Divide & Conquer divides, but doesn't conquer

[FeepingCreature]

On Sunday, 24 May 2020 at 23:40:48 UTC, Andrei Alexandrescu wrote:
> Consider staticMap's current version (there are a few upcoming 
> changes that don't change the point):
> 
>...
>
> In the instantiation staticMap!(pred, A, B, C, D, E, F, G, H), 
> recursion will instantiate:
>
> staticMap!(pred, A, B, C, D)
> staticMap!(pred, A, B)
> staticMap!(pred, A)
> staticMap!(pred, B)
> staticMap!(pred, C, D)
> staticMap!(pred, C)
> staticMap!(pred, D)
> staticMap!(pred, E. F, G, H)
> staticMap!(pred, E, F)
> staticMap!(pred, E)
> staticMap!(pred, F)
> staticMap!(pred, G, H)
> staticMap!(pred, G)
> staticMap!(pred, H)
>
> Total: 15 instantiations including original. This is because a 
> full tree with 8 leaves is being created. Generally, a tree 
> with N leaves has about 2N - 1 nodes total (exactly so when N 
> is a power of 2).
>
> The more naive version would simply use linear decomposition:
> ...
> There' no more need to handle the 1-element case, which is 
> already a plus. But that's not the topic here. The 
> instantiations created are:
>
> staticMap!(pred, B, C, D, E, F, G, H)
> staticMap!(pred, C, D, E, F, G, H)
> staticMap!(pred, D, E, F, G, H)
> staticMap!(pred, E, F, G, H)
> staticMap!(pred, F, G, H)
> staticMap!(pred, G, H)
> staticMap!(pred, H)
>
> Total: 8 instantiations including original. That's about half 
> the current number of instantiations.
>
> So it seems divide et impera doesn't quite help with certain 
> recursive templates.

To add to the good previous points: the divide-and-conquer 
strategy can take advantage of caching for the leaf 
instantiations with one parameter. That is, 8 template 
instantiations can trivially be reused, and the others can 
sometimes be reused if they hit a common subtree. The linear 
instantiation can only be reused once or twice at the very end.