Thread: Big Floating Number, 100! Not right.

Hello there Forum!

So, I'm new at programming C so my understanding about it is really rather limited. But I managed to put together a simple program to output factorials up to 100. It works fine until n!=18 but afterwards, when the numbers really are atronomical, only the few first digits of the output factorial are correct. The rest is replaced by 0's.

So, to 100! the output should be a 157 digit number with zeros for the last 24 digits, however, instead, the program returns a 157 digit number with zeros for the last 130 digits. Only the first 27 digits are correct.

What am I doing wrong?

Code:

#include<stdio.h>
int main(void){
    int i;
    double n;
    n=1;
    for(i=1;i<=100;i++){
                        n*=i;
                        printf("%.0f\n",n);}                      
    system("pause");
    return(0);
}

And also, I also made a program to output Euler's number, but I can only get it right up to 18 decimal places. How can I print about e to 100 decimal places?

Code:

#include<stdio.h>
int main(void){
    int i;
    float n,e,t;
    n=1;
    e=1;
    for(i=1;i<=30;i++){
                        n*=i;
                        t=n;
                        e+=1/t;
                        printf("%.20f\n",e);}                      
    system("pause");
    return(0);
}

That seems about right.

For each decimal digit, you need just over 3 bits in your number to represent it accurately. For a float, this equates to about 6 decimal digits. For doubles, you get about 15 decimal digits. Beyond that, anything you see is pure noise.

Floating point numbers are a fixed size (say 4 or 8 bytes). To achieve this, they sacrifice some precision (lots of accurate digits) for range (like being able to hold the most significant digits of 100!).

Now, if you want to store ALL the digits with total accuracy, you're going to have to use a bignum library like The GNU MP Bignum Library

Yes, something like that.

Though it is not the only one, and it is always possible to write your own (if that is the purpose of the exercise).

"There is no practical limit to the precision except the ones implied by the available memory in the machine GMP runs on. GMP has a rich set of functions, and the functions have a regular interface. "
1M digits would need about 350K of memory for each number.
It might take a while, but it can certainly store them on a decent modern machine.