docs/UserGuide/Operators-Functions/Mathematical.md

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## Arithmetic Operators and Functions

## Arithmetic Operators

### Unary Arithmetic Operators

Supported operators: `+`, `-`

Supported input data types: `INT32`, `INT64` and `FLOAT`

Output data type: consistent with the input data type

### Binary Arithmetic Operators

Supported operators: `+`, `-`, `*`, `/`, `%`

Supported input data types: `INT32`, `INT64`, `FLOAT` and `DOUBLE`

Output data type: `DOUBLE`

Note: Only when the left operand and the right operand under a certain timestamp are not  `null`, the binary arithmetic operation will have an output value.

### Example

```sql
select s1, - s1, s2, + s2, s1 + s2, s1 - s2, s1 * s2, s1 / s2, s1 % s2 from root.sg.d1
```

Result:

```
+-----------------------------+-------------+--------------+-------------+-------------+-----------------------------+-----------------------------+-----------------------------+-----------------------------+-----------------------------+
|                         Time|root.sg.d1.s1|-root.sg.d1.s1|root.sg.d1.s2|root.sg.d1.s2|root.sg.d1.s1 + root.sg.d1.s2|root.sg.d1.s1 - root.sg.d1.s2|root.sg.d1.s1 * root.sg.d1.s2|root.sg.d1.s1 / root.sg.d1.s2|root.sg.d1.s1 % root.sg.d1.s2|
+-----------------------------+-------------+--------------+-------------+-------------+-----------------------------+-----------------------------+-----------------------------+-----------------------------+-----------------------------+
|1970-01-01T08:00:00.001+08:00|          1.0|          -1.0|          1.0|          1.0|                          2.0|                          0.0|                          1.0|                          1.0|                          0.0|
|1970-01-01T08:00:00.002+08:00|          2.0|          -2.0|          2.0|          2.0|                          4.0|                          0.0|                          4.0|                          1.0|                          0.0|
|1970-01-01T08:00:00.003+08:00|          3.0|          -3.0|          3.0|          3.0|                          6.0|                          0.0|                          9.0|                          1.0|                          0.0|
|1970-01-01T08:00:00.004+08:00|          4.0|          -4.0|          4.0|          4.0|                          8.0|                          0.0|                         16.0|                          1.0|                          0.0|
|1970-01-01T08:00:00.005+08:00|          5.0|          -5.0|          5.0|          5.0|                         10.0|                          0.0|                         25.0|                          1.0|                          0.0|
+-----------------------------+-------------+--------------+-------------+-------------+-----------------------------+-----------------------------+-----------------------------+-----------------------------+-----------------------------+
Total line number = 5
It costs 0.014s
```

## Arithmetic Functions

Currently, IoTDB supports the following mathematical functions. The behavior of these mathematical functions is consistent with the behavior of these functions in the Java Math standard library.

| Function Name | Allowed Input Series Data Types | Output Series Data Type       | Corresponding Implementation in the Java Standard Library    |
| ------------- | ------------------------------- | ----------------------------- | ------------------------------------------------------------ |
| SIN           | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#sin(double)                                             |
| COS           | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#cos(double)                                             |
| TAN           | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#tan(double)                                             |
| ASIN          | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#asin(double)                                            |
| ACOS          | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#acos(double)                                            |
| ATAN          | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#atan(double)                                            |
| SINH          | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#sinh(double)                                            |
| COSH          | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#cosh(double)                                            |
| TANH          | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#tanh(double)                                            |
| DEGREES       | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#toDegrees(double)                                       |
| RADIANS       | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#toRadians(double)                                       |
| ABS           | INT32 / INT64 / FLOAT / DOUBLE  | Same type as the input series | Math#abs(int) / Math#abs(long) /Math#abs(float) /Math#abs(double) |
| SIGN          | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#signum(double)                                          |
| CEIL          | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#ceil(double)                                            |
| FLOOR         | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#floor(double)                                           |
| ROUND         | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#rint(double)                                            |
| EXP           | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#exp(double)                                             |
| LN            | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#log(double)                                             |
| LOG10         | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#log10(double)                                           |
| SQRT          | INT32 / INT64 / FLOAT / DOUBLE  | DOUBLE                        | Math#sqrt(double)                                            |

Example:

```   sql
select s1, sin(s1), cos(s1), tan(s1) from root.sg1.d1 limit 5 offset 1000;
```

Result:

```
+-----------------------------+-------------------+-------------------+--------------------+-------------------+
|                         Time|     root.sg1.d1.s1|sin(root.sg1.d1.s1)| cos(root.sg1.d1.s1)|tan(root.sg1.d1.s1)|
+-----------------------------+-------------------+-------------------+--------------------+-------------------+
|2020-12-10T17:11:49.037+08:00|7360723084922759782| 0.8133527237573284|  0.5817708713544664| 1.3980636773094157|
|2020-12-10T17:11:49.038+08:00|4377791063319964531|-0.8938962705202537|  0.4482738644511651| -1.994085181866842|
|2020-12-10T17:11:49.039+08:00|7972485567734642915| 0.9627757585308978|-0.27030138509681073|-3.5618602479083545|
|2020-12-10T17:11:49.040+08:00|2508858212791964081|-0.6073417341629443| -0.7944406950452296| 0.7644897069734913|
|2020-12-10T17:11:49.041+08:00|2817297431185141819|-0.8419358900502509| -0.5395775727782725| 1.5603611649667768|
+-----------------------------+-------------------+-------------------+--------------------+-------------------+
Total line number = 5
It costs 0.008s
```