About subtraction and reduction variables.

The following is allowed:
s = 0;
#pragma omp parallel for reduction(-: s) etc...
  for(k = 1; k <= n; k++) {
    expr_k = ...;
    s = s - expr_k; 
  }
The reason is that a thread can compute a partial sum (in any order)
and then these partial sums can be added together.

The final sum is -(expr_1 + expr_2 + ... + expr_n) and there is no problem
to divide the final sum into partial sums.

If we change s = s - expr_k; to s = expr_k - s; there will be a problem however.
Writing out the value of s for the first iterations we get:

k = 1: s = 0 - expr_1 = -expr_1
k = 2: s = expr_2 - s = expr_2 + expr_1
k = 3: s = expr_3 - s = expr_3 - expr_2 - expr_1
k = 4: s = expr_4 - s = expr_4 - expr_3 + expr_2 + expr_1
k = 5: s = expr_5 - s = expr_5 - expr_4 + expr_3 - expr_2 - expr_1

and we that an easy summation of partial sums is not possible due
to the alternation of sign.