android-10.0.0_r47/s

/* Copyright 2015 The TensorFlow Authors. All Rights Reserved.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

    http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
==============================================================================*/

#include "cuda/include/cublas_v2.h"
#include "cuda/include/cuda.h"

#define SE_CUDA_DATA_HALF CUDA_R_16F

#include "tensorflow/stream_executor/cuda/cuda_blas.h"

// Both Eigen Half.h and CUDA cuda_fp16.h provide similar typedef for __half. As
// such, there are two ways to get the typedef for __half:
//
// (1) Includes cuda_fp16.h and defines EIGEN_HAS_CUDA_FP16.
// (2) Neither includes cuda_fp16.h nor defines EIGEN_HAS_CUDA_FP16.
//
// Due to issue b/73793421, when the first approach is used and NVCC is used to
// compile this file, NVCC will complain duplicated definition for
// EIGEN_HAS_CUDA_FP16. On the other hand, when the second approach is used and
// clang is used to compile this file, clang will not understand __half
// due to missing the definition and macro EIGEN_HAS_CUDA_FP16.
//
// Because this file may be compiled with CLANG but will never be compiled with
// NVCC, we choose the first approach for CUDA < 9.0. For CUDA >= 9.0, we have
// to use the second approach because the data member in the __half defined
// by CUDA > 9.0 is `__x` while Eigen expects it to be `x`.
//
// TODO(b/73793421): Remove the following code block to switch to the second
// approach when the issue is fixed.
#if CUDA_VERSION < 9000
#include "cuda/include/cuda_fp16.h"
#define EIGEN_HAS_CUDA_FP16
#endif

#include "third_party/eigen3/Eigen/Core"

#include <assert.h>
#include <complex>

#include "absl/strings/str_cat.h"
#include "tensorflow/core/util/env_var.h"
#include "tensorflow/stream_executor/cuda/cuda_activation.h"
#include "tensorflow/stream_executor/cuda/cuda_gpu_executor.h"
#include "tensorflow/stream_executor/cuda/cuda_helpers.h"
#include "tensorflow/stream_executor/cuda/cuda_platform_id.h"
#include "tensorflow/stream_executor/cuda/cuda_stream.h"
#include "tensorflow/stream_executor/cuda/cuda_timer.h"
#include "tensorflow/stream_executor/device_memory.h"
#include "tensorflow/stream_executor/lib/env.h"
#include "tensorflow/stream_executor/lib/initialize.h"
#include "tensorflow/stream_executor/lib/status.h"
#include "tensorflow/stream_executor/lib/status_macros.h"
#include "tensorflow/stream_executor/lib/stringprintf.h"
#include "tensorflow/stream_executor/platform/logging.h"
#include "tensorflow/stream_executor/platform/port.h"
#include "tensorflow/stream_executor/plugin_registry.h"
#include "tensorflow/stream_executor/scratch_allocator.h"
#include "tensorflow/stream_executor/stream_executor.h"

namespace stream_executor {
namespace gpu {

PLUGIN_REGISTRY_DEFINE_PLUGIN_ID(kCuBlasPlugin);

static string ToString(cublasStatus_t status) {
  switch (status) {
    case CUBLAS_STATUS_SUCCESS:
      return "CUBLAS_STATUS_SUCCESS";
    case CUBLAS_STATUS_NOT_INITIALIZED:
      return "CUBLAS_STATUS_NOT_INITIALIZED";
    case CUBLAS_STATUS_ALLOC_FAILED:
      return "CUBLAS_STATUS_ALLOC_FAILED";
    case CUBLAS_STATUS_INVALID_VALUE:
      return "CUBLAS_STATUS_INVALID_VALUE";
    case CUBLAS_STATUS_ARCH_MISMATCH:
      return "CUBLAS_STATUS_ARCH_MISMATCH";
    case CUBLAS_STATUS_MAPPING_ERROR:
      return "CUBLAS_STATUS_MAPPING_ERROR";
    case CUBLAS_STATUS_EXECUTION_FAILED:
      return "CUBLAS_STATUS_EXECUTION_FAILED";
    case CUBLAS_STATUS_INTERNAL_ERROR:
      return "CUBLAS_STATUS_INTERNAL_ERROR";
#if CUDA_VERSION >= 8000
    case CUBLAS_STATUS_NOT_SUPPORTED:
      return "CUBLAS_STATUS_NOT_SUPPORTED";
    case CUBLAS_STATUS_LICENSE_ERROR:
      return "CUBLAS_STATUS_LICENSE_ERROR";
#endif
    default:
      return absl::StrCat("<invalid cublas status: ", status, ">");
  }
}

// Decide whether to enable TENSOR_OP_MATH
static bool TensorOpMathEnabled() {
  static bool is_enabled = [] {
    bool is_disabled;
    TF_CHECK_OK(
        tensorflow::ReadBoolFromEnvVar("TF_DISABLE_CUBLAS_TENSOR_OP_MATH",
                                       /*default_val=*/false, &is_disabled));
    return !is_disabled;
  }();
  return is_enabled;
}

// cuBLAS has interfaces that permit pointers to be passed from either the host
// memory space or the device memory space; however, you must instruct it as to
// which address space those pointers are in with cublasSetPointerMode.
//
// This helper sets the cuBLAS pointer mode to a desired value for a cuBLAS call
// you are about to perform in a given scope.
//
// The prior cuBLAS pointer mode is retained and restored when this object goes
// out of scope.
class ScopedCublasPointerMode {
 public:
  // Note that, because the setting of the cublas pointer mode is fallible,
  // construction of this scoped datatype must be paired with a call to
  // Init().
  //
  // Parameters:
  //  handle: The cublas library handle to act upon in setting the pointer mode.
  explicit ScopedCublasPointerMode(cublasHandle_t handle)
      : handle_(handle), ok_(false) {}

  // Attempts the switch to the requested scoped pointer mode, new_mode.
  //
  // Note that when false is returned, an appropriate error has already been
  // logged.
  bool Init(cublasPointerMode_t new_mode) {
    cublasStatus_t ret = cublasGetPointerMode(handle_, &old_mode_);
    if (ret != CUBLAS_STATUS_SUCCESS) {
      LOG(ERROR) << "failed to get old cublas pointer mode: " << ToString(ret);
      return ok_ = false;
    }

    ret = cublasSetPointerMode(handle_, new_mode);
    if (ret != CUBLAS_STATUS_SUCCESS) {
      LOG(ERROR) << "failed to set new cublas pointer mode: " << ToString(ret);
      return ok_ = false;
    }

    return ok_ = true;
  }

  // Switches back to the prior pointer mode, if the switch operation was
  // successful in the first place.
  ~ScopedCublasPointerMode() {
    if (ok_) {
      cublasStatus_t ret = cublasSetPointerMode(handle_, old_mode_);
      if (ret != CUBLAS_STATUS_SUCCESS) {
        LOG(ERROR) << "failed to set former cublas pointer mode: "
                   << ToString(ret);
      }
    }
  }

 private:
  cublasHandle_t handle_;  // Handle to the cuBLAS instance of interest.
  cublasPointerMode_t old_mode_;  // Prior cuBLAS pointer mode, to be restored.
  bool ok_;                       // Whether the change was successful.
};

#if CUDA_VERSION >= 9000
// cuBLAS has interfaces that permit computations to use the Volta hardware.
// This must be enabled via the cublasGet/SetMathMode APIs.
//
// This helper sets the cuBLAS math mode to a desired value for a cuBLAS call
// you are about to perform in a given scope.
//
// The prior cuBLAS math mode is retained and restored when this object goes
// out of scope.
class ScopedCublasMathMode {
 public:
  // Note that, because the setting of the cublas math mode is fallible,
  // construction of this scoped datatype must be paired with a call to
  // Init().
  //
  // Parameters:
  //  handle: The cublas library handle to act upon in setting the math mode.
  explicit ScopedCublasMathMode(cublasHandle_t handle)
      : handle_(handle), ok_(false) {}

  // Attempts the switch to the requested scoped math mode, new_mode.
  //
  // Note that when false is returned, an appropriate error has already been
  // logged.
  bool Init(cublasMath_t new_mode) {
    cublasStatus_t ret = cublasGetMathMode(handle_, &old_mode_);
    if (ret != CUBLAS_STATUS_SUCCESS) {
      LOG(ERROR) << "failed to get old cublas math mode: " << ToString(ret);
      return ok_ = false;
    }

    ret = cublasSetMathMode(handle_, new_mode);
    if (ret != CUBLAS_STATUS_SUCCESS) {
      LOG(ERROR) << "failed to set new cublas math mode: " << ToString(ret);
      return ok_ = false;
    }
    return ok_ = true;
  }

  // Switches back to the prior math mode, if the switch operation was
  // successful in the first place.
  ~ScopedCublasMathMode() {
    if (ok_) {
      cublasStatus_t ret = cublasSetMathMode(handle_, old_mode_);
      if (ret != CUBLAS_STATUS_SUCCESS) {
        LOG(ERROR) << "failed to set former cublas math mode: "
                   << ToString(ret);
      }
    }
  }

 private:
  cublasHandle_t handle_;  // Handle to the cuBLAS instance of interest.
  cublasMath_t old_mode_;  // Prior cuBLAS math mode, to be restored.
  bool ok_;                // Whether the change was successful.
};
#endif  // CUDA_VERSION >= 9000

bool CUDABlas::Init() {
  gpu::ScopedActivateExecutorContext sac{parent_};
  cublasStatus_t ret = cublasCreate(&blas_);
  if (ret != CUBLAS_STATUS_SUCCESS) {
    LOG(ERROR) << "failed to create cublas handle: " << ToString(ret);
    return false;
  }

  return true;
}

CUDABlas::CUDABlas(gpu::GpuExecutor *parent)
    : parent_(CHECK_NOTNULL(parent)), blas_(nullptr) {}

CUDABlas::~CUDABlas() {
  if (blas_ != nullptr) {
    gpu::ScopedActivateExecutorContext sac{parent_};
    cublasDestroy(blas_);
  }
}

bool CUDABlas::SetStream(Stream *stream) {
  CHECK(stream != nullptr);
  CHECK(AsGpuStreamValue(stream) != nullptr);
  CHECK(blas_ != nullptr);
  gpu::ScopedActivateExecutorContext sac{parent_};
  cublasStatus_t ret = cublasSetStream(blas_, AsGpuStreamValue(stream));
  if (ret != CUBLAS_STATUS_SUCCESS) {
    LOG(ERROR) << "failed to set stream for cuBLAS calls: " << ToString(ret);
    return false;
  }

  return true;
}

namespace {

// Helper functions transforming blas arguments into cuBLAS arguments.

cublasOperation_t CUDABlasTranspose(blas::Transpose trans) {
  switch (trans) {
    case blas::Transpose::kNoTranspose:
      return CUBLAS_OP_N;
    case blas::Transpose::kTranspose:
      return CUBLAS_OP_T;
    case blas::Transpose::kConjugateTranspose:
      return CUBLAS_OP_C;
    default:
      LOG(FATAL) << "Invalid value of blas::Transpose.";
  }
}

cublasFillMode_t CUDABlasUpperLower(blas::UpperLower uplo) {
  switch (uplo) {
    case blas::UpperLower::kUpper:
      return CUBLAS_FILL_MODE_UPPER;
    case blas::UpperLower::kLower:
      return CUBLAS_FILL_MODE_LOWER;
    default:
      LOG(FATAL) << "Invalid value of blas::UpperLower.";
  }
}

cublasDiagType_t CUDABlasDiagonal(blas::Diagonal diag) {
  switch (diag) {
    case blas::Diagonal::kUnit:
      return CUBLAS_DIAG_UNIT;
    case blas::Diagonal::kNonUnit:
      return CUBLAS_DIAG_NON_UNIT;
    default:
      LOG(FATAL) << "Invalid value of blas::Diagonal.";
  }
}

cublasSideMode_t CUDABlasSide(blas::Side side) {
  switch (side) {
    case blas::Side::kLeft:
      return CUBLAS_SIDE_LEFT;
    case blas::Side::kRight:
      return CUBLAS_SIDE_RIGHT;
    default:
      LOG(FATAL) << "Invalid value of blas::Side.";
  }
}

// CUDADataType<T>::type translates from a C++ type (e.g. float) to a
// cudaDataType_t (e.g. CUDA_R_32F).  CUDAComputationType(ty) translates from a
// blas::ComputationType to a cudaDataType_t.
//
// These are used to build the argument type and computation type args to
// cublasGemmEx.
template <typename T>
struct CUDADataType;

template <>
struct CUDADataType<Eigen::half> {
  static constexpr cudaDataType_t type = SE_CUDA_DATA_HALF;
};

template <>
struct CUDADataType<std::complex<Eigen::half>> {
  static constexpr cudaDataType_t type = CUDA_C_16F;
};

template <>
struct CUDADataType<float> {
  static constexpr cudaDataType_t type = CUDA_R_32F;
};

template <>
struct CUDADataType<std::complex<float>> {
  static constexpr cudaDataType_t type = CUDA_C_32F;
};

template <>
struct CUDADataType<double> {
  static constexpr cudaDataType_t type = CUDA_R_64F;
};

template <>
struct CUDADataType<std::complex<double>> {
  static constexpr cudaDataType_t type = CUDA_C_64F;
};

template <>
struct CUDADataType<int> {
  static constexpr cudaDataType_t type = CUDA_R_32I;
};

template <>
struct CUDADataType<int8> {
  static constexpr cudaDataType_t type = CUDA_R_8I;
};

template <>
struct CUDADataType<std::complex<int8>> {
  static constexpr cudaDataType_t type = CUDA_C_8I;
};

template <>
struct CUDADataType<uint8> {
  static constexpr cudaDataType_t type = CUDA_R_8U;
};

template <>
struct CUDADataType<std::complex<uint8>> {
  static constexpr cudaDataType_t type = CUDA_C_8U;
};

cudaDataType_t CUDAComputationType(blas::ComputationType ty) {
  switch (ty) {
    case blas::ComputationType::kF16:
      return CUDA_R_16F;
    case blas::ComputationType::kF32:
      return CUDA_R_32F;
    case blas::ComputationType::kF64:
      return CUDA_R_64F;
    case blas::ComputationType::kI32:
      return CUDA_R_32I;
    case blas::ComputationType::kComplexF32:
      return CUDA_C_32F;
    case blas::ComputationType::kComplexF64:
      return CUDA_C_64F;
  }
}
}  // namespace

template <typename FuncT, typename... Args>
bool CUDABlas::DoBlasInternalImpl(FuncT cublas_func, Stream *stream,
                                  bool pointer_mode_host, bool err_on_failure,
                                  bool use_tensor_op_math, Args... args) {
  mutex_lock lock(mu_);

  CHECK(blas_ != nullptr);
  if (!SetStream(stream)) {
    return false;
  }

  gpu::ScopedActivateExecutorContext sac{parent_};
  ScopedCublasPointerMode pointer_mode{blas_};
  if (!pointer_mode.Init(pointer_mode_host ? CUBLAS_POINTER_MODE_HOST
                                           : CUBLAS_POINTER_MODE_DEVICE)) {
    return false;
  }
#if CUDA_VERSION >= 9000
  ScopedCublasMathMode math_mode{blas_};
  if (use_tensor_op_math) {
    if (!math_mode.Init(CUBLAS_TENSOR_OP_MATH)) {
      return false;
    }
  }
#endif
  cublasStatus_t ret = cublas_func(blas_, args...);
  if ((err_on_failure || VLOG_IS_ON(3)) && ret != CUBLAS_STATUS_SUCCESS) {
    LOG(ERROR) << "failed to run cuBLAS routine: " << ToString(ret);
  }
  return ret == CUBLAS_STATUS_SUCCESS;
}

bool CUDABlas::DoBlasAsum(Stream *stream, uint64 elem_count,
                          const DeviceMemory<float> &x, int incx,
                          DeviceMemory<float> *result) {
  return DoBlasInternal(cublasSasum, stream, false /* = pointer_mode_host */,
                        elem_count, GpuMemory(x), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasAsum(Stream *stream, uint64 elem_count,
                          const DeviceMemory<double> &x, int incx,
                          DeviceMemory<double> *result) {
  return DoBlasInternal(cublasDasum, stream, false /* = pointer_mode_host */,
                        elem_count, GpuMemory(x), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasAsum(Stream *stream, uint64 elem_count,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          DeviceMemory<float> *result) {
  return DoBlasInternal(cublasScasum, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasAsum(Stream *stream, uint64 elem_count,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          DeviceMemory<double> *result) {
  return DoBlasInternal(cublasDzasum, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasAxpy(Stream *stream, uint64 elem_count, float alpha,
                          const DeviceMemory<float> &x, int incx,
                          DeviceMemory<float> *y, int incy) {
  return DoBlasInternal(cublasSaxpy, stream, true /* = pointer_mode_host */,
                        elem_count, &alpha, GpuMemory(x), incx,
                        GpuMemoryMutable(y), incy);
}

bool CUDABlas::DoBlasAxpy(Stream *stream, uint64 elem_count, double alpha,
                          const DeviceMemory<double> &x, int incx,
                          DeviceMemory<double> *y, int incy) {
  return DoBlasInternal(cublasDaxpy, stream, true /* = pointer_mode_host */,
                        elem_count, &alpha, GpuMemory(x), incx,
                        GpuMemoryMutable(y), incy);
}

bool CUDABlas::DoBlasAxpy(Stream *stream, uint64 elem_count,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          DeviceMemory<std::complex<float>> *y, int incy) {
  return DoBlasInternal(cublasCaxpy, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasAxpy(Stream *stream, uint64 elem_count,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          DeviceMemory<std::complex<double>> *y, int incy) {
  return DoBlasInternal(cublasZaxpy, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasCopy(Stream *stream, uint64 elem_count,
                          const DeviceMemory<float> &x, int incx,
                          DeviceMemory<float> *y, int incy) {
  return DoBlasInternal(cublasScopy, stream, true /* = pointer_mode_host */,
                        elem_count, GpuMemory(x), incx, GpuMemoryMutable(y),
                        incy);
}

bool CUDABlas::DoBlasCopy(Stream *stream, uint64 elem_count,
                          const DeviceMemory<double> &x, int incx,
                          DeviceMemory<double> *y, int incy) {
  return DoBlasInternal(cublasDcopy, stream, true /* = pointer_mode_host */,
                        elem_count, GpuMemory(x), incx, GpuMemoryMutable(y),
                        incy);
}

bool CUDABlas::DoBlasCopy(Stream *stream, uint64 elem_count,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          DeviceMemory<std::complex<float>> *y, int incy) {
  return DoBlasInternal(cublasCcopy, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasCopy(Stream *stream, uint64 elem_count,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          DeviceMemory<std::complex<double>> *y, int incy) {
  return DoBlasInternal(cublasZcopy, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasDot(Stream *stream, uint64 elem_count,
                         const DeviceMemory<float> &x, int incx,
                         const DeviceMemory<float> &y, int incy,
                         DeviceMemory<float> *result) {
  return DoBlasInternal(cublasSdot, stream, false /* = pointer_mode_host */,
                        elem_count, GpuMemory(x), incx, GpuMemory(y), incy,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasDot(Stream *stream, uint64 elem_count,
                         const DeviceMemory<double> &x, int incx,
                         const DeviceMemory<double> &y, int incy,
                         DeviceMemory<double> *result) {
  return DoBlasInternal(cublasDdot, stream, false /* = pointer_mode_host */,
                        elem_count, GpuMemory(x), incx, GpuMemory(y), incy,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasDotc(Stream *stream, uint64 elem_count,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          const DeviceMemory<std::complex<float>> &y, int incy,
                          DeviceMemory<std::complex<float>> *result) {
  return DoBlasInternal(cublasCdotc, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemory(y)), incy,
                        GpuComplex(GpuMemoryMutable(result)));
}

bool CUDABlas::DoBlasDotc(Stream *stream, uint64 elem_count,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          const DeviceMemory<std::complex<double>> &y, int incy,
                          DeviceMemory<std::complex<double>> *result) {
  return DoBlasInternal(cublasZdotc, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemory(y)), incy,
                        GpuComplex(GpuMemoryMutable(result)));
}

bool CUDABlas::DoBlasDotu(Stream *stream, uint64 elem_count,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          const DeviceMemory<std::complex<float>> &y, int incy,
                          DeviceMemory<std::complex<float>> *result) {
  return DoBlasInternal(cublasCdotu, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemory(y)), incy,
                        GpuComplex(GpuMemoryMutable(result)));
}

bool CUDABlas::DoBlasDotu(Stream *stream, uint64 elem_count,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          const DeviceMemory<std::complex<double>> &y, int incy,
                          DeviceMemory<std::complex<double>> *result) {
  return DoBlasInternal(cublasZdotu, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemory(y)), incy,
                        GpuComplex(GpuMemoryMutable(result)));
}

bool CUDABlas::DoBlasNrm2(Stream *stream, uint64 elem_count,
                          const DeviceMemory<float> &x, int incx,
                          DeviceMemory<float> *result) {
  return DoBlasInternal(cublasSnrm2, stream, false /* = pointer_mode_host */,
                        elem_count, GpuMemory(x), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasNrm2(Stream *stream, uint64 elem_count,
                          const DeviceMemory<double> &x, int incx,
                          DeviceMemory<double> *result) {
  return DoBlasInternal(cublasDnrm2, stream, false /* = pointer_mode_host */,
                        elem_count, GpuMemory(x), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasNrm2(Stream *stream, uint64 elem_count,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          DeviceMemory<float> *result) {
  return DoBlasInternal(cublasScnrm2, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasNrm2(Stream *stream, uint64 elem_count,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          DeviceMemory<double> *result) {
  return DoBlasInternal(cublasDznrm2, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasRot(Stream *stream, uint64 elem_count,
                         DeviceMemory<float> *x, int incx,
                         DeviceMemory<float> *y, int incy, float c, float s) {
  return DoBlasInternal(cublasSrot, stream, true /* = pointer_mode_host */,
                        elem_count, GpuMemoryMutable(x), incx,
                        GpuMemoryMutable(y), incy, &c, &s);
}

bool CUDABlas::DoBlasRot(Stream *stream, uint64 elem_count,
                         DeviceMemory<double> *x, int incx,
                         DeviceMemory<double> *y, int incy, double c,
                         double s) {
  return DoBlasInternal(cublasDrot, stream, true /* = pointer_mode_host */,
                        elem_count, GpuMemoryMutable(x), incx,
                        GpuMemoryMutable(y), incy, &c, &s);
}

bool CUDABlas::DoBlasRot(Stream *stream, uint64 elem_count,
                         DeviceMemory<std::complex<float>> *x, int incx,
                         DeviceMemory<std::complex<float>> *y, int incy,
                         float c, float s) {
  return DoBlasInternal(cublasCsrot, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemoryMutable(x)), incx,
                        GpuComplex(GpuMemoryMutable(y)), incy, &c, &s);
}

bool CUDABlas::DoBlasRot(Stream *stream, uint64 elem_count,
                         DeviceMemory<std::complex<double>> *x, int incx,
                         DeviceMemory<std::complex<double>> *y, int incy,
                         double c, double s) {
  return DoBlasInternal(cublasZdrot, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemoryMutable(x)), incx,
                        GpuComplex(GpuMemoryMutable(y)), incy, &c, &s);
}

bool CUDABlas::DoBlasRotg(Stream *stream, DeviceMemory<float> *a,
                          DeviceMemory<float> *b, DeviceMemory<float> *c,
                          DeviceMemory<float> *s) {
  return DoBlasInternal(cublasSrotg, stream, false /* = pointer_mode_host */,
                        GpuMemoryMutable(a), GpuMemoryMutable(b),
                        GpuMemoryMutable(c), GpuMemoryMutable(s));
}

bool CUDABlas::DoBlasRotg(Stream *stream, DeviceMemory<double> *a,
                          DeviceMemory<double> *b, DeviceMemory<double> *c,
                          DeviceMemory<double> *s) {
  return DoBlasInternal(cublasDrotg, stream, false /* = pointer_mode_host */,
                        GpuComplex(GpuMemoryMutable(a)), GpuMemoryMutable(b),
                        GpuMemoryMutable(c), GpuMemoryMutable(s));
}

bool CUDABlas::DoBlasRotg(Stream *stream, DeviceMemory<std::complex<float>> *a,
                          DeviceMemory<std::complex<float>> *b,
                          DeviceMemory<float> *c,
                          DeviceMemory<std::complex<float>> *s) {
  return DoBlasInternal(
      cublasCrotg, stream, false /* = pointer_mode_host */,
      GpuComplex(GpuMemoryMutable(a)), GpuComplex(GpuMemoryMutable(b)),
      GpuComplex(GpuMemoryMutable(c)), GpuComplex(GpuMemoryMutable(s)));
}

bool CUDABlas::DoBlasRotg(Stream *stream, DeviceMemory<std::complex<double>> *a,
                          DeviceMemory<std::complex<double>> *b,
                          DeviceMemory<double> *c,
                          DeviceMemory<std::complex<double>> *s) {
  return DoBlasInternal(
      cublasZrotg, stream, false /* = pointer_mode_host */,
      GpuComplex(GpuMemoryMutable(a)), GpuComplex(GpuMemoryMutable(b)),
      GpuComplex(GpuMemoryMutable(c)), GpuComplex(GpuMemoryMutable(s)));
}

bool CUDABlas::DoBlasRotm(Stream *stream, uint64 elem_count,
                          DeviceMemory<float> *x, int incx,
                          DeviceMemory<float> *y, int incy,
                          const DeviceMemory<float> &param) {
  return DoBlasInternal(cublasSrotm, stream, false /* = pointer_mode_host */,
                        elem_count, GpuMemoryMutable(x), incx,
                        GpuMemoryMutable(y), incy, GpuMemory(param));
}

bool CUDABlas::DoBlasRotm(Stream *stream, uint64 elem_count,
                          DeviceMemory<double> *x, int incx,
                          DeviceMemory<double> *y, int incy,
                          const DeviceMemory<double> &param) {
  return DoBlasInternal(cublasDrotm, stream, false /* = pointer_mode_host */,
                        elem_count, GpuMemoryMutable(x), incx,
                        GpuMemoryMutable(y), incy, GpuMemory(param));
}

bool CUDABlas::DoBlasRotmg(Stream *stream, DeviceMemory<float> *d1,
                           DeviceMemory<float> *d2, DeviceMemory<float> *x1,
                           const DeviceMemory<float> &y1,
                           DeviceMemory<float> *param) {
  return DoBlasInternal(cublasSrotmg, stream, false /* = pointer_mode_host */,
                        GpuMemoryMutable(d1), GpuMemoryMutable(d2),
                        GpuMemoryMutable(x1), GpuMemory(y1),
                        GpuMemoryMutable(param));
}

bool CUDABlas::DoBlasRotmg(Stream *stream, DeviceMemory<double> *d1,
                           DeviceMemory<double> *d2, DeviceMemory<double> *x1,
                           const DeviceMemory<double> &y1,
                           DeviceMemory<double> *param) {
  return DoBlasInternal(cublasDrotmg, stream, false /* = pointer_mode_host */,
                        GpuMemoryMutable(d1), GpuMemoryMutable(d2),
                        GpuMemoryMutable(x1), GpuMemory(y1),
                        GpuMemoryMutable(param));
}

bool CUDABlas::DoBlasScal(Stream *stream, uint64 elem_count, float alpha,
                          DeviceMemory<float> *x, int incx) {
  return DoBlasInternal(cublasSscal, stream, true /* = pointer_mode_host */,
                        elem_count, &alpha, GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasScal(Stream *stream, uint64 elem_count, double alpha,
                          DeviceMemory<double> *x, int incx) {
  return DoBlasInternal(cublasDscal, stream, true /* = pointer_mode_host */,
                        elem_count, &alpha, GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasScal(Stream *stream, uint64 elem_count, float alpha,
                          DeviceMemory<std::complex<float>> *x, int incx) {
  return DoBlasInternal(cublasCsscal, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(&alpha),
                        GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasScal(Stream *stream, uint64 elem_count, double alpha,
                          DeviceMemory<std::complex<double>> *x, int incx) {
  return DoBlasInternal(cublasZdscal, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(&alpha),
                        GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasScal(Stream *stream, uint64 elem_count,
                          std::complex<float> alpha,
                          DeviceMemory<std::complex<float>> *x, int incx) {
  return DoBlasInternal(cublasCscal, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(&alpha),
                        GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasScal(Stream *stream, uint64 elem_count,
                          std::complex<double> alpha,
                          DeviceMemory<std::complex<double>> *x, int incx) {
  return DoBlasInternal(cublasZscal, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(&alpha),
                        GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasSwap(Stream *stream, uint64 elem_count,
                          DeviceMemory<float> *x, int incx,
                          DeviceMemory<float> *y, int incy) {
  return DoBlasInternal(cublasSswap, stream, true /* = pointer_mode_host */,
                        elem_count, GpuMemoryMutable(x), incx,
                        GpuMemoryMutable(y), incy);
}

bool CUDABlas::DoBlasSwap(Stream *stream, uint64 elem_count,
                          DeviceMemory<double> *x, int incx,
                          DeviceMemory<double> *y, int incy) {
  return DoBlasInternal(cublasDswap, stream, true /* = pointer_mode_host */,
                        elem_count, GpuMemoryMutable(x), incx,
                        GpuMemoryMutable(y), incy);
}

bool CUDABlas::DoBlasSwap(Stream *stream, uint64 elem_count,
                          DeviceMemory<std::complex<float>> *x, int incx,
                          DeviceMemory<std::complex<float>> *y, int incy) {
  return DoBlasInternal(cublasCswap, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemoryMutable(x)), incx,
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasSwap(Stream *stream, uint64 elem_count,
                          DeviceMemory<std::complex<double>> *x, int incx,
                          DeviceMemory<std::complex<double>> *y, int incy) {
  return DoBlasInternal(cublasZswap, stream, true /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemoryMutable(x)), incx,
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasIamax(Stream *stream, uint64 elem_count,
                           const DeviceMemory<float> &x, int incx,
                           DeviceMemory<int> *result) {
  return DoBlasInternal(cublasIsamax, stream, false /* = pointer_mode_host */,
                        elem_count, GpuMemory(x), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasIamax(Stream *stream, uint64 elem_count,
                           const DeviceMemory<double> &x, int incx,
                           DeviceMemory<int> *result) {
  return DoBlasInternal(cublasIdamax, stream, false /* = pointer_mode_host */,
                        elem_count, GpuMemory(x), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasIamax(Stream *stream, uint64 elem_count,
                           const DeviceMemory<std::complex<float>> &x, int incx,
                           DeviceMemory<int> *result) {
  return DoBlasInternal(cublasIcamax, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasIamax(Stream *stream, uint64 elem_count,
                           const DeviceMemory<std::complex<double>> &x,
                           int incx, DeviceMemory<int> *result) {
  return DoBlasInternal(cublasIzamax, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasIamin(Stream *stream, uint64 elem_count,
                           const DeviceMemory<float> &x, int incx,
                           DeviceMemory<int> *result) {
  return DoBlasInternal(cublasIsamin, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasIamin(Stream *stream, uint64 elem_count,
                           const DeviceMemory<double> &x, int incx,
                           DeviceMemory<int> *result) {
  return DoBlasInternal(cublasIdamin, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasIamin(Stream *stream, uint64 elem_count,
                           const DeviceMemory<std::complex<float>> &x, int incx,
                           DeviceMemory<int> *result) {
  return DoBlasInternal(cublasIcamin, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasIamin(Stream *stream, uint64 elem_count,
                           const DeviceMemory<std::complex<double>> &x,
                           int incx, DeviceMemory<int> *result) {
  return DoBlasInternal(cublasIzamin, stream, false /* = pointer_mode_host */,
                        elem_count, GpuComplex(GpuMemory(x)), incx,
                        GpuMemoryMutable(result));
}

bool CUDABlas::DoBlasGbmv(Stream *stream, blas::Transpose trans, uint64 m,
                          uint64 n, uint64 kl, uint64 ku, float alpha,
                          const DeviceMemory<float> &a, int lda,
                          const DeviceMemory<float> &x, int incx, float beta,
                          DeviceMemory<float> *y, int incy) {
  return DoBlasInternal(cublasSgbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(trans), m, n, kl, ku, &alpha,
                        GpuMemory(a), lda, GpuMemory(x), incx, &beta,
                        GpuMemoryMutable(y), incy);
}

bool CUDABlas::DoBlasGbmv(Stream *stream, blas::Transpose trans, uint64 m,
                          uint64 n, uint64 kl, uint64 ku, double alpha,
                          const DeviceMemory<double> &a, int lda,
                          const DeviceMemory<double> &x, int incx, double beta,
                          DeviceMemory<double> *y, int incy) {
  return DoBlasInternal(cublasDgbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(trans), m, n, kl, ku, &alpha,
                        GpuMemory(a), lda, GpuMemory(x), incx, &beta,
                        GpuMemoryMutable(y), incy);
}

bool CUDABlas::DoBlasGbmv(Stream *stream, blas::Transpose trans, uint64 m,
                          uint64 n, uint64 kl, uint64 ku,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          std::complex<float> beta,
                          DeviceMemory<std::complex<float>> *y, int incy) {
  return DoBlasInternal(cublasCgbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(trans), m, n, kl, ku,
                        GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(x)), incx, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasGbmv(Stream *stream, blas::Transpose trans, uint64 m,
                          uint64 n, uint64 kl, uint64 ku,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          std::complex<double> beta,
                          DeviceMemory<std::complex<double>> *y, int incy) {
  return DoBlasInternal(cublasZgbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(trans), m, n, kl, ku,
                        GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(x)), incx, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasGemv(Stream *stream, blas::Transpose trans, uint64 m,
                          uint64 n, float alpha, const DeviceMemory<float> &a,
                          int lda, const DeviceMemory<float> &x, int incx,
                          float beta, DeviceMemory<float> *y, int incy) {
  return DoBlasInternal(cublasSgemv, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(trans), m, n, &alpha, GpuMemory(a),
                        lda, GpuMemory(x), incx, &beta, GpuMemoryMutable(y),
                        incy);
}

bool CUDABlas::DoBlasGemv(Stream *stream, blas::Transpose trans, uint64 m,
                          uint64 n, double alpha, const DeviceMemory<double> &a,
                          int lda, const DeviceMemory<double> &x, int incx,
                          double beta, DeviceMemory<double> *y, int incy) {
  return DoBlasInternal(cublasDgemv, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(trans), m, n, &alpha, GpuMemory(a),
                        lda, GpuMemory(x), incx, &beta, GpuMemoryMutable(y),
                        incy);
}

bool CUDABlas::DoBlasGemv(Stream *stream, blas::Transpose trans, uint64 m,
                          uint64 n, std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          std::complex<float> beta,
                          DeviceMemory<std::complex<float>> *y, int incy) {
  return DoBlasInternal(cublasCgemv, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(trans), m, n, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(a)), lda, GpuComplex(GpuMemory(x)),
                        incx, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasGemv(Stream *stream, blas::Transpose trans, uint64 m,
                          uint64 n, std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          std::complex<double> beta,
                          DeviceMemory<std::complex<double>> *y, int incy) {
  return DoBlasInternal(cublasZgemv, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(trans), m, n, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(a)), lda, GpuComplex(GpuMemory(x)),
                        incx, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasGer(Stream *stream, uint64 m, uint64 n, float alpha,
                         const DeviceMemory<float> &x, int incx,
                         const DeviceMemory<float> &y, int incy,
                         DeviceMemory<float> *a, int lda) {
  return DoBlasInternal(cublasSger, stream, true /* = pointer_mode_host */, m,
                        n, &alpha, GpuMemory(x), incx, GpuMemory(y), incy,
                        GpuMemoryMutable(a), lda);
}

bool CUDABlas::DoBlasGer(Stream *stream, uint64 m, uint64 n, double alpha,
                         const DeviceMemory<double> &x, int incx,
                         const DeviceMemory<double> &y, int incy,
                         DeviceMemory<double> *a, int lda) {
  return DoBlasInternal(cublasDger, stream, true /* = pointer_mode_host */, m,
                        n, &alpha, GpuMemory(x), incx, GpuMemory(y), incy,
                        GpuMemoryMutable(a), lda);
}

bool CUDABlas::DoBlasGerc(Stream *stream, uint64 m, uint64 n,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          const DeviceMemory<std::complex<float>> &y, int incy,
                          DeviceMemory<std::complex<float>> *a, int lda) {
  return DoBlasInternal(cublasCgerc, stream, true /* = pointer_mode_host */, m,
                        n, GpuComplex(&alpha), GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemory(y)), incy,
                        GpuComplex(GpuMemoryMutable(a)), lda);
}

bool CUDABlas::DoBlasGerc(Stream *stream, uint64 m, uint64 n,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          const DeviceMemory<std::complex<double>> &y, int incy,
                          DeviceMemory<std::complex<double>> *a, int lda) {
  return DoBlasInternal(cublasZgerc, stream, true /* = pointer_mode_host */, m,
                        n, GpuComplex(&alpha), GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemory(y)), incy,
                        GpuComplex(GpuMemoryMutable(a)), lda);
}

bool CUDABlas::DoBlasGeru(Stream *stream, uint64 m, uint64 n,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          const DeviceMemory<std::complex<float>> &y, int incy,
                          DeviceMemory<std::complex<float>> *a, int lda) {
  return DoBlasInternal(cublasCgeru, stream, true /* = pointer_mode_host */, m,
                        n, GpuComplex(&alpha), GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemory(y)), incy,
                        GpuComplex(GpuMemoryMutable(a)), lda);
}

bool CUDABlas::DoBlasGeru(Stream *stream, uint64 m, uint64 n,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          const DeviceMemory<std::complex<double>> &y, int incy,
                          DeviceMemory<std::complex<double>> *a, int lda) {
  return DoBlasInternal(cublasZgeru, stream, true /* = pointer_mode_host */, m,
                        n, GpuComplex(&alpha), GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemory(y)), incy,
                        GpuComplex(GpuMemoryMutable(a)), lda);
}

bool CUDABlas::DoBlasHbmv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          uint64 k, std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          std::complex<float> beta,
                          DeviceMemory<std::complex<float>> *y, int incy) {
  return DoBlasInternal(cublasChbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, k, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(a)), lda, GpuComplex(GpuMemory(x)),
                        incx, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasHbmv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          uint64 k, std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          std::complex<double> beta,
                          DeviceMemory<std::complex<double>> *y, int incy) {
  return DoBlasInternal(cublasZhbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, k, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(a)), lda, GpuComplex(GpuMemory(x)),
                        incx, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasHemv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          std::complex<float> beta,
                          DeviceMemory<std::complex<float>> *y, int incy) {
  return DoBlasInternal(cublasChemv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(a)), lda, GpuComplex(GpuMemory(x)),
                        incx, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasHemv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          std::complex<double> beta,
                          DeviceMemory<std::complex<double>> *y, int incy) {
  return DoBlasInternal(cublasZhemv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(a)), lda, GpuComplex(GpuMemory(x)),
                        incx, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasHer(Stream *stream, blas::UpperLower uplo, uint64 n,
                         float alpha,
                         const DeviceMemory<std::complex<float>> &x, int incx,
                         DeviceMemory<std::complex<float>> *a, int lda) {
  return DoBlasInternal(cublasCher, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha,
                        GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemoryMutable(a)), lda);
}

bool CUDABlas::DoBlasHer(Stream *stream, blas::UpperLower uplo, uint64 n,
                         double alpha,
                         const DeviceMemory<std::complex<double>> &x, int incx,
                         DeviceMemory<std::complex<double>> *a, int lda) {
  return DoBlasInternal(cublasZher, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha,
                        GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemoryMutable(a)), lda);
}

bool CUDABlas::DoBlasHer2(Stream *stream, blas::UpperLower uplo, uint64 n,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          const DeviceMemory<std::complex<float>> &y, int incy,
                          DeviceMemory<std::complex<float>> *a, int lda) {
  return DoBlasInternal(cublasCher2, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemory(y)), incy,
                        GpuComplex(GpuMemoryMutable(a)), lda);
}

bool CUDABlas::DoBlasHer2(Stream *stream, blas::UpperLower uplo, uint64 n,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          const DeviceMemory<std::complex<double>> &y, int incy,
                          DeviceMemory<std::complex<double>> *a, int lda) {
  return DoBlasInternal(cublasZher2, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemory(y)), incy,
                        GpuComplex(GpuMemoryMutable(a)), lda);
}

bool CUDABlas::DoBlasHpmv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &ap,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          std::complex<float> beta,
                          DeviceMemory<std::complex<float>> *y, int incy) {
  return DoBlasInternal(cublasChpmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(ap)), GpuComplex(GpuMemory(x)),
                        incx, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasHpmv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &ap,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          std::complex<double> beta,
                          DeviceMemory<std::complex<double>> *y, int incy) {
  return DoBlasInternal(cublasZhpmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(ap)), GpuComplex(GpuMemory(x)),
                        incx, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(y)), incy);
}

bool CUDABlas::DoBlasHpr(Stream *stream, blas::UpperLower uplo, uint64 n,
                         float alpha,
                         const DeviceMemory<std::complex<float>> &x, int incx,
                         DeviceMemory<std::complex<float>> *ap) {
  return DoBlasInternal(cublasChpr, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemoryMutable(ap)));
}

bool CUDABlas::DoBlasHpr(Stream *stream, blas::UpperLower uplo, uint64 n,
                         double alpha,
                         const DeviceMemory<std::complex<double>> &x, int incx,
                         DeviceMemory<std::complex<double>> *ap) {
  return DoBlasInternal(cublasZhpr, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, GpuComplex(&alpha),
                        GpuComplex(GpuMemory(x)), incx,
                        GpuComplex(GpuMemoryMutable(ap)));
}

bool CUDABlas::DoBlasHpr2(Stream *stream, blas::UpperLower uplo, uint64 n,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &x, int incx,
                          const DeviceMemory<std::complex<float>> &y, int incy,
                          DeviceMemory<std::complex<float>> *ap) {
  return DoBlasInternal(
      cublasChpr2, stream, true /* = pointer_mode_host */,
      CUDABlasUpperLower(uplo), n, GpuComplex(&alpha), GpuComplex(GpuMemory(x)),
      incx, GpuComplex(GpuMemory(y)), incy, GpuComplex(GpuMemoryMutable(ap)));
}

bool CUDABlas::DoBlasHpr2(Stream *stream, blas::UpperLower uplo, uint64 n,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &x, int incx,
                          const DeviceMemory<std::complex<double>> &y, int incy,
                          DeviceMemory<std::complex<double>> *ap) {
  return DoBlasInternal(
      cublasZhpr2, stream, true /* = pointer_mode_host */,
      CUDABlasUpperLower(uplo), n, GpuComplex(&alpha), GpuComplex(GpuMemory(x)),
      incx, GpuComplex(GpuMemory(y)), incy, GpuComplex(GpuMemoryMutable(ap)));
}

bool CUDABlas::DoBlasSbmv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          uint64 k, float alpha, const DeviceMemory<float> &a,
                          int lda, const DeviceMemory<float> &x, int incx,
                          float beta, DeviceMemory<float> *y, int incy) {
  return DoBlasInternal(cublasSsbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, k, &alpha, GpuMemory(a),
                        lda, GpuMemory(x), incx, &beta, GpuMemoryMutable(y),
                        incy);
}

bool CUDABlas::DoBlasSbmv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          uint64 k, double alpha, const DeviceMemory<double> &a,
                          int lda, const DeviceMemory<double> &x, int incx,
                          double beta, DeviceMemory<double> *y, int incy) {
  return DoBlasInternal(cublasDsbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, k, &alpha, GpuMemory(a),
                        lda, GpuMemory(x), incx, &beta, GpuMemoryMutable(y),
                        incy);
}

bool CUDABlas::DoBlasSpmv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          float alpha, const DeviceMemory<float> &ap,
                          const DeviceMemory<float> &x, int incx, float beta,
                          DeviceMemory<float> *y, int incy) {
  return DoBlasInternal(cublasSspmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(ap),
                        GpuMemory(x), incx, &beta, GpuMemoryMutable(y), incy);
}

bool CUDABlas::DoBlasSpmv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          double alpha, const DeviceMemory<double> &ap,
                          const DeviceMemory<double> &x, int incx, double beta,
                          DeviceMemory<double> *y, int incy) {
  return DoBlasInternal(cublasDspmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(ap),
                        GpuMemory(x), incx, &beta, GpuMemoryMutable(y), incy);
}

bool CUDABlas::DoBlasSpr(Stream *stream, blas::UpperLower uplo, uint64 n,
                         float alpha, const DeviceMemory<float> &x, int incx,
                         DeviceMemory<float> *ap) {
  return DoBlasInternal(cublasSspr, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(x), incx,
                        GpuMemoryMutable(ap));
}

bool CUDABlas::DoBlasSpr(Stream *stream, blas::UpperLower uplo, uint64 n,
                         double alpha, const DeviceMemory<double> &x, int incx,
                         DeviceMemory<double> *ap) {
  return DoBlasInternal(cublasDspr, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(x), incx,
                        GpuMemoryMutable(ap));
}

bool CUDABlas::DoBlasSpr2(Stream *stream, blas::UpperLower uplo, uint64 n,
                          float alpha, const DeviceMemory<float> &x, int incx,
                          const DeviceMemory<float> &y, int incy,
                          DeviceMemory<float> *ap) {
  return DoBlasInternal(cublasSspr2, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(x), incx,
                        GpuMemory(y), incy, GpuMemoryMutable(ap));
}

bool CUDABlas::DoBlasSpr2(Stream *stream, blas::UpperLower uplo, uint64 n,
                          double alpha, const DeviceMemory<double> &x, int incx,
                          const DeviceMemory<double> &y, int incy,
                          DeviceMemory<double> *ap) {
  return DoBlasInternal(cublasDspr2, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(x), incx,
                        GpuMemory(y), incy, GpuMemoryMutable(ap));
}

bool CUDABlas::DoBlasSymv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          float alpha, const DeviceMemory<float> &a, int lda,
                          const DeviceMemory<float> &x, int incx, float beta,
                          DeviceMemory<float> *y, int incy) {
  return DoBlasInternal(cublasSsymv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(a), lda,
                        GpuMemory(x), incx, &beta, GpuMemoryMutable(y), incy);
}

bool CUDABlas::DoBlasSymv(Stream *stream, blas::UpperLower uplo, uint64 n,
                          double alpha, const DeviceMemory<double> &a, int lda,
                          const DeviceMemory<double> &x, int incx, double beta,
                          DeviceMemory<double> *y, int incy) {
  return DoBlasInternal(cublasDsymv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(a), lda,
                        GpuMemory(x), incx, &beta, GpuMemoryMutable(y), incy);
}

bool CUDABlas::DoBlasSyr(Stream *stream, blas::UpperLower uplo, uint64 n,
                         float alpha, const DeviceMemory<float> &x, int incx,
                         DeviceMemory<float> *a, int lda) {
  return DoBlasInternal(cublasSsyr, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(x), incx,
                        GpuMemoryMutable(a), lda);
}

bool CUDABlas::DoBlasSyr(Stream *stream, blas::UpperLower uplo, uint64 n,
                         double alpha, const DeviceMemory<double> &x, int incx,
                         DeviceMemory<double> *a, int lda) {
  return DoBlasInternal(cublasDsyr, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(x), incx,
                        GpuMemoryMutable(a), lda);
}

bool CUDABlas::DoBlasSyr2(Stream *stream, blas::UpperLower uplo, uint64 n,
                          float alpha, const DeviceMemory<float> &x, int incx,
                          const DeviceMemory<float> &y, int incy,
                          DeviceMemory<float> *a, int lda) {
  return DoBlasInternal(cublasSsyr2, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(x), incx,
                        GpuMemory(y), incy, GpuMemoryMutable(a), lda);
}

bool CUDABlas::DoBlasSyr2(Stream *stream, blas::UpperLower uplo, uint64 n,
                          double alpha, const DeviceMemory<double> &x, int incx,
                          const DeviceMemory<double> &y, int incy,
                          DeviceMemory<double> *a, int lda) {
  return DoBlasInternal(cublasDsyr2, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), n, &alpha, GpuMemory(x), incx,
                        GpuMemory(y), incy, GpuMemoryMutable(a), lda);
}

bool CUDABlas::DoBlasTbmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          uint64 k, const DeviceMemory<float> &a, int lda,
                          DeviceMemory<float> *x, int incx) {
  return DoBlasInternal(cublasStbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, k, GpuMemory(a), lda,
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTbmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          uint64 k, const DeviceMemory<double> &a, int lda,
                          DeviceMemory<double> *x, int incx) {
  return DoBlasInternal(cublasDtbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, k, GpuMemory(a), lda,
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTbmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          uint64 k, const DeviceMemory<std::complex<float>> &a,
                          int lda, DeviceMemory<std::complex<float>> *x,
                          int incx) {
  return DoBlasInternal(cublasCtbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, k, GpuComplex(GpuMemory(a)),
                        lda, GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasTbmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          uint64 k, const DeviceMemory<std::complex<double>> &a,
                          int lda, DeviceMemory<std::complex<double>> *x,
                          int incx) {
  return DoBlasInternal(cublasZtbmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, k, GpuComplex(GpuMemory(a)),
                        lda, GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasTbsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          uint64 k, const DeviceMemory<float> &a, int lda,
                          DeviceMemory<float> *x, int incx) {
  return DoBlasInternal(cublasStbsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, k, GpuMemory(a), lda,
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTbsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          uint64 k, const DeviceMemory<double> &a, int lda,
                          DeviceMemory<double> *x, int incx) {
  return DoBlasInternal(cublasDtbsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, k, GpuMemory(a), lda,
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTbsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          uint64 k, const DeviceMemory<std::complex<float>> &a,
                          int lda, DeviceMemory<std::complex<float>> *x,
                          int incx) {
  return DoBlasInternal(cublasCtbsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, k, GpuComplex(GpuMemory(a)),
                        lda, GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasTbsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          uint64 k, const DeviceMemory<std::complex<double>> &a,
                          int lda, DeviceMemory<std::complex<double>> *x,
                          int incx) {
  return DoBlasInternal(cublasZtbsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, k, GpuComplex(GpuMemory(a)),
                        lda, GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasTpmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<float> &ap, DeviceMemory<float> *x,
                          int incx) {
  return DoBlasInternal(cublasStpmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuMemory(ap),
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTpmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<double> &ap,
                          DeviceMemory<double> *x, int incx) {
  return DoBlasInternal(cublasDtpmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuMemory(ap),
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTpmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<std::complex<float>> &ap,
                          DeviceMemory<std::complex<float>> *x, int incx) {
  return DoBlasInternal(cublasCtpmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuComplex(GpuMemory(ap)),
                        GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasTpmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<std::complex<double>> &ap,
                          DeviceMemory<std::complex<double>> *x, int incx) {
  return DoBlasInternal(cublasZtpmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuComplex(GpuMemory(ap)),
                        GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasTpsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<float> &ap, DeviceMemory<float> *x,
                          int incx) {
  return DoBlasInternal(cublasStpsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuMemory(ap),
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTpsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<double> &ap,
                          DeviceMemory<double> *x, int incx) {
  return DoBlasInternal(cublasDtpsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuMemory(ap),
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTpsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<std::complex<float>> &ap,
                          DeviceMemory<std::complex<float>> *x, int incx) {
  return DoBlasInternal(cublasCtpsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuComplex(GpuMemory(ap)),
                        GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasTpsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<std::complex<double>> &ap,
                          DeviceMemory<std::complex<double>> *x, int incx) {
  return DoBlasInternal(cublasZtpsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuComplex(GpuMemory(ap)),
                        GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasTrmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<float> &a, int lda,
                          DeviceMemory<float> *x, int incx) {
  return DoBlasInternal(cublasStrmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuMemory(a), lda,
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTrmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<double> &a, int lda,
                          DeviceMemory<double> *x, int incx) {
  return DoBlasInternal(cublasDtrmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuMemory(a), lda,
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTrmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          DeviceMemory<std::complex<float>> *x, int incx) {
  return DoBlasInternal(cublasCtrmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuComplex(GpuMemory(a)),
                        lda, GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasTrmv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          DeviceMemory<std::complex<double>> *x, int incx) {
  return DoBlasInternal(cublasZtrmv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuComplex(GpuMemory(a)),
                        lda, GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasTrsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<float> &a, int lda,
                          DeviceMemory<float> *x, int incx) {
  return DoBlasInternal(cublasStrsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuMemory(a), lda,
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTrsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<double> &a, int lda,
                          DeviceMemory<double> *x, int incx) {
  return DoBlasInternal(cublasDtrsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuMemory(a), lda,
                        GpuMemoryMutable(x), incx);
}

bool CUDABlas::DoBlasTrsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          DeviceMemory<std::complex<float>> *x, int incx) {
  return DoBlasInternal(cublasCtrsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuComplex(GpuMemory(a)),
                        lda, GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasTrsv(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, blas::Diagonal diag, uint64 n,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          DeviceMemory<std::complex<double>> *x, int incx) {
  return DoBlasInternal(cublasZtrsv, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans),
                        CUDABlasDiagonal(diag), n, GpuComplex(GpuMemory(a)),
                        lda, GpuComplex(GpuMemoryMutable(x)), incx);
}

bool CUDABlas::DoBlasGemm(
    Stream *stream, blas::Transpose transa,
    blas::Transpose transb, uint64 m, uint64 n, uint64 k,
    float alpha, const DeviceMemory<Eigen::half> &a, int lda,
    const DeviceMemory<Eigen::half> &b, int ldb, float beta,
    DeviceMemory<Eigen::half> *c, int ldc) {
#if CUDA_VERSION >= 7050
  VLOG(1) << port::Printf(
      "doing cuBLAS SGEMM: at=%d bt=%d m=%llu n=%llu "
      "k=%llu alpha=%f a=%p lda=%d b=%p ldb=%d beta=%f "
      "c=%p ldc=%d",
      static_cast<int>(transa), static_cast<int>(transb), m, n, k, alpha,
      a.opaque(), lda, b.opaque(), ldb, beta, c->opaque(), ldc);
  if (transa == blas::Transpose::kNoTranspose) {
    if (lda < static_cast<int64>(m)) {
      LOG(WARNING) << "GEMM lda was smaller than m (no transpose case); "
                      "precondition violation";
    }
  } else {
    if (lda < static_cast<int64>(k)) {
      LOG(WARNING) << "GEMM lda (" << lda << ") was smaller than k (" << k
                   << ") (transpose case); precondition violation";
    }
  }
  if (transb == blas::Transpose::kNoTranspose) {
    if (ldb < static_cast<int64>(k)) {
      LOG(WARNING) << "GEMM ldb (" << ldb << ") was smaller than k (" << k
                   << ") (no transpose case); precondition violation";
    }
  } else {
    if (ldb < static_cast<int64>(n)) {
      LOG(WARNING) << "GEMM ldb was smaller than n (transpose case); "
                      "precondition violation";
    }
  }

  bool use_tensor_ops = false;
#if CUDA_VERSION >= 9000
  int cc_major, cc_minor;
  stream->parent()->GetDeviceDescription().cuda_compute_capability(&cc_major,
                                                                   &cc_minor);

  // GPUs < sm_70 don't support tensor ops.
  if (cc_major >= 7 && TensorOpMathEnabled()) {
    use_tensor_ops = true;
  }
#endif

  return DoBlasInternalImpl(
      cublasSgemmEx, stream, true /* = pointer_mode_host */,
      true /* = err_on_failure= */, use_tensor_ops, CUDABlasTranspose(transa),
      CUDABlasTranspose(transb), m, n, k, &alpha, GpuMemory(a),
      SE_CUDA_DATA_HALF, lda, GpuMemory(b), SE_CUDA_DATA_HALF, ldb, &beta,
      GpuMemoryMutable(c), SE_CUDA_DATA_HALF, ldc);

#else
  LOG(ERROR) << "fp16 sgemm is not implemented in this cuBLAS version "
             << "(need at least CUDA 7.5)";
  return false;
#endif
}

bool CUDABlas::DoBlasGemm(Stream *stream, blas::Transpose transa,
                          blas::Transpose transb, uint64 m, uint64 n, uint64 k,
                          float alpha, const DeviceMemory<float> &a, int lda,
                          const DeviceMemory<float> &b, int ldb, float beta,
                          DeviceMemory<float> *c, int ldc) {
  VLOG(1) << port::Printf(
      "doing cuBLAS SGEMM: at=%d bt=%d m=%llu n=%llu "
      "k=%llu alpha=%f a=%p lda=%d b=%p ldb=%d beta=%f "
      "c=%p ldc=%d",
      static_cast<int>(transa), static_cast<int>(transb), m, n, k, alpha,
      a.opaque(), lda, b.opaque(), ldb, beta, c->opaque(), ldc);
  if (transa == blas::Transpose::kNoTranspose) {
    if (lda < static_cast<int64>(m)) {
      LOG(WARNING) << "GEMM lda was smaller than m (no transpose case); "
                      "precondition violation";
    }
  } else {
    if (lda < static_cast<int64>(k)) {
      LOG(WARNING) << "GEMM lda (" << lda << ") was smaller than k (" << k
                   << ") (transpose case); precondition violation";
    }
  }
  if (transb == blas::Transpose::kNoTranspose) {
    if (ldb < static_cast<int64>(k)) {
      LOG(WARNING) << "GEMM ldb (" << ldb << ") was smaller than k (" << k
                   << ") (no transpose case); precondition violation";
    }
  } else {
    if (ldb < static_cast<int64>(n)) {
      LOG(WARNING) << "GEMM ldb was smaller than n (transpose case); "
                      "precondition violation";
    }
  }
  return DoBlasInternal(cublasSgemm, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(transa), CUDABlasTranspose(transb), m,
                        n, k, &alpha, GpuMemory(a), lda, GpuMemory(b), ldb,
                        &beta, GpuMemoryMutable(c), ldc);
}

bool CUDABlas::DoBlasGemm(Stream *stream, blas::Transpose transa,
                          blas::Transpose transb, uint64 m, uint64 n, uint64 k,
                          double alpha, const DeviceMemory<double> &a, int lda,
                          const DeviceMemory<double> &b, int ldb, double beta,
                          DeviceMemory<double> *c, int ldc) {
  return DoBlasInternal(cublasDgemm, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(transa), CUDABlasTranspose(transb), m,
                        n, k, &alpha, GpuMemory(a), lda, GpuMemory(b), ldb,
                        &beta, GpuMemoryMutable(c), ldc);
}

bool CUDABlas::DoBlasGemm(Stream *stream, blas::Transpose transa,
                          blas::Transpose transb, uint64 m, uint64 n, uint64 k,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          const DeviceMemory<std::complex<float>> &b, int ldb,
                          std::complex<float> beta,
                          DeviceMemory<std::complex<float>> *c, int ldc) {
  return DoBlasInternal(cublasCgemm, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(transa), CUDABlasTranspose(transb), m,
                        n, k, GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(b)), ldb, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasGemm(Stream *stream, blas::Transpose transa,
                          blas::Transpose transb, uint64 m, uint64 n, uint64 k,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          const DeviceMemory<std::complex<double>> &b, int ldb,
                          std::complex<double> beta,
                          DeviceMemory<std::complex<double>> *c, int ldc) {
  return DoBlasInternal(cublasZgemm, stream, true /* = pointer_mode_host */,
                        CUDABlasTranspose(transa), CUDABlasTranspose(transb), m,
                        n, k, GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(b)), ldb, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasGemvWithProfiling(
    Stream *stream, blas::Transpose trans, uint64 m, uint64 n, float alpha,
    const DeviceMemory<float> &a, int lda, const DeviceMemory<float> &x,
    int incx, float beta, DeviceMemory<float> *y, int incy,
    blas::ProfileResult *output_profile_result) {
  return DoBlasGemvWithProfilingImpl(stream, trans, m, n, alpha, a, lda, x,
                                     incx, beta, y, incy,
                                     output_profile_result);
}

bool CUDABlas::DoBlasGemvWithProfiling(
    Stream *stream, blas::Transpose trans, uint64 m, uint64 n, double alpha,
    const DeviceMemory<double> &a, int lda, const DeviceMemory<double> &x,
    int incx, double beta, DeviceMemory<double> *y, int incy,
    blas::ProfileResult *output_profile_result) {
  return DoBlasGemvWithProfilingImpl(stream, trans, m, n, alpha, a, lda, x,
                                     incx, beta, y, incy,
                                     output_profile_result);
}

bool CUDABlas::DoBlasGemvWithProfiling(
    Stream *stream, blas::Transpose trans, uint64 m, uint64 n,
    std::complex<float> alpha, const DeviceMemory<std::complex<float>> &a,
    int lda, const DeviceMemory<std::complex<float>> &x, int incx,
    std::complex<float> beta, DeviceMemory<std::complex<float>> *y, int incy,
    blas::ProfileResult *output_profile_result) {
  return DoBlasGemvWithProfilingImpl(stream, trans, m, n, alpha, a, lda, x,
                                     incx, beta, y, incy,
                                     output_profile_result);
}

bool CUDABlas::DoBlasGemvWithProfiling(
    Stream *stream, blas::Transpose trans, uint64 m, uint64 n,
    std::complex<double> alpha, const DeviceMemory<std::complex<double>> &a,
    int lda, const DeviceMemory<std::complex<double>> &x, int incx,
    std::complex<double> beta, DeviceMemory<std::complex<double>> *y, int incy,
    blas::ProfileResult *output_profile_result) {
  return DoBlasGemvWithProfilingImpl(stream, trans, m, n, alpha, a, lda, x,
                                     incx, beta, y, incy,
                                     output_profile_result);
}

bool CUDABlas::DoBlasGemmWithProfiling(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, float alpha, const DeviceMemory<Eigen::half> &a,
    int lda, const DeviceMemory<Eigen::half> &b, int ldb, float beta,
    DeviceMemory<Eigen::half> *c, int ldc,
    blas::ProfileResult *output_profile_result) {
  return DoBlasGemmWithProfilingImpl(stream, transa, transb, m, n, k, alpha, a,
                                     lda, b, ldb, beta, c, ldc,
                                     output_profile_result);
}

bool CUDABlas::DoBlasGemmWithProfiling(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, float alpha, const DeviceMemory<float> &a, int lda,
    const DeviceMemory<float> &b, int ldb, float beta, DeviceMemory<float> *c,
    int ldc, blas::ProfileResult *output_profile_result) {
  return DoBlasGemmWithProfilingImpl(stream, transa, transb, m, n, k, alpha, a,
                                     lda, b, ldb, beta, c, ldc,
                                     output_profile_result);
}

bool CUDABlas::DoBlasGemmWithProfiling(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, double alpha, const DeviceMemory<double> &a, int lda,
    const DeviceMemory<double> &b, int ldb, double beta,
    DeviceMemory<double> *c, int ldc,
    blas::ProfileResult *output_profile_result) {
  return DoBlasGemmWithProfilingImpl(stream, transa, transb, m, n, k, alpha, a,
                                     lda, b, ldb, beta, c, ldc,
                                     output_profile_result);
}

bool CUDABlas::DoBlasGemmWithProfiling(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, std::complex<float> alpha,
    const DeviceMemory<std::complex<float>> &a, int lda,
    const DeviceMemory<std::complex<float>> &b, int ldb,
    std::complex<float> beta, DeviceMemory<std::complex<float>> *c, int ldc,
    blas::ProfileResult *output_profile_result) {
  return DoBlasGemmWithProfilingImpl(stream, transa, transb, m, n, k, alpha, a,
                                     lda, b, ldb, beta, c, ldc,
                                     output_profile_result);
}

bool CUDABlas::DoBlasGemmWithProfiling(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, std::complex<double> alpha,
    const DeviceMemory<std::complex<double>> &a, int lda,
    const DeviceMemory<std::complex<double>> &b, int ldb,
    std::complex<double> beta, DeviceMemory<std::complex<double>> *c, int ldc,
    blas::ProfileResult *output_profile_result) {
  return DoBlasGemmWithProfilingImpl(stream, transa, transb, m, n, k, alpha, a,
                                     lda, b, ldb, beta, c, ldc,
                                     output_profile_result);
}

template <typename T>
bool CUDABlas::DoBlasGemvWithProfilingImpl(
    Stream *stream, blas::Transpose trans, uint64 m, uint64 n, const T &alpha,
    const DeviceMemory<T> &a, int lda, const DeviceMemory<T> &x, int incx,
    const T &beta, DeviceMemory<T> *y, int incy,
    blas::ProfileResult *output_profile_result) {
  std::unique_ptr<GpuTimer, GpuTimerDeleter> timer;
  if (output_profile_result != nullptr) {
    timer.reset(new GpuTimer(parent_));
    if (!timer->Init() || !timer->Start(AsGpuStream(stream))) {
      return false;
    }
  }

  // Call blasGemm
  bool result =
      DoBlasGemv(stream, trans, m, n, alpha, a, lda, x, incx, beta, y, incy);

  if (timer != nullptr && result) {
    // GpuTimer will CHECK-fail if we Stop() it while the stream is in an error
    // state.
    if (!timer->Stop(AsGpuStream(stream))) {
      return false;
    }
    output_profile_result->set_is_valid(true);
    output_profile_result->set_algorithm(blas::kDefaultBlasGemv);
    output_profile_result->set_elapsed_time_in_ms(
        timer->GetElapsedMilliseconds());
  }
  return result;
}

template <typename T, typename ParamType>
bool CUDABlas::DoBlasGemmWithProfilingImpl(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, const ParamType &alpha, const DeviceMemory<T> &a,
    int lda, const DeviceMemory<T> &b, int ldb, const ParamType &beta,
    DeviceMemory<T> *c, int ldc, blas::ProfileResult *output_profile_result) {
  std::unique_ptr<GpuTimer, GpuTimerDeleter> timer;
  if (output_profile_result != nullptr) {
    timer.reset(new GpuTimer(parent_));
    if (!timer->Init() || !timer->Start(AsGpuStream(stream))) {
      return false;
    }
  }

  // Call blasGemm
  bool result = DoBlasGemm(stream, transa, transb, m, n, k, alpha, a, lda, b,
                           ldb, beta, c, ldc);

  if (timer != nullptr && result) {
    // GpuTimer will CHECK-fail if we Stop() it while the stream is in an error
    // state.
    if (!timer->Stop(AsGpuStream(stream))) {
      return false;
    }
    output_profile_result->set_is_valid(true);
    output_profile_result->set_algorithm(blas::kDefaultBlasGemm);
    output_profile_result->set_elapsed_time_in_ms(
        timer->GetElapsedMilliseconds());
  }
  return result;
}

static bool UsesTensorOps(blas::AlgorithmType algo) {
#if CUDA_VERSION >= 9000
  cublasGemmAlgo_t cublas_algo = static_cast<cublasGemmAlgo_t>(algo);
  return cublas_algo >= CUBLAS_GEMM_DEFAULT_TENSOR_OP;
#else
  return false;
#endif
}

template <typename InType>
static bool TensorOpsAvailable(int cc_major) {
#if CUDA_VERSION >= 9000
  // cublas *does* allow tensor ops on inputs that are not fp16, so this is not
  // strictly correct.  We can't simply enable it, though, as that would change
  // clients' behavior significantly: Using tensor ops on fp32 inputs cause them
  // to be rounded to fp16.
  if (cc_major >= 7 && TensorOpMathEnabled() &&
      std::is_same<InType, Eigen::half>::value) {
    return true;
  }
#endif
  return false;
}

template <typename InT, typename OutT, typename CompT>
bool CUDABlas::DoBlasGemmWithAlgorithmImpl(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, const HostOrDeviceScalar<CompT> &alpha,
    const DeviceMemory<InT> &a, int lda, const DeviceMemory<InT> &b, int ldb,
    const HostOrDeviceScalar<CompT> &beta, DeviceMemory<OutT> *c, int ldc,
    blas::ComputationType computation_type, blas::AlgorithmType algorithm,
    blas::ProfileResult *output_profile_result) {
  // GPUs < sm_50 don't support cublasGemmEx.
  int cc_major, cc_minor;
  if (stream->parent()->GetDeviceDescription().cuda_compute_capability(
          &cc_major, &cc_minor) &&
      cc_major < 5) {
    VLOG(2) << "DoBlasGemmWithAlgorithm returning false because sm" << cc_major
            << cc_minor << " devices don't support explicit gemm algorithms.";
    return false;
  }

  if (UsesTensorOps(algorithm) && !TensorOpsAvailable<InT>(cc_major)) {
    if (std::is_same<InT, Eigen::half>::value) {
      VLOG(2) << "DoBlasGemmWithAlgorithm returning false because algorithm "
              << algorithm
              << " uses tensor ops, but tensor ops are not available in sm"
              << cc_major << "X devices.";
    } else {
      VLOG(2) << "DoBlasGemmWithAlgorithm returning false because algorithm "
              << algorithm
              << " uses tensor ops, but the input data type is not fp16.";
    }
    return false;
  }

  // Either both 'alpha' and 'beta' need to be pointers to device memory, or
  // they need to be both host scalars.
  if (alpha.is_pointer() != beta.is_pointer()) {
    VLOG(2) << "DoBlasGemmWithAlgorithm returning false because one of `alpha` "
               "and `beta` is a pointer, but the other is not.";
    return false;
  }

  std::unique_ptr<GpuTimer, GpuTimerDeleter> timer;
  if (output_profile_result != nullptr) {
    timer.reset(new GpuTimer(parent_));
    if (!timer->Init() || !timer->Start(AsGpuStream(stream))) {
      VLOG(2) << "DoBlasGemmWithAlgorithm returning false because "
                 "output_profile_result was given, but we were unable to "
                 "create a GpuTimer.";
      return false;
    }
  }

  // Return false if we might be hitting a cuBLAS bug that produces the wrong
  // result. See nvbugs/2156201, b/79126339.
#if CUDA_VERSION >= 9000 && CUDA_VERSION < 9020
  if ((algorithm == CUBLAS_GEMM_DEFAULT || algorithm >= CUBLAS_GEMM_ALGO13) &&
      std::max({m, n, k}) >= 2097153 && cc_major < 7) {
    VLOG(2) << "DoBlasGemmWithAlgorithm returning false to work around cudnn "
               "<9.2 bug with m, n, or k >= 2097153.  See b/79126339.";
    return false;
  }
#endif

  cudaDataType_t cuda_in_type = CUDADataType<InT>::type;
  // Since we are converting 'algorithm' to cublasGemmAlgo_t by static_cast,
  // we do the following compile-time check on the default value:
  static_assert(blas::kDefaultGemmAlgo == CUBLAS_GEMM_DFALT, "");
  // If 'alpha' and 'beta' are host scalars and CompT is Eigen::half, we
  // essentially reinterpet_cast to __half, which is safe because Eigen::half
  // inherits from __half.
  bool result = DoBlasInternalFailureOK(
      cublasGemmEx, stream, /* pointer_mode_host = */ !alpha.is_pointer(),
      CUDABlasTranspose(transa), CUDABlasTranspose(transb), m, n, k,
      alpha.is_pointer() ? GpuMemory(alpha.pointer()) : &alpha.value(),
      GpuMemory(a), cuda_in_type, lda, GpuMemory(b), cuda_in_type, ldb,
      beta.is_pointer() ? GpuMemory(beta.pointer()) : &beta.value(),
      GpuMemoryMutable(c), CUDADataType<OutT>::type, ldc,
      CUDAComputationType(computation_type),
      static_cast<cublasGemmAlgo_t>(algorithm));

  if (timer != nullptr && result) {
    // GpuTimer will CHECK-fail if we Stop() it while the stream is in an error
    // state.
    if (!timer->Stop(AsGpuStream(stream))) {
      VLOG(2) << "DoBlasGemmWithAlgorithm returning false; unable to stop "
                 "GpuTimer.";
      return false;
    }
    output_profile_result->set_is_valid(true);
    output_profile_result->set_algorithm(algorithm);
    output_profile_result->set_elapsed_time_in_ms(
        timer->GetElapsedMilliseconds());
  }
  return result;
}

bool CUDABlas::GetBlasGemmAlgorithms(
    std::vector<blas::AlgorithmType> *out_algorithms) {
  // cublasGemmAlgo_t (and the function that accepts this type, cublasGemmEx)
  // were first introduced in CUDA 8.
  //
  // Note that when CUDA version and compute capability is not sufficient, we
  // still return the out_algorithms. Caller needs to make sure that in this
  // case, the returned vector is empty.
  *out_algorithms = {
    CUBLAS_GEMM_DFALT,
    CUBLAS_GEMM_ALGO0,
    CUBLAS_GEMM_ALGO1,
    CUBLAS_GEMM_ALGO2,
    CUBLAS_GEMM_ALGO3,
    CUBLAS_GEMM_ALGO4,
    CUBLAS_GEMM_ALGO5,
    CUBLAS_GEMM_ALGO6,
    CUBLAS_GEMM_ALGO7,
#if CUDA_VERSION >= 9000
    CUBLAS_GEMM_ALGO8,
    CUBLAS_GEMM_ALGO9,
    CUBLAS_GEMM_ALGO10,
    CUBLAS_GEMM_ALGO11,
    CUBLAS_GEMM_ALGO12,
    CUBLAS_GEMM_ALGO13,
    CUBLAS_GEMM_ALGO14,
    CUBLAS_GEMM_ALGO15,
    CUBLAS_GEMM_ALGO16,
    CUBLAS_GEMM_ALGO17,
    CUBLAS_GEMM_DFALT_TENSOR_OP,
    CUBLAS_GEMM_ALGO0_TENSOR_OP,
    CUBLAS_GEMM_ALGO1_TENSOR_OP,
    CUBLAS_GEMM_ALGO2_TENSOR_OP,
    CUBLAS_GEMM_ALGO3_TENSOR_OP,
    CUBLAS_GEMM_ALGO4_TENSOR_OP,
#endif
#if CUDA_VERSION >= 9020
    CUBLAS_GEMM_ALGO18,
    CUBLAS_GEMM_ALGO19,
    CUBLAS_GEMM_ALGO20,
    CUBLAS_GEMM_ALGO21,
    CUBLAS_GEMM_ALGO22,
    CUBLAS_GEMM_ALGO23,
    CUBLAS_GEMM_ALGO5_TENSOR_OP,
    CUBLAS_GEMM_ALGO6_TENSOR_OP,
    CUBLAS_GEMM_ALGO7_TENSOR_OP,
    CUBLAS_GEMM_ALGO8_TENSOR_OP,
    CUBLAS_GEMM_ALGO9_TENSOR_OP,
    CUBLAS_GEMM_ALGO10_TENSOR_OP,
    CUBLAS_GEMM_ALGO11_TENSOR_OP,
    CUBLAS_GEMM_ALGO12_TENSOR_OP,
    CUBLAS_GEMM_ALGO13_TENSOR_OP,
    CUBLAS_GEMM_ALGO14_TENSOR_OP,
    CUBLAS_GEMM_ALGO15_TENSOR_OP,
#endif
  };
  return true;
}

bool CUDABlas::DoBlasGemmWithAlgorithm(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, const HostOrDeviceScalar<int> &alpha,
    const DeviceMemory<int8> &a, int lda, const DeviceMemory<int8> &b, int ldb,
    const HostOrDeviceScalar<int> &beta, DeviceMemory<int> *c, int ldc,
    blas::ComputationType computation_type, blas::AlgorithmType algorithm,
    blas::ProfileResult *output_profile_result) {
  return DoBlasGemmWithAlgorithmImpl(
      stream, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc,
      computation_type, algorithm, output_profile_result);
}

bool CUDABlas::DoBlasGemmWithAlgorithm(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, const HostOrDeviceScalar<Eigen::half> &alpha,
    const DeviceMemory<Eigen::half> &a, int lda,
    const DeviceMemory<Eigen::half> &b, int ldb,
    const HostOrDeviceScalar<Eigen::half> &beta, DeviceMemory<Eigen::half> *c,
    int ldc, blas::ComputationType computation_type,
    blas::AlgorithmType algorithm, blas::ProfileResult *output_profile_result) {
  if (computation_type == blas::ComputationType::kF32) {
    if (alpha.is_pointer() || beta.is_pointer()) {
      // We cannot easily convert a pointer to f16 memory to a pointer to f32
      // memory from here, so we don't support this for now.
      // TODO(akuegel): Investigate whether we can do the conversion before
      // calling DoBlasGemmWithAlgorithm.
      return false;
    }
    HostOrDeviceScalar<float> float_alpha(static_cast<float>(alpha.value()));
    HostOrDeviceScalar<float> float_beta(static_cast<float>(beta.value()));
    return DoBlasGemmWithAlgorithmImpl(
        stream, transa, transb, m, n, k, float_alpha, a, lda, b, ldb,
        float_beta, c, ldc, computation_type, algorithm, output_profile_result);
  }

  CHECK_EQ(computation_type, blas::ComputationType::kF16);
  return DoBlasGemmWithAlgorithmImpl(
      stream, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc,
      computation_type, algorithm, output_profile_result);
}

bool CUDABlas::DoBlasGemmWithAlgorithm(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, const HostOrDeviceScalar<float> &alpha,
    const DeviceMemory<float> &a, int lda, const DeviceMemory<float> &b,
    int ldb, const HostOrDeviceScalar<float> &beta, DeviceMemory<float> *c,
    int ldc, blas::ComputationType computation_type,
    blas::AlgorithmType algorithm, blas::ProfileResult *output_profile_result) {
  return DoBlasGemmWithAlgorithmImpl(
      stream, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc,
      computation_type, algorithm, output_profile_result);
}

bool CUDABlas::DoBlasGemmWithAlgorithm(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, const HostOrDeviceScalar<double> &alpha,
    const DeviceMemory<double> &a, int lda, const DeviceMemory<double> &b,
    int ldb, const HostOrDeviceScalar<double> &beta, DeviceMemory<double> *c,
    int ldc, blas::ComputationType computation_type,
    blas::AlgorithmType algorithm, blas::ProfileResult *output_profile_result) {
  return DoBlasGemmWithAlgorithmImpl(
      stream, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc,
      computation_type, algorithm, output_profile_result);
}

bool CUDABlas::DoBlasGemmWithAlgorithm(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, const HostOrDeviceScalar<std::complex<float>> &alpha,
    const DeviceMemory<std::complex<float>> &a, int lda,
    const DeviceMemory<std::complex<float>> &b, int ldb,
    const HostOrDeviceScalar<std::complex<float>> &beta,
    DeviceMemory<std::complex<float>> *c, int ldc,
    blas::ComputationType computation_type, blas::AlgorithmType algorithm,
    blas::ProfileResult *output_profile_result) {
  return DoBlasGemmWithAlgorithmImpl(
      stream, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc,
      computation_type, algorithm, output_profile_result);
}

bool CUDABlas::DoBlasGemmWithAlgorithm(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, const HostOrDeviceScalar<std::complex<double>> &alpha,
    const DeviceMemory<std::complex<double>> &a, int lda,
    const DeviceMemory<std::complex<double>> &b, int ldb,
    const HostOrDeviceScalar<std::complex<double>> &beta,
    DeviceMemory<std::complex<double>> *c, int ldc,
    blas::ComputationType computation_type, blas::AlgorithmType algorithm,
    blas::ProfileResult *output_profile_result) {
  return DoBlasGemmWithAlgorithmImpl(
      stream, transa, transb, m, n, k, alpha, a, lda, b, ldb, beta, c, ldc,
      computation_type, algorithm, output_profile_result);
}

template <typename T>
struct HalfAsFloat {
  typedef T type;
};

template <>
struct HalfAsFloat<Eigen::half> {
  typedef float type;
};

template <typename T, typename Scalar, typename FuncT>
port::Status CUDABlas::DoBlasGemmBatchedInternal(
    FuncT cublas_func, Stream *stream, blas::Transpose transa,
    blas::Transpose transb, uint64 m, uint64 n, uint64 k, Scalar alpha,
    const port::ArraySlice<DeviceMemory<T> *> &a_ptrs_to_wrappers, int lda,
    const port::ArraySlice<DeviceMemory<T> *> &b_ptrs_to_wrappers, int ldb,
    Scalar beta, const port::ArraySlice<DeviceMemory<T> *> &c_ptrs_to_wrappers,
    int ldc, int batch_count, ScratchAllocator *scratch_allocator) {
  std::vector<T *> a_raw_ptrs, b_raw_ptrs, c_raw_ptrs;
  for (int i = 0; i < batch_count; ++i) {
    a_raw_ptrs.push_back(static_cast<T *>(a_ptrs_to_wrappers[i]->opaque()));
    b_raw_ptrs.push_back(static_cast<T *>(b_ptrs_to_wrappers[i]->opaque()));
    c_raw_ptrs.push_back(static_cast<T *>(c_ptrs_to_wrappers[i]->opaque()));
  }

  typedef typename HalfAsFloat<typename GpuComplexT<T>::type>::type CUDA_T;

  const size_t size = batch_count * sizeof(CUDA_T *);

  // Device-side copy of pointers to matrices.
  DeviceMemory<CUDA_T *> a;
  DeviceMemory<CUDA_T *> b;
  DeviceMemory<CUDA_T *> c;

  // If temporary space is allocated for device-side copies of pointers to
  // matrices, that temporary space should not be freed until this function
  // returns. Although the values for these unique_ptrs are not set here, they
  // are declared at this scope so they will be destroyed when the function
  // returns.
  //
  // If a scratch allocator is provided, these pointers will not be used at all.
  std::unique_ptr<TemporaryDeviceMemory<CUDA_T *>> a_temporary;
  std::unique_ptr<TemporaryDeviceMemory<CUDA_T *>> b_temporary;
  std::unique_ptr<TemporaryDeviceMemory<CUDA_T *>> c_temporary;

  // Decide how to allocate device-side copy of pointers to matrices based on
  // whether a scratch allocator was passed.
  if (scratch_allocator != nullptr) {
    SE_ASSIGN_OR_RETURN(DeviceMemory<uint8> a_bytes,
                        scratch_allocator->AllocateBytes(stream, size));
    SE_ASSIGN_OR_RETURN(DeviceMemory<uint8> b_bytes,
                        scratch_allocator->AllocateBytes(stream, size));
    SE_ASSIGN_OR_RETURN(DeviceMemory<uint8> c_bytes,
                        scratch_allocator->AllocateBytes(stream, size));
    a = DeviceMemory<CUDA_T *>(a_bytes);
    b = DeviceMemory<CUDA_T *>(b_bytes);
    c = DeviceMemory<CUDA_T *>(c_bytes);
  } else {
    SE_ASSIGN_OR_RETURN(a_temporary,
                        stream->AllocateTemporaryArray<CUDA_T *>(batch_count));
    SE_ASSIGN_OR_RETURN(b_temporary,
                        stream->AllocateTemporaryArray<CUDA_T *>(batch_count));
    SE_ASSIGN_OR_RETURN(c_temporary,
                        stream->AllocateTemporaryArray<CUDA_T *>(batch_count));
    a = DeviceMemory<CUDA_T *>(*a_temporary->mutable_device_memory());
    b = DeviceMemory<CUDA_T *>(*b_temporary->mutable_device_memory());
    c = DeviceMemory<CUDA_T *>(*c_temporary->mutable_device_memory());
  }

  if (!stream->ThenMemcpy(&a, a_raw_ptrs.data(), size).ok() ||
      !stream->ThenMemcpy(&b, b_raw_ptrs.data(), size).ok() ||
      !stream->ThenMemcpy(&c, c_raw_ptrs.data(), size).ok()) {
    return port::Status(port::error::INTERNAL,
                        "failed to copy memory from host to device in "
                        "CUDABlas::DoBlasGemmBatched");
  }

  cudaDataType_t data_type = CUDADataType<T>::type;

#if CUDA_VERSION >= 9010
  int cc_major, cc_minor;
  if (stream->parent()->GetDeviceDescription().cuda_compute_capability(
          &cc_major, &cc_minor) &&
      cc_major >= 5) {
    bool use_tensor_ops = TensorOpMathEnabled() && data_type == CUDA_R_16F;
    cublasGemmAlgo_t algo =
        (use_tensor_ops ? CUBLAS_GEMM_DFALT_TENSOR_OP : CUBLAS_GEMM_DFALT);
    cudaDataType_t compute_type =
        (data_type == CUDA_R_16F ? CUDA_R_32F : data_type);
    const void **a_void_ptrs = reinterpret_cast<const void **>(
        const_cast<const CUDA_T **>(GpuMemory(a)));
    const void **b_void_ptrs = reinterpret_cast<const void **>(
        const_cast<const CUDA_T **>(GpuMemory(b)));
    void **c_void_ptrs =
        reinterpret_cast<void **>(const_cast<CUDA_T **>(GpuMemory(c)));
    bool ok;
    ok = DoBlasInternalImpl(
        cublasGemmBatchedEx, stream, true /* = pointer_mode_host */,
        true /* = err_on_failure */, use_tensor_ops, CUDABlasTranspose(transa),
        CUDABlasTranspose(transb), m, n, k, &alpha, a_void_ptrs, data_type, lda,
        b_void_ptrs, data_type, ldb, &beta, c_void_ptrs, data_type, ldc,
        batch_count, compute_type, algo);
    if (ok) {
      return port::Status::OK();
    }
    return port::Status(port::error::INTERNAL,
                        "failed BLAS call, see log for details");
  }
#endif
  // either CUDA_VERSION < 9.1 or SM < 5.0
  if (data_type != CUDA_R_16F) {
    bool ok = DoBlasInternal(
        cublas_func, stream, true /* = pointer_mode_host */,
        CUDABlasTranspose(transa), CUDABlasTranspose(transb), m, n, k,
        GpuComplex(&alpha), const_cast<const CUDA_T **>(GpuMemory(a)), lda,
        const_cast<const CUDA_T **>(GpuMemory(b)), ldb, GpuComplex(&beta),
        const_cast<CUDA_T **>(GpuMemory(c)), ldc, batch_count);
    if (ok) {
      return port::Status::OK();
    }
    return port::Status(port::error::INTERNAL,
                        "failed BLAS call, see log for details");
  } else {
    // Fall back to a loop for fp16
    for (int b = 0; b < batch_count; ++b) {
      const DeviceMemory<T> &a_matrix = *a_ptrs_to_wrappers[b];
      const DeviceMemory<T> &b_matrix = *b_ptrs_to_wrappers[b];
      DeviceMemory<T> *c_matrix = c_ptrs_to_wrappers[b];
      bool ok = DoBlasGemm(stream, transa, transb, m, n, k, alpha, a_matrix,
                           lda, b_matrix, ldb, beta, c_matrix, ldc);
      if (!ok) {
        return port::Status(port::error::INTERNAL,
                            "failed BLAS call, see log for details");
      }
    }
    return port::Status::OK();
  }
}

bool CUDABlas::DoBlasGemmBatched(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, float alpha,
    const port::ArraySlice<DeviceMemory<Eigen::half> *> &a_array, int lda,
    const port::ArraySlice<DeviceMemory<Eigen::half> *> &b_array, int ldb,
    float beta, const port::ArraySlice<DeviceMemory<Eigen::half> *> &c_array,
    int ldc, int batch_count, ScratchAllocator *scratch_allocator) {
  // Note: The func passed here (cublasSgemmBatched) is not actually called,
  // due to special handling of fp16 inside DoBlasGemmBatchedInternal.
  port::Status status = DoBlasGemmBatchedInternal(
      cublasSgemmBatched, stream, transa, transb, m, n, k, alpha, a_array, lda,
      b_array, ldb, beta, c_array, ldc, batch_count, scratch_allocator);
  if (!status.ok()) {
    LOG(ERROR) << status;
  }
  return status.ok();
}

bool CUDABlas::DoBlasGemmBatched(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, float alpha,
    const port::ArraySlice<DeviceMemory<float> *> &a_array, int lda,
    const port::ArraySlice<DeviceMemory<float> *> &b_array, int ldb, float beta,
    const port::ArraySlice<DeviceMemory<float> *> &c_array, int ldc,
    int batch_count, ScratchAllocator *scratch_allocator) {
  port::Status status = DoBlasGemmBatchedInternal(
      cublasSgemmBatched, stream, transa, transb, m, n, k, alpha, a_array, lda,
      b_array, ldb, beta, c_array, ldc, batch_count, scratch_allocator);
  if (!status.ok()) {
    LOG(ERROR) << status;
  }
  return status.ok();
}

bool CUDABlas::DoBlasGemmBatched(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, double alpha,
    const port::ArraySlice<DeviceMemory<double> *> &a_array, int lda,
    const port::ArraySlice<DeviceMemory<double> *> &b_array, int ldb,
    double beta, const port::ArraySlice<DeviceMemory<double> *> &c_array,
    int ldc, int batch_count, ScratchAllocator *scratch_allocator) {
  port::Status status = DoBlasGemmBatchedInternal(
      cublasDgemmBatched, stream, transa, transb, m, n, k, alpha, a_array, lda,
      b_array, ldb, beta, c_array, ldc, batch_count, scratch_allocator);
  if (!status.ok()) {
    LOG(ERROR) << status;
  }
  return status.ok();
}

bool CUDABlas::DoBlasGemmBatched(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, std::complex<float> alpha,
    const port::ArraySlice<DeviceMemory<std::complex<float>> *> &a_array,
    int lda,
    const port::ArraySlice<DeviceMemory<std::complex<float>> *> &b_array,
    int ldb, std::complex<float> beta,
    const port::ArraySlice<DeviceMemory<std::complex<float>> *> &c_array,
    int ldc, int batch_count, ScratchAllocator *scratch_allocator) {
  port::Status status = DoBlasGemmBatchedInternal(
      cublasCgemmBatched, stream, transa, transb, m, n, k, alpha, a_array, lda,
      b_array, ldb, beta, c_array, ldc, batch_count, scratch_allocator);
  if (!status.ok()) {
    LOG(ERROR) << status;
  }
  return status.ok();
}

bool CUDABlas::DoBlasGemmBatched(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, std::complex<double> alpha,
    const port::ArraySlice<DeviceMemory<std::complex<double>> *> &a_array,
    int lda,
    const port::ArraySlice<DeviceMemory<std::complex<double>> *> &b_array,
    int ldb, std::complex<double> beta,
    const port::ArraySlice<DeviceMemory<std::complex<double>> *> &c_array,
    int ldc, int batch_count, ScratchAllocator *scratch_allocator) {
  port::Status status = DoBlasGemmBatchedInternal(
      cublasZgemmBatched, stream, transa, transb, m, n, k, alpha, a_array, lda,
      b_array, ldb, beta, c_array, ldc, batch_count, scratch_allocator);
  if (!status.ok()) {
    LOG(ERROR) << status;
  }
  return status.ok();
}

bool CUDABlas::DoBlasGemmStridedBatched(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, float alpha, const DeviceMemory<Eigen::half> &a,
    int lda, int64 stride_a, const DeviceMemory<Eigen::half> &b, int ldb,
    int64 stride_b, float beta, DeviceMemory<Eigen::half> *c, int ldc,
    int64 stride_c, int batch_count) {
  bool use_tensor_ops = false;
#if CUDA_VERSION >= 9000
  int cc_major, cc_minor;
  if (stream->parent()->GetDeviceDescription().cuda_compute_capability(
          &cc_major, &cc_minor)) {
    // GPUs < sm_70 don't support tensor ops.
    if (cc_major >= 7 && TensorOpMathEnabled()) {
      use_tensor_ops = true;
    }
#if CUDA_VERSION >= 9010
    if (cc_major >= 5) {
      cublasGemmAlgo_t algo =
          (use_tensor_ops ? CUBLAS_GEMM_DFALT_TENSOR_OP : CUBLAS_GEMM_DFALT);
      bool ok = DoBlasInternalImpl(
          cublasGemmStridedBatchedEx, stream, true /* = pointer_mode_host */,
          true /* = err_on_failure */, use_tensor_ops,
          CUDABlasTranspose(transa), CUDABlasTranspose(transb), m, n, k, &alpha,
          GpuMemory(a), CUDA_R_16F, lda, stride_a, GpuMemory(b), CUDA_R_16F,
          ldb, stride_b, &beta, GpuMemoryMutable(c), CUDA_R_16F, ldc, stride_c,
          batch_count, CUDA_R_32F, algo);
      if (ok) {
        return true;
      }
      LOG(ERROR) << "failed BLAS call, see log for details";
      return false;
    }
#endif
  }
#endif
  // Either CUDA_VERSION < 9.1 or SM < 5.0. Fall back to a loop.
  for (int batch = 0; batch < batch_count; ++batch) {
    const auto *a_matrix =
        reinterpret_cast<const __half *>(GpuMemory(a) + batch * stride_a);
    const auto *b_matrix =
        reinterpret_cast<const __half *>(GpuMemory(b) + batch * stride_b);
    auto *c_matrix =
        reinterpret_cast<__half *>(GpuMemoryMutable(c) + batch * stride_c);
    bool ok = DoBlasInternalImpl(
        cublasSgemmEx, stream, true /* = pointer_mode_host */,
        true /* = err_on_failure= */, use_tensor_ops, CUDABlasTranspose(transa),
        CUDABlasTranspose(transb), m, n, k, &alpha, a_matrix, SE_CUDA_DATA_HALF,
        lda, b_matrix, SE_CUDA_DATA_HALF, ldb, &beta, c_matrix,
        SE_CUDA_DATA_HALF, ldc);
    if (!ok) {
      LOG(ERROR) << "failed BLAS call, see log for details";
      return false;
    }
  }
  return true;
}

bool CUDABlas::DoBlasGemmStridedBatched(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, float alpha, const DeviceMemory<float> &a, int lda,
    int64 stride_a, const DeviceMemory<float> &b, int ldb, int64 stride_b,
    float beta, DeviceMemory<float> *c, int ldc, int64 stride_c,
    int batch_count) {
  return DoBlasInternal(
      cublasSgemmStridedBatched, stream, true /* = pointer_mode_host */,
      CUDABlasTranspose(transa), CUDABlasTranspose(transb), m, n, k, &alpha,
      GpuMemory(a), lda, stride_a, GpuMemory(b), ldb, stride_b, &beta,
      GpuMemoryMutable(c), ldc, stride_c, batch_count);
}

bool CUDABlas::DoBlasGemmStridedBatched(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, double alpha, const DeviceMemory<double> &a, int lda,
    int64 stride_a, const DeviceMemory<double> &b, int ldb, int64 stride_b,
    double beta, DeviceMemory<double> *c, int ldc, int64 stride_c,
    int batch_count) {
  return DoBlasInternal(
      cublasDgemmStridedBatched, stream, true /* = pointer_mode_host */,
      CUDABlasTranspose(transa), CUDABlasTranspose(transb), m, n, k, &alpha,
      GpuMemory(a), lda, stride_a, GpuMemory(b), ldb, stride_b, &beta,
      GpuMemoryMutable(c), ldc, stride_c, batch_count);
}

bool CUDABlas::DoBlasGemmStridedBatched(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, std::complex<float> alpha,
    const DeviceMemory<std::complex<float>> &a, int lda, int64 stride_a,
    const DeviceMemory<std::complex<float>> &b, int ldb, int64 stride_b,
    std::complex<float> beta, DeviceMemory<std::complex<float>> *c, int ldc,
    int64 stride_c, int batch_count) {
  return DoBlasInternal(
      cublasCgemmStridedBatched, stream, true /* = pointer_mode_host */,
      CUDABlasTranspose(transa), CUDABlasTranspose(transb), m, n, k,
      GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda, stride_a,
      GpuComplex(GpuMemory(b)), ldb, stride_b, GpuComplex(&beta),
      GpuComplex(GpuMemoryMutable(c)), ldc, stride_c, batch_count);
}

bool CUDABlas::DoBlasGemmStridedBatched(
    Stream *stream, blas::Transpose transa, blas::Transpose transb, uint64 m,
    uint64 n, uint64 k, std::complex<double> alpha,
    const DeviceMemory<std::complex<double>> &a, int lda, int64 stride_a,
    const DeviceMemory<std::complex<double>> &b, int ldb, int64 stride_b,
    std::complex<double> beta, DeviceMemory<std::complex<double>> *c, int ldc,
    int64 stride_c, int batch_count) {
  return DoBlasInternal(
      cublasZgemmStridedBatched, stream, true /* = pointer_mode_host */,
      CUDABlasTranspose(transa), CUDABlasTranspose(transb), m, n, k,
      GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda, stride_a,
      GpuComplex(GpuMemory(b)), ldb, stride_b, GpuComplex(&beta),
      GpuComplex(GpuMemoryMutable(c)), ldc, stride_c, batch_count);
}

bool CUDABlas::DoBlasHemm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, uint64 m, uint64 n,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          const DeviceMemory<std::complex<float>> &b, int ldb,
                          std::complex<float> beta,
                          DeviceMemory<std::complex<float>> *c, int ldc) {
  return DoBlasInternal(cublasChemm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo), m, n,
                        GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(b)), ldb, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasHemm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, uint64 m, uint64 n,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          const DeviceMemory<std::complex<double>> &b, int ldb,
                          std::complex<double> beta,
                          DeviceMemory<std::complex<double>> *c, int ldc) {
  return DoBlasInternal(cublasZhemm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo), m, n,
                        GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(b)), ldb, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasHerk(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, uint64 n, uint64 k,
                          float alpha,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          float beta, DeviceMemory<std::complex<float>> *c,
                          int ldc) {
  return DoBlasInternal(cublasCherk, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        &beta, GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasHerk(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, uint64 n, uint64 k,
                          double alpha,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          double beta, DeviceMemory<std::complex<double>> *c,
                          int ldc) {
  return DoBlasInternal(cublasZherk, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        &beta, GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasHer2k(Stream *stream, blas::UpperLower uplo,
                           blas::Transpose trans, uint64 n, uint64 k,
                           std::complex<float> alpha,
                           const DeviceMemory<std::complex<float>> &a, int lda,
                           const DeviceMemory<std::complex<float>> &b, int ldb,
                           float beta, DeviceMemory<std::complex<float>> *c,
                           int ldc) {
  return DoBlasInternal(cublasCher2k, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(b)), ldb, &beta,
                        GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasHer2k(Stream *stream, blas::UpperLower uplo,
                           blas::Transpose trans, uint64 n, uint64 k,
                           std::complex<double> alpha,
                           const DeviceMemory<std::complex<double>> &a, int lda,
                           const DeviceMemory<std::complex<double>> &b, int ldb,
                           double beta, DeviceMemory<std::complex<double>> *c,
                           int ldc) {
  return DoBlasInternal(cublasZher2k, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(b)), ldb, &beta,
                        GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasSymm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, uint64 m, uint64 n,
                          float alpha, const DeviceMemory<float> &a, int lda,
                          const DeviceMemory<float> &b, int ldb, float beta,
                          DeviceMemory<float> *c, int ldc) {
  return DoBlasInternal(cublasSsymm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo), m, n,
                        &alpha, GpuMemory(a), lda, GpuMemory(b), ldb, &beta,
                        GpuMemoryMutable(c), ldc);
}

bool CUDABlas::DoBlasSymm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, uint64 m, uint64 n,
                          double alpha, const DeviceMemory<double> &a, int lda,
                          const DeviceMemory<double> &b, int ldb, double beta,
                          DeviceMemory<double> *c, int ldc) {
  return DoBlasInternal(cublasDsymm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo), m, n,
                        &alpha, GpuMemory(a), lda, GpuMemory(b), ldb, &beta,
                        GpuMemoryMutable(c), ldc);
}

bool CUDABlas::DoBlasSymm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, uint64 m, uint64 n,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          const DeviceMemory<std::complex<float>> &b, int ldb,
                          std::complex<float> beta,
                          DeviceMemory<std::complex<float>> *c, int ldc) {
  return DoBlasInternal(cublasCsymm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo), m, n,
                        GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(b)), ldb, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasSymm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, uint64 m, uint64 n,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          const DeviceMemory<std::complex<double>> &b, int ldb,
                          std::complex<double> beta,
                          DeviceMemory<std::complex<double>> *c, int ldc) {
  return DoBlasInternal(cublasZsymm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo), m, n,
                        GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(b)), ldb, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasSyrk(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, uint64 n, uint64 k,
                          float alpha, const DeviceMemory<float> &a, int lda,
                          float beta, DeviceMemory<float> *c, int ldc) {
  return DoBlasInternal(cublasSsyrk, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, &alpha, GpuMemory(a), lda, &beta,
                        GpuMemoryMutable(c), ldc);
}

bool CUDABlas::DoBlasSyrk(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, uint64 n, uint64 k,
                          double alpha, const DeviceMemory<double> &a, int lda,
                          double beta, DeviceMemory<double> *c, int ldc) {
  return DoBlasInternal(cublasDsyrk, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, &alpha, GpuMemory(a), lda, &beta,
                        GpuMemoryMutable(c), ldc);
}

bool CUDABlas::DoBlasSyrk(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, uint64 n, uint64 k,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          std::complex<float> beta,
                          DeviceMemory<std::complex<float>> *c, int ldc) {
  return DoBlasInternal(cublasCsyrk, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(&beta), GpuComplex(GpuMemoryMutable(c)),
                        ldc);
}

bool CUDABlas::DoBlasSyrk(Stream *stream, blas::UpperLower uplo,
                          blas::Transpose trans, uint64 n, uint64 k,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          std::complex<double> beta,
                          DeviceMemory<std::complex<double>> *c, int ldc) {
  return DoBlasInternal(cublasZsyrk, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(&beta), GpuComplex(GpuMemoryMutable(c)),
                        ldc);
}

bool CUDABlas::DoBlasSyr2k(Stream *stream, blas::UpperLower uplo,
                           blas::Transpose trans, uint64 n, uint64 k,
                           float alpha, const DeviceMemory<float> &a, int lda,
                           const DeviceMemory<float> &b, int ldb, float beta,
                           DeviceMemory<float> *c, int ldc) {
  return DoBlasInternal(cublasSsyr2k, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, &alpha, GpuMemory(a), lda, GpuMemory(b), ldb, &beta,
                        GpuMemoryMutable(c), ldc);
}

bool CUDABlas::DoBlasSyr2k(Stream *stream, blas::UpperLower uplo,
                           blas::Transpose trans, uint64 n, uint64 k,
                           double alpha, const DeviceMemory<double> &a, int lda,
                           const DeviceMemory<double> &b, int ldb, double beta,
                           DeviceMemory<double> *c, int ldc) {
  return DoBlasInternal(cublasDsyr2k, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, &alpha, GpuMemory(a), lda, GpuMemory(b), ldb, &beta,
                        GpuMemoryMutable(c), ldc);
}

bool CUDABlas::DoBlasSyr2k(Stream *stream, blas::UpperLower uplo,
                           blas::Transpose trans, uint64 n, uint64 k,
                           std::complex<float> alpha,
                           const DeviceMemory<std::complex<float>> &a, int lda,
                           const DeviceMemory<std::complex<float>> &b, int ldb,
                           std::complex<float> beta,
                           DeviceMemory<std::complex<float>> *c, int ldc) {
  return DoBlasInternal(cublasCsyr2k, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(b)), ldb, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasSyr2k(Stream *stream, blas::UpperLower uplo,
                           blas::Transpose trans, uint64 n, uint64 k,
                           std::complex<double> alpha,
                           const DeviceMemory<std::complex<double>> &a, int lda,
                           const DeviceMemory<std::complex<double>> &b, int ldb,
                           std::complex<double> beta,
                           DeviceMemory<std::complex<double>> *c, int ldc) {
  return DoBlasInternal(cublasZsyr2k, stream, true /* = pointer_mode_host */,
                        CUDABlasUpperLower(uplo), CUDABlasTranspose(trans), n,
                        k, GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemory(b)), ldb, GpuComplex(&beta),
                        GpuComplex(GpuMemoryMutable(c)), ldc);
}

bool CUDABlas::DoBlasTrmm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, blas::Transpose transa,
                          blas::Diagonal diag, uint64 m, uint64 n, float alpha,
                          const DeviceMemory<float> &a, int lda,
                          DeviceMemory<float> *b, int ldb) {
  return DoBlasInternal(cublasStrmm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo),
                        CUDABlasTranspose(transa), CUDABlasDiagonal(diag), m, n,
                        &alpha, GpuMemory(a), lda, GpuMemoryMutable(b), ldb,
                        GpuMemoryMutable(b), ldb);
}

bool CUDABlas::DoBlasTrmm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, blas::Transpose transa,
                          blas::Diagonal diag, uint64 m, uint64 n, double alpha,
                          const DeviceMemory<double> &a, int lda,
                          DeviceMemory<double> *b, int ldb) {
  return DoBlasInternal(cublasDtrmm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo),
                        CUDABlasTranspose(transa), CUDABlasDiagonal(diag), m, n,
                        &alpha, GpuMemory(a), lda, GpuMemoryMutable(b), ldb,
                        GpuMemoryMutable(b), ldb);
}

bool CUDABlas::DoBlasTrmm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, blas::Transpose transa,
                          blas::Diagonal diag, uint64 m, uint64 n,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          DeviceMemory<std::complex<float>> *b, int ldb) {
  return DoBlasInternal(cublasCtrmm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo),
                        CUDABlasTranspose(transa), CUDABlasDiagonal(diag), m, n,
                        GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemoryMutable(b)), ldb,
                        GpuComplex(GpuMemoryMutable(b)), ldb);
}

bool CUDABlas::DoBlasTrmm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, blas::Transpose transa,
                          blas::Diagonal diag, uint64 m, uint64 n,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          DeviceMemory<std::complex<double>> *b, int ldb) {
  return DoBlasInternal(cublasZtrmm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo),
                        CUDABlasTranspose(transa), CUDABlasDiagonal(diag), m, n,
                        GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemoryMutable(b)), ldb,
                        GpuComplex(GpuMemoryMutable(b)), ldb);
}

bool CUDABlas::DoBlasTrsm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, blas::Transpose transa,
                          blas::Diagonal diag, uint64 m, uint64 n, float alpha,
                          const DeviceMemory<float> &a, int lda,
                          DeviceMemory<float> *b, int ldb) {
  return DoBlasInternal(cublasStrsm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo),
                        CUDABlasTranspose(transa), CUDABlasDiagonal(diag), m, n,
                        &alpha, GpuMemory(a), lda, GpuMemoryMutable(b), ldb);
}

bool CUDABlas::DoBlasTrsm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, blas::Transpose transa,
                          blas::Diagonal diag, uint64 m, uint64 n, double alpha,
                          const DeviceMemory<double> &a, int lda,
                          DeviceMemory<double> *b, int ldb) {
  return DoBlasInternal(cublasDtrsm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo),
                        CUDABlasTranspose(transa), CUDABlasDiagonal(diag), m, n,
                        &alpha, GpuMemory(a), lda, GpuMemoryMutable(b), ldb);
}

bool CUDABlas::DoBlasTrsm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, blas::Transpose transa,
                          blas::Diagonal diag, uint64 m, uint64 n,
                          std::complex<float> alpha,
                          const DeviceMemory<std::complex<float>> &a, int lda,
                          DeviceMemory<std::complex<float>> *b, int ldb) {
  return DoBlasInternal(cublasCtrsm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo),
                        CUDABlasTranspose(transa), CUDABlasDiagonal(diag), m, n,
                        GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemoryMutable(b)), ldb);
}

bool CUDABlas::DoBlasTrsm(Stream *stream, blas::Side side,
                          blas::UpperLower uplo, blas::Transpose transa,
                          blas::Diagonal diag, uint64 m, uint64 n,
                          std::complex<double> alpha,
                          const DeviceMemory<std::complex<double>> &a, int lda,
                          DeviceMemory<std::complex<double>> *b, int ldb) {
  return DoBlasInternal(cublasZtrsm, stream, true /* = pointer_mode_host */,
                        CUDABlasSide(side), CUDABlasUpperLower(uplo),
                        CUDABlasTranspose(transa), CUDABlasDiagonal(diag), m, n,
                        GpuComplex(&alpha), GpuComplex(GpuMemory(a)), lda,
                        GpuComplex(GpuMemoryMutable(b)), ldb);
}

}  // namespace gpu

void initialize_cublas() {
  port::Status status =
      PluginRegistry::Instance()->RegisterFactory<PluginRegistry::BlasFactory>(
          cuda::kCudaPlatformId, gpu::kCuBlasPlugin, "cuBLAS",
          [](internal::StreamExecutorInterface *parent) -> blas::BlasSupport * {
            gpu::GpuExecutor *cuda_executor =
                dynamic_cast<gpu::GpuExecutor *>(parent);
            if (cuda_executor == nullptr) {
              LOG(ERROR)
                  << "Attempting to initialize an instance of the cuBLAS "
                  << "support library with a non-CUDA StreamExecutor";
              return nullptr;
            }

            gpu::CUDABlas *blas = new gpu::CUDABlas(cuda_executor);
            if (!blas->Init()) {
              // Note: Init() will log a more specific error.
              delete blas;
              return nullptr;
            }
            return blas;
          });

  if (!status.ok()) {
    LOG(ERROR) << "Unable to register cuBLAS factory: "
               << status.error_message();
  }

  PluginRegistry::Instance()->SetDefaultFactory(
      cuda::kCudaPlatformId, PluginKind::kBlas, gpu::kCuBlasPlugin);
}

}  // namespace stream_executor

REGISTER_MODULE_INITIALIZER(register_cublas,
                            { stream_executor::initialize_cublas(); });