NAG CL Interface
s10abc (sinh)
1
Purpose
s10abc returns the value of the hyperbolic sine, .
2
Specification
| double |
s10abc (double x,
NagError *fail) |
|
The function may be called by the names: s10abc, nag_specfun_sinh or nag_sinh.
3
Description
s10abc 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 function 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:
– double
Input
-
On entry: the argument of the function.
-
2:
– NagError *
Input/Output
-
The NAG error argument (see
Section 7 in the Introduction to the NAG Library CL Interface).
6
Error Indicators and Warnings
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
- NE_INTERNAL_ERROR
-
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact
NAG for assistance.
See
Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
- NE_NO_LICENCE
-
Your licence key may have expired or may not have been installed correctly.
See
Section 8 in the Introduction to the NAG Library CL Interface for further information.
- NE_REAL_ARG_GT
-
On entry, .
Constraint: .
The function 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.
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
s10abc 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
