s10ac returns the value of the hyperbolic cosine, coshx.

Syntax

C#
public static double s10ac(
	double x,
	out int ifail
)
Visual Basic
Public Shared Function s10ac ( _
	x As Double, _
	<OutAttribute> ByRef ifail As Integer _
) As Double
Visual C++
public:
static double s10ac(
	double x, 
	[OutAttribute] int% ifail
)
F#
static member s10ac : 
        x : float * 
        ifail : int byref -> float 

Parameters

x
Type: System..::..Double
On entry: the argument x of the function.
ifail
Type: System..::..Int32%
On exit: ifail=0 unless the method detects an error or a warning has been flagged (see [Error Indicators and Warnings]).

Return Value

s10ac returns the value of the hyperbolic cosine, coshx.

Description

s10ac calculates an approximate value for the hyperbolic cosine, coshx.
For xE1,  coshx=12ex+e-x.
For x>E1, the method fails owing to danger of setting overflow in calculating ex. The result returned for such calls is coshE1, i.e., it returns the result for the nearest valid argument. The value of machine-dependent constant E1 may be given in the Users' Note for your implementation.

References

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

Error Indicators and Warnings

Errors or warnings detected by the method:
ifail=1
The method has been called with an argument too large in absolute magnitude. There is a danger of overflow. The result returned is the value of coshx at the nearest valid argument.
ifail=-9000
An error occured, see message report.

Accuracy

If δ and ε are the relative errors in the argument and result, respectively, then in principle
εxtanhx×δ.
That is, the relative error in the argument, x, is amplified by a factor, at least xtanhx. 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
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 x2 
εxδ=Δ
where Δ is the absolute error in the argument x.

Parallelism and Performance

None.

Further Comments

None.

Example

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

Example program (C#): s10ace.cs

Example program data: s10ace.d

Example program results: s10ace.r

See Also