.. _softmax_prot:

Softmax Prototype and Function List
-----------------------------------

Description
^^^^^^^^^^^

This kernel performs Softmax activation function that is a generalization of the 
logistic function that transforms the input vector according to the following formula:

.. math:: y_{i} = \frac{e^{x_{i}}}{\sum_{j}^{}e^{x_{j}}}

Where:

   :math:`x_{i}` *–* :math:`i_{\text{th}}` *value in input data subset*

   :math:`x_{j}` *–* :math:`j_{\text{th}}` *value in the same input data
   subset*

   :math:`y_{i}` *–* :math:`i_{\text{th}}` *value in output data subset*
	
The softmax function might be applied to the whole tensor, or along a specific axis. 
In the first case, all the input values are involved in the calculation of each output value. 
If an axis is specified, then the softmax function is applied to each slice along the 
specific axis independently. 

This kernel uses a look-up table (LUTs) to perform data transformation. 
See :ref:`lut_prot` section and the pseudo-code sample for more details on LUT structure preparation.
Use the following functions for the purpose:

 - :code:`mli_krn_softmax_get_lut_size`
 - :code:`mli_krn_softmax_create_lut`

Functions
^^^^^^^^^

Kernels which implement softmax functions have the following prototype:

.. code:: c

   mli_status mli_krn_softmax_<data_format>(
      const mli_tensor *in,
      const mli_lut *lut,
      const mli_softmax_cfg *cfg,
     mli_tensor *out);
..

where ``data_format`` is one of the data formats listed in Table :ref:`mli_data_fmts` and the function 
parameters are shown in the following table:

.. table:: Softmax Function Parameters
   :align: center
   :widths: auto
   
   +----------------+-------------------------+-----------------------------------------------+
   | **Parameter**  | **Type**                | **Description**                               |
   +================+=========================+===============================================+
   | ``in``         | ``mli_tensor *``        | [IN] Pointer to constant input tensor.        |
   +----------------+-------------------------+-----------------------------------------------+
   | ``lut``        | ``mli_lut *``           | [IN] Pointer to a valid LUT table             |
   |                |                         | structure prepared for softmax activation.    |
   +----------------+-------------------------+-----------------------------------------------+
   | ``cfg``        | ``mli_softmax_cfg *``   | [IN] Pointer to softmax parameters structure. |
   +----------------+-------------------------+-----------------------------------------------+
   | ``out``        | ``mli_tensor *``        | [IN | OUT] Pointer to output tensor.          |
   |                |                         | Result is stored here                         |
   +----------------+-------------------------+-----------------------------------------------+
..

``mli_softmax_cfg`` is defined as:

.. code:: c

   typedef mli_prelu_cfg mli_softmax_cfg;
..
  
See Table :ref:`t_mli_prelu_cfg_desc` for more details.

.. table:: List of Available Softmax Functions
   :align: center
   :widths: auto
   
   +---------------------------+------------------------------------+
   | **Function Name**         | **Details**                        |
   +===========================+====================================+
   | ``mli_krn_softmax_sa8``   | All tensors data format: **sa8**   |
   +---------------------------+------------------------------------+
   | ``mli_krn_softmax_fx16``  | All tensors data format: **fx16**  |
   +---------------------------+------------------------------------+
..

Conditions
^^^^^^^^^^

Ensure that you satisfy the following general conditions before calling the function:

 - ``in`` and ``out`` tensors must be valid (see :ref:`mli_tnsr_struc`)
   and satisfy data requirements of the used version of the kernel.

 - ``in`` and ``out`` tensors must be of the same shape

 - ``lut`` structure must be valid and prepared for the softmax activation function (see :ref:`lut_prot`).

 - ``mem_stride`` of the innermost dimension must be equal to 1 for all the tensors.

 - ``axis`` parameter of ``cfg`` structure can be negative and must be less than ``in`` tensor rank.

For **sa8** versions of kernel, in addition to general conditions, ensure that you satisfy 
the following quantization conditions before calling the function:

 - ``in`` tensors must be quantized on the tensor level. This 
   implies that the tensor contains a single scale factor and a single zero offset.

 - Zero offset of ``in`` tensor must be within [-128, 127] range.

Ensure that you satisfy the platform-specific conditions in addition to those listed above 
(see the :ref:`platform_spec_chptr` chapter).

Result
^^^^^^

These functions modify:

 - Memory pointed by ``out.data.mem`` field.  
 - ``el_params`` field of ``out`` tensor. 

The range of this function is (0, 1).  Depending on the data type, quantization parameters of the output 
tensor are configured in the following way:

 - **fx16**

    - ``out.el_params.fx.frac_bits`` is set to 15. Hence, the maximum representable value of softmax is
      equivalent to 0.999969482421875 (not 1.0).

 - **sa8**

    - ``out.el_params.sa.zero_point.mem.i16`` is set to -128

    - ``out.el_params.sa.scale.mem.i16`` is set to 1

    - ``out.el_params.sa.scale_frac_bits.mem.i8`` is set to 8

The kernel supports in-place computation. It means that ``out`` and ``in`` tensor structures 
can point to the same memory with the same memory strides but without shift.
It can affect performance for some platforms.

.. warning::

  Only an exact overlap of starting address and memory stride of the ``in`` and ``out`` 
  tensors is acceptable. Partial overlaps result in undefined behavior.
..

Depending on the debug level (see section :ref:`err_codes`) this function performs a parameter 
check and returns the result as an ``mli_status`` code as described in section :ref:`kernl_sp_conf`.