Geodesic
A Mathematical Basis for an Interval Arithmetic Standard
Serdica Journal of Computing, Tome 4 (2010) no. 1, pp. 29-42.

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Basic concepts for an interval arithmetic standard are discussed in the paper. Interval arithmetic deals with closed and connected sets of real numbers. Unlike floating-point arithmetic it is free of exceptions. A complete set of formulas to approximate real interval arithmetic on the computer is displayed in section 3 of the paper. The essential comparison relations and lattice operations are discussed in section 6. Evaluation of functions for interval arguments is studied in section 7. The desirability of variable length interval arithmetic is also discussed in the paper. The requirement to adapt the digital computer to the needs of interval arithmetic is as old as interval arithmetic. An obvious, simple possible solution is shown in section 8.
Keywords: Interval Arithmetic, IEEE Standardization, Variable Precision Interval Arithmetic, Evaluation of Functions, Hardware Support 
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Bohlender, Gerd; Kulisch, Ulrich. A Mathematical Basis for an Interval Arithmetic Standard. Serdica Journal of Computing, Tome 4 (2010) no. 1, pp. 29-42. http://geodesic.mathdoc.fr/item/SJC_2010_4_1_a3/