Error Estimation of Floating Point Calculations by a New Floating Point Type That Tracks the Errors

摘要

A new floating point type called the precise floating point type is developed to limit and track the accumulation of calculation errors during floating point calculations and qualify the calculation results, by reinterpreting the polymorphic representation of the conventional floating point types. The validity of this strategy is demonstrated by tracking the calculation error and qualifying the results of Fast Fourier Transformation in various conditions. Using this type, the calculation error seems to propagate according to Boltzman distribution.