NAG Library Function Document
nag_arccosh (s11acc) returns the value of the inverse hyperbolic cosine, . The result is in the principal positive branch.
||nag_arccosh (double x,
nag_arccosh (s11acc) calculates an approximate value for the inverse hyperbolic cosine,
. It is based on the relation
This form is used directly for
, and the machine uses approximately
decimal place arithmetic.
is equal to
to within the accuracy of the machine and hence we can guard against premature overflow and, without loss of accuracy, calculate
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, x
must not be less than 1.0:
is not defined and the result returned is zero.
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 apply if
is greater than the machine precision
due to data error etc.), but if
is simply a result of round-off in the machine representation, it is possible that an extra figure may be lost in internal calculation and round-off.
It should be noted that for
the factor is always less than 1.0. For large
we have the absolute error
in the result, in principle, given by
This means that eventually accuracy is limited by machine precision
. More significantly for
close to 1,
, the above analysis becomes inapplicable due to the fact that both function and argument are bounded,
. In this region we have
That is, there will be approximately half as many decimal places correct in the result as there were correct figures 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 (s11acce.c)
9.2 Program Data
Program Data (s11acce.d)
9.3 Program Results
Program Results (s11acce.r)