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Transcendental Functions

Computing transcendental functions is performed as follows. Suppose we wish to compute the value f(x), we find a sequence or series in terms of x which either which tends towards a limit f(x) with a known rate of convergence, or converges to but oscillates round the limit f(x). Once we have this we can generate a sequence of upper and lower bounds on this limit at each term of the original sequence. We know that the sequence converges, so we can use this fact to generate an infinite and strictly nested stream of intervals containing the limit of the sequence. Once we have this stream, we can then converted it into a signed binary representation of the desired result using the method described in section 5.1.

We now give some sequences satisfying these conditions for a number of trigonometric and logarithmic transcendental functions.


Martin Escardo