Please Help with e^x estimating program

[intro2Cpp]

Hello,

I have been trying to figure out what I'm doing wrong on my program for two days. My professor keeps "forgetting " about me. It is due tomorrow. We are supposed to use the "summing estimator" to calculate an estimated value for exp(x) using the formula 1+ x^n/n! for a user entered value for x, and values for n from 1 to 100. I know my problem is in the logic of how to implement the formula in C++ because it compiles but gives the wrong values. I can't figure it out. Please help. Here is my program so far:

//
//
// This program will take an entered value 'x'
// and run an estimated calculation for e^x and
// also a calculation based on existing c++ exponent
// functions.
//
#include <iostream>
#include <cmath>
#include <iomanip>

using namespace std;

double x; // Value entered by the user
double factorial(doubl e n);
double sum (double factors);

int main()
{

double estimate;

cout << setiosflags(ios ::fixed) << setprecision(5) ;

cout << "Enter a value for 'x' =>";
cin >> x;

estimate = 1 + sum(x);

cout << "The estimated value for pi is " << estimate << ".\n";

return 0;
}

// Function calculates n!

double factorial (double n)
{
double ans;
if (n<=1)
ans = 1;
else
ans = n * factorial(n-1);
return ans;
}

double sum (double factors)
{
double sum;
for (double n=1; n<=100; n++)
sum = pow(x,n)/factorial(x);

return sum;
}

[D_C]

double sum (double factors)
{
        double sum;
        for (double n=1; n<=100; n++)
        [b]sum = pow(x,n)/factorial(x);[/b]

return sum;
}

should be

sum += pow(x,n) / factorial(x);

Also, the first term of the series is 1, so you could start the loop at 0 instead of assigning

estimate = 1 + sum(x);

[intro2Cpp]

double sum (double factors)
{
        double sum;
        for (double n=1; n<=100; n++)
        [b]sum = pow(x,n)/factorial(x);[/b]

return sum;
}

should be

sum += pow(x,n) / factorial(x);

Also, the first term of the series is 1, so you could start the loop at 0 instead of assigning

estimate = 1 + sum(x);

THANK YOU SO VERY MUCH! I will enter that in and give it a whirl!

[intro2Cpp]

THANK YOU SO VERY MUCH! I will enter that in and give it a whirl!

Okay, I did that, but now all it will return no matter what I enter as the 'x' value is 1.000. That would normally tell me there is an integer division, but I intentionally used 'double' type for everything. Please help???

[D_C]

The formula is summation (x^n)/n! and you are calculating summation (x^n)/x!. Change your parameter for factorial from x to n. You could also do an iterative version, it would be much faster.

#include <iostream>
#include <iomanip>

using namespace std;


int main()
{
    cout << setiosflags(ios::fixed) << setprecision(5);

    double x;
    cout << "Enter a value for 'x' =>";
    cin >> x;

    double estimate = 0;
    double exp = 1;
    double fact = 1;
    double r;
    int n = 1;

    do
    {
        r = exp / fact;
        estimate += r;

        exp *= x; // x^n
        fact *= n++; // n!
    }   while(r > 10e-6);

    cout << "The estimated value for pi is " << estimate << ".\n";

    system("PAUSE");
    return EXIT_SUCCESS;
}

[Banfa]

You could also do an iterative version, it would be much faster.

Are you sure about that? can you provide references.

I only ask becasue to call a function requires a branch and the creation of a stack frame, where as a loop requires a branch and possibly the additional increment of a variable so it would seem to me that looping would be faster.

[tyreld]

Are you sure about that? can you provide references.

I only ask becasue to call a function requires a branch and the creation of a stack frame, where as a loop requires a branch and possibly the additional increment of a variable so it would seem to me that looping would be faster.

I suspect you have misread iterative as recursive. The factorial function is currently implemented recursively. Changing it to a loop (ie. iterative implementation) would make it faster. Leaving you both in agreement. ;)