### LOG1P 

#### Description
The `LOG1P` function is used to calculate the value of the expression `log(1 + expr)`. This function is very useful in numerical computations, especially when dealing with values close to zero, as it can avoid numerical instability issues that may arise from directly calculating the `log` function.

#### Syntax
```
LOG1P(expr)
```
#### Parameters
- `expr`: A double type value for which the `log(1 + expr)` value needs to be calculated.

#### Return Value
Returns the calculation result, which is of type double.

#### Example Usage

1. Calculate the value of `log1p(0)`:
   ```sql
   SELECT LOG1P(0);
   ```
Result:
   ```
   0.0
   ```
2. Calculate the `log1p` value of a series of numbers:
   ```sql
   SELECT LOG1P(0.1), LOG1P(0.01), LOG1P(0.001);
   ```

Result:
   ```
  0.09531017980432487 0.009950330853168083 9.995003330835331E-4
   ```
3. In practical applications, you can use the `LOG1P` function to calculate the log-odds value in probability models:
   ```sql
   SELECT LOG1P(2) - LOG1P(1) AS log_odds;
   ```
 Result: 
   ```
    0.4054651081081643
   ```
#### Precautions
- When `expr` is negative, the `LOG1P` function will return `NULL`.
- When using the `LOG1P` function, ensure that the input value does not cause the result to exceed the range of the double type.