利用公式近似计算log2(x)

公式详见程序设计基础（清华大学出版社）P102解题时，注意应向log2函数传递的参数的选取及其类型即可代码如下：#include <iostream>
#include <cmath>
using namespace std;
const double q = 1e-6;
double s[100000], a[100000], b[100000];

int main()
{
b[0] = 1;
s[0] = 0;
double x;
int i, n;
for (i = 0; i < 100000; i++) // define b[i]
b[i] = pow(0.5, i);
for (i = 1; ; i++) // define n
{
if (pow(0.5, i) <= q)
break;
}
n = i;
while (cin >> x && x)
{
cout << log2(x) << endl;
}
return 0;
}

double log2(double x, int n)
{
b[0] = 1;
s[0] = 0;
int i;
for (i = 0; i < 100000; i++) // define b[i]
b[i] = pow(0.5, i);
a[0] = x;
for (i = 1; i <= n; i++) // define a[i]
{
if (a[i - 1] * a[i - 1] < 2)
a[i] = a[i - 1] * a[i - 1];
else
a[i] = a[i - 1] * a[i - 1] / 2.0;
}
for (i = 1; i <= n; i++)
{
if (a[i - 1] * a[i - 1] < 2)
s[i] = s[i - 1];
else
s[i] = s[i - 1] + b[i];
}
if (x > 0 && x < 1)
cout << -log2(1/x) << endl;
else if (x > pow (2.0, n))
cout << n + log2(x / pow(2.0, n)) << endl;
else
cout << s
<< endl;
}