Binary summation

In discussing his binary summation method [1] Linz mentions two defects: “It is more difficult to program than the standard method, and it is difficult to use unless all numbers are available at the start of the summation.” A defect not mentioned is the extra storage space (approximately N words) required for the Sij. The last two of these three defects can be removed by proper combination of partial sums. In the adjacent PL/I program, the only storage needed is for the M-component vector T, where M ≧ [log2 N]. N must be even, and B is a number not expressible as a sum of A(I)'s, e.g. B = -1 if A(I) ≥ 0, or B = 1E + 75 for reasonably sized A(I).

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