nag_sinh (s10abc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_sinh (s10abc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_sinh (s10abc) returns the value of the hyperbolic sine, sinhx .

2  Specification

#include <nag.h>
#include <nags.h>
double  nag_sinh (double x, NagError *fail)

3  Description

nag_sinh (s10abc) calculates an approximate value for the hyperbolic sine of its argument, sinhx .
For x 1  the function is based on a Chebyshev expansion.
For 1 < x E 1 , (where E 1  is a machine-dependent constant), sinhx = 1 2 e x - e -x .
For x > E 1 , the function fails owing to the danger of setting overflow in calculating e x . The result returned for such calls is sinh signx E 1 , i.e., it returns the result for the nearest valid argument.

4  References

Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications

5  Arguments

1:     xdoubleInput
On entry: the argument x  of the function.
2:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_REAL_ARG_GT
On entry, x=value.
Constraint: xvalue.
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 ).

7  Accuracy

If δ  and ε  are the relative errors in the argument and result, respectively, then in principle
ε x cothx δ .
That is, the relative error in the argument, x , is amplified by a factor, approximately x cothx . The equality should hold if δ  is greater than the machine precision ( δ  is a result of data errors etc.), but if δ  is simply a result of round-off in the machine representation of x , then it is possible that an extra figure may be lost in internal calculation round-off.
It should be noted that for x 2  
ε x δ = Δ
where Δ  is the absolute error in the argument.

8  Further Comments

None.

9  Example

The following program reads values of the argument x  from a file, evaluates the function at each value of x  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)


nag_sinh (s10abc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012