NAG Library Routine Document
S10ABF returns the value of the hyperbolic sine, , via the function name.
|REAL (KIND=nag_wp) S10ABF
S10ABF calculates an approximate value for the hyperbolic sine of its argument,
it uses the Chebyshev expansion
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.
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 setting overflow. The result is the value of
at the closest argument for which a valid call could be made. (See Section 3
and the Users' Note
for your implementation.)
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
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 (s10abfe.f90)
9.2 Program Data
Program Data (s10abfe.d)
9.3 Program Results
Program Results (s10abfe.r)