Binary {#dev_guide_binary}
====================

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

## General

The binary primitive computes the result of a binary elementwise operation
between tensors source 0 and source 1 (the variable names follow the standard
@ref dev_guide_conventions):

\f[
    \dst(\overline{x}) =
        \src_0(\overline{x}) \mathbin{op} \src_1(\overline{x}),
\f]

where \f$op\f$ is one of the following operators: addition (\f$+\f$), 
subtraction (\f$-\f$), multiplication (\f$\times\f$), division (\f$\div\f$), 
greater than or equal to (\f$\geq\f$), greater than (\f$>\f$), 
less than or equal to (\f$\leq\f$), less than (\f$<\f$), equal to (\f$=\f$), 
not equal to (\f$\neq\f$), get maximum value (\f$\max(\cdot)\f$), 
get minimum value (\f$\min(\cdot)\f$), and conditional select operation.
For the conditional select operation, the binary primitive uses a third input 
tensor \f$src_2\f$ to select between the two source tensors:

\f[
    \dst[i] = \src_2[i] ? \src_0[i] : \src_1[i]
\f]

The binary primitive does not have a notion of forward or backward propagations.

## 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                                                  |
|-----------------------------|---------------------------------------------------------------------------|
| \f$\src_0\f$                | DNNL_ARG_SRC_0                                                            |
| \f$\src_1\f$                | DNNL_ARG_SRC_1                                                            |
| \f$\src_2\f$                | DNNL_ARG_SRC_2                                                            |
| \dst                        | DNNL_ARG_DST                                                              |
| \f$\text{binary post-op}\f$ | DNNL_ARG_ATTR_MULTIPLE_POST_OP(binary_post_op_position) \| DNNL_ARG_SRC_1,|
|                             | DNNL_ARG_ATTR_MULTIPLE_POST_OP(binary_post_op_position) \| DNNL_ARG_SRC_2 |
| \f$binary scale0\f$         | DNNL_ARG_ATTR_SCALES \| DNNL_ARG_SRC_0                                    |
| \f$binary scale1\f$         | DNNL_ARG_ATTR_SCALES \| DNNL_ARG_SRC_1                                    |

## Implementation Details

### General Notes

 * The binary primitive requires all source and destination tensors to have the
   same number of dimensions.

 * The binary primitive supports implicit broadcast semantics for source 0 and
   source 1. This means that if a dimension size is one, that single value
   will be broadcast (used to compute an operation with each point of the other
   source) for that dimension. It is recommended to use broadcast for source 1
   to get better performance. Generally it should match the syntax below:
   `{N,1}x{C,1}x{D,1}x{H,1}x{W,1}:{N,1}x{C,1}x{D,1}x{H,1}x{W,1} -> NxCxDxHxW`.
   It is consistent with [PyTorch broadcast semantic]
   (https://pytorch.org/docs/stable/notes/broadcasting.html).

 * The dimensions of both sources must match unless either is equal to one.

 * \f$\src_1\f$ and \dst memory formats can be either specified explicitly or by
   #dnnl::memory::format_tag::any (recommended), in which case the primitive
   will derive the most appropriate memory format based on the format of the
   source 0 tensor. The \dst tensor dimensions must match the ones of the
   source 0 and source 1 tensors (except for broadcast dimensions).

 * The binary primitive supports in-place operations, meaning that source 0
   tensor may be used as the destination, in which case its data will
   be overwritten. In-place mode requires the \dst and source 0 data types to be
   the same. Different data types will unavoidably lead to correctness issues.

 * For the binary select operation, broadcast semantics are not supported for 
   the third conditional input tensor. For this case, the dimensions and layout 
   of the conditional input tensor must match that of the source 0 tensor. 

### Post-Ops and Attributes

The following attributes are supported:

| Type      | Operation                                       | Description                                                                    | Restrictions
| :--       | :--                                             | :--                                                                            | :--
| Attribute | [Scales](@ref dnnl::primitive_attr::set_scales_mask) | Scales the corresponding input tensor by the given scale factor(s).            | Only one scale per tensor is supported. Input tensors only. |
| Post-op   | [Sum](@ref dnnl::post_ops::append_sum)          | Adds the operation result to the destination tensor instead of overwriting it. |                                                             |
| Post-op   | [Eltwise](@ref dnnl::post_ops::append_eltwise)  | Applies an @ref dnnl_api_eltwise operation to the result.                      |                                                             |
| Post-op   | [Binary](@ref dnnl::post_ops::append_binary)    | Applies a @ref dnnl_api_binary operation to the result                         | General binary post-op restrictions                         |

### Data Types Support

The source and destination tensors may have `f32`, `bf16`, `f16`, `s32` or `s8/u8`
data types.
For the binary select operation, the conditional input tensor can only be 
of `s8` data type. 
The binary primitive supports the following combinations of data types:

| Source 0 / 1                | Destination                 |
|:----------------------------|:----------------------------|
| f32, bf16, f16, s32, u8, s8 | f32, bf16, f16, s32, u8, s8 |

@warning
    There might be hardware and/or implementation specific restrictions.
    Check [Implementation Limitations](@ref dg_binary_impl_limits) section
    below.

### Data Representation

#### Sources, Destination

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

@anchor dg_binary_impl_limits
## 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

1. Whenever possible, avoid specifying different memory formats for source
   tensors.

## Examples

* @ref binary_example_cpp
* @ref bnorm_u8_via_binary_postops_cpp
