public static double s10aa(
	double x
)

Public Shared Function s10aa ( _
	x As Double _
) As Double

public:
static double s10aa(
	double x
)

static member s10aa : 
        x : float -> float 

s10aa returns a value for the hyperbolic tangent, $\tanh x$.

s10aa calculates an approximate value for the hyperbolic tangent of its argument, $\tanh x$.

For $\left|x\right|\le 1$ it is based on the Chebyshev expansion where $-1\le x\le 1\text{, \hspace{1em}}-1\le t\le 1\text{, \hspace{1em} and \hspace{1em}}t=2x^2-1$.

For $1<\left|x\right|<E_1$ (see the Users' Note for your implementation for value of $E_1$) For $\left|x\right|\ge E_1$, $\tanh x=\mathrm{sign} x$ to within the representation accuracy of the machine and so this approximation is used.

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

None.

If $\delta$ and $\epsilon$ are the relative errors in the argument and the result respectively, then in principle, That is, a relative error in the argument, $x$, is amplified by a factor approximately $\frac{2x}{\sinh 2x}$, in the result.

The equality should hold if $\delta$ is greater than the machine precision ($\delta$ due to data errors etc.) but if $\delta$ is due simply to the round-off in the machine representation it is possible that an extra figure may be lost in internal calculation round-off.

The behaviour of the amplification factor is shown in the following graph:

It should be noted that this factor is always less than or equal to $1.0$ and away from $x=0$ the accuracy will eventually be limited entirely by the precision of machine representation.

None.

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This example reads values of the argument $x$ from a file, evaluates the function at each value of $x$ and prints the results.