nag_cosh (s10acc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_cosh (s10acc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_cosh (s10acc) returns the value of the hyperbolic cosine, coshx .

2  Specification

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

3  Description

nag_cosh (s10acc) calculates an approximate value for the hyperbolic cosine, coshx .
For x E 1 , (where E 1  is a machine-dependent constant) coshx = 1 2 e x + e -x .
For x > E 1 , the function fails owing to danger of setting overflow in calculating e x . The result returned for such calls is coshE 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

On entry, x=value.
Constraint: xvalue.
The function has been called with an argument too large in absolute magnitude. There is a danger of overflow. The result returned is the value of coshx  at the nearest valid argument.

7  Accuracy

If δ  and ε  are the relative errors in the argument and result, respectively, then in principle
ε x tanhx δ .
That is, the relative error in the argument, x , is amplified by a factor at least x tanhx  in the result. The equality should hold if δ  is greater than the machine precision ( δ  is due to 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 near x=0  where this amplification factor tends to zero the accuracy will be limited eventually by the machine precision. Also for x 2  
ε x δ = Δ
where Δ  is the absolute error in the argument x .

8  Further Comments


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 (s10acce.c)

9.2  Program Data

Program Data (s10acce.d)

9.3  Program Results

Program Results (s10acce.r)

nag_cosh (s10acc) (PDF version)
s Chapter Contents
s Chapter Introduction
NAG C Library Manual

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