nag_cosh (s10acc) calculates an approximate value for the hyperbolic cosine, .
For , the function fails owing to danger of setting overflow in calculating . The result returned for such calls is , i.e., it returns the result for the nearest valid argument. The value of machine-dependent constant may be given in the Users' Note for your implementation.
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 22.214.171.124 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 too large in absolute magnitude. There is a danger of overflow. The result returned is the value of at the nearest valid argument.
If and are the relative errors in the argument and result, respectively, then in principle
That is, the relative error in the argument, , is amplified by a factor, at least . The equality should hold if is greater than the machine precision ( is due to data errors etc.) but if is simply a result of round-off in the machine representation of then it is possible that an extra figure may be lost in internal calculation round-off.
The behaviour of the error amplification factor is shown by the following graph:
It should be noted that near where this amplification factor tends to zero the accuracy will be limited eventually by the machine precision. Also for
where is the absolute error in the argument .
8 Parallelism and Performance
nag_cosh (s10acc) 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.