A simple benchmark

I was recently wondering if I could speed up the access to the element of a matrix in OCaml, using Bigarrays. As the benchmark below shows, it turns out that no, Bigarray was actually slower than matrix operations.

However, a couple of interesting observations can also be made: inlining manually provided a huge increase of the performance for nested arrays, and Owl is actually the fastest solution available (but not by a lot).

```
open Owl
let n = 10000
let array_at m i j =
Array.unsafe_get (Array.unsafe_get m i ) j
let sum_array_no_inline n m =
let a = ref 0. in
for i = 0 to (n-1) do
for j = 0 to (n-1) do
a := !a +. array_at m i j
done;
done;
!a
let sum_array n m =
let a = ref 0. in
for i = 0 to (n-1) do
for j = 0 to (n-1) do
a := !a +. (Array.unsafe_get (Array.unsafe_get m i ) j )
done;
done;
!a
let sum_big_array n m =
let a = ref 0. in
for i = 0 to (n-1) do
for j = 0 to (n-1) do
a := !a +. (Bigarray.Array2.unsafe_get m i j);
done;
done;
!a
let sum_owl_array n m =
let a = ref 0. in
for i = 0 to (n-1) do
for j = 0 to (n-1) do
a := !a +. Mat.get m i j;
done;
done;
!a
let sum_owl_array_lib n m =
Mat.sum' m
let time f x =
let start = Unix.gettimeofday () in
let res = f x in
let stop = Unix.gettimeofday () in
Printf.printf "Execution time: %fs\n%!" (stop -. start);
res
let () =
let arr = Array.init n (fun i -> Array.init n (fun j -> (Random.float 1.0))) in
print_string "[ArrayNoInline] ";
let a1 = time (sum_array_no_inline n) arr in
print_string "[Array] ";
let a2 = time (sum_array n) arr in
let big_arr = Bigarray.Array2.of_array Bigarray.float32 Bigarray.c_layout arr in
print_string "[BigArray] ";
let b = time (sum_big_array n) big_arr in
let owl_arr = Mat.of_arrays arr in
print_string "[OwlArray] ";
let c = time (sum_owl_array n) owl_arr in
print_string "[OwlArrayLib] ";
let d = time (sum_owl_array_lib n) owl_arr in
print_string "\n";
print_float a1;
print_string "\n";
print_float a2;
print_string "\n";
print_float b;
print_string "\n";
print_float c;
print_string "\n";
print_float d;
()
```

And the results

```
[ArrayNoInline] Execution time: 0.432230s
[Array] Execution time: 0.105445s
[BigArray] Execution time: 3.037937s
[OwlArray] Execution time: 2.177349s
[OwlArrayLib] Execution time: 0.080217s
```