Public Shared Function s10ab ( _ x As Double, _ <OutAttribute> ByRef ifail As Integer _ ) As Double
public: static double s10ab( double x, [OutAttribute] int% ifail )
- Type: System..::..DoubleOn entry: the argument of the function.
s10ab calculates an approximate value for the hyperbolic sine of its argument, .
For it uses the Chebyshev expansion
where is a machine-dependent constant, details of which are given in the Users' Note for your implementation.
For , the method fails owing to the danger of setting overflow in calculating . The result returned for such calls is , 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
Errors or warnings detected by the method:
If and are the relative errors in the argument and result, respectively, then in principle
That is the relative error in the argument, , is amplified by a factor, approximately . The equality should hold if is greater than the machine precision ( is a result of data errors etc.) but, if is simply a result of round-off in the machine representation of , then it is possible that an extra figure may be lost in internal calculation round-off.
It should be noted that for
where is the absolute error in the argument.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.