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# Variation Trend Calculation Functions
Currently, IoTDB supports the following variation trend calculation functions:
| Function Name | Allowed Input Series Data Types | Output Series Data Type | Description |
| ----------------------- | ----------------------------------------------- | ----------------------------- | ------------------------------------------------------------ |
| TIME_DIFFERENCE | INT32 / INT64 / FLOAT / DOUBLE / BOOLEAN / TEXT | INT64 | Calculates the difference between the time stamp of a data point and the time stamp of the previous data point. There is no corresponding output for the first data point. |
| DIFFERENCE | INT32 / INT64 / FLOAT / DOUBLE | Same type as the input series | Calculates the difference between the value of a data point and the value of the previous data point. There is no corresponding output for the first data point. |
| NON_NEGATIVE_DIFFERENCE | INT32 / INT64 / FLOAT / DOUBLE | Same type as the input series | Calculates the absolute value of the difference between the value of a data point and the value of the previous data point. There is no corresponding output for the first data point. |
| DERIVATIVE | INT32 / INT64 / FLOAT / DOUBLE | DOUBLE | Calculates the rate of change of a data point compared to the previous data point, the result is equals to DIFFERENCE / TIME_DIFFERENCE. There is no corresponding output for the first data point. |
| NON_NEGATIVE_DERIVATIVE | INT32 / INT64 / FLOAT / DOUBLE | DOUBLE | Calculates the absolute value of the rate of change of a data point compared to the previous data point, the result is equals to NON_NEGATIVE_DIFFERENCE / TIME_DIFFERENCE. There is no corresponding output for the first data point. |
Example:
``` sql
select s1, time_difference(s1), difference(s1), non_negative_difference(s1), derivative(s1), non_negative_derivative(s1) from root.sg1.d1 limit 5 offset 1000;
```
Result:
```
+-----------------------------+-------------------+-------------------------------+--------------------------+---------------------------------------+--------------------------+---------------------------------------+
| Time| root.sg1.d1.s1|time_difference(root.sg1.d1.s1)|difference(root.sg1.d1.s1)|non_negative_difference(root.sg1.d1.s1)|derivative(root.sg1.d1.s1)|non_negative_derivative(root.sg1.d1.s1)|
+-----------------------------+-------------------+-------------------------------+--------------------------+---------------------------------------+--------------------------+---------------------------------------+
|2020-12-10T17:11:49.037+08:00|7360723084922759782| 1| -8431715764844238876| 8431715764844238876| -8.4317157648442388E18| 8.4317157648442388E18|
|2020-12-10T17:11:49.038+08:00|4377791063319964531| 1| -2982932021602795251| 2982932021602795251| -2.982932021602795E18| 2.982932021602795E18|
|2020-12-10T17:11:49.039+08:00|7972485567734642915| 1| 3594694504414678384| 3594694504414678384| 3.5946945044146785E18| 3.5946945044146785E18|
|2020-12-10T17:11:49.040+08:00|2508858212791964081| 1| -5463627354942678834| 5463627354942678834| -5.463627354942679E18| 5.463627354942679E18|
|2020-12-10T17:11:49.041+08:00|2817297431185141819| 1| 308439218393177738| 308439218393177738| 3.0843921839317773E17| 3.0843921839317773E17|
+-----------------------------+-------------------+-------------------------------+--------------------------+---------------------------------------+--------------------------+---------------------------------------+
Total line number = 5
It costs 0.014s
```
| Function Name | Allowed Input Series Data Types | Attributes | Output Series Data Type | Description |
|---------------|---------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|-------------------------|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|
| DIFF | INT32 / INT64 / FLOAT / DOUBLE | `ignoreNull`:optional,default is true. If is true, the previous data point is ignored when it is null and continues to find the first non-null value forwardly. If the value is false, previous data point is not ignored when it is null, the result is also null because null is used for subtraction | DOUBLE | Calculates the difference between the value of a data point and the value of the previous data point. There is no corresponding output for the first data point, so output is null |
### Example
#### RawData
```
+-----------------------------+------------+------------+
| Time|root.test.s1|root.test.s2|
+-----------------------------+------------+------------+
|1970-01-01T08:00:00.001+08:00| 1| 1.0|
|1970-01-01T08:00:00.002+08:00| 2| null|
|1970-01-01T08:00:00.003+08:00| null| 3.0|
|1970-01-01T08:00:00.004+08:00| 4| null|
|1970-01-01T08:00:00.005+08:00| 5| 5.0|
|1970-01-01T08:00:00.006+08:00| null| 6.0|
+-----------------------------+------------+------------+
```
#### Not use `ignoreNull` attribute (Ignore Null)
SQL:
```sql
SELECT DIFF(s1), DIFF(s2) from root.test;
```
Result:
```
+-----------------------------+------------------+------------------+
| Time|DIFF(root.test.s1)|DIFF(root.test.s2)|
+-----------------------------+------------------+------------------+
|1970-01-01T08:00:00.001+08:00| null| null|
|1970-01-01T08:00:00.002+08:00| 1.0| null|
|1970-01-01T08:00:00.003+08:00| null| 2.0|
|1970-01-01T08:00:00.004+08:00| 2.0| null|
|1970-01-01T08:00:00.005+08:00| 1.0| 2.0|
|1970-01-01T08:00:00.006+08:00| null| 1.0|
+-----------------------------+------------------+------------------+
```
#### Use `ignoreNull` attribute
SQL:
```sql
SELECT DIFF(s1, 'ignoreNull'='false'), DIFF(s2, 'ignoreNull'='false') from root.test;
```
Result:
```
+-----------------------------+----------------------------------------+----------------------------------------+
| Time|DIFF(root.test.s1, "ignoreNull"="false")|DIFF(root.test.s2, "ignoreNull"="false")|
+-----------------------------+----------------------------------------+----------------------------------------+
|1970-01-01T08:00:00.001+08:00| null| null|
|1970-01-01T08:00:00.002+08:00| 1.0| null|
|1970-01-01T08:00:00.003+08:00| null| null|
|1970-01-01T08:00:00.004+08:00| null| null|
|1970-01-01T08:00:00.005+08:00| 1.0| null|
|1970-01-01T08:00:00.006+08:00| null| 1.0|
+-----------------------------+----------------------------------------+----------------------------------------+
```