A memory-efficient canonical data structure for decimal floating point arithmetic systems modeling and verification

Abstract

Decimal floating point (DFP) number representation was proposed in IEEE-754-2008 in order to overcome binary floating point inaccuracy. Neglecting binary floating point verification has resulted in significant validity and economic losses. Formal verification can be a solution to similar DFP design problems. Verification techniques aiming atDFP are limited to functional methods whereas formal approaches have been neglected and traditional decision diagrams cannot model DFP representation complexity. In this paper, we propose an efficient canonical data structure that can model DFP properties. Our novel data structure models coefficient, exponent, sign, and bias of a DFP number. We will prove mathematically that our data structure is canonical. We will also show that the size of the proposed data structure will grow linearly for a DFP number for all format lengths, so our data structure can be built with a reasonable amount of memory and run time. Experimental results support our mathematical discussion for linear growth of the DFP data structure. Moreover, comparison of our data structure with integer decision diagrams reveals that our model is also efficient for modeling integer functions when utilized as an integer level diagram.

Metrology and Measurement Systems

“…It was verified that the values in variables stored during the algorithm operation had up to about 12 or even 16 digits significant for the results of calculations, due to the specifics of the simulation method chosen. These values lie at the limit of the accuracy range of the binary variables in C#, which is between 15 and 16 decimal places [2]. It was verified that the change of arithmetic from decimal to binary causes slight differences in the transmission spectrum of the Bragg grating obtained as a result of the simulation.…”

“…The simulations were carried out in a handwritten application dedicated to this purpose, written in the C# programming language, having a graphical interface based on the Windows Forms technology. The program uses decimal data types, thanks to which, in the calculations performed by the application, the accuracy of 28 decimal places was obtained [2]. It was verified that the values in variables stored during the algorithm operation had up to about 12 or even 16 digits significant for the results of calculations, due to the specifics of the simulation method chosen.…”

“…6 [3]. (2). Calculating the difference between the obtained transmission coefficients (3) and determining the average value (4); Determining the wavelength for which the function assumes the calculated value (5).…”