Lazy evaluation & performance

[Benoit de Boursetty <debourse@email.enst.fr>]

Hello,

Has anybody done benchmarks to eval the cost of lazy computation
encapsulation, in terms of time, memory, garbage collection? I have no
idea of how this is implemented...

Here's my personal case :

There is a function f which I want to compute for several arguments
x_1,...x_n.

let f x =
  [beginning]
  let intermediate_value = ... in
  [end]

only that I want to compute it thoroughly just for the x_i that has the
highest intermediate_value among x_i's. This intermediate value is used
anyway for the [end] part.

Naive design (design a):

let f x =
  [beginning]
  let intermediate_value = ... in
  (intermediate_value, lazy [end])
 
the lazy computation of the [end] being forced only for the x_i that has
the highest intermediate_value

Another possible design (less elegant) (design b):

let intermediate_value x =
  [beginning]
  let intermediate_value = ... in
  intermediate_value

let f x =
  [beginning]
  [end]

I compute the intermediate value and then recompute all over again
for the x I want to compute.

Comparison of time costs:

if
  B is the cost for [beginning]
  E is the cost for [end]
  L is the cost for encapsulating the lazy computation of [end]
then
design a costs n*(B+L) + E
design b costs (n+1)*B + E
(very roughly I suppose)

Clearly, deciding which design to adopt is a trade-off depending on n, B,
L. I suppose L also depends on the number of results from [beginning] that
the computer will need to "remember" for [end]? Also, encapsulating lazy
computations means more memory allocation, means more garbage collecting,
doesn't it?

In my case the efficiency bottleneck is E not B, and n is about 10 (i.e.
high) so I'm not expecting a wonderful overall time gain. I'm just
wondering if it's costly to implement it in the way that corresponds best
to reality (design a). "B" is only a dozen flops.

Could anybody give me a hint about the order of magnitude of L?

Thanks very much in advance for your answers.

Benoit de Boursetty.