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[Caml-list] Bigarray map & set/get (long)
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Date: -- (:)
From: Christophe TROESTLER <Christophe.Troestler@u...>
Subject: [Caml-list] Bigarray map & set/get (long)
Hi everybody,

I am in the process of writing some numerical code (nonlinear ODE/PDE
solvers with C^1 finite elements).  I would like to share some remarks
and ask some questions about the Bigarray module.  As an example of
the operations I need, I chose the matrix assignment

OUT <- A + B .* C

where .* denotes elementwise multiplication.  Direct implementation in
CAML is

let mac out a b c =
  for i = 1 to Array2.dim1 a do
    for j = 1 to Array2.dim2 a do
      out.{i,j} <- a.{i,j} +. b.{i,j} *. c.{i,j}
    done
  done;
  out

Typical matrices are of dimension 1000x1000 and above and computations
like the previous one may need to be repeated several thousand of
times.  Now, I also wrote such computation in C (I mean C called from
CAML).  On my machine (Athlon 1GHz, 512Mb) for a matrix of size
1300x1300, the C version run in 0.16 sec while the above CAML code
takes 2.14 secs; that is, about 13 times more.  Now, if I specify the
full type of the arrays I want (here

type mat =
  (float, Bigarray.float64_elt, Bigarray.fortran_layout) Bigarray.Array2.t

) then the code runs much faster: 0.87 sec (still more than 5 times
the C version unfortunately).  That sould be mentioned in
http://caml.inria.fr/ocaml/speed.html IMHO -- and maybe this page
could be better advertised?.

I tried two other things.  First I wrote a callback version, that is a
"map" function written in C that calls the CAML function passed as
argument.  Its interface looks like:

val map3 :
  out:mat -> (float -> float -> float -> float) -> mat -> mat -> mat -> mat

which allows to write the previous function [mac out a b c] as

map3 ~out (fun a b c -> a +. b *. c) a b c

Now, this does not work so bad (considering it is very naively
written): 0.35 sec (about twice as much as C).  I also wrote in C safe
and unsafe (and specialized to mat) versions and set/get but the the
result is not what is expected: 1.16 sec (about 7 times slower than C)
with little difference between safe/unsafe.

So (eventually :-) here a my questions:

* The Lacaml modules does contain some "matlab like" operations on
  vectors (and, in the future, on 2D arrays).  That will make easy to
  write fast code for this example.  However, one thing that will
  always be necessary is to make CAML functions act on arrays.
  Therefore why not add some carefully designed "map" and "fold"
  functions to the Bigarray module.  Such functions would need making
  bound checks and checks for the type of the array only once, before
  the loop.  To be useful they would need to have optional arguments
  like ~from (index of the start) ~inc (increment, default [|1;
  1;... |]) ~to (max index).  ~out can also be made optional if one
  wants to match more closely the map/fold of Array but it is
  necessary to be able to specify it -- and it may be one of the input
  arrays.

  In the same vein, what can be done to write a faster map-like
  function?

* Are bound checks responsible for the difference between the "fully
  typed" version [mac (out:mat) (a:mat) (b:mat) (c:mat)] and C??  How
  to write specialized (fully typed) versions of set/get (possibly
  unsafe) that will run as fast as C?  What is the difference with the
  set/get for Arrays that allows them to run as fast as C (for a float
  array of the size 1690000 = 1300 * 1300).

Have a good weekend,
Christophe


P.S.  Is it possible to write a "let module A = B" (i.e., module
renaming) in camlp4?  That is very useful when one wants to be able to
switch between different modules with the same interface but do not
want to open them (for name conflicts reasons for example).
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