The report is structured as follows:

In chapter 2 we discuss real arithmetic in general terms, examine some approaches to performing it on a computer, and introduce exact real arithmetic.

Chapter 3 defines the the representations used, chapter 4 develops the algorithms for the basic operations, and chapter 5 those for higher level transcendental functions. Proofs of correctness are included for some algorithms.

In chapter 6, the implementation of the algorithms is discussed, and in chapter 7 some experimentation and analysis of the work is given.

In the conclusion, chapter 8, we draw together the work, make some concluding remarks, and discuss potential extensions and directions for future work.