Abstract
The article presents a parallel hardware-oriented algorithm designed to speed up the division of two octonions. The advantage of the proposed algorithm is that the number of real multiplications is halved as compared to the naive method for implementing this operation. In the synthesis of the discussed algorithm, the matrix representation of this operation was used, which allows us to present the division of octonions by means of a vector–matrix product. Taking into account a specific structure of the matrix multiplicand allows for reducing the number of real multiplications necessary for the execution of the octonion division procedure.
Highlights
This is at the expense of increasing the number of addition operations from 63 to 133, which is an increase of approximately 106.3%
This means that the matrix D16 entries can be computed in advance only once and stored in the read-only memory (ROM) of the computational system
The paper presented a new parallel algorithm for calculating the quotient of two octonions. The use of this algorithm reduces the multiplicative complexity of dividing octonion operation, reducing its hardware implementation complexity
Summary
The dynamic development of science and technology of data processing as well as the need to implement more and more complex problems and practical applications require the use of ever more complex mathematical methods and formalisms. When performing the aforementioned hypercomplex-valued algorithms, the most time-consuming macro operations are multiplication and division, since they require several dozen of the nested real multiplications and additions [29,30]. The intention of developers of highly efficient algorithms for processing hypercomplex data has always been to look for ways to reduce the number of arithmetic operations in these algorithms.
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