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Mod operation specification refactoring. (#4703)

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* Mod operation specification refactoring.

* Add dummy broadcast_rules.md.

* Minor fixes, e.g. capitalize operation names, typos.

* Add comment about division by zero.

* Division by zero update.

Co-authored-by: jdanieck <jozef.daniecki@intel.com>
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Szymon Durawa 2021-03-09 20:59:32 +01:00 committed by GitHub
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docs/ops/arithmetic/Mod_1.md
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@ -4,9 +4,16 @@
**Category**: Arithmetic binary operation
**Short description**: *Mod* returns an element-wise division reminder with two given tensors applying multi-directional broadcast rules.
The result here is consistent with a truncated divide (like in C programming language): `truncated(x / y) * y + truncated_mod(x, y) = x`.
The sign of the result is equal to a sign of a dividend.
**Short description**: *Mod* performs an element-wise modulo operation with two given tensors applying broadcasting rule specified in the *auto_broadcast* attribute.
**Detailed description**
As a first step input tensors *a* and *b* are broadcasted if their shapes differ. Broadcasting is performed according to `auto_broadcast` attribute specification. As a second step *Mod* operation is computed element-wise on the input tensors *a* and *b* according to the formula below:
\f[
o_{i} = a_{i} % b_{i}
\f]
*Mod* operation computes a reminder of a truncated division. It is the same behaviour like in C programming language: `truncated(x / y) * y + truncated_mod(x, y) = x`. The sign of the result is equal to a sign of a dividend. The result of division by zero is undefined.
**Attributes**:
@ -14,20 +21,21 @@ The sign of the result is equal to a sign of a dividend.
* **Description**: specifies rules used for auto-broadcasting of input tensors.
* **Range of values**:
* *none* - no auto-broadcasting is allowed, all input shapes should match
* *numpy* - numpy broadcasting rules, aligned with ONNX Broadcasting. Description is available in <a href="https://github.com/onnx/onnx/blob/master/docs/Broadcasting.md">ONNX docs</a>.
* *none* - no auto-broadcasting is allowed, all input shapes must match
* *numpy* - numpy broadcasting rules, description is available in [Broadcast Rules For Elementwise Operations](../broadcast_rules.md)
* **Type**: string
* **Default value**: "numpy"
* **Required**: *no*
**Inputs**
* **1**: A tensor of type T. Required.
* **2**: A tensor of type T. Required.
* **1**: A tensor of type T and arbitrary shape. Required.
* **2**: A tensor of type T and arbitrary shape. Required.
**Outputs**
* **1**: The element-wise division reminder. A tensor of type T.
* **1**: The result of element-wise modulo operation. A tensor of type T with shape equal to broadcasted shape of two inputs.
**Types**
@ -35,10 +43,11 @@ The sign of the result is equal to a sign of a dividend.
**Examples**
*Example 1*
*Example 1 - no broadcasting*
```xml
<layer ... type="FloorMod">
<layer ... type="Mod">
<data auto_broadcast="none"/>
<input>
<port id="0">
<dim>256</dim>
@ -58,9 +67,10 @@ The sign of the result is equal to a sign of a dividend.
</layer>
```
*Example 2: broadcast*
*Example 2: numpy broadcasting*
```xml
<layer ... type="FloorMod">
<layer ... type="Mod">
<data auto_broadcast="numpy"/>
<input>
<port id="0">
<dim>8</dim>