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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 The user{interface is similar to that of the built{in data type double. All comparison operators f>;; <;;=g are exact. In order to determine the sign of a real number x the data type rst computes a rational number q such that jxj q implies x = 0 and then computes an approximation of x of sucient precision to decide the sign of x. The user may assist the data type by providing a separation bound q. The data type also allows to evaluate real expressions with arbitrary precision. One may either set the mantissae length of the underlying oating point sys-tem 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 most q