Cache structs to save memory use on repeated calls to _taylorinteg!

[PerezHz]

This PR introduces some cache structs which allow reusing memory on repeated calls to _taylorinteg!.

[coveralls]

coverage: 95.078% (-0.6%) from 95.697%
when pulling 3b40df6 on jp/cache
into de3e06a on main.

[PerezHz]

This is ready for review @lbenet @LuEdRaMo

[lbenet]

Thanks @PerezHz for the nice addition. Do you have some comparisons/benchmarks? I'll have a look into it in the next few days!

[PerezHz]

@lbenet I'm trying out some changes in this PR which will help re-use more memory while making this cache concept more user-friendly. I'll run benchmarks once this is ready.

[LuEdRaMo]

@PerezHz: If I create a cache object once and then reuse it, do I have to update de cache.t, cache.x and cache.dx variables before every integration? If so, I think it would be nice to have a function for this.

[PerezHz]

@PerezHz: If I create a cache object once and then reuse it, do I have to update de cache.t, cache.x and cache.dx variables before every integration? If so, I think it would be nice to have a function for this.

Thank you for the suggestion! Right now, the workflow with these caches looks as follows:

# allocation
cache = TaylorIntegration.init_cache(Val(true), t0, q0, maxsteps, order)
# handle parsing
parse_eqs, rv = TaylorIntegration._determine_parsing!(true, f!, cache.t, cache.x, cache.dx, params);
# first integration
sol = taylorinteg!(Val(true), f!, q0, t0, tmax, abstol, rv, cache, params; parse_eqs, maxsteps)
# update
t0 = # new time
q0 = # new initial condition
# second integration
sol2 = taylorinteg!(Val(true), f!, q0, t0, tmax, abstol, rv, cache, params; parse_eqs, maxsteps)

That is, the cache is initialized only once, and the update to the new initial condition is handled internally by taylorinteg!.