Evaluating elementary functions with guaranteed precision (Q5951256)

The numerical algorithms to evaluate trigonometrical, exponential and logarithmic functions are adapted to the double precision calculation in IEEE-754 standard. The operation time for above evaluations makes about 50\% of that for the standard methods, but the number of precalculated constants is considerably increased (up to about 10000 constants for each function). Each algorithm starts from the evaluation in the so called ``good'' interval by means of the Taylor expansion with Peano remainder. For instance the \(sin\) is first evaluated at the rational points \(\frac{n}{512}\in[0,\frac{\pi}{2}]\) and next the calculation is extended outside the ``good'' interval with estimation of error.