Constant and power-of-2 segmentation algorithms for a high speed numerical function generator

• Main Author: Valenzuela, Zaldy M.
• Other Authors: Butler, Jon T.
• Format: Others
• Published: Monterey California. Naval Postgraduate School 2012
• Subjects: Numerical functions; Approximation theory
• Online Access: http://hdl.handle.net/10945/1881

The realization of high-speed numeric computation is a sought-after commodity for real world applications, including high-speed scientific computation, digital signal processing, and embedded computers. An example of this is the generation of elementary functions, such as sin( ) x , x e and log( ) x . Sasao, Butler and Reidel [Ref. 1] developed a high speed numeric function generator using a look-up table (LUT) cascade. Their method used a piecewise linear segmentation algorithm to generate the functions [Ref. 1]. In this thesis, two alternative segmentation algorithms are proposed and compared to the results of Sasao, Butler and Reidel [Ref.1]. The first algorithm is the Constant Approximation. This algorithm uses lines of slope zero to approximate a curve. The second algorithm is the power-of-2-approximation. This method uses 2i x to approximate a curve. The constant approximation eliminates the need for a multiplier and adder, while the power-of-2-approximations eliminates the need for multiplier, thus improving the computation speed. Tradeoffs between the three methods are examined. Specifically, the implementation of the piecewise linear algorithm requires the most amount of hardware and is slower than the other two. The advantage that it has is that it yields the least amount of segments to generate a function. The constant approximation requires the most amount of hardware to realize a function, but is the fastest implementation. The power-of-2 approximation is an intermediate choice that balances speed and hardware requirements.