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: . x is too large and positive. The function returns zero.
On entry, .
Constraint: . x is too large and negative. The function returns zero.
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.
For negative arguments the function is oscillatory and hence absolute error is the appropriate measure. In the positive region the function is essentially exponential-like and here relative error is appropriate. The absolute error, , and the relative error, , are related in principle to the relative error in the argument, , by
In practice, approximate equality is the best that can be expected. When , or is of the order of the machine precision, the errors in the result will be somewhat larger.
For small , errors are strongly damped by the function and hence will be bounded by the machine precision.
For moderate negative , the error behaviour is oscillatory but the amplitude of the error grows like
However, the phase error will be growing roughly like and hence all accuracy will be lost for large negative arguments due to the impossibility of calculating sin and cos to any accuracy if .
For large positive arguments, the relative error amplification is considerable:
This means a loss of roughly two decimal places accuracy for arguments in the region of . However, very large arguments are not possible due to the danger of setting underflow and so the errors are limited in practice.
8Parallelism and Performance
Background information to multithreading can be found in the Multithreading documentation.
s17agf 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.