[C++] Implement logarithm compute functions

[asfimport]

ln, log, log2?

Reporter: David Li / @lidavidm
Assignee: David Li / @lidavidm

Related issues:

• [C++] Arithmetic kernels for numeric arrays (is a child of)
• [C++] Implement logN compute function (is related to)
• [R] Bindings for log and trig functions (is depended upon by)

PRs and other links:

• GitHub Pull Request #10567

_{Note: This issue was originally created as ARROW-13096. Please see the migration documentation for further details.}

[asfimport]

Eduardo Ponce / @edponce:
I consider having (1) ln, (2) log10, and (3) log2 is a good starting point, and the missing variants are:
(4) log(x, base) = log(x) / log(base), note that log(base) is a constant w.r.t. to Datum x so optimizations can be made
(5) log1p(x) = log(1+x)

Note that (4) is the most general variant as it can represent any of the other variants, so it might be worthwhile to consider adding it to Arrow.

As additional context, here is the partial landscape of log functions across library/languages:

• C++ math library supports (1,2,3,5)
• Python math module supports (1-5)
• Python numpy supports (1,2,3,5)
• R supports (1-5)
• Rust math support (1-5)
• MySQL supports (1-4)
• PostgreSQL supports (1,2,4)

[asfimport]

David Li / @lidavidm:
Thanks for looking all these over. I think we can add #5 easily. For #4, would we pass the log base as a kernel option? Or as another argument? (We'd only be able to optimize in the former case, I guess, unless we required a scalar argument)

[asfimport]

yibocai#1:
Issue resolved by pull request 10567
#10567