Add SQL function overload `LOG(base, x)` for logarithm of x to base

[stuartcarnie]

Is your feature request related to a problem or challenge? Please describe what you are trying to do.

As a user, I would like to determine the logarithm of a value, $x$ to base $b$.

Describe the solution you'd like

Add an overload to the log function, which takes two arguments. Using PostgreSQL for inspiration per the documentation:

log ( b numeric, x numeric ) → numeric
Logarithm of $x$ to base $b$
log(2.0, 64.0) → 6.0000000000000000

Describe alternatives you've considered

DataFusion strives for PostgreSQL compatibility, so it makes sense to use the PostgreSQL solution.

Additional context

[comphead]

@alamb on top of my head we dont have overloaded scalar functions yet?
We know how to to create different aliases for the same function, but not overloading

[stuartcarnie]

@comphead there are already examples in DF of this, for example the ltrim function takes 1 or 2 arguments:

https://github.com/apache/arrow-datafusion/blob/ac876dbc9729b16e272e00496c51e53d9f649173/datafusion/physical-expr/src/string_expressions.rs#L355-L369

[comphead]

Thanks @stuartcarnie with log I came out to the similar solution, inspecting len() :) but was wondering if we already have something more elegant to provide default values, seems we dont have it yet

[stuartcarnie]

In the case of the LOG function, if there is a single argument, it is assumed to be LOG $x$ base 10:

log ( numeric ) → numeric
log ( double precision ) → double precision
     Base 10 logarithm
     log(100) → 2

[stuartcarnie]

@comphead no worries – I looked for other solutions too, but that is all I could find for now.

[comphead]

Thats okay, I'll implement it using len() but going forward probably we may want to think how we can substitute default values, in case of different signatures for the same scalar function

[stuartcarnie]

@comphead awesome, thanks for doing that!