FPBern is a tool for computation of roundoff error bounds using Bernstein expansion.
We consider the roundoff error r of a program implementing a polynomial function f(x):
r(x,e) = l(x, e) + h(x, e)
with l(x, e) the part of r(x, e) linear w.r.t. e and h(x, e) the part of r(x, e) non-linear w.r.t. e.
FPBern computes an upper bound of |l(x, e)| with x lying in a box, and e being bounded by a given machine epsilon.
For instance, one can consider f(x) = x1^3 + (3/4) x1 x2^2, with x1 in [-1, 1] and x2 in [-2, 2].
FPBern is divided in two independant modules:
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FPBern(a): computes the roundoff error with a C++ implementation.
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FPBern(b): computes the roundoff error with a Matlab2015a implementation.
Please refer to the the specific README of each module for details on the installation and usage.