- Type: System..::..DoubleOn entry: the argument of the function.
s10aa calculates an approximate value for the hyperbolic tangent of its argument, .
For it is based on the Chebyshev expansion
For (see the Users' Note for your implementation for value of )
For , 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
If and 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 and away from the accuracy will eventually be limited entirely by the precision of machine representation.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.