s10ab returns the value of the hyperbolic sine, sinhx.


public static double s10ab(
	double x,
	out int ifail
Visual Basic
Public Shared Function s10ab ( _
	x As Double, _
	<OutAttribute> ByRef ifail As Integer _
) As Double
Visual C++
static double s10ab(
	double x, 
	[OutAttribute] int% ifail
static member s10ab : 
        x : float * 
        ifail : int byref -> float 


Type: System..::..Double
On entry: the argument x of the function.
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

s10ab returns the value of the hyperbolic sine, sinhx.


s10ab calculates an approximate value for the hyperbolic sine of its argument, sinhx.
For x1 it uses the Chebyshev expansion
where t=2x2-1.
For 1<xE1,  sinhx=12ex-e-x
where E1 is a machine-dependent constant, details of which are given in the Users' Note for your implementation.
For x>E1, the method fails owing to the danger of setting overflow in calculating ex. The result returned for such calls is sinhsignxE1, i.e., it returns the result for the nearest valid argument.


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:
The method has been called with an argument too large in absolute magnitude. There is a danger of setting overflow. The result is the value of sinhx at the closest argument for which a valid call could be made. (See [Description] and the Users' Note for your implementation.)
An error occured, see message report.


If δ and ε 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, approximately xcothx. The equality should hold if δ is greater than the machine precision (δ is a result of 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 can be seen in the following graph:
Figure 1
Figure 1
It should be noted that for x2 
where Δ is the absolute error in the argument.

Parallelism and Performance


Further Comments



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#): s10abe.cs

Example program data: s10abe.d

Example program results: s10abe.r

See Also