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, .
it is based on the Chebyshev expansion
(see the Users' Note
for your implementation for value of
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.
The behaviour of the amplification factor is shown in the following graph:
It should be noted that this factor is always less than or equal to and away from the accuracy will eventually be limited entirely by the precision of machine representation.
8 Parallelism and Performance
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
10.1 Program Text
Program Text (s10aace.c)
10.2 Program Data
Program Data (s10aace.d)
10.3 Program Results
Program Results (s10aace.r)