tensor_cpu-inl.h

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#ifndef MSHADOW_TENSOR_CPU_INL_H_
#define MSHADOW_TENSOR_CPU_INL_H_
#include <cstring>
#include <functional>
#include <utility>
#include <vector>
#include "./base.h"
#include "./tensor.h"
#include "./packet-inl.h"
#include "./dot_engine-inl.h"

namespace mshadow {
template<>
inline void InitTensorEngine<cpu>(int dev_id) {
}
template<>
inline void ShutdownTensorEngine<cpu>(void) {
}

template<>
inline void SetDevice<cpu>(int devid) {
}
template<>
inline Stream<cpu> *NewStream<cpu>(bool create_blas_handle,
                                   bool create_dnn_handle,
                                   int dev_id) {
  return new Stream<cpu>();
}
template<>
inline void DeleteStream<cpu>(Stream<cpu> *stream) {
  delete stream;
}

template<int ndim>
inline std::ostream &operator<<(std::ostream &os, const Shape<ndim> &shape) { // NOLINT(*)
  os << '(';
  for (int i = 0; i < ndim; ++i) {
    if (i != 0) os << ',';
    os << shape[i];
  }
  // python style tuple
  if (ndim == 1) os << ',';
  os << ')';
  return os;
}

template<typename xpu>
inline void *AllocHost_(size_t size);
template<typename xpu>
inline void FreeHost_(void * dptr);

#ifdef __CUDACC__
template<>
inline void *AllocHost_<gpu>(size_t size) {
  void *dptr;
  MSHADOW_CUDA_CALL(cudaMallocHost(&dptr, size, cudaHostAllocPortable));
  return dptr;
}
template<>
inline void FreeHost_<gpu>(void *dptr) {
  MSHADOW_CUDA_CALL(cudaFreeHost(dptr));
}
#endif

template<>
inline void *AllocHost_<cpu>(size_t size) {
  size_t pitch;
  return packet::AlignedMallocPitch(&pitch, size, 1);
}
template<>
inline void FreeHost_<cpu>(void *dptr) {
  packet::AlignedFree(dptr);
}

template<typename xpu, int dim, typename DType>
inline void AllocHost(Tensor<cpu, dim, DType> *obj) {
  obj->stride_ = obj->size(dim - 1);
  CHECK_EQ(obj->CheckContiguous(), true) << "AllocHost";
  void *dptr = AllocHost_<xpu>(obj->MSize() * sizeof(DType));
  obj->dptr_ = reinterpret_cast<DType*>(dptr);
}
template<typename xpu, int dim, typename DType>
inline void FreeHost(Tensor<cpu, dim, DType> *obj) {
  if (obj->dptr_ == NULL) {
    LOG(FATAL) << "FreeHost:: double free";
  }
  FreeHost_<xpu>(obj->dptr_);
  obj->dptr_ = NULL;
}

template<int dim, typename DType>
inline void AllocSpace(Tensor<cpu, dim, DType> *obj, bool pad) {
  size_t pitch;
  void *dptr;
  if (pad) {
    dptr = packet::AlignedMallocPitch
        (&pitch, obj->size(dim - 1) * sizeof(DType), obj->shape_.FlatTo2D()[0]);
    obj->stride_ = static_cast<index_t>(pitch / sizeof(DType));
  } else {
    obj->stride_ = obj->size(dim - 1);
    dptr = packet::AlignedMallocPitch
        (&pitch, obj->shape_.Size() * sizeof(DType), 1);
  }
  obj->dptr_ = reinterpret_cast<DType*>(dptr);
}
template<typename Device, typename DType, int dim>
inline Tensor<Device, dim, DType>
NewTensor(const Shape<dim> &shape, DType initv, bool pad, Stream<Device> *stream_) {
  Tensor<Device, dim, DType> obj(shape);
  obj.stream_ = stream_;
  AllocSpace(&obj, pad);
  MapExp<sv::saveto>(&obj, expr::ScalarExp<DType>(initv));
  return obj;
}
template<int dim, typename DType>
inline void FreeSpace(Tensor<cpu, dim, DType> *obj) {
  packet::AlignedFree(obj->dptr_);
  obj->dptr_ = NULL;
}
template<int dim, typename DType>
inline void Copy(Tensor<cpu, dim, DType> _dst,
                 const Tensor<cpu, dim, DType> &_src,
                 Stream<cpu> *stream) {
  CHECK_EQ(_dst.shape_, _src.shape_)
      << "Copy:shape mismatch:" << _dst.shape_ << " vs " << _src.shape_;
  if (_dst.CheckContiguous() && _src.CheckContiguous()) {
    memcpy(_dst.dptr_, _src.dptr_, sizeof(DType) * _dst.shape_.Size());
  } else {
    Tensor<cpu, 2, DType> dst = _dst.FlatTo2D();
    Tensor<cpu, 2, DType> src = _src.FlatTo2D();
    for (index_t y = 0; y < dst.size(0); ++y) {
      memcpy(dst[y].dptr_, src[y].dptr_, sizeof(DType) * dst.size(1));
    }
  }
}

template<typename Saver, typename R, int dim,
         typename DType, typename E>
inline void MapPlan(TRValue<R, cpu, dim, DType> *dst,
                    const expr::Plan<E, DType> &plan) {
  Shape<2> shape = expr::ShapeCheck<dim, R>::Check(dst->self()).FlatTo2D();
  expr::Plan<R, DType> dplan = expr::MakePlan(dst->self());
#ifndef __CUDACC__
  #pragma omp parallel for
#endif
  // temp remove openmp, as default setting throttles CPU
  for (openmp_index_t y = 0; y < shape[0]; ++y) {
    for (index_t x = 0; x < shape[1]; ++x) {
      // trust your compiler! -_- they will optimize it
      Saver::template Save<DType>(dplan.REval(y, x), plan.Eval(y, x));
    }
  }
}
// code to handle SSE optimization
template<bool pass_check, typename Saver,
         typename R, int dim,
         typename DType, typename E, int etype>
struct MapExpCPUEngine {
  inline static void Map(TRValue<R, cpu, dim, DType> *dst,
                         const expr::Exp<E, DType, etype> &exp) {
    MapPlan<Saver>(dst, MakePlan(exp.self()));
  }
};

template<typename SV, int dim, typename DType, typename E, int etype>
struct MapExpCPUEngine<true, SV, Tensor<cpu, dim, DType>,
                       dim, DType, E, etype> {
  inline static void Map(Tensor<cpu, dim, DType> *dst,
                         const expr::Exp<E, DType, etype> &exp) {
    if (expr::PacketAlignCheck<dim, E, MSHADOW_DEFAULT_PACKET>::Check(exp.self()) &&
        expr::PacketAlignCheck<dim, Tensor<cpu, dim, DType>, MSHADOW_DEFAULT_PACKET>::Check(*dst)) {
      expr::MapPacketPlan<SV>(dst->self(),
                              expr::MakePacketPlan<MSHADOW_DEFAULT_PACKET>(exp.self()));
    } else {
      MapPlan<SV>(dst, MakePlan(exp.self()));
    }
  }
};


template<typename Saver, typename R, int dim,
         typename DType, typename E, int etype>
inline void MapExp(TRValue<R, cpu, dim, DType> *dst,
                   const expr::Exp<E, DType, etype> &exp) {
  expr::TypeCheckPass<expr::TypeCheck<cpu, dim, DType, E>::kMapPass>
      ::Error_All_Tensor_in_Exp_Must_Have_Same_Type();
  Shape<dim> eshape = expr::ShapeCheck<dim, E>::Check(exp.self());
  Shape<dim> dshape = expr::ShapeCheck<dim, R>::Check(dst->self());
  CHECK(eshape[0] == 0 || eshape == dshape)
      << "Assignment: Shape of Tensors are not consistent with target, "
      << "eshape: " << eshape << " dshape:" << dshape;
  MapExpCPUEngine<expr::PacketCheck<E, MSHADOW_DEFAULT_PACKET>::kPass,
                  Saver, R, dim, DType, E, etype>
  ::Map(dst->ptrself(), exp);
}

template<typename Saver, typename Reducer,
         typename R, typename DType, typename E, int etype>
inline void MapReduceKeepLowest(TRValue<R, cpu, 1, DType> *dst,
                                const expr::Exp<E, DType, etype> &exp,
                                DType scale) {
  expr::TypeCheckPass<expr::TypeCheck<cpu, 1, DType, E>::kRedPass>
      ::Error_TypeCheck_Not_Pass_For_Reduce_Exp();
  Shape<2> eshape = expr::ShapeCheck<expr::ExpInfo<E>::kDim, E>
      ::Check(exp.self()).FlatTo2D();
  Shape<1> dshape = expr::ShapeCheck<1, R>::Check(dst->self());
  CHECK_EQ(eshape[1], dshape[0]) << "MapReduceKeepLowest::reduction dimension do not match";
  CHECK_NE(eshape[0], 0U) << "can not reduce over empty tensor";
  // execution
  expr::Plan<R, DType> dplan = MakePlan(dst->self());
  expr::Plan<E, DType> splan = MakePlan(exp.self());
#ifndef __CUDACC__
  #pragma omp parallel for
#endif
  for (openmp_index_t x = 0; x < eshape[1]; ++x) {
    DType res = splan.Eval(0, x);
    for (index_t y = 1; y < eshape[0]; ++y) {
      Reducer::Reduce(res, splan.Eval(y, x));
    }
    Saver::template Save<DType>(dplan.REval(0, x), res * scale);
  }
}

template<typename Saver, typename Reducer, int dimkeep,
         typename R, typename DType, typename E, int etype>
inline void MapReduceKeepHighDim(TRValue<R, cpu, 1, DType> *dst,
                                 const expr::Exp<E, DType, etype> &exp,
                                 DType scale) {
  expr::TypeCheckPass<expr::TypeCheck<cpu, dimkeep, DType, E>::kRedPass>
      ::Error_TypeCheck_Not_Pass_For_Reduce_Exp();
  typedef Shape<expr::ExpInfo<E>::kDim> EShape;
  EShape eshape = expr::ShapeCheck<expr::ExpInfo<E>::kDim, E>
      ::Check(exp.self());
  Shape<1> dshape = expr::ShapeCheck<1, R>::Check(dst->self());
  CHECK_EQ(eshape[dimkeep], dshape[0])
    << "MapReduceKeepHighDim::reduction dimension do not match";
  // use equvalent form
  Shape<4> pshape = Shape4(eshape.ProdShape(0, dimkeep),
                           eshape[dimkeep],
                           eshape.ProdShape(dimkeep + 1, EShape::kSubdim),
                           eshape[EShape::kSubdim]);
  // execution
  expr::Plan<R, DType> dplan = MakePlan(dst->self());
  expr::Plan<E, DType> splan = MakePlan(exp.self());
#ifndef __CUDACC__
  #pragma omp parallel for
#endif
  for (openmp_index_t c = 0; c < pshape[1]; ++c) {
    DType res; Reducer::SetInitValue(res);
    for (index_t n = 0; n < pshape[0]; ++n) {
      DType tres; Reducer::SetInitValue(tres);
      for (index_t y = 0; y < pshape[2]; ++y) {
        for (index_t x = 0; x < pshape[3]; ++x) {
          Reducer::Reduce(tres,
                          splan.Eval((n * pshape[1] + c) * pshape[2] + y, x));
        }
      }
      Reducer::Reduce(res, tres);
    }
    Saver::template Save<DType>(dplan.REval(0, c), DType(res * scale));
  }
}

template<typename DType>
inline void Softmax(Tensor<cpu, 1, DType> dst,
                    const Tensor<cpu, 1, DType> &energy) {
  DType mmax = energy[0];
  for (index_t x = 1; x < dst.size(0); ++x) {
    if (mmax < energy[x]) mmax = energy[x];
  }
  DType sum = DType(0.0f);
  for (index_t x = 0; x < dst.size(0); ++x) {
    dst[x] = std::exp(energy[x] - mmax);
    sum += dst[x];
  }
  for (index_t x = 0; x < dst.size(0); ++x) {
    dst[x] /= sum;
  }
}

template<typename DType>
inline void SoftmaxGrad(Tensor<cpu, 2, DType> dst,
                        const Tensor<cpu, 2, DType> &src,
                        const Tensor<cpu, 1, DType> &label) {
#pragma omp parallel for
  for (openmp_index_t y = 0; y < dst.size(0); ++y) {
    const index_t k = static_cast<int>(label[y]);
    for (index_t x = 0; x < dst.size(1); ++x) {
      if (x == k) {
        dst[y][k] = src[y][k] - 1.0f;
      } else {
        dst[y][x] = src[y][x];
      }
    }
  }
}

template<typename DType>
inline void SmoothSoftmaxGrad(Tensor<cpu, 2, DType> dst,
                        const Tensor<cpu, 2, DType> &src,
                        const Tensor<cpu, 1, DType> &label,
                        const float alpha) {
  const float smooth_grad = (alpha / (dst.size(1) - 1));
#pragma omp parallel for
  for (openmp_index_t y = 0; y < dst.size(0); ++y) {
    const index_t k = static_cast<int>(label[y]);
    for (index_t x = 0; x < dst.size(1); ++x) {
      if (x == k) {
        dst[y][k] = src[y][k] - 1.0f + alpha;
      } else {
        dst[y][x] = src[y][x] - smooth_grad;
      }
    }
  }
}


template<typename DType>
inline void SoftmaxGrad(Tensor<cpu, 2, DType> dst,
                        const Tensor<cpu, 2, DType> &src,
                        const Tensor<cpu, 1, DType> &label,
                        const DType &ignore_label) {
#pragma omp parallel for
  for (openmp_index_t y = 0; y < dst.size(0); ++y) {
    const int k = static_cast<int>(label[y]);
    for (int x = 0; x < static_cast<int>(dst.size(1)); ++x) {
      if (static_cast<int>(ignore_label) == k) {
        dst[y][x] = 0.0f;
      } else {
        if (x == k) {
          dst[y][k] = src[y][k] - 1.0f;
        } else {
          dst[y][x] = src[y][x];
        }
      }
    }
  }
}

template<typename DType>
inline void SmoothSoftmaxGrad(Tensor<cpu, 2, DType> dst,
                              const Tensor<cpu, 2, DType> &src,
                              const Tensor<cpu, 1, DType> &label,
                              const DType &ignore_label,
                              const float alpha) {
  const float smooth_grad = (alpha / (dst.size(1) - 1));
#pragma omp parallel for
  for (openmp_index_t y = 0; y < dst.size(0); ++y) {
    const int k = static_cast<int>(label[y]);
    for (int x = 0; x < static_cast<int>(dst.size(1)); ++x) {
      if (static_cast<int>(ignore_label) == k) {
        dst[y][x] = 0.0f;
      } else {
        if (x == k) {
          dst[y][k] = src[y][k] - 1.0f + alpha;
        } else {
          dst[y][x] = src[y][x] - smooth_grad;
        }
      }
    }
  }
}

template<typename DType>
inline void SoftmaxGrad(Tensor<cpu, 3, DType> dst,
                        const Tensor<cpu, 3, DType> &src,
                        const Tensor<cpu, 2, DType> &label) {
#pragma omp parallel for
  for (openmp_index_t n = 0; n < dst.size(2); ++n) {
    for (index_t y = 0; y < dst.size(0); ++y) {
      const int k = static_cast<int>(label[y][n]);
      for (int x = 0; x < static_cast<int>(dst.size(1)); ++x) {
        if (x == k) {
          dst[y][k][n] = src[y][k][n] - 1.0f;
        } else {
          dst[y][x][n] = src[y][x][n];
        }
      }
    }
  }
}

template<typename DType>
inline void SmoothSoftmaxGrad(Tensor<cpu, 3, DType> dst,
                        const Tensor<cpu, 3, DType> &src,
                        const Tensor<cpu, 2, DType> &label,
                        const float alpha) {
  const float smooth_grad = (alpha / (dst.size(1) - 1));
#pragma omp parallel for
  for (openmp_index_t n = 0; n < dst.size(2); ++n) {
    for (index_t y = 0; y < dst.size(0); ++y) {
      const int k = static_cast<int>(label[y][n]);
      for (int x = 0; x < static_cast<int>(dst.size(1)); ++x) {
        if (x == k) {
          dst[y][k][n] = src[y][k][n] - 1.0f + alpha;
        } else {
          dst[y][x][n] = src[y][x][n] - smooth_grad;
        }
      }
    }
  }
}

template<typename DType>
inline void SoftmaxGrad(Tensor<cpu, 3, DType> dst,
                        const Tensor<cpu, 3, DType> &src,
                        const Tensor<cpu, 2, DType> &label,
                        const DType &ignore_label) {
#pragma omp parallel for
  for (openmp_index_t n = 0; n < dst.size(2); ++n) {
    for (index_t y = 0; y < dst.size(0); ++y) {
      const int k = static_cast<int>(label[y][n]);
      if (k == static_cast<int>(ignore_label)) {
        for (int x = 0; x < static_cast<int>(dst.size(1)); ++x) {
          dst[y][x][n] = DType(0.0f);
        }
      } else {
        for (int x = 0; x < static_cast<int>(dst.size(1)); ++x) {
          if (x == k) {
            dst[y][k][n] = src[y][k][n] - 1.0f;
          } else {
            dst[y][x][n] = src[y][x][n];
          }
        }
      }
    }
  }
}

template<typename DType>
inline void SmoothSoftmaxGrad(Tensor<cpu, 3, DType> dst,
                        const Tensor<cpu, 3, DType> &src,
                        const Tensor<cpu, 2, DType> &label,
                        const DType &ignore_label,
                        const float alpha) {
  const float smooth_grad = (alpha / (dst.size(1) - 1));
#pragma omp parallel for
  for (openmp_index_t n = 0; n < dst.size(2); ++n) {
    for (index_t y = 0; y < dst.size(0); ++y) {
      const int k = static_cast<int>(label[y][n]);
      if (k == static_cast<int>(ignore_label)) {
        for (int x = 0; x < static_cast<int>(dst.size(1)); ++x) {
          dst[y][x][n] = DType(0.0f);
        }
      } else {
        for (int x = 0; x < static_cast<int>(dst.size(1)); ++x) {
          if (x == k) {
            dst[y][k][n] = src[y][k][n] - 1.0f + alpha;
          } else {
            dst[y][x][n] = src[y][x][n] - smooth_grad;
          }
        }
      }
    }
  }
}

template<typename DType>
inline void Softmax(Tensor<cpu, 2, DType> dst,
                    const Tensor<cpu, 2, DType> &energy) {
  CHECK_EQ(dst.shape_, energy.shape_) << "Softmax: shape mismatch";
#pragma omp parallel for
  for (openmp_index_t y = 0; y < dst.size(0); ++y) {
    Softmax(dst[y], energy[y]);
  }
}

template<typename DType>
inline void Softmax(Tensor<cpu, 3, DType> dst,
                    const Tensor<cpu, 3, DType> &energy) {
  CHECK_EQ(dst.shape_, energy.shape_) << "Softmax: shape mismatch";
#pragma omp parallel for
  for (openmp_index_t y = 0; y < dst.size(0); ++y) {
    for (index_t n = 0; n < dst.size(2); ++n) {
      DType mmax = energy[y][0][n];
      for (index_t x = 1; x < dst.size(1); ++x) {
        if (mmax < energy[y][x][n]) mmax = energy[y][x][n];
      }
      DType sum = DType(0.0f);
      for (index_t x = 0; x < dst.size(1); ++x) {
        dst[y][x][n] = std::exp(energy[y][x][n] - mmax);
        sum += dst[y][x][n];
      }
      for (index_t x = 0; x < dst.size(1); ++x) {
        dst[y][x][n] /= sum;
      }
    }
  }
}

template<bool clip, typename IndexType, typename DType>
inline void AddTakeGrad(Tensor<cpu, 2, DType> dst,
                        const Tensor<cpu, 1, IndexType>& index,
                        const Tensor<cpu, 2, DType> &src) {
  const int K = dst.shape_[0];
  for (index_t y = 0; y < index.size(0); ++y) {
    int j = index[y];
    if (clip) {
      if (j <= 0) j = 0;
      else if (j >= K) j = K - 1;
    } else {
      j %= K;
      if (j < 0) j += K;
    }
    dst[j] += src[y];
  }
}

template<typename IndexType, typename DType>
inline void AddTakeGradLargeBatch(Tensor<cpu, 2, DType> dst,
                                  const Tensor<cpu, 1, IndexType>& sorted,
                                  const Tensor<cpu, 1, IndexType>& index,
                                  const Tensor<cpu, 2, DType> &src) {
  for (index_t y = 0; y < sorted.size(0); ++y) {
    dst[sorted[y]] += src[index[y]];
  }
}

template<typename IndexType, typename DType>
inline void IndexFill(Tensor<cpu, 2, DType> dst,
                      const Tensor<cpu, 1, IndexType>& index,
                      const Tensor<cpu, 2, DType> &src) {
  for (index_t y = 0; y < index.size(0); ++y) {
    for (index_t j = 0; j < src.size(1); j++) {
      dst[index[y]][j] = src[y][j];
    }
  }
}

template<typename KDType, typename VDType>
inline void SortByKey(Tensor<cpu, 1, KDType> keys, Tensor<cpu, 1, VDType> values,
                      bool is_ascend) {
  CHECK_EQ(keys.CheckContiguous(), true);
  CHECK_EQ(values.CheckContiguous(), true);
  CHECK_EQ(keys.size(0), values.size(0))
    << "The sizes of key/value are not equal! keys_size: " << keys.size(0)
    << "values_size: " << values.size(0);
  std::vector<size_t> idx(keys.size(0));
  std::vector<KDType> keys_vec(keys.size(0));
  std::vector<VDType> values_vec(values.size(0));
  for (int i = 0; i < keys.size(0); i++) {
    idx[i] = i;
    keys_vec[i] = keys[i];
    values_vec[i] = values[i];
  }
  if (is_ascend) {
    std::stable_sort(idx.begin(), idx.end(),
                     [&keys_vec](size_t i1, size_t i2)
                       {return keys_vec[i1] < keys_vec[i2]; });
  } else {
    std::stable_sort(idx.begin(), idx.end(),
                     [&keys_vec](size_t i1, size_t i2)
                       {return keys_vec[i1] > keys_vec[i2]; });
  }
  for (index_t i = 0; i < values.size(0); i++) {
    keys[i] = keys_vec[idx[i]];
    values[i] = values_vec[idx[i]];
  }
}

template<typename Device, typename VDType, typename SDType>
inline void VectorizedSort(Tensor<Device, 1, VDType> values, Tensor<Device, 1, SDType> segments) {
  // We can sort each segments using two stable sorts
  SortByKey(values, segments, true);
  SortByKey(segments, values, true);
}

// blas related
template<typename Device, typename DType>
inline void VectorDot(Tensor<Device, 1, DType> dst,
                      const Tensor<Device, 1, DType> &lhs,
                      const Tensor<Device, 1, DType> &rhs) {
  CHECK_EQ(lhs.size(0), rhs.size(0))
      << "VectorDot: Shape mismatch";
  CHECK_EQ(dst.size(0), 1U)
      << "VectorDot: expect dst to be scalar";
  expr::BLASEngine<Device, DType>::SetStream(lhs.stream_);
  mshadow::expr::BLASEngine<Device, DType>::dot(
      lhs.stream_, lhs.size(0), lhs.dptr_, 1, rhs.dptr_, 1, dst.dptr_);
}

template<bool transpose_left, bool transpose_right, typename Device, typename DType>
inline void BatchGEMM(Tensor<Device, 3, DType> dst,
                      const Tensor<Device, 3, DType> &lhs,
                      const Tensor<Device, 3, DType> &rhs,
                      DType alpha,
                      DType beta,
                      Tensor<Device, 1, DType*> workspace) {
  index_t batch_size = dst.shape_[0];
  expr::BLASEngine<Device, DType>::SetStream(dst.stream_);
  Shape<3> sleft = transpose_left ? Shape3(lhs.shape_[0], lhs.shape_[2], lhs.shape_[1])
    : lhs.shape_;
  Shape<3> sright = transpose_right ? Shape3(rhs.shape_[0], rhs.shape_[2], rhs.shape_[1])
    : rhs.shape_;
  CHECK_EQ(dst.CheckContiguous(), true);
  CHECK_EQ(lhs.CheckContiguous(), true);
  CHECK_EQ(rhs.CheckContiguous(), true);
  CHECK(sleft[0] == batch_size && sright[0] == batch_size)
    << "BatchGEMM: batchsize must be equal."
    << "dst: " << dst.shape_ << "\n"
    << "lhs: " << sleft << "\n"
    << "rhs: " << sright << "\n";
  CHECK(dst.size(1) == sleft[1] && dst.size(2) == sright[2] && sleft[2] == sright[1])
    << "BatchGEMM: matrix shape mismatch"
    << "dst: " << dst.shape_ << "\n"
    << "lhs: " << sleft << "\n"
    << "rhs: " << sright << "\n";
  CHECK(workspace.size(0) >= 3 * batch_size)
    << "Workspace Size must be bigger than " << 3 * batch_size;
  CHECK_EQ(workspace.CheckContiguous(), true);
  // use column major argument to compatible with most BLAS
  expr::BLASEngine<Device, DType>::batched_gemm
    (dst.stream_,
    transpose_right, transpose_left,
    transpose_right ? rhs.size(1) : rhs.size(2),
    transpose_left ? lhs.size(2) : lhs.size(1),
    transpose_right ? rhs.size(2) : rhs.size(1),
    alpha,
    rhs.dptr_, rhs.stride_,
    lhs.dptr_, lhs.stride_,
    beta,
    dst.dptr_, dst.stride_, batch_size,
    workspace.dptr_);
}
}  // namespace mshadow
#endif  // MSHADOW_TENSOR_CPU_INL_H_