public static double s10ac(
	double x,
	out int ifail
)

Public Shared Function s10ac ( _
	x As Double, _
	<OutAttribute> ByRef ifail As Integer _
) As Double

public:
static double s10ac(
	double x, 
	[OutAttribute] int% ifail
)

static member s10ac : 
        x : float * 
        ifail : int byref -> float 

s10ac returns the value of the hyperbolic cosine, $\cosh x$.

s10ac calculates an approximate value for the hyperbolic cosine, $\cosh x$.

For $\left|x\right|\le E_1\text{, \hspace{1em}}\cosh x=\frac{1}{2}\left(e^x+e^{-x}\right)$.

For $\left|x\right|>E_1$, the method fails owing to danger of setting overflow in calculating $e^x$. The result returned for such calls is $\cosh E_1$, i.e., it returns the result for the nearest valid argument. The value of machine-dependent constant $E_1$ may be given in the Users' Note for your implementation.

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

Errors or warnings detected by the method:

If $\delta$ and $\epsilon$ are the relative errors in the argument and result, respectively, then in principle That is, the relative error in the argument, $x$, is amplified by a factor, at least $x\tanh x$. The equality should hold if $\delta$ is greater than the machine precision ($\delta$ is due to data errors etc.) but if $\delta$ 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:

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 $\left|x\right|\ge 2$  where $\Delta$ is the absolute error in the argument $x$.

None.

None.

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