#include <iostream>
#include <math.h>
using namespace std;
int main()
{
    int i=1;
    float x, result, sum, temp=0, sumhigh, temphigh;
    cout<<"Please give a value of x for the function f(x) = sinh(x)\nx = "; // Tom Ellaby. Tuesday Afternoon Session.
    cin>>x;
    if (fabs(x)>5)                                                          // This checks whether to use the taylor expansion for small values of x
    {                                                                       // or large values. Since sinh is an odd function, the absolute value is
        if (x<0)                                                            // checked.
        {
            sum=-0.5*exp(fabs(x));                                          // This part simply inverts the sign if a negative value was entered,
        }                                                                   // since the large approximation does not deal with this as the small
        else                                                                // approximation does.
        {                                                                   //
            sum=0.5*exp(fabs(x));                                           //
        }                                                                   //
    }
    else                                                                    // if  the entered value was small, the expansion is used as an
    {                                                                       // instead.
        result=x;                                                           //
        sum=result;                                                         //
        do                                                                  //
        {                                                                   //
            result=result*((x*x)/((i+1)*(i+2)));                            // This line calculates each term in the sequence from the previous, and
            temp=sum;                                                       // assigns it to the variable 'result'. These values are then summed,
            sum+=result;                                                    // giving the value of sinh x, which becomes more accurate with each
            i=i+2;                                                          // iteration.
            temphigh=10000*temp;                                            // This sets the current value for sinh(x) and the value from the previous
            sumhigh=10000*sum;                                              // iteration to 10000 times their actual value. This is done so that it
            //cout<<result<<", "<<i<<", "<<sum<<endl;                       // can be seen when the next value calculated is the same as the last to
        }                                                                   // 4 decimal places. The loop is finished when this happens, as the
        while ((int)temphigh!=(int)sumhigh);                                // desired accuracy has been reached.
    }
    cout<<"f(x) = "<<sum;                                                   // This line simply prints the calculated value of sinh(x)

    return 0;
}