sqrt函数实现（多种算法比较）

短命女 2023-01-06 11:56 114阅读 0赞

### 本文有错误，待修改 ###

### 参考链接 ###

*  [Best Square Root Method - Algorithm - Function (Precision VS Speed)][Best Square Root Method - Algorithm - Function _Precision VS Speed]

### 测试文件下载 ###

[链接1][1]  
  [所有文件][Link 1]

### 运行结果 ###

![在这里插入图片描述][watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80Mzk2NDk5Mw_size_16_color_FFFFFF_t_70]

### 速率较快的代码 ###

float sqrt3(const float x)  
    { 
      union
      { 
        int i;
        float x;
      } u;
    
      u.x = x;
      u.i = (1<<29) + (u.i >> 1) - (1<<22); 
      return u.x;
    }

float sqrt7(float x)
     { 
       unsigned int i = *(unsigned int*) &x; 
       // adjust bias
       i  += 127 << 23;
       // approximation of square root
       i >>= 1; 
       return *(float*) &i;
     }

#define SQRT_MAGIC_F 0x5f3759df 
    float  sqrt2(const float x)
    { 
      const float xhalf = 0.5f*x;
     
      union // get bits for floating value
      { 
        float x;
        int i;
      } u;
      u.x = x;
      u.i = SQRT_MAGIC_F - (u.i >> 1);  // gives initial guess y0
      return x*u.x*(1.5f - xhalf*u.x*u.x);// Newton step, repeating increases accuracy 
    }

float sqrt1(const float x)  
    { 
      union
      { 
        int i;
        float x;
      } u;
      u.x = x;
      u.i = (1<<29) + (u.i >> 1) - (1<<22); 
      
      // Two Babylonian Steps (simplified from:)
      // u.x = 0.5f * (u.x + x/u.x);
      // u.x = 0.5f * (u.x + x/u.x);
      u.x =       u.x + x/u.x;
      u.x = 0.25f*u.x + x/u.x;
    
      return u.x;
    }

//神奇的方法
    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
    	x = *(float*)&i; // convert bits BACK to float
    	x = x*(1.5f-xhalf*x*x); // Newton step, repeating increases accuracy
    	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;
    }

--------------------

**相关文章：**

*  [二分法开方sqrt函数编写][sqrt]
 *  [一个Sqrt函数引发的血案][Sqrt]
 *  [sqrt函数实现（神奇的算法）][sqrt 1]
 *  [sqrt函数实现（神奇的算法）][sqrt 2]
 *  [Best Square Root Method - Algorithm - Function (Precision VS Speed)][Best Square Root Method - Algorithm - Function _Precision VS Speed]
 *  [金庸老先生笔下的数学谜题][Link 2]
 *  [面试题：实现一个开方函数][Link 3]
 *  [【算法 | Python】二分法求函数在区间\[a,b\]中的根][_ Python_a_b]

[Best Square Root Method - Algorithm - Function _Precision VS Speed]: https://www.codeproject.com/Articles/69941/Best-Square-Root-Method-Algorithm-Function-Precisi
[1]: https://wwa.lanzous.com/il9IXke4lva
[Link 1]: https://wwa.lanzous.com/ielNZke4tmj
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3dlaXhpbl80Mzk2NDk5Mw_size_16_color_FFFFFF_t_70]: /images/20221119/ba187aa8cdbd4b99b25a7a4a3cb25cec.png
[sqrt]: https://blog.csdn.net/weixin_43964993/article/details/112602194
[Sqrt]: https://diducoder.com/sotry-about-sqrt.html
[sqrt 1]: https://blog.csdn.net/qq_26499321/article/details/73724763
[sqrt 2]: https://blog.csdn.net/weixin_43964993/article/details/112604518
[Link 2]: https://k.sina.cn/article_2897328623_acb1b9ef01900cfkm.html
[Link 3]: https://blog.csdn.net/mynameisbill2/article/details/100185542
[_ Python_a_b]: https://blog.csdn.net/weixin_43964993/article/details/108351554