NAG Library Function Document
nag_tanh (s10aac) returns a value for the hyperbolic tangent, .
||nag_tanh (double x)
nag_tanh (s10aac) calculates an approximate value for the hyperbolic tangent of its argument, .
For the function is based on a Chebyshev expansion.
is a machine-dependent constant),
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
x – doubleInput
On entry: the argument of the function.
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.
It should be noted that this factor is always less than or equal to 1.0 and away from the accuracy will eventually be limited entirely by the machine precision.
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 (s10aace.c)
9.2 Program Data
Program Data (s10aace.d)
9.3 Program Results
Program Results (s10aace.r)