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