Public Shared Function s09ab ( _ x As Double, _ <OutAttribute> ByRef ifail As Integer _ ) As Double
public: static double s09ab( double x, [OutAttribute] int% ifail )
- Type: System..::..DoubleOn entry: the argument of the function.Constraint: .
s09ab calculates an approximate value for the inverse circular cosine, . It is based on the Chebyshev expansion
For is undefined and the method fails.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
Errors or warnings detected by the method:
- s09ab has been called with , for which arccos is undefined. A zero result is returned.
If and are the relative errors in the argument and the result, respectively, then in principle
The equality should hold if is greater than the machine precision ( is due to data errors etc.), but if is due simply to round-off in the machine it is possible that rounding etc. in internal calculations may lose one extra figure.
The behaviour of the amplification factor is shown in the graph below.
In the region of this factor tends to zero and the accuracy will be limited by the machine precision. For close to one, , the above analysis is not applicable owing to the fact that both the argument and the result are bounded , .
In the region of we have , that is the result will have approximately half as many correct significant figures as the argument.
In the region , we have that the absolute error in the result, , is given by , that is the result will have approximately half as many decimal places correct as there are correct figures in the argument.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.