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 at DFP 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.
Highlights
Decimal floating point (DFP) number representation, standardized in IEEE-754-R, results in a higher level of computation accuracy compared to binary floating point (BFP) for arithmetic operations
In order to experimentally show that the proposed DFP data structure grows linearly for a DFP number, we measure the memory consumption of our data structure
It was shown that the presented model grows linearly for a DFP number
Summary
Decimal floating point (DFP) number representation, standardized in IEEE-754-R, results in a higher level of computation accuracy compared to binary floating point (BFP) for arithmetic operations. In order to formally verify DFP DSP systems, a novel and efficient data structure that is capable of modeling both DFP numbers and basic arithmetic operations is required. The IEEE-754 standard [3] for BFP number representation is a widespread standard used for arithmetic calculations. It could represent a large range of numbers. Many other works like [8] provided arithmetic architectures for DFP operations.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
