Avoid if-def branching for threading code

[wds15]

Description

Currently we if-def around single-core vs multi-core implementation of functions which implement parallelism. The if-def asks for the availability of STAN_THREADS being set or not during compilation. Since the TBB simplifies on a single core to just run with 1 process (if configured to do so), we should drop the if-def while ensuring that we instruct C++ users accordingly to setup the TBB task_arena things run in to just have 1 core.

Example

Code should be easier to maintain due to fewer if-def.

Expected Output

No change in outputs.

Current Version:

v4.1.0

[t4c1]

Does single thread code using TBB exhibit the same performance as sequential code without TBB?

[wds15]

There are two cases to discriminate:

• The user defines STAN_THREADS... then then AD tape is thread local for which you pay a bit of performance (quite platform dependent). In this case the user anyway wants to use parallelism.
• The user does not define STAN_THREADS... in that case you gain a bit of performance due to AD tape not being thread local. When a user now calls a TBB based function, then that function may incur a minor performance penalty which I would doubt that you can measure it. However, if a user intends to go sequential then he should anyway not call out to the TBB based functions.

So I think we are safe to simplify our code.