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Exact Real Computer Arithmetic (1997) [16 citations — 9 self]

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@MISC{Potts97exactreal,
    author = {Peter John Potts and Peter John and Abbas Edalat},
    title = {Exact Real Computer Arithmetic},
    year = {1997}
}

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Abstract:

Introduction Real numbers are usually represented by finite strings of digits belonging to some digit set. The real number representation specifies a function that maps strings to real numbers or real intervals with distinct end-points. For example, IEEE 754 single precision floating point [9] is encoded in 32 binary bits using 1 bit for the sign s, 8 bits for the biased exponent e, and 23 bits for the normalised mantissa m without the leading 1. The basic format represents the real number (\Gamma1) s 2 e\Gamma127 (1:m): However, finite strings of digits can only represent a limited subset of the real numbers exactly because many real numbers have too many significant digits (such as or p 2) or are too large or too small. This means that most real numbers are represented by nearby real numbers or enclosing real

Citations

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