The Harmonized Parabolic Synthesis Methodology for Hardware Efficient Function Generation with Full Error Control

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 with moderate accuracy for ASIC implementation. These functions are extensively used in computer graphics, communication systems and many other application areas. For these high-speed applications, software solutions are 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 complexity operations, thus being simple to implement in hardware. A difference compared to other approximation methodologies is that it is a multiplicative, and not additive, methodology. Compared to the Parabolic Synthesis methodologies it is possible to significantly enhance the performance in terms of reducing chip area, computation delay and power consumption. Furthermore, it increases the possibility to tailor the characteristics of the error, improving conditions for subsequent calculations. To evaluate the methodology, the fractional part of the logarithm is implemented and its performance is compared to the Parabolic Synthesis methodology. The comparison is made with 15-bit resolution. The design implemented using the proposed methodology performs 3× better than the Parabolic Synthesis implementation in terms of throughput, while consuming 90% less energy. The chip area is 70% smaller than for the Parabolic Synthesis methodology. In summary, the new technology further increases the advantages of Parabolic Synthesis