Divide & Conquer divides, but doesn't conquer

[johnsmith101]

On Monday, 25 May 2020 at 05:59:41 UTC, FeepingCreature wrote:
> 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.

Thank u so much for taking time to help.