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: $| x | \leq E_{1}$ .
The function has been called with an argument too large in absolute magnitude. There is a danger of overflow. The result returned is the value of $\cosh x$ at the nearest valid argument.

7 Accuracy

δ

and

ε

are the relative errors in the argument and result, respectively, then in principle

ε ≃ x \tanh x \times δ .

That is, the relative error in the argument,

x

, is amplified by a factor, at least

x \tanh x

. The equality should hold if

δ

is greater than the machine precision (

δ

is due to data errors etc.) but if

δ

is simply a result of round-off in the machine representation of

x

then it is possible that an extra figure may be lost in internal calculation round-off.

The behaviour of the error amplification factor is shown by the following graph:

Figure 1

It should be noted that near

x = 0

where this amplification factor tends to zero the accuracy will be limited eventually by the machine precision. Also, for

| x | \geq 2

ε \sim x δ = Δ

where

Δ

is the absolute error in the argument

x

s10acc 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.

s10ac: FL CL CPP AD