NAG Library Function Document
nag_cosh (s10acc) returns the value of the hyperbolic cosine, .
||nag_cosh (double x,
nag_cosh (s10acc) calculates an approximate value for the hyperbolic cosine, .
For , (where is a machine-dependent constant) .
For , the function 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.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
x – doubleInput
On entry: the argument of the function.
fail – NagError *Input/Output
The NAG error argument (see Section 3.6
in the Essential Introduction).
6 Error Indicators and Warnings
On entry, .
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 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
in the result. 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.
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
The following program 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 (s10acce.c)
9.2 Program Data
Program Data (s10acce.d)
9.3 Program Results
Program Results (s10acce.r)