Custom Operators (Custom-based)

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Overview

When built-in operators cannot meet requirements during network development, you can call the Python API Custom primitive defined in MindSpore to quickly create different types of custom operators for use.

Traditional methods to add a custom operator need three steps: registering the operator primitive, implementing the operator, and registering the operator information.

The related concepts are as follows:

  • Operator primitive: defines the frontend API prototype of an operator on the network. It is the basic unit for forming a network model and includes the operator name, attribute (optional), input and output names, output shape inference method, and output data type inference method.

  • Operator implementation: defines a Python function (JIT custom operators) or a C++ class (GPU and CPU custom operators), which describes the implementation of the internal computation logic of an operator.

  • Operator information: describes basic information about an operator, such as the operator name, supported input and output data types, supported input and output data formats, and attributes. It is the basis for the backend to select and map operators.

Compared with traditional custom operator creating methods, creating custom operators based on Custom primitive has several advantages:

  • Different custom operators use the same Custom primitive, there is no need to define a primitive for every operator. The above three parts of work can be implemented in a network script in a unified way and used as part of the network expression, there is no need to modify and recompile the source codes of MindSpore.

  • It unifies the interface and usage for different kinds of custom operators, which is convenient for network developers to flexibly choose which kind of custom operator to use according to their needs.

  • Supports defining custom operators with hybrid expression, which can be used across platforms.

The operator development methods supported by custom operator based on the Custom primitive include: hybrid,aot, pyfunc, julia, and akg.

The difference between these operator development methods are as follows:

Defining Methods

Development Language

Compilation Method

Supported Platforms

Recommended Scenarios

pyfunc

Python

JIT

CPU

Fast algorithm verification, need to interact with Python and other scenarios

hybrid

MindSpore HYBRID DSL

N/A

GPU CPU

General development and rapid validation for all platforms

akg

MindSpore AKG DSL

JIT

GPU

GPU platform general scenarios

aot

C/C++/CUDA

AOT

GPU CPU

high-performance scenarios / use third-party operators scenarios

julia

Julia

N/A

CPU

Science compute scenarios / use Julia scenarios

  • The full name of DSL is Domain Specific Language.

  • AOT(Ahead Of Time) compiling means the operator implementation needs to be compiled into a dynamic library in advance and then automatically called by the framework when the network is running. JIT(Just In Time) compiling does not need to compile the operator implementation in advance, the operator implementation will be directly called by the framework during network compilation or runtime.

  • In order to distinguish the types and compilation methods of custom operators, in the following text, the lowercase aot is used to refer to the type of the custom operator, and the uppercase AOT is used to refer to the compilation method of the custom operator.

The recommended methods for all platforms under different scenarios are as follows:

  • GPU: hybrid(general purpose development), aot(high performance development based on CUDA);

  • CPU: hybrid(general purpose development), aot(high performance development based on C++).

Different custom operator defining methods use different development languages to implement the operator, but the development process is the same, including operator implementation, operator output shape, data type inference, and operator information registration (optional). You can choose which one to use based on needs. The defining methods of these custom operators will be introduced here, and examples are provided for each method.

More examples can be found in the MindSpore source code tests/st/ops/graph_kernel/custom.

The Introduction to Custom Operator: An Example

To help users quickly get started with custom operators, here is an example of a pyfunc type custom operator to help users understand the definition process of custom operators. The following defines a custom operator that implements the sin calculation based on the pyfunc pattern. Custom operators of type pyfunc use native Python syntax to define operator implementation functions, describing the implementation of the operator's internal computational logic. During the network runtime, framework will automatically call this function. In order to express the calculation of a custom operator, we write a Python native function based on numpy to calculate the sine function.

import numpy as np

def sin_by_numpy(x):
    return np.sin(x)

Then we need to define two more functions. One is the infer shape function, while the other is the infer dtype function. Here's something to keep in mind:

  • The derivative function of the tensor shape is the shape of the input tensor;

  • The derivative function of the tensor dtype is the dtype of the input tensor;

def infer_shape(x):

    #    1. here x is the shape of the input tensor
    #    2. sin is elements, so the shape of the output is the same as that of the input.
    return x

def infer_dtype(x):

    #    1. here x is the dtype of the input tensor
    #    2. sin keeps the dtype, so the dtype of the output is the same as that of the input.
    return x

Then we use the above functions to create a custom operator, and the inputs include:

  • func: the computation function of the custom op. Here we use sin_by_numpy above;

  • out_shape: the infer shape function. Here we use infer_shape above;

  • out_dtype: the infer dtype function. Here we use infer_dtype above;

  • func_type: the mode of the custom operator. Here we use "pyfunc".

from mindspore import ops

sin_by_numpy_op = ops.Custom(func = sin_by_numpy, # this is for the computation function
                             out_shape = infer_shape, # this is for the infer shape function
                             out_dtype = infer_dtype, # this is for the infer dtype function
                             func_type = "pyfunc" # this is for the custom op mode
                            )

Adding other environment dependencies and operator call statements, we obtain the complete custom operator use case as follows.

import numpy as np
import mindspore as ms
from mindspore import ops

ms.set_context(mode=ms.GRAPH_MODE, device_target="CPU")

def sin_by_numpy(x):
    return np.sin(x)

def infer_shape(x):
    return x

def infer_dtype(x):
    return x

sin_by_numpy_op = ops.Custom(func = sin_by_numpy,
                             out_shape = infer_shape,
                             out_dtype = infer_dtype,
                             func_type = "pyfunc" )
input_tensor = ms.Tensor([0,1, 0.2, 0.3, 0.4], dtype=ms.float32)
result_cus = sin_by_numpy_op(input_tensor)
print(result_cus)

Then we have the following results as sin values of above inputs.

[0.         0.84147096 0.19866933 0.29552022 0.38941833]

Then we have completed the definition of a custom operator of type pyfunc. For more complete examples of pyfunc-type custom operators, see the use cases in the MindSpore source code.

JIT Compiled Custom Operator

JIT (Just In Time) refers to operators compiled directly by the framework during network compilation or runtime. Users can define custom operators of this type directly in their network scripts using Python scripts, and then call the corresponding operator compiler to automatically compile them based on the operator and backend types. This type of custom operator definition is convenient and has better backend adaptability.

Defining Custom Operator of Hybrid Type

A custom operator of Hybrid type is the default defined type of a custom operator. By using a custom operator of the Hybrid type, users can describe the operator calculation logic in Python-like syntax without paying attention to the engineering details defined by the operator for the MindSpore framework, allowing the user to focus on the algorithm itself.

Custom operators of Hybrid type use MindSpore Hybrid DSL to describe the implementation of the calculation logic inside the operator. Functions defined with MindSpore Hybrid DSL can be parsed by the AKG Operator Compiler for JIT compilation to generate efficient operators for use in training reasoning for large-scale models. At the same time, the function defined by MindSpore Hybrid DSL can be called directly as a numpy function, which is convenient for users to debug and flexibly switch to pyfunc type custom operator, so that when developed, custom operator expressions are reused for multiple modes, multiple platforms and multiple scenes.

The following example (test_custom_hybrid.py) shows how to write a custom operator of the hybrid type. The operator computes the sum of two tensors. Notice that custom operators of Hybrid type use the source to source transformation method to connect the graph compiler and the operator compiler. Users can use the keywords of MindSpore Hybrid DSL directly in the script, such as output_tensor below, without importing any Python modules. For more information about the keywords, refer to MindSpore Hybrid DSL Keywords.

import numpy as np
from mindspore import ops
import mindspore as ms
from mindspore.ops import kernel

ms.set_context(device_target="GPU")

# Operator implementation, Hybrid DSL
@kernel
def add(a, b):
    c = output_tensor(a.shape, a.dtype)
    for i0 in range(a.shape[0]):
        for i1 in range(a.shape[1]):
            c[i0, i1] = a[i0, i1] + b[i0, i1]
    return c

if __name__ == "__main__":
    # Define custom operators of the hybrid type (Custom's default mode)
    op = ops.Custom(add)

    x0 = np.array([[0.0, 0.0], [1.0, 1.0]]).astype(np.float32)
    x1 = np.array([[2.0, 2.0], [3.0, 3.0]]).astype(np.float32)
    output = op(ms.Tensor(x0), ms.Tensor(x1))
    print(output)

In this case,

  • The Hybrid type is the default type for Custom.

  • The input of custom operators with Hybrid type must be a function with @kernel.

  • When defining a custom operator for the Hybrid type, you can use the built-in automatic shape/dtype derivation function, or you can manually enter the shape/dtype deduction function.

Execute case:

python test_custom_hybrid.py

The execution result is as follows:

[[2. 2.]
 [4. 4.]]

For more complete examples of hybrid-type custom operators, see the use cases in the MindSpore source code.

Defining Custom Operator of akg Type

The custom operator of akg type uses the MindSpore AKG operator DSL to describe the internal calculation logic of the operator. MindSpore AKG is an operator development and compilation framework based on TVM(Tensor Virtual Machine) and Polyhedral technology, and it supports multiple types of operator DSL, such as Hybrid, IR builder and TVM compute.

Operator output shape and data type inference can be realized by defining Python functions to describe the inference logic of operator output shape and data type.

If the operator contains attributes or only supports specific input and output data types or data formats, operator information needs to be registered, and for how to generate operator information, see Registering the Operator Information. If the operator information is not registered, when operator selection and mapping are made in the backend, the operator information is derived from the input of the current operator.

The following is an example of the development process of a custom operator of type akg in test_custom_akg.py, where the custom operator implements the addition of two input tensors.

Here is the content of test_custom_akg.py:

import numpy as np
import mindspore as ms
import mindspore.ops as ops

ms.set_context(device_target="GPU")

# Operator implementation, Hybrid DSL
def add(a, b):
    c = output_tensor(a.shape, a.dtype)
    for i0 in range(a.shape[0]):
        for i1 in range(a.shape[1]):
            c[i0, i1] = a[i0, i1] + b[i0, i1]
    return c

if __name__ == "__main__":
    # Define a custom operator of akg type
    op = ops.Custom(add, out_shape=lambda x, _: x, out_dtype=lambda x, _: x, func_type="akg")

    x0 = np.array([[0.0, 0.0], [1.0, 1.0]]).astype(np.float32)
    x1 = np.array([[2.0, 2.0], [3.0, 3.0]]).astype(np.float32)
    output = op(ms.Tensor(x0), ms.Tensor(x1))
    print(output)

The following points need to be explained in this example:

  • set_context(device_target="GPU") indicates that the operator runs on the GPU platform.

  • Use Python lambda functions to infer the output shape and data type, and pass them to the out_shape and out_dtype parameters of the Custom primitive. In this example, the lambda function indicates that the output shape and data type are the same as the information of the first input tensor.

  • The operator information is not registered, so the operator information of the custom operator will be inferred from the inputs.

Execute case:

python test_custom_akg.py

The execution result is as follows:

[[2. 2.]
 [4. 4.]]

For more complete examples of akg-type custom operators, see the use cases in the MindSpore source code.

AOT-Compiled Custom Operator

AOT type of customized operator means that the user compiles the operator into a binary file beforehand and then accesses the network. Usually, users optimize their implementations using programming languages such as C/C++/CUDA and compile their operators as dynamic libraries to accelerate MindSpore networks. As a result, users can perform ultimate optimization on their operators and leverage the performance of the corresponding backend hardware. Here, we will introduce some basic knowledge about AOT type custom operators. For more advanced usage and functionality of AOT type custom operators, please refer to Advanced Usage of AOT Type Custom Operators.

Defining Custom Operator of aot Type

The custom operator of aot type adopts the AOT compilation method, which requires network developers to hand-write the source code file of the operator implementation based on a specific interface and compiles the source code file into a dynamic library in advance, and then the framework will automatically call and run the function defined in the dynamic library. In terms of the development language of the operator implementation, the GPU platform supports CUDA, and the CPU platform supports C and C++. The interface specification of the operator implementation in the source file is as follows:

extern "C" int func_name(int nparam, void **params, int *ndims, int64_t **shapes, const char **dtypes, void *stream, void *extra);

where the function name func_name can be replaced with any valid function name. The return value is of type int. 0 means normal exit, and non-zero means an exception occurs. The meaning of the parameter list is as follows:

  • nparam (int): The number of inputs and outputs. For example, if an operator has 2 inputs and 1 output, then the value of nparam is 3.

  • params (void **): An array of pointers, with each pointer pointing to the input or output data. For example, if an operator has 2 inputs and 1 output, then params[0] points to the first input data, params[1] points to the second input data, params[2] points to the output data.

  • ndims (int *): An array of integers, each integer represents the dimensions of the shape of input or output. For example, if params[i] is a tensor with shape [1024, 1024], then ndims[i] is 2.

  • shapes (int64_t **): An array of shapes, each element in array represents for the shape of input or output. For example, if params[i] is a tensor with shape [1024, 1024], then shapes[i][0] is 1024, shapes[i][1] is 1024.

  • dtypes (const char **): Array of data types, each element in array represents for the data type of input or output. The value of data type can be "float32", "float16", "float", "float64", "int", "int8", "int16", "int32", "int64", "uint", "uint8", "uint16", "uint32", "uint64", "bool".

  • stream (void *): Stream pointer, only used in Cuda file.

  • extra (void *): Used for further extension.

In the Python script, the format for the func input in Custom is Path_To_Func:CustomFunc, where CustomFunc is the name of the function above and Path_To_Func is the path to the corresponding function source file or binary library.

  • MindSpore recognizes the automatic compilation through the file name suffix. To use the automatic compilation feature, please use source files with suffixes such as cpp, cc, or cu. Otherwise, MindSpore will treat it as a binary library path;

  • To prevent malicious third-party libraries from tampering, please set the environment variable MS_CUSTOM_AOT_WHITE_LIST to the path of legitimate third-party libraries. Only files in the directories specified by MS_CUSTOM_AOT_WHITE_LIST and its subdirectories will be called by custom operators.

Operator output shape and data type inference can be realized by defining Python functions to describe the inference logic.

If the operator only supports some specific input and output data types, the operator information needs to be registered. For the creation of operator information, please refer to Registering the Operator Information.

The following examples introduce the development process of aot type custom operator on GPU platform and CPU platform, where the custom operator implements the function of adding two input tensors.

A GPU Example

Use the CUDA language to write the source file add.cu for the operator implementation:

#define THREADS 1024
__global__ void CustomAddKernel(float *input1, float *input2, float *output, size_t size) {
  auto idx = blockIdx.x * THREADS + threadIdx.x;
  if (idx < size) {
    output[idx] = input1[idx] + input2[idx];
  }
}

extern "C" int CustomAdd(int nparam, void **params, int *ndims, int64_t **shapes, const char **dtypes, void *stream,
                         void *extra) {
  cudaStream_t custream = static_cast<cudaStream_t>(stream);
  if (nparam != 3) return 1;
  void *input1 = params[0];
  void *input2 = params[1];
  void *output = params[2];
  size_t size = 1;

  for (int i = 0; i < ndims[2]; i++) {
    size *= shapes[2][i];
  }
  int n = size / THREADS;
  for (int i = 0; i < nparam; i++) {
    if (strcmp(dtypes[i], "float32") != 0) {
      return 2;
    }
  }
  CustomAddKernel<<<n + 1, THREADS, 0, custream>>>(static_cast<float *>(input1), static_cast<float *>(input2),
                                                   static_cast<float *>(output), size);
  return 0;
}

Compile add.cu into a dynamic library add.so:

nvcc --shared -Xcompiler -fPIC -o add.so add.cu

Write the test case test_custom_aot.py:

import numpy as np
import mindspore as ms
import mindspore.ops as ops

ms.set_context(device_target="GPU")

if __name__ == "__main__":
    # Define a custom operator of aot type
    op = ops.Custom("./add.so:CustomAdd", out_shape=lambda x, _: x, out_dtype=lambda x, _: x, func_type="aot")

    x0 = np.array([[0.0, 0.0], [1.0, 1.0]]).astype(np.float32)
    x1 = np.array([[2.0, 2.0], [3.0, 3.0]]).astype(np.float32)
    output = op(ms.Tensor(x0), ms.Tensor(x1))
    print(output)

The following points need to be explained in this example:

  • In this example, you need to place test_custom_aot.py and add.so in the same directory. If add.so is in another directory, you need to replace the value of the first parameter of Custom primitive with the absolute path of add.so.

  • Use Python lambda functions to infer the output shape and data type, and pass them to the out_shape and out_dtype parameters of the Custom primitive. In this example, the lambda function indicates that the output shape and data type are the same as the information of the first input tensor.

  • The operator information is not registered, so the operator information of the custom operator will be inferred from the inputs.

Execute case:

python test_custom_aot.py

The execution result is as follows:

[[2. 2.]
 [4. 4.]]

A CPU Example

Use C/C++ language to write the source file add.cc for the operator implementation:

#include <string.h>
using size_t = decltype(sizeof(int));
using int64_t = decltype(sizeof(long));

extern "C" int CustomAdd(int nparam, void **params, int *ndims, int64_t **shapes, const char **dtypes, void *stream, void *extra) {
  if (nparam != 3) return 1;
  float *input1 = static_cast<float *>(params[0]);
  float *input2 = static_cast<float *>(params[1]);
  float *output = static_cast<float *>(params[2]);
  size_t size = 1;
  for (int i = 0; i < ndims[2]; i++) {
    size *= shapes[2][i];
  }
  for (int i = 0; i < nparam; i++) {
    if (strcmp(dtypes[i], "float32") != 0) {
      return 2;
    }
  }
  for (int i = 0; i < size; i++) {
    output[i] = input1[i] + input2[i];
  }
  return 0;
}

Compile add.cc into a dynamic library add.so:

g++ --shared -fPIC -o add.so add.cc

Write the test case test_custom_aot.py:

import numpy as np
import mindspore as ms
import mindspore.ops as ops

ms.set_context(device_target="CPU")

if __name__ == "__main__":
    # Define a custom operator of aot type
    op = ops.Custom("./add.so:CustomAdd", out_shape=lambda x, _: x, out_dtype=lambda x, _: x, func_type="aot")

    x0 = np.array([[0.0, 0.0], [1.0, 1.0]]).astype(np.float32)
    x1 = np.array([[2.0, 2.0], [3.0, 3.0]]).astype(np.float32)
    output = op(ms.Tensor(x0), ms.Tensor(x1))
    print(output)

The following points need to be explained in this example:

  • In this example, you need to place test_custom_aot.py and add.so in the same directory. If add.so is in another directory, you need to replace the value of the first parameter of Custom primitive with the absolute path of add.so.

  • Use Python lambda functions to infer the output shape and data type, and pass them to the out_shape and out_dtype parameters of the Custom primitive. In this example, the lambda function indicates that the output shape and data type are the same as the information of the first input tensor.

  • The operator information is not registered, so the operator information of the custom operator will be inferred from the inputs.

Execute case:

python test_custom_aot.py

The execution result is as follows:

[[2. 2.]
 [4. 4.]]

For more complete examples of aot-type custom operators, see the use cases in the MindSpore source code.

Custom Operator with Third Party Frontend

As one of the future development goals of MindSpore, the fusion of AI and scientific computing draws more and more attention from the industry. Based on the flexibility of the representation, MindSpore custom operator also makes exploration on the scientific computing, and introduces the programming frontend for HPC to MindSpore via custom operator.

Defining Custom Operator of julia Type

Julia is a high level general programming language which has high performance and is easy to use. Julia is firstly designed for scientific computing, and also gain the favor of general users due to its high effience. The custom operator of julia type uses Julia to describe the internal calculation logic of the operator. The framework will automatically call this function during the network runtime.

Operator output shape and data type inference can be realized by defining Python functions to describe the inference logic of the operator output shape and the data type.

If the custom operator only supports specific input and output data types, you need to define the operator information. For the creation of operator information, please refer to Registering the Operator Information.

Takes the function of adding two input tensors as an example to introduce how to define a custom operator of julia type.

Firstly, users need to implement Julia functions via separate files, such as (add.jl):

# add.jl
module Add
# inputs: x, y, output: z, output should use .= to inplace assign
function add(x, y, z)
    z .= x + y
end
end

Secondly, refer to the Julia function written above in a custom operator in the network script, taking test_custom_julia.py as an example:

import numpy as np
import mindspore as ms
import mindspore.ops as ops

ms.set_context(device_target="CPU")

if __name__ == "__main__":
    op = ops.Custom("./add.jl:Add:add", out_shape=lambda x, _: x, out_dtype=lambda x, _: x, func_type="julia")
    x0 = np.array([[0.0, 0.0], [1.0, 1.0]]).astype(np.float32)
    x1 = np.array([[2.0, 2.0], [3.0, 3.0]]).astype(np.float32)
    output = op(ms.Tensor(x0), ms.Tensor(x1))
    print(output)

The following points need to be explained in this example:

  • Use Python lambda functions to infer the output shape and data type, and pass them to the out_shape and out_dtype parameters of the Custom primitive. In this example, the lambda function indicates that the output shape and data type are the same as the information of the first input tensor.

  • The operator information is not registered, so the operator information of the custom operator will be inferred from the inputs.

Execute case:

python test_custom_julia.py

The execution result is as follows:

[[2. 2.]
 [4. 4.]]

Matters need attention:

  1. User should make sure to download the correct version of Julia, that is, version >= 1.6.0.

  2. User is required to set julia/lib to LD_LIBRARY_PATH, because the Julia C API called at runtime is obtained from libjulia.so, taking julia-1.6.5 as an example:

    # download julia-1.6.5
    wget https://julialang-s3.julialang.org/bin/linux/x64/1.6/julia-1.6.5-linux-x86_64.tar.gz
    # for arm server
    # wget https://julialang-s3.julialang.org/bin/linux/aarch64/1.6/julia-1.6.5-linux-aarch64.tar.gz
    # extract file
    tar xvf julia-1.6.5-linux-x86_64.tar.gz
    # if $JULIA_DIR not exist
    export LD_LIBRARY_PATH=$PWD/julia-1.6.5/lib:$LD_LIBRARY_PATH
    # else
    export LD_LIBRARY_PATH=$JULIA_DIR/lib:$LD_LIBRARY_PATH
    
  3. Custom operator's first arg func should keep format like file_name:module_name:func_name, file_name should include path, suggest using absolute path.

  4. Julia file should include module, module include function, both ends with end.

  5. The input and output order of the Julia function needs to be consistent with the input and output order of the operator.

  6. The final output of the Julia function, i.e. assignment of kernel output, needs to use .=, otherwise the result cannot be written to memory.

  7. Julia code supports Julia's common syntax, users need to ensure that the syntax is correct and the function can be executed correctly.

  8. Users who want to use Julia's third-party software packages in Julia files need to download the corresponding software to ensure that they can call it correctly, which can be called through import pkg; pkg.add ("somepkg") to install.

  9. julia array is column major arranged in memory, while numpy array is row major. If Julia and numpy are compared, non-elemwise calculations need to consider memory arrangement. In the Julia function, the conversion of numpy array and julia array can be performed by following the following code example:An example of MatMul:

    function change_input_to_row_major(x)
       return permutedims(reshape(x, reverse(size(x))), length(size(x)):-1:1)
    end
    
    function change_output_to_row_major(x)
       return reshape(permutedims(x, length(size(x)):-1:1), size(x))
    end
    

Taking matrix multiplication as an example:

# julia array is column-major, numpy array is row-major
# user should change julia or numpy's layout to keep same behavior
#= EXAMPLE
A[2,3]               B[3,4]               C[2,4]
NUMPY:
[[1, 2, 3]       [[1, 2, 3, 4]         [[38, 44, 50,  56]
 [4, 5, 6]]       [5, 6, 7, 8]          [83, 98, 113,128]]
                  [9,10,11,12]]
JULIA:
change_input_to_row_major:
1.inputs read numpy data from memory:
[[1, 3, 5]       [[1, 4, 7,10]
 [2, 4, 6]]       [2, 5, 8,11]
                  [3, 6, 9,12]]
2.inputs after reshape(reverse(shape)):
[[1, 4]          [[1, 5, 9]
 [2, 5]           [2, 6,10]
 [3, 6]]          [3, 7,11]
                  [4, 8,12]]
3.inputs after transpose/permutedims:
[[1, 2, 3]       [[1, 2, 3, 4]         [[38, 44, 50,  56]
 [4, 5, 6]]       [5, 6, 7, 8]          [83, 98, 113,128]]
                  [9,10,11,12]]
change_output_to_row_major:
1.output after transpose/permutedims:
                                       [[38, 83]
                                        [44, 98]
                                        [50,113]
                                        [56,128]
2.output after reshape:
                                       [[38, 50, 83, 113]
                                        [44, 56, 98, 128]]
3.output read numpy data from memory:
                                       [[38, 44, 50,  56]
                                        [83, 98,113, 128]]
=#
function foo!(x, y, z)
    x = change_input_to_row_major(x)
    y = change_input_to_row_major(y)
    z .= gemm(x, y, z)
    z .= change_output_to_row_major(z)
end

For more complete examples of julia-type custom operators, see the use cases in the MindSpore source code.