ForCE provides a number type that is more accurate than hardware-supported floating-point types and provides error estimates. For example, a system that supports only single-precision IEEE numbers can use ForCE to obtain better precision results, at the same time as obtaining a roundoff error estimate.
Test it by navigating to the /tests folder and typing
make
ForCE uses a variant of CENA, a method for the correction of floating-point
roundoff errors. The original CENA method uses previously-published formulas
to compute the local error introduced by operators (e.g. +-*/), and
takes inspiration from the reverse-mode of automatic differentiation to combine
local errors into a global error estimate. This error estimate is often so
precise that it can be subtracted from the result to obtain a better result.
Instead of the reverse-propagation that the original CENA method is built on, ForCE uses forward-mode AD. This allows us to save memory, reduce complexity, and offer an operator-overloading-based implementation that can be easily used in an existing C++ program. ForCE naturally works in parallel OpenMP programs.