NAG Library Routine Document
S10ACF returns the value of the hyperbolic cosine, , via the function name.
|REAL (KIND=nag_wp) S10ACF
S10ACF calculates an approximate value for the hyperbolic cosine, .
, the routine fails owing to danger of setting overflow in calculating
. The result returned for such calls is
, i.e., it returns the result for the nearest valid argument. The value of machine-dependent constant
may be given in the Users' Note
for your implementation.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
- 1: X – REAL (KIND=nag_wp)Input
On entry: the argument of the function.
- 2: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction 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 parameter, 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
6 Error Indicators and Warnings
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
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 nearest valid argument.
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, at least
. The equality should hold if
is greater than the machine precision
is due to 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 is shown by the following graph:
It should be noted that near
where this amplification factor tends to zero the accuracy will be limited eventually by the machine precision
. Also for
is the absolute error in the argument
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
9.1 Program Text
Program Text (s10acfe.f90)
9.2 Program Data
Program Data (s10acfe.d)
9.3 Program Results
Program Results (s10acfe.r)