[Caml-list] Re: float boxing (was: matrix-matrix multiply)

[Christophe TROESTLER <debian00@tiscalinet.be>]

On Sun, 20 Oct 2002, Issac Trotts <ijtrotts@ucdavis.edu> wrote:
> 
> You might try converting your references to mutable fields.
>
> let x = ref 1.0 in
> let n = int_of_string Sys.argv.(1) in
> for i = 1 to n do x := !x +. 1.0 done
> 
> ./ref 100000000  2.51s user 0.00s system 99% cpu 2.515 total
> 
> type t = { mutable f:float };;
> let x = { f = 1.0 } in
> let n = int_of_string Sys.argv.(1) in
> for i = 1 to n do x.f <- x.f +. 1.0 done
>
> ./ref2 100000000  1.54s user 0.01s system 100% cpu 1.542 total

A few questions in view of this.  First, on my machine (AMD Athlon
1GHz running GNU/Linux), the timings give a preference to ref.ml

time ./ref 100000000
real    0m1.279s user    0m1.280s sys     0m0.000s
time ./ref2 100000000
real    0m1.411s user    0m1.380s sys     0m0.000s

What could be a reason for that?

Second, ain't references be optimized when their type is statically
known to be a float ref (I thought so, please confirm or correct)?

It seems to me there are three main issues concerning floats:
* storing       (avoid unnecessary indirections but take care of GC)
* comparisons   (= is not reflexive in IEEE 754 arithmetic)
* conversions

About "conversions", float : int -> float seems to be slow (compared
to a cast in C at least).  Is there any way to optimize it when it
intervene in an algebraic expression?  (Frequently on has to write
things like: for i=0 to n do let x = float i / float n in ... done)

I understand that float values need to be boxed to "dialog" with
polymorphic functions.  Let me picture it as

    +--------+  f : float -> float   +--------+
    |        | --------------------> |        |
    +--------+                       +--------+
        |                                |
        V                                V
    +--------+                       +--------+
    | double |                       | double |
    +--------+                       +--------+

However, couldn't we imagine that functions with float arguments or
return value have "two interfaces": the standard one (where one knows
the pointer) and another one (which gives the value) :

    +--------+  f : float -> float   +--------+
    |        | --------------------> |        |
    +--------+                       +--------+
        |                                |
        V                                V
    +--------+  f': float -> float   +--------+
    | double | --------------------> | double |
    +--------+                       +--------+

The _idea_, in C parlance, is to declare f(x) as &(f'(*x)).  Now, the
boxing should allow the GC to take care of these values.  But, if a
function returning a float feeds another function expecting a float,
the compiler could connect the "bottom lines" instead of passing
through the pointers:

     f : 'a -> float   +--------+      +--------+  g : float -> 'b
    -----------------> |        |      |        | -----------------> 
                       +--------+      +--------+                   
                           |               |                        
                           V               V                        
     f': 'a -> float   +--------+      +--------+  g': float -> 'b   
    -----------------> | double |----->| double | -----------------> 
                       +--------+      +--------+ 

This kind of idea could also apply to recursive functions passing
float values along the recursion...

My question is: is this type of idea workable?  Is it difficult to
implement?  (In a way it just generalize the special treatment of
arithmetic expressions.)  Maybe this can be generalized further to put
float references & equalities under the same umbrella?

Bear in mind I am not a compiler expert (and people even giving
compiling courses here are not very helpful), so my questions are also
a way for me to learn a little something...

Cheers,
ChriS
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