Multi-threaded `MultipleShooting` and `TrapezoidalCollocation`

[franckgaga]

@baggepinnen

I want to add conditional multi-threading for MultipleShooting and TrapezoidalCollocation, similar to DyadControl. I managed to get multi-threaded computations for the nonlinear equality constraints (the state defects over the prediction horizon) by using:

Threads.@threads for j=1:Hp
    # I fill the the equality constraint vectors `geq` here.
    # I never use Threads.threadid() and there is seperate
    # memory space for each iteration, so race conditions
    # are theoretically impossible.
end

Now what's the best way to do condtionnal multi-threading without code duplication ? The copilot suggested:

if use_threads
    Threads.@threads for j in 1:Hp
        # loop body
    end
else
    for j in 1:Hp
        # loop body
    end
end

but the loop body will be duplicated. I also tried to create this macro:

macro maybe_threads(use_threads, loop)
    if use_threads
        return esc(:(Threads.@threads $loop))
    else
        return esc(loop)
    end
end

but the only way to use it is with boolean literals, that is @maybe_threads true for j=1:Hp or @maybe_threads false for j=1:Hp. It does not work with variable nor parametric struct with "value-as-parameter".

Thanks!

[baggepinnen]

The macro has to escape and interpolate the use_threads variable if you want to use a non-literal

[franckgaga]

Easy enough! Macros are not my strength, as you can see XD.

[franckgaga]

Woah, I just understood that it's impossible to multi-thread the TrapezoidalCollocation(1), with the FOH, using the tricks that calls the state derivative f function only once per time step. The iterations needs to be "re-orderable" for multithreading. If we call the f function only once per time steps, we need the results from the previous time steps, which may or may not be computed at the time of execution, giving a race condition.

Multi-threading can gets very tricky...

edit : I'll do some branching if multi-threading is activated when h=1, it won't be cute 😆