How can I code exp(x) in c?

Question

There is a serie for the exp function whitch looks like this: exp(x) = (x^0)/0! + (x^1)/1! + (x^2)/2! + (x^3)/3! + ···. And I'm trying to compute it for different values of x, checking my results with a calculator and I found that for big values, 20 for example, my results stop increasing and get stuck in a value that is almost the real one. I get 485165184.00 and the real value is 485165195.4.

I must do this code in a for cycle or a recursive function, since it is a homework assignment.

My code looks as following

#include <stdio.h>
#define N 13
#define xi 3

double fun7(int n, int m){
    int i;
    double res=1, aux=0;
    for(i=1, aux=1; i<(n+1); i++){
    res += aux;
    aux *= m;
    aux /= i;
    }
    return res-1;
}



int main() {
    int a, b, pot, x[xi];
    float R[N][xi];

    x[0] = 5;
    x[1] = 10;
    x[2] = 20;

    for(b=0; b<xi; b++){
        for (a=0, pot=1; a<N; a++){
            R[a][b] = fun7(pot, x[b]);
            pot *= 2;
        }
    }

    for(b=0; b<xi; b++){
        for (a=0, pot=1; a<N; a++){
            printf("%d\t%f\n", pot, R[a][b]);
            pot *= 2;
        }
        printf("\n");
    }

    return 0;
}

Answer 1

The float data type can normally represent numbers with a tad more than 7 decimal digits of precision.

485165184 has 9 decimal digits. The last two digits are just meaningless noise as far as float goes. You really should be showing 4.851652e8, which is the correct value for exp(20) with the given level of precision.

If you want to increase precision, try using double or long double data types.