The routine may be called by the names s10acf or nagf_specfun_cosh.
s10acf calculates an approximate value for the hyperbolic cosine, .
For , the routine 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.
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, .
The routine 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.
An unexpected error has been triggered by this routine. Please
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
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 .
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s10acf is not threaded in any implementation.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.