NAG FL Interface
s10abf (sinh)
1
Purpose
s10abf returns the value of the hyperbolic sine, , via the function name.
2
Specification
Fortran Interface
| Real (Kind=nag_wp) |
:: |
s10abf |
| Integer, Intent (Inout) |
:: |
ifail |
| Real (Kind=nag_wp), Intent (In) |
:: |
x |
|
C Header Interface
|
#include <nag.h>
| double |
s10abf_ (const double *x, Integer *ifail) |
|
C++ Header Interface
|
#include <nag.h> extern "C" {
| double |
s10abf_ (const double &x, Integer &ifail) |
}
|
The routine may be called by the names s10abf or nagf_specfun_sinh.
3
Description
s10abf calculates an approximate value for the hyperbolic sine of its argument,
.
For
it uses the Chebyshev expansion
where
.
For
where
is a machine-dependent constant, details of which are given in the
Users' Note for your implementation.
For , the routine 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.
4
References
5
Arguments
-
1:
– Real (Kind=nag_wp)
Input
-
On entry: the argument of the function.
-
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: .
The routine has been called with an argument too large in absolute magnitude. There is a danger of overflow. The result returned is the value of at the closest argument for which a valid call could be made.
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 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.
The behaviour of the error amplification factor can be seen in the following graph:
It should be noted that for
where
is the absolute error in the argument.
8
Parallelism and Performance
s10abf 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
