Thread: Help Understanding Logic of these two programs to print the value of e and e^x

I get the factorial part but what is why have we used n . What is accuracy, degree, and what is meant by while( n <= accuracy )
Write a program to compute the value of e
e=1+1/1!+1/2!+1/3!+⋯

Code:

#include<stdio.h>
int main()
    
{
  int n = 0;                 /* loop counter for accuracy */
  int fact = 1;              /* current n factorial */
  int accuracy = 10;         /*degree of accuracy */
  double e = 0;              /* current estimated value of e */
                             /* loop until degree of accuracy */
      while (n <= accuracy)
    {
    if (n == 0)
       {
      fact *= 1;
      }
   
    else {
      fact *= n;
    }
    e += 1.0 / fact;
    ++n;
    }
  printf("e is %f\n", e);   /* display estimated value */
  return 0;
}

> What is accuracy, degree, and what is meant by while( n <= accuracy )
Why don't you edit the program to say

int accuracy = 0;
compile and run

Then
int accuracy = 1;
compile and run


Or better yet,
for ( accuracy = 0 ; accuracy <= 10 ; accuracy++ )

It's called software for a reason.
You can change it however you want. Make a prediction, make a change, observe the result.

What does line 14 actually achieve?

Edit: I should say that I actually like that you compute the factorial as a "running total" (but my question still stands)

Originally Posted by Izzy98

0! = 1

Yes, of course... but it's already 1 (because you initialised it to 1)

Edit: In my test program I changed it to:

Code:

if (n > 1) {
    fact *= n;
}

I wonder if there is a way to improve accuracy/precision by rearranging the equation?

On my computer:

Code:

for n == 18 e is identical to the previous value of e
for n == 19 e is identical to the previous value of e
for n == 20 e is identical to the previous value of e
for n == 21 e is identical to the previous value of e

This is due to hitting the limit of double's precision.

For what it's worth I think the name of the variable "accuracy" is misleading. It's not really a measure of accuracy, it's the number of terms to sum in an infinite sum (for this method of estimating e which I think Newton first described). Because the particular continuing fraction is asymptotic the greater the number of terms in the sum the closer the calculated value of e is to the real value of e. Edit: this isn't really a measure of the "accuracy" though.

Edit 2: "degree" is sometimes used in mathematics and often synonymous with "order" which is simply the number of times something happens, or the size of something. (In this case the number of iterations). I don't think I'd use the word degree or order for this particular problem though.