Alan A. Jorgensen, University of Nevada, Las Vegas
Floating point, the method computers use to represent real numbers, is prone to errors. Because the floating point is represented in a fixed space, it is prone to two types of error, rounding and Cancellation. Rounding error occurs when significant digits must be discarded and accounted for by rounding up or down. Cancellation error occurs when similar numbers are subtracted and consequently lose significant leading digits. These errors are incompatible because rounding error is linear and cancellation error is exponential. The accumulation of these errors can be catastrophic with no visible indication of a failure. In general, prior methods of error mitigation do not account for both rounding and cancellation errors, both of which may exist in a complex computation. The patent, Jorgensen, 2017, US9817662 defines a mechanism that calculates and saves the range of error associated with a standard floating point value consequently making floating point error visible and therefore making floating point safe and reliable.