Mathematical model and implementation of rational processing

作者：

Highlights：

• It is introduced a formal framework for processing rational numbers.

• A representation system based on positional notation system is described.

• A method for calculating the addition function is detailed.

• Experiments and application example have been made to validate the model.

摘要

•It is introduced a formal framework for processing rational numbers.•A representation system based on positional notation system is described.•A method for calculating the addition function is detailed.•Experiments and application example have been made to validate the model.

论文关键词：Computer arithmetic,Computational methods,Exact computation,Rational processing,Mathematical model,Computational efficiency

论文评审过程：Received 10 November 2015, Revised 27 April 2016, Available online 18 May 2016, Version of Record 29 August 2016.

论文官网地址：https://doi.org/10.1016/j.cam.2016.05.001