The routine may be called by the names s01eaf or nagf_specfun_exp_complex.
s01eaf evaluates the exponential function , taking care to avoid machine overflow, and giving a warning if the result cannot be computed to more than half precision. The function is evaluated as , where and are the real and imaginary parts respectively of .
Since and are less than or equal to in magnitude, it is possible that may overflow although or does not. In this case the alternative formula is used for the real part of the result, and for the imaginary part. If either part of the result still overflows, a warning is returned through argument ifail.
If is too large, precision may be lost in the evaluation of and . Again, a warning is returned through ifail.
1: – Complex (Kind=nag_wp)Input
On entry: the argument of the function.
2: – IntegerInput/Output
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:
Argument z causes overflow in real part of result: .
Argument z causes overflow in imaginary part of result: .
Argument z causes overflow in both real and imaginary parts of result: .
The imaginary part of argument z is so large that the result is accurate to less than half precision: .
The imaginary part of argument z is so large that the result has no precision: .
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.
Accuracy is limited in general only by the accuracy of the standard functions in the computation of , and , where , . As gets larger, precision will probably be lost due to argument reduction in the evaluation of the sine and cosine functions, until the warning error occurs when gets larger than , where is the machine precision. Note that on some machines, the intrinsic functions SIN and COS will not operate on arguments larger than about , and so ifail can never return as .
In the comparatively rare event that the result is computed by the formulae and , a further small loss of accuracy may be expected due to rounding errors in the logarithmic function.
8Parallelism and Performance
s01eaf 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.