# Build recursion in parallel?

Problem

Let's define a simple recursion.

f[1] = 1;
f[n_] := f[n] = f[n - 1]*n;

If I evaluate f in parallel

ParallelTable[f[i], {i, 10}];

and then query f

?f
Globalf
f[1]=1
f[n_]:=f[n]=f[n-1] n

Question

How can I tell the sub kernels to build up the recursion, so that

?f

Globalf

f[1]=1
....
f[10]=3628800

f[n_]:=f[n]=f[n-1] n

Thanks !

PS: of course the actual function is not that trivial.

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Does SetSharedFunction[f] do what you want? – sebhofer Aug 7 '12 at 16:49
Indeed, thank you! Should I remove my question? – chris Aug 7 '12 at 17:18
On the other hand it does not re-export to the different kernels the known definitions. Table[f[i], {i, 5000}]; // Timing (* {0.005126,Null} ) ParallelTable[f[i], {i, 5000}]; // Timing ( {6.69067,Null} *) – chris Aug 7 '12 at 17:22
Indeed. I can remember that I once ran into that problem but I couldn't find a solution to distribute DownValues from the subkernels. Maybe you can formulate your question more generally (with a different title?), so you get more attention! – sebhofer Aug 7 '12 at 18:05

@sebhofer provides a partial answer via the command

SetSharedFunction[f]

which collects to the master kernel the accumulated downvalues. On the other hand, the slave kernels seem unaware of these.

Indeed

ParallelTable[f[i], {i, 5000}];
Table[f[i], {i, 5000}]; // Timing

(* {0.005126,Null} *)

which suggests the master kernel does remember the previous definitions. On the other hand,

ParallelTable[f[i], {i, 5000}]; // Timing

(* {6.69067,Null} *)

still takes quite some time.

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The reason the second invocation takes a while has changed, though--f exists only in the master kernel and is fetched using a callback every time it's referenced in one of the slaves. This is still basically a serial operation, but now it involves a lot of communication overhead. Unfortunately it isn't easy to do what you want given the way the Parallel` package works. I thought you could perhaps try something like f[n_]:=g[n]=f[n-1] n with SetSharedFunction[g]; DistributeDefinitions[f], but this doesn't seem to work... sorry, no time for a more considered response! – Oleksandr R. Aug 8 '12 at 8:20