NAG FL Interface
s09aaf (arcsin)
1
Purpose
s09aaf returns the value of the inverse circular sine, , via the function name. The value is in the principal range .
2
Specification
Fortran Interface
| Real (Kind=nag_wp) |
:: |
s09aaf |
| Integer, Intent (Inout) |
:: |
ifail |
| Real (Kind=nag_wp), Intent (In) |
:: |
x |
|
C Header Interface
|
#include <nag.h>
| double |
s09aaf_ (const double *x, Integer *ifail) |
|
C++ Header Interface
|
#include <nag.h> extern "C" {
| double |
s09aaf_ (const double &x, Integer &ifail) |
}
|
The routine may be called by the names s09aaf or nagf_specfun_arcsin.
3
Description
s09aaf calculates an approximate value for the inverse circular sine,
. It is based on the Chebyshev expansion
where
and
.
For .
For .
For is undefined and the routine fails.
4
References
5
Arguments
-
1:
– Real (Kind=nag_wp)
Input
-
On entry: the argument of the function.
Constraint:
.
-
2:
– Integer
Input/Output
-
On entry:
ifail must be set to
,
or
to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value
or
is recommended. If message printing is undesirable, then the value
is recommended. Otherwise, the value
is recommended.
When the value or is used it is essential to test the value of ifail on exit.
On exit:
unless the routine detects an error or a warning has been flagged (see
Section 6).
6
Error Indicators and Warnings
If on entry
or
, explanatory error messages are output on the current error message unit (as defined by
x04aaf).
Errors or warnings detected by the routine:
-
On entry, .
Constraint: .
An unexpected error has been triggered by this routine. Please
contact
NAG.
See
Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See
Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See
Section 9 in the Introduction to the NAG Library FL Interface for further information.
7
Accuracy
If
and
are the relative errors in the argument and result, respectively, then in principle
That is, a relative error in the argument
is amplified by at least a factor
in the result.
The equality should hold if is greater than the machine precision ( is a result of data errors etc.) but if is produced simply by round-off error in the machine it is possible that rounding in internal calculations may lose an extra figure in the result.
This factor stays close to one except near where its behaviour is shown in the following graph.
For close to unity, , the above analysis is no longer applicable owing to the fact that both argument and result are subject to finite bounds, ( and ). In this region ; that is the result will have approximately half as many correct significant figures as the argument.
For the result will be correct to full machine precision.
8
Parallelism and Performance
s09aaf is not threaded in any implementation.
None.
10
Example
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
10.1
Program Text
10.2
Program Data
10.3
Program Results
