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ABSTRACT

Floating-point operations are an essential requisite in a wide range of computational and engineering applications that need good performance and high precision. Current advances in VLSI technology raised the density integration fast enough, allowing the designers to develop directly in hardware several floating-point operations commonly implemented in software. Until now, most of the research has not focused on the tradeoff among the need of high performance and the cost of the size of logic area, associated with the level of precision, parameters that are very important in a wide variety of applications such as robotics, image and digital signal processing. This paper describes an FPGA implementation of a parameterizable floating-point library for addition/subtraction, multiplication, division and square root operations. Architectures based on Goldschmidt algorithm were implemented for computing floating-point division and square root. The library is parameterizable by bit-width and number of iterations. An analysis of the mean square error and the cost in area consumption is done in order to find, for general purpose applications, the feasible bit-width representation, number of iterations and number of addressable words for storing initial seeds of the Goldschmidt algorithm.

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INDEX TERMS

General Terms:
Algorithms, Performance

Keywords:
FPGA, computer arithmetic, floating-point, goldschmidt