A parallel/vectorized double-precision exponential core to accelerate computational science applications

ABSTRACT

Many natural processes exhibit exponential decay and, consequently, computational scientists make extensive use of e^-χx in computer simulation experiments. While it is common to implement transcendental functions (sine, cosine, exponentiation, etc.) in hardware using the well-known CORDIC algorithm, many contemporary FPGA implementations either use fixed point or reduced precision floating-point operations (which suffers from a high average/mean error). Unfortunately, these solutions are unacceptable for many computational scientist who require the accuracy of doubleprecision values.

This paper presents a direct implementation of an IEEE 754 double-precision e^-χx FPGA core to support computational science applications. The design is similar to CORDIC but has been modified to specifically support exponentiation; it is pipelined and parallel to efficiently handle large vectors of parameters. Compared to solutions described in the literature, it consumes lesser logical gates, enabling more e^-χx cores per FPGA. The paper compares the implementation to the current prevailing approaches. Results shows that the implementation on the Virtex 4 XC4VFX60 FPGA achieves a correct precise double-precision e^-χx values, with a high throughput.

INDEX TERMS

Primary Classification:
  B. Hardware
  B.2 ARITHMETIC AND LOGIC STRUCTURES
      B.2.1 Design Styles
          Subjects: Parallel

Additional Classification:
  B. Hardware
  B.2 ARITHMETIC AND LOGIC STRUCTURES
      B.2.1 Design Styles
          Subjects: Pipeline

General Terms:
Design

Keywords:
cordic, exponential core, fpga