NAG Library Function Document
nag_sinh (s10abc) returns the value of the hyperbolic sine, .
||nag_sinh (double x,
nag_sinh (s10abc) calculates an approximate value for the hyperbolic sine of its argument, .
For the function is based on a Chebyshev expansion.
For , (where is a machine-dependent constant), .
For , the function fails owing to the 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
The function has been called with an argument too large in absolute magnitude. There is a danger of setting overflow. The result is the value of sinh at the closest argument for which a valid call could be made. (See Section 3
and the Users' Note for your implementation ).
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, approximately
. The equality should hold if
is greater than the machine precision
is a result of 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 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 (s10abce.c)
9.2 Program Data
Program Data (s10abce.d)
9.3 Program Results
Program Results (s10abce.r)