# Just a crazy fool who needs to know...

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This might seem like a weird question, but I just *have* to know. I wrote a short and sweet program to calculate factorials:
#include "stdafx.h"
#include <iostream>
using namespace std;

unsigned int Factorial( unsigned int in )
{
if( 1 == in )
{
return 1;
}

return in + ( Factorial( in - 1 ) );
}

int _tmain(int argc, _TCHAR* argv[])
{
unsigned int theX = 4, theFact;
while( theX >= 0 )
{
cout << "Enter number:  ";
cin >> theX;
theFact = Factorial( theX );
cout << "\n" << theX << "! is:  " <<  theFact << endl;
}

return 0;
}

When I run it the program can only handle values of up to 4795 as an imput value (4795! is 11498110 by the way). If I enter any higher number it shuts down. I've tried using different data types, but the same thing happens. My question is this: Why does this limitation exist? I know this is an odd question, but like I said, I *need* to know. [grin]

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Well, one, 4795! is a lot bigger than 11498110.

Two, the factorial funciton is the culmutive multplication of successive integers, not the addition. ie.
in + ( Factorial( in - 1 ) )

should be
in * ( Factorial( in - 1 ) )

Three, I'm guessing you're getting a stack overflow, which is what happens when you recurse too deeply.

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Factorial's are multiplications? Oops... [oh]

Well I think you've answered my question anyhow. A stack overflow would explain it all away! Thanks [grin]

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im pretty sure that value (4795!) couldn't be stored in an int either

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By my calculations, the actual value of 4795! is approximately 1015567. It is, in other words, rather large.

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Quote:
 Original post by SneftelBy my calculations, the actual value of 4795! is approximately 1015567. It is, in other words, rather large.

Yup, rather.

The largest most 10-digit-calculators can display is 69!, which is 1.71122452 × 10^98, or...

171122452000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

:)

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If you need to write the program so it can handle larger values, there are some math APIs out there that have perfect-precision data types that you could use. Of course, they would also almost certainly have a factorial function, which would probably be heavily optimized. If this is your own personal project, then just do what you need to =)

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There are much better ways of calculating factorials than recursion or even iteration through all the numbers. The factorial example is just used by programming teachers because it is a good way of learning recursive algorithms. :)

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Yeah, I know there are probably a lot of much better optimisations out there. I was just messing around really and I saw this weird limit which seemed to have nothing to do with the size of an int, and it bugged me that I didn't know why. Of course a useful side-effect of this curiosity was learning that I knew *nothing* about factorials. ;)

By the way I rewrote it so it actually *does* do factorials. It's slightly worse than a calculator! Anything above 65! it pumps out a zero. That's using unsigned __int64 as the data type.

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Quote:
 Original post by SneftelBy my calculations, the actual value of 4795! is approximately 1015567. It is, in other words, rather large.

I can't believe it only took you half an hour to work that out! I'm only up to 1768! so far!

:)

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