1: $x$ – double Input: On entry: the argument $x$ of the function.

Constraint: $x > 0.0$ .
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_LE: On entry, $x = ⟨ value ⟩$ .
Constraint: $x > 0.0$ .
The function has been called with an argument less than or equal to zero for which $Ci (x)$ is not defined.

7 Accuracy

E

and

ε

are the absolute and relative errors in the result and

δ

is the relative error in the argument then in principle these are related by

| E | ≃ | δ \cos x | and ​ | ε | ≃ | \frac{δ \cos x}{Ci (x)} | .

That is accuracy will be limited by machine precision near the origin and near the zeros of

\cos x

, but near the zeros of

Ci (x)

only absolute accuracy can be maintained.

The behaviour of this amplification is shown in Figure 1.

Figure 1

For large values of

x

Ci (x) \sim \frac{\sin x}{x}

, therefore,

ε \sim δ x \cot x

and since

δ

is limited by the finite precision of the machine it becomes impossible to return results which have any relative accuracy. That is, when

x \geq 1 / δ

we have that

| Ci (x) | \leq 1 / x \sim E

and hence is not significantly different from zero.

Hence

x_{hi}

is chosen such that for values of

x \geq x_{hi}

Ci (x)

in principle would have values less than the machine precision and so is essentially zero.

Background information to multithreading can be found in the Multithreading documentation.

s13acc 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.

s13ac: FL CL CPP AD PY MB