PowerAda 130

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(130) The accuracy of certain elementary functions for parameters beyond the angle threshold.

See G.2.4(10).

The accuracy of the trig functions is determined by the C math libraries.

For detailed, official information on the accuracy of these functions please contact the supplier of these libraries (normally IBM for AIX). However, for an idea of the accuracy of these functions, our research shows that on AIX version 4.x parameter reduction is done with a 128 bit long double with about 106 bits of precision (twice that of a double). Given parameter X this gives a maximum absolute (not relative) error of the reduced X of about 2.0**(long_float'exponent(X)-104). For a few values of X very close to a multiple of Pi, this will result in a greater relative error than normal for values of a given magnitude. For values with exponent greater than about 105, the values of the these functions are not particularly related to the correct mathematical result at all. Despite the advanced accuracy of these functions, We do not recommend making use of them for large values because any rounding (or related) errors in such a large value will result in huge errors in the result of these functions.