Combining the parabolic synthesis methodology with second-degree interpolation

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

“…The second sub-function is a second-degree interpolation [3,13,14] specifically shown in [12], where the number of intervals in the interpolation decides the final accuracy of the approximation and allows the distribution of the error to be tailored. When developing an approximation with the proposed methodology, an empirical design methodology is the only feasible approach since the sub-functions are designed as a complete unity to fulfill the design criteria.…”

“…Second, the Parabolic Synthesis methodology allows full control of the characteristics and distribution of the error, which opens an opportunity to design with shorter word lengths and thereby gain in area, speed and power. As reported in [12], a further improvement of the Parabolic Synthesis methodology was developed by combining it with second-degree interpolation [3,13,14].…”

“…As a summary, the approximation is computed as a polynomial with two variables and with the total degree of 2 + 2 = 4. An attractive feature with the Parabolic Synthesis methodology combined with Second-Degree Interpolation [12] is that it enables a rough internal error adjustment as part of the approximation. The error compensation can be performed in order to improve the distribution of the error to suit the properties required of the approximation.…”

“…The error compensation can be performed in order to improve the distribution of the error to suit the properties required of the approximation. Compared to the Parabolic Synthesis methodology the Parabolic Synthesis methodology Combined with Second-Degree Interpolation accomplishes the following [12]: A reduction in chip area because the number of second-order functions is reduced to two; a reduction of the critical path delays because the number of second-order functions is reduced to two; a reduction in power consumption because of reduced chip area and critical path delay. And last, the improved possibilities to tailor the distribution of the error.…”

“…Using accuracy as the only comparison criterion is not enough; other characteristics of the error, most notably its distribution, are equally important. An illustrative example is the comparison in [12] between an implementation based on one of the Parabolic Synthesis methodologies and an implementation performed with the CORDIC method (which, by far, is the most commonly used approximation method today). It is shown that the implementation performed using Parabolic Synthesis combined with seconddegree interpolation outperforms the CORDIC implementation in all aspects.…”