1: $x$ – double Input: On entry: the argument $x$ of the function.
2: $fail$ – NagError * Input/Output: The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_INTERNAL_ERROR: 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.
NE_NO_LICENCE: 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.
NE_REAL_ARG_GT: On entry, $x = ⟨ value ⟩$ .
Constraint: $| x | \leq ⟨ value ⟩$ .
$| x |$ is too large and the function returns the approximate value of $I_{1} (x)$ at the nearest valid argument.

7 Accuracy

Let

δ

and

ε

be the relative errors in the argument and result respectively.

δ

is somewhat larger than the machine precision (i.e., if

δ

is due to data errors etc.), then

ε

and

δ

are approximately related by:

ε ≃ | \frac{x I_{0} (x) - I_{1} (x)}{I_{1} (x)} | δ .

Figure 1 shows the behaviour of the error amplification factor

| \frac{x I_{0} (x) - I_{1} (x)}{I_{1} (x)} | .

Figure 1

However, if

δ

is of the same order as machine precision, then rounding errors could make

ε

slightly larger than the above relation predicts.

For small

x

ε ≃ δ

and there is no amplification of errors.

For large

x

ε ≃ x δ

and we have strong amplification of errors. However, the function must fail for quite moderate values of

x

because

I_{1} (x)

would overflow; hence in practice the loss of accuracy for large

x

is not excessive. Note that for large

x

, the errors will be dominated by those of the standard math library function exp.

s18afc is not threaded in any implementation.

None.

This example reads values of the argument

x

from a file, evaluates the function at each value of

x

and prints the results.

s18af: FL CL CPP AD