David McClain writes:
 > ....well, I hate to say this... but I did recode the innermost loop in C and
 > it now runs more than 5 times faster... Straight recoding into C bought 4x,
 > and using better math brought that up to 5x.
 > 
 > I think the big thing here is that the OCaml code was producing huge amounts
 > of garbage, despite preallocated buffers with which all the processing was
 > reading and writing data. The ancillary closures and tuple args were just
 > eating my shirt...

I can easily imagine that, with two caveats: tuples passed directly to
functions do seem to get elided, while on the other hand apparently
atomic float accumulators can cause more garbage than you might think.
E.g.

        let a = ref 0. in
        for i = 0 to n-1 do
          a := !a +. Array.unsafe_get xs i
        done

makes garbage---`a' isn't unboxed---while

        type floatref = { mutable it: float }

        let a = { it = 0. } in
        for i = 0 to n-1 do
          a := !a +. Array.unsafe_get xs i
        done

doesn't.  The effect on the visible quality of the assembler for the
inner loop is dramatic, and so is the speed improvement ... basically
using polymorphic data structures is a bad idea.  I wonder if this is
a limitation you have run up against?

Some years ago I made a library using camlp4 for supporting tensor
notation, e.g.

        tens x[I] = a[I J] b[J]

using both automatically generated C and vanilla caml.  When I
recently noticed the above point about not using polymorphic
references, I found there was rather little difference in performane
between the C and ocaml versions.
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