Abstract
We develop an online-algorithm for multiplication of real numbers which runs in time O(M(n)log(n)), where M denotes the Schönhage-Strassen-bound for integer multiplication which is defined by M(m)=m log(m) log log(m), and n refers to the output precision (1/2)n. Our computational model is based on Type-2-machines: The real numbers are given by infinite sequences of symbols which approximate the reals with increasing precision. While reading more and more digits of the input reals, an algorithm for a real function produces more and more precise approximations of the desired result. An algorithm M is called online, if for every n ∈ ℕ the input-precision, which M requires for producing the result with precision (1/2)n, is approximately the same as the topologically necessary precision.
This work was supported by the Deutsche Forschungsgemeinschaft.
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© 1997 Springer-Verlag Berlin Heidelberg
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Schröder, M. (1997). Fast online multiplication of real numbers. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023450
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DOI: https://doi.org/10.1007/BFb0023450
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