ACCURACY-AWARE APPROXIMATIONS FOR ERROR ANALYSIS

Abstract

With expensive hardware, users grew more tolerant to errors jeopardising answer quality for speed. Transistors have gradually become inexpensive and bandwidth has become very precious, but there is no significant change in the approach towards approximation. This work demonstrates the need for predictive approximations and automatic error analysis. Results from 6 DSP programs show that tuning the bitwidth of floating point programs to their arbitrary precision fixed point equivalents can yield upto 82 and 66 percent average reduction in resources when compared to the double precision and single precision versions respectively. The need for accuracy-aware computing is studied through roundoff error analysis by comparing floating point with multi-precision floating point and interval arithmetic libraries and Universal Numbers (UNUMs) through selected case studies. Results emphasize the need to address some of the important challenges like automatic error analysis, programmer productivity, performance and achieving the desired accuracy with limited precision.