Minior: Add negative tests about log function

[caicancai]

Which issue does this PR close?

Fractions in the log function are an important test because the results of 2.0/3 and 2/3 are completely different

Rationale for this change

What changes are included in this PR?

Are these changes tested?

Are there any user-facing changes?

[caicancai]

@alamb Hello, I have a question about logX(0). In arrow-datafusion, logX(0) returns -Infinity. From a mathematical point of view, I think there is no problem. However, I tested that mysql returns null and postgres returns error. , consider modifying the arrow-datafusion part.
calcite is currently experiencing similar problems

[gruuya]

In arrow-datafusion, logX(0) returns -Infinity.
consider modifying the arrow-datafusion part.

On a similar note the log with base zero returns zero

❯ select log(0, 3);
+------------------------+
| log(Int64(0),Int64(3)) |
+------------------------+
| 0.0                    |
+------------------------+

Mathematically that's undefined, while in Postgres/DuckDB it leads to an error (cannot take logarithm of zero).

[caicancai]

Mathematically that's undefined, while in Postgres/DuckDB it leads to an error (cannot take logarithm of zero).

I think log2, log10, and log should be the same set of functions, which is fine, and maybe we all feel that the current handling of log10(0) could be improved

[Jefffrey]

FYI some relevant previous discussion/work on log:

• Make log function to be in sync with PostgresSql #5259
• [DOC] Update math expression documentation  #5316

[caicancai]

FYI some relevant previous discussion/work on log:

* [Make `log` function to be in sync with PostgresSql #5259](https://github.com/apache/arrow-datafusion/issues/5259)

* [[DOC] Update math expression documentation  #5316](https://github.com/apache/arrow-datafusion/pull/5316)

Thank you for your reply. I'm sorry that I didn't notice the content in the document before.

[alamb]

Thank you @caicancai for adding the tests to document this feature more fully in code

I am hoping this type of "what should log do in corner cases" will have a better story once we have done #8045 -- and thus if someone wants a different set of log function behavior they can just register a different log UDF

[caicancai]

Thank you @caicancai for adding the tests to document this feature more fully in code

I am hoping this type of "what should log do in corner cases" will have a better story once we have done #8045 -- and thus if someone wants a different set of log function behavior they can just register a different log UDF

so cool, I think this is a very good idea, as a single sql engine can output the corresponding result expected by the user according to the user's custom behavior, which means that we do not need to adapt the negative test of each function in any dialect, but only need to concentrate on adapting most of the common functions.

[comphead]

lgtm thanks @caicancai