程序代码：

/*
手工开根号：<span style="color: #008000; text-decoration: underline;">http://wenku.baidu.com/view/e048aa651eb91a37f1115c16.html[/color]
*/

#include <stdio.h>

#define LEN_RESULT     100
#define LEN            102

int comp(int *a, int *b, int n)
{    //return a > b;
    int i;

    for (i = n;i <= 2*n+1;++i)
    {
        if (a[i] < b[i])    return 0;
        if (a[i] > b[i])    return 1;
    }
    return 0;
}
/*
其实可以写乘法的，这里是变乘为加，
以为会更好写，结果画蛇添足

(20a+n+1)*(n+1) - (20a+n)*n = 20a+2*n+1
*/
void add(int *a, int *b, int *c, int n, int m)
{
    int i, j, res = 0;
    
    for (i = n*2+1;i >= n;c[i] = a[i], --i);
    for (i = n*2, j = n-1;j >= 0;--i, --j)
    {
        res += c[i] + b[j] * 2;
        c[i] = res % 10, res /= 10;
    }
    while (res)    c[i--] += res % 10, res /= 10;

    i = n * 2 + 1, res = m * 2 + 1;
    while (res)
    {
        res += c[i];
        c[i--] = res % 10, res /= 10;
    }
}

void sub(int *a, int *b, int n)
{
    int i, j;

    for (i = n*2+1;i >= n;--i)
    {
        a[j = i] -= b[i];
        while (a[j] < 0)    a[j] += 10, --a[--j];
    }
}
/*
得到 结果 a的第 n位，试商。
tmp[n] = (20a + n) * n
*/
int get_ans(int *a, int *b, int n)
{
    int i, j, tmp[10][LEN*2] = {0};

    for (i = n*2, j = n-1;j >= 0;--i, --j)
        tmp[0][i] = a[j] * 2;

    tmp[0][n*2+1] = 1;
    if (comp(tmp[0], b, n))    return 0;

    for (i = 1;i < 10;++i)
    {
        add(tmp[i-1], a, tmp[i], n, i);
        if (comp(tmp[i], b, n))    break;
    }
    sub(b, tmp[i-1], n);
    return i;
}

void fun(int *a, int *b)
{
    int i;

    //a = sqrt(5);
    for (i = 0;i <= LEN_RESULT;++i)
    {
        a[i] = get_ans(a, b, i);
    }

    //ans = ( sqrt(5) - 1 ) / 2
    for (a[0]--, i = 0;i < LEN_RESULT;++i)
    {
        a[i+1] += (a[i] % 2) * 10;
        a[i] /= 2;
    }
}

int main()
{
    int i, ans[LEN] = {0};
    int s[LEN*2] = {0, 5};
    
    fun(ans, s);

    for (i = 0; i < LEN_RESULT;++i)
        printf("%d", ans[i]);
    printf("\n");
    return 0;
}