nag_cos_integral (s13acc) calculates an approximate value for .
For it is based on the Chebyshev expansion
For where the value of is given in the Users' Note for your implementation,
where and ,
For , to within the accuracy possible (see Section 7).
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
On entry: the argument of the function.
– NagError *Input/Output
The NAG error argument (see Section 2.7 in How to Use the NAG Library and its Documentation).
6 Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 220.127.116.11 in How to Use the NAG Library and its Documentation for further information.
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
An unexpected error has been triggered by this function. Please contact NAG.
See Section 2.7.6 in How to Use the NAG Library and its Documentation for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.
On entry, .
The function has been called with an argument less than or equal to zero for which is not defined.
If and are the absolute and relative errors in the result and is the relative error in the argument then in principle these are related by
That is accuracy will be limited by machine precision near the origin and near the zeros of , but near the zeros of only absolute accuracy can be maintained.
The behaviour of this amplification is shown in Figure 1.
For large values of , therefore and since is limited by the finite precision of the machine it becomes impossible to return results which have any relative accuracy. That is, when we have that and hence is not significantly different from zero.
Hence is chosen such that for values of , in principle would have values less than the machine precision and so is essentially zero.
8 Parallelism and Performance
nag_cos_integral (s13acc) is not threaded in any implementation.
9 Further Comments
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.