Divider for calculating by summation the quotient and remainder

Details Divider for calculating by summation the quotient and remainder Divider for calculating by summation the quotient and remainder

1980-07-08

1982-06-08

Malzahn, David H.

Boots, shoes, and leggings

364900, G06F 752

Patent

active

043342850

ABSTRACT:
For division by a Mersenne number (2.sup.n -1), a divided P is expressed as: ##EQU1## A first summing unit sums up the coefficients a.sub.i 's to provide a sum of a carry multiplied by 2.sup.n and a sum portion less than 2.sup.n. The carry is added to the sum portion to provide a similar sum. When the sum portion of such a sum becomes less than 2.sup.n, the sum portion provides the remainder if it is less than the Mersenne number. If not, the remainder is rendered zero with an additional carry produced. A second summing unit calculates ##STR1## for i=1 to (k-2). Each summation is given by a carry multiplied by 2.sup.n plus a sum portion with the carry from the first summing unit and the additional carry added to the summation for i=1 and with the carry from the summation i=i-1 added to the summation for i=i. The sum portions calculated by the second summing unit with successive addition of the carries provide zeroth through (k-2)-th coefficients to (2.sup.n).sup.O through (2.sup.n).sup.k-2 of a polynomial representative of the quotient, in which the carry from the summation for i=k-2, if not zero, provides the coefficient for (2.sup.n).sup.k-1. For a parallel processor system, a Mersenne prime is used as the number of memory modules. The system preferably comprises a divider of the type described.

REFERENCES:
patent: 3527930 (1970-09-01), Cocke et al.

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