POJ 2661 Factstone Benchmark

Description

Amtel has announced that it will release a 128-bit computer chip by 2010, a 256-bit computer by 2020, and so on, continuing its strategy of doubling the word-size every ten years. (Amtel released a 64-bit computer in 2000, a 32-bit computer in 1990, a 16-bit computer in 1980, an 8-bit computer in 1970, and a 4-bit computer, its first, in 1960.)
Amtel will use a new benchmark - the Factstone - to advertise the vastly improved capacity of its new chips. The Factstone rating is defined to be the largest integer n such that n! can be represented as an unsigned integer in a computer word.
Given a year 1960 <= y <= 2160, what will be the Factstone rating of Amtel's most recently released chip?
Input

There are several test cases. For each test case, there is one line of input containing y. A line containing 0 follows the last test case.
Output

For each test case, output a line giving the Factstone rating.
Sample Input

1960
1981
0
Sample Output

3
8
由于这是高精度没法用普通方式计算阶乘，否则会TLE
可以用斯特林(Stirling)公式求解
斯特林（Stirling）公式：

[html] 
#include <stdio.h> 
int main() 
{ 
    int year; 
    int endflag; 
    int n; 
    double sum; 
    while(scanf("%d", &year),year) 
    { 
        endflag = 1<<((year - 1960) / 10 + 2); 
        n = 2; 
        sum = 0; 
        while(sum <= endflag) 
        { 
            sum += log(n) / log(2); 
            ++n; 
        } 
        printf("%d/n", n - 2); 
    } 
    return 0; 
}