Title :
A priori worst-case error bounds for floating-point computations
Author_Institution :
Inst. fur Wissenschaftliches Rechnen und Math. Modellbildung, Karlsruhe Univ., Germany
Abstract :
A new technique for the a-priori calculation of rigorous error bounds for floating-point computations is introduced. The theorems given in this paper, combined with interval arithmetic, lead to the implementation of reliable software routines which enable the user to compute the desired error bounds automatically by a suitable computer program. As a prominent example, a table-lookup algorithm for calculating the function exp(x)-1 that has been published by Tang (1992) is analyzed using these new tools. The result shows the high quality of the new approach
Keywords :
error analysis; floating point arithmetic; function evaluation; software reliability; subroutines; table lookup; a-priori worst-case error bounds; exponential function; floating-point computations; interval arithmetic; reliable software routines; table-lookup algorithm; Algorithm design and analysis; Computer errors; Digital arithmetic; Equations; Error analysis; Floating-point arithmetic; Linear systems; Reliability theory;
Conference_Titel :
Computer Arithmetic, 1997. Proceedings., 13th IEEE Symposium on
Conference_Location :
Asilomar, CA
Print_ISBN :
0-8186-7846-1
DOI :
10.1109/ARITH.1997.614880
