@INPROCEEDINGS{ChevillardLauter2007,
  author = {S.~Chevillard and C.~Lauter},
  title = {A certified infinite norm for the implementation of elementary functions},
  booktitle = {QSIC 2007, Proceedings of the Seventh International Conference on
	Quality Software},
  year = {2007},
  editor = {A.~Mathur and W.~E.~Wong and M.~F.~Lau},
  pages = {153--160},
  address = {Los Alamitos, CA},
  month = {October},
  publisher = {IEEE Computer Society},
  abstract = {The high-quality floating-point implementation of useful functions
	$f : \R \rightarrow \R$, such as $\exp$, $\sin$, $\erf$ requires
	bounding the error $\epsilon = \frac{p -f }{f}$ of an approximation
	$p$ with regard to the function~$f$. This involves bounding the infinite
	norm $\ninf{\epsilon}$ of the error function. Its value must not
	be underestimated when implementations must be safe.
	
	
	Previous approaches for computing infinite norm are shown to be either
	unsafe, not sufficiently tight or too tedious in manual work.
	
	
	We present a safe and self-validating algorithm for automatically
	upper- and lower-bounding infinite norms of error functions. The
	algorithm is based on enhanced interval arithmetic. It can overcome
	high cancellation and high condition number around points where the
	error function is defined only by continuous extension.
	
	
	The given algorithm is implemented in a software tool. It can generate
	a proof of correctness for each instance on which it is run.},
  keywords = {Certified infinite norm, interval arithmetic, elementary functions}
}