Sum {#dev_guide_sum}
====================

>
> [API Reference](@ref dnnl_api_sum)
>

## General

The sum primitive sums \f$N\f$ tensors (the variable names follow the standard
@ref dev_guide_conventions):

\f[
    \dst(\overline{x}) =
        \sum\limits_{i = 1}^{N}
        scales(i) \cdot
        \src_i(\overline{x})
\f]

The sum primitive does not have a notion of forward or backward propagations.
The backward propagation for the sum operation is simply an identity operation.

## Execution Arguments

When executed, the inputs and outputs should be mapped to an execution
argument index as specified by the following table.

| primitive input/output | execution argument index |
|------------------------|--------------------------|
| \src                   | DNNL_ARG_MULTIPLE_SRC    |
| \dst                   | DNNL_ARG_DST             |

## Implementation Details

### General Notes

 * The \dst memory format can be either specified by a user or derived
   the most appropriate one by the primitive. The recommended way is to allow
   the primitive to choose the appropriate format.

 * The sum primitive requires all source and destination tensors to have the
   same shape.
   Implicit broadcasting is not supported.

 * The sum primitive supports in-place operation, meaning that the \f$\src_0\f$
   tensor can be used as both input and output. In-place operation overwrites
   the original data. Using in-place operation requires the memory footprint of
   the output tensor to be either bigger than or equal to the size of the \dst
   memory descriptor used for primitive creation.

### Post-Ops and Attributes

The sum primitive does not support any post-ops or attributes.

### Data Types Support

The sum primitive supports arbitrary data types for source and destination
tensors according to the @ref dev_guide_data_types page.

### Data Representation

#### Sources, Destination

The sum primitive works with arbitrary data tensors. There is no special
meaning associated with any logical dimensions.


## Implementation Limitations

1. Refer to @ref dev_guide_data_types for limitations related to data types
   support.

2. **GPU**
   - Only tensors of 6 or fewer dimensions are supported.


## Performance Tips

 * Whenever possible do not specify the destination memory format so that the
   primitive is able to choose the most appropriate one.

 * The sum primitive is highly optimized for the cases when all source tensors
   have same memory format and data type matches the destination tensor data
   type. For other cases more general but slower code is working. Consider
   reordering sources to the same data format before the sum primitive.

 * Use in-place operations whenever possible (see caveats in General Notes).

## Examples

* @ref sum_example_cpp
