## Range<a name="Range"></a> {#openvino_docs_ops_generation_Range_4}

**Versioned name**: *Range-4*

**Category**: Generation

**Short description**: *Range* operation generates a sequence of numbers according input values [start, stop) with a step.

**Attributes**:

* *output_type*

  * **Description**: the output tensor type
  * **Range of values**: any numeric type
  * **Type**: string
  * **Default value**: None
  * **Required**: *Yes*

**Inputs**:

* **1**: "start" - A scalar of type T1. **Required.**
* **2**: "stop" - A scalar of type T2. **Required.**
* **3**: "step" - A scalar of type T3. If `step` is equal to zero after casting to `output_type`, behavior is undefined. **Required.**

**Outputs**:

* **1**: A tensor with type specified by attribute *output_type*.

**Types**

* *T1*, *T2*, *T3*: any numeric type.

**Detailed description**:

*Range* operation generates a sequence of numbers starting from the value in the first input (`start`) up to but not including the value in the second input (`stop`) with a `step` equal to the value in the third input, according to the following formula:

For a positive `step`:

\f[
start<=val[i]<stop,
\f]

for a negative `step`:

\f[
start>=val[i]>stop,
\f]

the i-th element is calculated by the following formula:

\f[
val[i+1]=val[i]+step.
\f]

The calculations are done after casting all values to `accumulate_type(output_type)`. `accumulate_type` is a type that have better or equal accuracy for accumulation than `output_type` on current hardware, e.g. `fp64` for `fp16`. The number of elements is calculated in the floating point type according to the following formula:

\f[
max(ceil((end − start) / step), 0)
\f]

This is aligned with PyTorch's operation `torch.arange`, to align with tensorflow operation `tf.range` all inputs must be casted to `output_type` before calling *Range*. The rounding for casting values are done towards zero.

**Examples**

*Example 1: positive step*

```xml
<layer ... type="Range">
    <data output_type="i32">
    <input>
        <port id="0">  <!-- start value: 2 -->
        </port>
        <port id="1">  <!-- stop value: 23 -->
        </port>
        <port id="2">  <!-- step value: 3 -->
        </port>
    </input>
    <output>
        <port id="3">
            <dim>7</dim> <!-- [ 2,  5,  8, 11, 14, 17, 20] -->
        </port>
    </output>
</layer>
```

*Example 2: negative step*

```xml
<layer ... type="Range">
    <data output_type="i32">
    <input>
        <port id="0">  <!-- start value: 23 -->
        </port>
        <port id="1">  <!-- stop value: 2 -->
        </port>
        <port id="2">  <!-- step value: -3 -->
        </port>
    </input>
    <output>
        <port id="3">
            <dim>7</dim> <!-- [23, 20, 17, 14, 11, 8, 5] -->
        </port>
    </output>
</layer>
```

*Example 3: floating point*

```xml
<layer ... type="Range">
    <data output_type="f32">
    <input>
        <port id="0">  <!-- start value: 1 -->
        </port>
        <port id="1">  <!-- stop value: 2.5 -->
        </port>
        <port id="2">  <!-- step value: 0.5 -->
        </port>
    </input>
    <output>
        <port id="3">
            <dim>3</dim> <!-- [ 1.0,  1.5,  2.0] -->
        </port>
    </output>
</layer>
```

