arXiv Open Access 2023

Efficient Generic Quotients Using Exact Arithmetic

Stephen M. Watt

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Abstrak

The usual formulation of efficient division uses Newton iteration to compute an inverse in a related domain where multiplicative inverses exist. On one hand, Newton iteration allows quotients to be calculated using an efficient multiplication method. On the other hand, working in another domain is not always desirable and can lead to a library structure where arithmetic domains are interdependent. This paper uses the concept of a whole shifted inverse and modified Newton iteration to compute quotients efficiently without leaving the original domain. The iteration is generic to domains having a suitable shift operation, such as integers or polynomials with coefficients that do not necessarily commute.

Topik & Kata Kunci

cs.SC

Penulis (1)

Stephen M. Watt

Format Sitasi

APA MLA BibTeX

Watt, S.M. (2023). Efficient Generic Quotients Using Exact Arithmetic. https://arxiv.org/abs/2304.01753

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓