Re: caml (special) light and numerics

Pierre Weis
 Thorsten Ohl
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Date:  19951018 (17:41) 
From:  Thorsten Ohl <ohl@c...> 
Subject:  Re: caml (special) light and numerics 
>>>>> "Pierre" == Pierre Weis <Pierre.Weis@inria.fr> writes: Pierre> If your code does not explicitely allocate a new array in the Pierre> body of the procedure, CAML won't allocate any temporary Pierre> array. How can I get around Array.new in val f : float array > float array let f x = let n = Array.length x in let y = Array.new n 0.0 in for i = 0 to n do for j = 0 to n do y.(i) < y.(i) +. a.(i).(j) *. x.(j) done done The problem is that I cannot modify `x' in place (even if I know that I won't need it later). The solution val g : float array > float array > unit let f x y = let n = Array.length x in for i = 0 to n do for j = 0 to n do y.(i) < y.(i) +. a.(i).(j) *. x.(j) done done comes to mind, but it forces me to think of the operation in terms of side efects, not in a functional way. I was hoping to build a library in which I could use functors to build different incarnations of an algorithm: a slow multidimentional one using arrays and a fast one for one dimensional problems. functor (In : Vectorspace, Out : Vectorspace) > sig val f : In.type > Out.type ... end But it seems that I will have to use references for the onedimensional case too. BTW: If this sound like sensless babble to you, please warn me that I'm wasting my time and should better buy a Fortran90 compiler ... Pierre> However, our compilers are rather good at optimizing these Pierre> tail calls (not only recursive ones). So if it is reasonably Pierre> evident, your Caml compiler must do it. I'll take your word for it. Pierre> I would like to end this answer on efficiency considerations Pierre> by telling a little true story: [...] After a bit of brain Pierre> storming, changing the algorithm leads to a program that runs Pierre> within 100 words of memory, runs exponentially faster, and Pierre> gives the result after a few minutes :) This is the effect I'm looking for  and I won't be satified with anything less :). Pierre> My feeling is that, if efficiency is a problem, you Pierre> have to change the complexity of the algorithm, not to try to Pierre> change the code generated by the compiler! Sure. However: if we assume for simplicity that the compiler induces a multiplicative overhead (wrt. low level languages like FORTRAN), and I manage to reduce the complexity by one power FORTRAN: C_F * O(n^2) CSL: C_C * O(n) then I have to estimate (roughly) C_C/C_F to find out where the break even point is. Otherwise I will not be able to convince anyone. Pierre> And if you need to test and change your programs rapidly, the Pierre> readibility and expressiveness of Caml programs may help Pierre> you... No doubt about that, but I'm trying to figure out if it is _likely_ that also production level code can be produced. Cslopt is certainly an example, but from a very different field. I'm thinking about implementing a nontrivial system and I need _some_ idea if it has a chance to fly. Flashes of genius that reduce an exponential solution to a power law are nice, but rare in numerics. OTOH, a factor of ten can be painful if it means that you have to wait a week, instead of of a night. Thanks for your patience, Thorsten /// Thorsten Ohl, TH Darmstadt, Schlossgartenstr. 9, D64289 Darmstadt, Germany //////////////// net: ohl@crunch.ikp.physik.thdarmstadt.de, ohl@gnu.ai.mit.edu /// voice: +496151163116, secretary: +496151162072, fax: +496151162421