Implementation of Elementary Functions for a Fixed Point SIMD DSP Coprocessor

Orri Tomasson

This thesis is about implementing the functions for reciprocal, square root, inverse square root and logarithms on a DSP platform. A multi-core DSP platform that consists of one master processor core and several SIMD coprocessor cores is currently being designed by a team at the Computer Engineering Department of Linköping University. The SIMD coprocessors’ arithmetic logic unit (ALU) has 16 multipliers to support vector multiplication instructions. By efficiently using the 16 multipliers, it is possible to evaluate polynomials very fast. The ALU does not have (hardware) support for floating point arithmetic, so the challenge is to get good precision by using fixed point arithmetic. Precise and fast solutions to implement the mathematical functions are found by converting the fixed point input to a soft floating point format before polynomial approximation, choosing a polynomial based on an error analysis of the polynomial approximation, and using Newton-Raphson or Goldschmidt iterations to improve the precision of the polynomial approximations. Finally, suggestions are made of changes and additions to the instruction set architecture, in order to make the implementations faster, by efficiently using the currently existing hardware.