Exact Real Algorithms for Transcendent Functions

In computations with numbers in the floating point format, the numbers are rounded up after each arithmetical operation. This usually works quite well, but sometimes, the successive roundings yield wrong results. Exact arithmetical algorithms, on the other hand, work with real numbers specified to an arbitrary precision. The precision of the result depends on the precision of the operands. To compute a transcendent function to arbitrary precision we use its expression by continued fractions obtained from Padé approximants. On input, the algorithm chooses between reading next letter of the input and reading next term of the continued fraction. We show that this choice is well balanced and the algorithm is fast and effective. The exact real computation is therefore a feasible alternative to the floating point computation, at least in the tasks, in which the precision of the results matters.