The harmonized parabolic synthesis methodology for function generation in hardware
(English)Manuscript (preprint) (Other academic)
The Harmonized Parabolic Synthesis methodology is a further development of the Parabolic Synthesis methodology for approximation of unary functions such as trigonometric functions, logarithms and the square root, as well as binary functions such as division, in hardware.These functions are extensively used in computer graphics, digital signal processing, communication systems, robotics, astrophysics, fluid physics and many other application areas. For these high-speed applications, software solutions are in many cases not sufficient and a hardware implementation is therefore needed. The Harmonized Parabolic Synthesis methodology has two outstanding advantages: it is parallel, thus reducing the execution time, and it is based on low 2complexity operations, thus is simple to implement in hardware. A notable difference in the Harmonized Parabolic Synthesis methodology compared to many other approximation methodologies is that it is a multiplicative and not an additive methodology. Without harming the favorable distribution of the approximation error presented in earlier described Parabolic Synthesis methodologies it is possible to significantly enhances the performance of the Harmonized Parabolic Synthesis methodology, in terms of reducing chip area, computation delay and power consumption. Furthermore it increases the possibility to tailor the characteristics of the error, which improves the conditions for subsequent calculations. It also extends the set of unary functions that approximations can be performed upon since the possibilities to elaborate with the characteristics and distribution of the error increases. To evaluate the proposed methodology, the fractional part of the logarithm has been implemented and its performance is compared to the Parabolic Synthesis methodology. The comparison is made with 15-bit resolution. The design implemented using the Harmonized Parabolic Synthesis methodology performs 3x better than the Parabolic Synthesis implementation in terms of throughput. In terms of energy consumption, the new methodology consumes 90% less. The chip area is 70% smaller than for the Parabolic Synthesis methodology. In summary, the new technology presented in this paper further increases the advantages of Parabolic Synthesis.
Approximation, parabolic synthesis, unary functions, elementary functions, second-degree interpolation, arithmetic computation, look-up table, VLSI
IdentifiersURN: urn:nbn:se:hh:diva-30859OAI: oai:DiVA.org:hh-30859DiVA: diva2:927006
Som manuskript i avhandling. / As manuscript in dissertation.2016-05-102016-05-102016-12-01Bibliographically approved