is too large, the result underflows. contains zero. The threshold value is the same as for NE_REAL_ARG_GT in s19acc
, as defined in the Users' Note for your implementation.
, the function is undefined. contains .
5: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, .
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.
See Section 7.5 in the Introduction to the NAG Library CL 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 CL Interface for further information.
On entry, at least one value of x was invalid.
Check ivalid for more information.
Let be the absolute error in the result, be the relative error in the result and be the relative error in the argument. If is somewhat larger than the machine precision, then we have:
For very small , the relative error amplification factor is approximately given by , which implies a strong attenuation of relative error. However, in general cannot be less than the machine precision.
For small , errors are damped by the function and hence are limited by the machine precision.
For medium and large , the error behaviour, like the function itself, is oscillatory, and hence only the absolute accuracy for the function can be maintained. For this range of , the amplitude of the absolute error decays like which implies a strong attenuation of error. Eventually, , which asymptotically behaves like , becomes so small that it cannot be calculated without causing underflow, and the function returns zero. Note that for large the errors are dominated by those of the standard function exp.
8Parallelism and Performance
s19aqc is not threaded in any implementation.
Underflow may occur for a few values of close to the zeros of , below the limit which causes a failure with NW_IVALID.
This example reads values of x from a file, evaluates the function at each value of and prints the results.