Comparison of Universal Number with the IEEE 754 Standard with Respect to Validation Criterion

Abstract

Improving the accuracy of computations is a topical line of research in the field of theoretical informatics due to a large volume of scientific and engineering problems. The IEEE 754 standard used for representing floating-point numbers has certain drawbacks and involves limitations for being directly used in high-precision computations. To ensure the reliability of the computation results, a numerical analysis is necessary, but in many cases such analysis is not carried out. Due to lack of analysis, incorrect results may occur in performing calculations, leading to unknown behavior of the calculation program. Incorrect results can cause serious consequences in software that is critical to the accuracy of calculations. In 2014, John Gustafson proposed a so-called universal number format, in which reliability of the obtained results was guaranteed by adding additional fields in the bit string to represent the number and introduce the advantages of interval arithmetic. The use of interval arithmetic ensures reliability of the results, and the additional fields in the universal number can reduce the memory bus bandwidth requirements, as well as reduce the computer system power consumption requirements. The universal number automatically adjusts the length of the bit string to the computation requirements. The article describes the IEEE 754 and the universal number formats, and compares them in carrying out arithmetic calculations, solving systems of linear equations, and calculating a convex hull. Results demonstrating that the use of universal number for solving computational problems makes it possible to improve the reliability of calculations as compared with those performed using the IEEE 754 format are presented.