NAG Library Routine Document
s10aaf returns a value for the hyperbolic tangent, , via the function name.
|Real (Kind=nag_wp)||:: ||s10aaf|
|Integer, Intent (Inout)||:: ||ifail|
|Real (Kind=nag_wp), Intent (In)||:: ||x|C Header Interface
s10aaf_ (const double *x, Integer *ifail)|
s10aaf calculates an approximate value for the hyperbolic tangent of its argument, .
it is based on the Chebyshev expansion
(see the Users' Note
for your implementation for value of
to within the representation accuracy of the machine and so this approximation is used.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
- 1: – Real (Kind=nag_wp)Input
On entry: the argument of the function.
- 2: – IntegerInput/Output
must be set to
. If you are unfamiliar with this argument you should refer to Section 3.4
in How to Use the NAG Library and its Documentation for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this argument, the recommended value is
. When the value is used it is essential to test the value of ifail on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
Error Indicators and Warnings
are the relative errors in the argument and the result respectively, then in principle,
That is, a relative error in the argument,
, is amplified by a factor approximately
, in the result.
The equality should hold if is greater than the machine precision ( due to data errors etc.) but if is due simply to the round-off in the machine representation it is possible that an extra figure may be lost in internal calculation round-off.
The behaviour of the amplification factor is shown in the following graph:
It should be noted that this factor is always less than or equal to and away from the accuracy will eventually be limited entirely by the precision of machine representation.
Parallelism and Performance
s10aaf is not threaded in any implementation.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
Program Text (s10aafe.f90)
Program Data (s10aafe.d)
Program Results (s10aafe.r)