The routine may be called by the names s10abf or nagf_specfun_sinh.
3Description
s10abf calculates an approximate value for the hyperbolic sine of its argument,
.
For it uses the Chebyshev expansion
where .
For
where is a machine-dependent constant
, details of which are given in the Users' Note for your implementation.
For , the routine fails owing to the danger of setting overflow in calculating . The result returned for such calls is , i.e., it returns the result for the nearest valid argument.
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, .
Constraint: .
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 closest argument for which a valid call could be made.
An unexpected error has been triggered by this routine. Please
contact NAG.
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.
7Accuracy
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, approximately . The equality should hold if is greater than the machine precision ( is a result of 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 can be seen in the following graph:
Figure 1
It should be noted that for
where is the absolute error in the argument.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s10abf is not threaded in any implementation.
9Further Comments
None.
10Example
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.