thr_mma, tCrA(_,_,k_block), tCrB(_,_,k_block), tCrC);
  }

  //
  // Epilogue
  //

  Tensor cC   = make_identity_tensor(make_shape(BLK_M, BLK_N));      // (BLK_M,BLK_N) -> (blk_m,blk_n)
  Tensor tCcC = thr_mma.partition_C(cC);                             // (MMA, 1, 1)   -> (blk_m,blk_n)

  const bool isBetaZero = (beta == Beta{});

  // Custom axpby_if for now
  CUTE_UNROLL
  for (int m = 0; m < size<1>(tCsC); ++m)
  {
    CUTE_UNROLL
    for (int n = 0; n < size<2>(tCsC); ++n)
    {
      CUTE_UNROLL
      for (int i = 0; i < size<0>(tCsC); ++i)
      {
        if ((m_residue == BLK_M || m < size<1>(tCrC)-1 || get<0>(tCcC(i)) < m_residue) &&
            (n_residue == BLK_N || n < size<2>(tCrC)-1 || get<1>(tCcC(i)) < n_residue))
        {
          tCsC(i,m,n) = isBetaZero ? alpha * tCrC(i,m,n) : alpha * tCrC(i,m,n) + beta * tCsC(i,m,n);
        }
      }
    }
  }
}

template <class... Args,
          class Alpha, class TA, class ALayout, class TB, class BLayout,
          class Beta,  class TC, class CLayout,
          __CUTE_REQUIRES(ALayout::rank == 2 && is_smem<TA>::value &&
                          BLayout::rank == 2 && is_smem<TB>::value &&
                          CLayout::rank == 2 && is_smem<TC>::value)>
CUTE_HOST_DEVICE
void
gemm(ThrMMA<Args...> const& thr_mma,
     Alpha const& alpha,
     Tensor<TA, ALayout> sA,
     Tensor<TB, BLayout> sB,
     Beta  const& beta,
     Tensor<TC, CLayout> sC)
{
  gemm(thr_mma, alpha, sA, sB, beta, sC, identity() /* sA_load_op */, identity() /* sB_load_op */);
}

} // end namespace cute
