Back to the calculator. Go to the RetroFactorial page to see how your parents calculated the factorial.
Back to the Homepage of Factorial Algorithms. 1: string factorial(int n)
2: {
3: var ex = 0.0;
4: var x = (double)n;
5: x = x + x + 1;
6:
7: if (x > 1)
8: {
9: x = (Math.log(2.0 * Math.Pi) + Math.log(x / 2.0) * x - x
10: - (1.0 - 7.0 / (30.0 * x * x)) / (6.0 * x)) / 2.0;
11: x = x / Math.log(10);
12: ex = Math.floor(x);
13: x = Math.pow(10, x - ex);
14: }
15:
16: var res = x.toString();
17: return res.substring(0, 6) + " E " + ex.toString();
18: }
19:
20: void calc()
21: {
22: Console.writeLine(factorial(134217728));
23: }
Clearly, this method has it's limitations, but it is amazingly powerful. The charm of the formula lies in the small integer coefficients: 2,1,7,30,6,2. Therefore it is also well suited for the use with a pocket calculator. (The order of the formula is O(n-5).) Some obsolete browsers may use a float instead of a double and run into floating point trouble.
Our small calculator computes 134217728! ~ 8.3459 E 1032606161 using this formula. A better approximation is
8.34597925944327661772882039785919428429176258950852382 E 1032606161.
This approximation can for example be calculated as described in this section
'
A higher precision approximation'.
Back to the calculator.
Go to the RetroFactorial page to see how your parents calculated the factorial.
Back to the Homepage of Factorial Algorithms.