The function takes a string input and shifts each alphabetical character by 16 positions in the alphabet, wrapping around when necessary. Numeric characters are not altered.

[CODE]:
```python
def approx_function(input_str):
    output_str = ""
    for char in input_str:
        if char.isalpha():
            shift = 16
            if char.islower():
                new_char = chr(((ord(char) - ord('a') + shift) % 26) + ord('a'))
            else:  # char.isupper()
                new_char = chr(((ord(char) - ord('A') + shift) % 26) + ord('A'))
            output_str += new_char
        else:
            output_str += char
    return output_str
```

To validate the description and code, let's test the function with some additional inputs.
COMMAND: PYTHON(./temp/function.py "Caesar" "Cypher" "77Times" "alphaBET23")