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The LEDA class real number

By Christoph Burnikel, Kurt Mehlhorn and Stefan Schirra


We describe the implementation of the LEDA [MN95, Nah95] data type real. Every integer is a real and reals are closed under the operations addition, subtraction, multiplication, division and squareroot. The main features of the data type real are ffl The user-interface is similar to that of the built--in data type double. ffl All comparison operators f?; ; !; ; =g are exact. In order to determine the sign of a real number x the data type first computes a rational number q such that jxj q implies x = 0 and then computes an approximation of x of sufficient precision to decide the sign of x. The user may assist the data type by providing a separation bound q. ffl The data type also allows to evaluate real expressions with arbitrary precision. One may either set the mantissae length of the underlying floating point system and then evaluate the expression with that mantissa length or one may specify an error bound q. The data type then computes an approximation with absolute error at ..

Year: 1996
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