. However, In applications often interval operations A ? B for thick intervals A, B are executed. The wider A and B are, the less is the gain of Algorithm 1 compared to

S. Boldo and J. Muller, Some Functions Computable with a Fused-Mac, 17th IEEE Symposium on Computer Arithmetic (ARITH'05), pp.52-58, 2005.
DOI : 10.1109/ARITH.2005.39
URL : https://hal.archives-ouvertes.fr/inria-00000895

W. J. Cody, J. , and J. T. Coonen, Algorithm 722; Functions to support the IEEE standard for binary floating-point arithmetic, ACM Transactions on Mathematical Software, vol.19, issue.4, pp.443-451, 1993.
DOI : 10.1145/168173.168185

R. B. Kearfott, M. Dawande, K. Du, and C. Hu, Algorithm 737; INTLIB: a portable Fortran 77 interval standard-function library, ACM Transactions on Mathematical Software, vol.20, issue.4, pp.447-459, 1994.
DOI : 10.1145/198429.198433

S. M. Rump, T. Ogita, and S. Oishi, Accurate Floating-point Summation Part I: Faithful Rounding Accepted for publication in SISC, 2008.

M. Daumas, L. Rideau, and L. Théry, A Generic Library for Floating-Point Numbers and Its Application to Exact Computing, 14th International Conference on Theorem Proving in Higher Order Logics, pp.169-184, 2001.
DOI : 10.1007/3-540-44755-5_13
URL : https://hal.archives-ouvertes.fr/hal-00157285

S. Boldo, Preuves formelles en arithmétiquesarithmétiquesà virgule flottante, 2004.