用泰勒级数计算任何 x 的 e^x

Question

I know its pretty bad beginner code but I think it should work, why doesn't it?

It's probably my condidtion haufen != haufen_alt that causes some problems but maybe I'm doing something else wrong.

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

double fak(k){
    double i, f_haufen = 1;

    for (i=1; i <= k; i++){
        f_haufen = f_haufen*i;
    }
    return f_haufen;
}

double e_hoch (double x){
    double haufen, haufen_alt, k;

    haufen = 0;
    haufen_alt = 0;
    k = 0;
    do{
        haufen_alt = haufen;
        haufen += (pow(x,k))/(fak(k));
        k++;
    }while(haufen != haufen_alt);

    return haufen;
}

int main (void){
    double x_main;
    printf("x=");
    scanf("%lf", &x_main);

    printf("e^%.2f = %f",x_main, e_hoch(x_main));
}

Answer 1

haufen and haufen_alt will always be different by a nonzero factor of (pow(x,k))/(fak(k)) . The factor will get smaller and smaller approaching zero, but it won't actually reach zero since the numerator is nonzero.

The standard procedure is to decide on some epsilon threshold close to zero you want to stop at. When the next addend drops below epsilon, or when the difference between successive terms is less than epsilon, stop. That lets you tune how accurate you want the result to be. The smaller epsilon the more accurate it'll be but the longer it'll take.