A Novel Approach to Tight Bouonds and Statistical Information of Rounding Errors

Friday, October 15, 2010 - 1:25pm - 2:25pm
Vincent 16
Ping Tak Tang (D. E. Shaw Research)
Obtaining tight bounds on rounding errors has been so specialized and labor-intensive a task that it is seldom carried out during normal engineering practice in industry. It turns out that for absolute error analysis related to fixed point arithmetic, an automatic method can be devised for computation of linear transform. This method, implemented as a software tool, allows practicing engineers to obtain tight bounds as well as a vast amount of statistical information on forward rounding errors. The method consists of modeling the rounding error process in a way that allows mechanical computation on its propagation. When this model and propagation computation is implemented with objects and overloading in an object oriented manner, engineers can obtain detailed error information by means of algorithm implementation, not by actually carrying out error analysis. In this talk we will describe this method and illustrate its application on the very important Fast Fourier Transform.