如何修复我的e ^ x近似C程序？

Question

I have written a C program that should compute and print the approximation of e^x for all values up to n. I am using this equation to implement my program.

f(x, n) = e^x = the sum of i=0 up to n= x^i/x! = x^0/0! + x^1/1! + x^2/2! +....+ x^n/n!

This is my code:

#include <stdio.h>
#include <math.h>
#include <stdlib.h>

double factorial(int n){
        double fac =1;
        int i;
        for(i =1; i <= n; i++){ 
                fac *=n;
        }
        return fac;
}
double exponent(double x, int n){
        double sum, i;
        for(i = 0; i <=n; i++){
                sum +=  (pow(x, i)/ factorial(i));
        } 
        return sum;
}

int main(int argc, char *argv[]){
        int n = atoi(argv[1]);
        double x = atof(argv[2]);
        printf("\ti\tApproximantion\n");
        printf("-------------------------------------\n");
        int i;
        for(i =0; i <=n; i++){
               printf("\t%d\t%f\n", i, exponent(x,i));
        }
        printf("Exact Value =\t%12f\n", exp(x));
        return 0;
}//main

I am using iteration instead of recursion. My current output using ./aprroximation 10 2.2 is:

        i       Approximation
-------------------------------------
        0       1.000000
        1       3.200000
        2       4.410000
        3       4.804370
        4       7.895877
        5       8.912368
        6       9.914798
        7       10.915101
        8       11.915134
        9       12.915137
        10      13.915137
Exact Value =       9.025013

the output should be: (ignore the space/tabbing)

   i Approximation
--------------------------------
   0   1.0000000000
   1   3.2000000000
   2   5.6200000000
   3   7.3946666667
   4   8.3707333333
   5   8.8002026667
   6   8.9576747556
   7   9.0071659835
   8   9.0207760712
   9   9.0241029815
   10   9.0248349018
Exact Value = 9.0250134994

I can't seem to find the problem in my code. I have looked at some pseudo-code for factorial and power functions and nothing stands out. My results continue to be wrong. Any thoughts?

Answer 1

There are two problems:

1. In the exponent function you don't initialize sum
2. Your factorial function is wrong.

If you had tested the factorial function separately you would have found out easily by yourself at least that problem.

Answer 2

I see, you didn't initialize the variable sum inside the exponent() function. Initialize it to zero, otherwise the exponent() function looks ok.

double exponent(double x, int n){
    double sum = 0, i;
    for(i = 0; i <=n; i++){
        sum += pow(x, i)/ factorial(i);
    } 
    return sum;
}

---

Update

I spot another problem in the factorial() function. Just think, whether the statement inside the for loop is correct!

for(i=1; i<=n; i++){ 
    fac *= n;
}

What you are computing here is not n! , it is n^n . You should do the following.

for(i=1; i<=n; i++){ 
    fac *= i;
}