Showing papers on "Divisor published in 1987"

Apparatus for dividing elements of a Galois Field GF (2QM)

Abstract: The invention is an apparatus and/or method which enables one to divide two elements, A and B, of GF(2 2M ), that is, perform the operation B/A, by finding the multiplicative inverse of the divisor A, and then multiplying the inverse by the numerator, B. The multiplicative inverse, A -1 , of A is found by computing a conversion factor, D, and then multiplying A by D to convert it to an element C, where C is also an element of a smaller Galois Field, GF(2 M ), which is a subfield of GF(2 2M ). Specifically, C is equal to A 2 .spsp.M.sbsp.+1), or A 2 .spsp.M *A, in the field GF(2 2M ). Next, the multiplicative inverse, C -1 , of C in GF(2 M ) is found by appropriately entering a stored look-up table containing the 2 M elements of GF(2 M ). The multiplicative inverse, C -1 , of C is thereafter converted, by multiplying it by the conversion factor D calculated above, to the element of GF(2 2M ) which is the multiplicative inverse, A -1 , of the original divisor, A. The multiplicative inverse, A -1 , of A is then multiplied by B to calculate the quotient, B/A.

A radix-4 on-line division algorithm

Abstract: We present an on-line algorithm for radix-4 floating point division. The divisor is first transformed in to a range such that the quotient digits are computed as a function of the scaled partial remainder only.

A Shift-Remainder GCD Algorithm

Abstract: This paper studies an integer greatest common divisor algorithm which uses a "shift-divide" instruction to compute the gcd of two integers u, v. If u > v, the worst case run-time is [log2v]+1, and for uniformly distributed integers in the range [0,u-1] , the average run-time is experimentally 0.555 ln u.

N-decimal number subtraction processing system

Abstract: PURPOSE:To speed up processing by specifically setting the value of a quotient in accordance with the size of a dividend and a divisor when the number of upper digits C (C is an integer >=2) of the dividend coincides with that of the divisor. CONSTITUTION:Whether the number of upper digits C of a dividend to be processed and expressed by an n-decimal number coincides with that of the divisor or not is processed by a checking part 1, and when both the values coincide with each other, the dividend and the divisor are compared by a size comparison processing part 2. When the dividend is larger or smaller than the divisor, the 1st or 2nd quotient preset processing part 3 or 4 executes its processing. The processing part 3 sets up (n-1) forcedly by (C-1) digits on the basis of the quotient and the processing part 4 sets up value '0' forcedly by (C-1) digits on the basis of the digits in the quotient.

Divisors of polynomial matrices: Theory and applications

Abstract: In this note divisors G(s) of a given polynomial matrix N(s) are discussed. The note deals with the following problems: extraction of a greatest right (left) divisor of N(s) , computation for a given state-space system (C, A, B) a state-space feedback making the system (C, A + BF, B) maximally or appropriately observable, and determination for a given system (C, A, B, O, W, O) a disturbance rejection feedback F . The developed methods are very simple from a computational point of view and can be easily implemented in the software via existing computer library procedures.

Bi-unitary perfect polynomials overGF(g)

Abstract: This paper continues the author's excursions into the arithmetic of polynomials over finite fields. For monic polynomials A, B e GF[q, x] where p is a prime, q=pdand d ⩾ 1: The divisor B of A is a bi-unitary divisor of A provided 1 is the greatest common unitary divisor of the polynomials B and A/B, and we say that A is bi-unitary perfect (b.u.p.) over GF(q) provided A equals the sum σ**(A) of the distinct bi-unitary divisors of A in GF[q, x]. A diversity of b.u.p. polynomials over GF(q) is found, some of which are neither perfect nor unitary perfect. For p > 2 we can only conjecture a characterisation of the b.u.p. polynomials which split in GF[p, x], so several open questions remain. Examples of non-splitting b.u.p. polynomials over GF(p) are given for p=2, 3, 5 which, in turn, allow the construction of such examples over GF(pd) for these p.