#include<iostream>
#include<cmath>
using namespace std;

float Sqrt(float x);

float InvSqrt(float x);

int main(void)
{       
    system("color F0"); 
    cout.setf(ios::fixed);                     
    cout.setf(ios::showpoint);
    cout.precision(10);  


    //高速算法
    double result1,result2;
    result1=Sqrt(635);
    //系统方法
    double a=635;
    result2=sqrt(a);


    cout<<result1<<endl;
    cout<<result2<<endl;


    system("pause");
    return 0;
}




//浮点数平方根高速算法
float Sqrt(float x)
{
float xhalf = 0.5f*x;
int i = *(int*)&x;      // get bits for floating value
i = 0x5f375a86- (i>>1); // gives initial guess y0                     迅速找出第一次比較接近的迭代结果
x = *(float*)&i;        // convert bits BACK to float
x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy  牛顿迭代法，次数越多越准确
x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy
x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy


return 1/x;

}

//实现平方根的倒数
float InvSqrt(float x)
{
float xhalf = 0.5f*x;
int i = *(int*)&x;      // get bits for floating value
i = 0x5f375a86- (i>>1); // gives initial guess y0                     迅速找出第一次比較接近的迭代结果
x = *(float*)&i;        // convert bits BACK to float
x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy  牛顿迭代法，次数越多越准确
x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy
x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy


return x;

}