Square root cube root

Preface

square root

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1. Dichotomy

The code is as follows （ Example ）：

double SQRT_Binary(double n)
{
    
    double l = 0, r = n;
    if(n<0) l=n,r=0;
    while(l<r)
    {
    
        double mid = (l + r) / 2;
        if(mid * mid > n)
        //if(mid*mid*mid)>n  Cube root 
        //if(mid*mid*mid<E||mid*mid*mid>-E) return mid; Less than a certain threshold output 
        //
            r = mid;
        else if(mid * mid < n)
            l = mid;
        else return mid;
    }
    
}

2. Newton's iteration

The code is as follows （ Example ）：

double SQRT_Newton(double n)
{
    
    double x0 = n;
    double x1;
    while(1)
    {
    
        //x1 = -(x0 * x0 - n) / (2 * x0) + x0;
        x1 = (x0 * x0 + n) / (2 * x0);
        //x1=(x0*x0*x0+n)/(3*x0*x0)
        double val = x1 * x1 - n;
        if(val <= inf && val >= -inf)
            return x1;
        x0 = x1;
    }
    return 0;
}

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