Abstract
One possible approach to exact real arithmetic is to use linear fractional transformations to represent real numbers and computations on real numbers. In this paper, we show that the bit sizes of the (integer) parameters of nearly all transformations used in computations are proportional to the number of basic computational steps executed so far. Here, a basic step means consuming one digit of the argument(s) or producing one digit of the result.
Most of the results in this paper were found during a visiting fellowship of the author at Imperial College, London. This visit was organised by Abbas Edalat and funded by EPSRC.
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Heckmann, R. (1998). The appearance of big integers in exact real arithmetic based on Linear Fractional Transformations. In: Nivat, M. (eds) Foundations of Software Science and Computation Structures. FoSSaCS 1998. Lecture Notes in Computer Science, vol 1378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0053549
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DOI: https://doi.org/10.1007/BFb0053549
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