Precedence and associativity with infix operators

[mooreryan]

This is related to #21.

The infix operators seem to break with what you would expect normal math operator precedence to have. I'm just wondering if this is the intended behavior or not.

Here's an example.

# module M = Owl.Mat;;
# module Op = Owl.Dense.Matrix.Operator;;

# let x = M.linspace 0. 10. 6
val x : M.mat = 
   C0 C1 C2 C3 C4 C5 
R0  0  2  4  6  8 10 

(* Okay *)
# Op.(x *$ 2. +$ 1.);;
- : (float, Bigarray.float64_elt) Owl_dense_matrix_generic.t =

   C0 C1 C2 C3 C4 C5 
R0  1  5  9 13 17 21 


(* Not what you would expect... *)
# Op.(2. $* x +$ 1.);;
- : (float, Bigarray.float64_elt) Owl_dense_matrix_generic.t =

   C0 C1 C2 C3 C4 C5 
R0  2  6 10 14 18 22 

I assume this is because of OCaml's rules about operator precedence and associativity. Particularly the fact that operators starting with + (like +$) have a higher precedence than those starting with $ (like $*).

So then you have a case where scalar * matrix multiplication ($*) has a lower precedence than matrix * scalar multiplication (*$).

In particular, you can see that, scalar * matrix multiplication ($*) has a lower precedence than matrix + scalar (+$) addition.

Just for reference, here is numpy with the same example.

>>> import numpy as np
>>> x = np.linspace(0, 10, num=6)
>>> 2 * x + 1
array([ 1.,  5.,  9., 13., 17., 21.])
>>> x * 2 + 1
array([ 1.,  5.,  9., 13., 17., 21.])