Calaulate sqrt(x) using magic number method

SqrtByMagicNumber.cxx

#include <iostream>
#include <cmath>

#define SQRT_MAGIC32 0x5F375A86
#define SQRT_MAGIC64 0x5FE6EB50C7B537A9

using namespace std;

float Sqrt32(float x) {
    uint32_t i;			                                   // The integer interpretation of x
    float   x_half = x * 0.5F;
    float   r_sqrt = x;
    
    i = *(uint32_t *) &r_sqrt;
    i = SQRT_MAGIC32 - (i >> 1);
    r_sqrt = *(float *) &i;
    
    r_sqrt = r_sqrt * (1.5F - (x_half * r_sqrt * r_sqrt)); // 1st Newton iteration
    r_sqrt = r_sqrt * (1.5F - (x_half * r_sqrt * r_sqrt)); // 2nd Newton iteration
    
    return x * r_sqrt; // x * (1/sqrt(x)) := sqrt(x)
}


double Sqrt64(double x) {
    uint64_t i;			                                   // The integer interpretation of x
    double   x_half = x * 0.5;
    double   r_sqrt = x;
    
    i = *(uint64_t *) &r_sqrt;
    i = SQRT_MAGIC64 - (i >> 1);
    r_sqrt = *(double *) &i;
    
    r_sqrt = r_sqrt * (1.5 - (x_half * r_sqrt * r_sqrt)); // 1st Newton iteration
    r_sqrt = r_sqrt * (1.5 - (x_half * r_sqrt * r_sqrt)); // 2nd Newton iteration
    
    return x * r_sqrt; // x * (1/sqrt(x)) := sqrt(x)
}

int main(int argc, char** argv) {
    float input32 = 17.0F;
    cout << "[By C++ library]: " << sqrtf(input32)  << endl;
    cout << "[By fast method]: " << Sqrt32(input32) << endl;
    
    double input64 = 17.0;
    cout << "[By C++ library]: " << sqrt(input64)   << endl;
    cout << "[By fast method]: " << Sqrt64(input64) << endl;
}

Reference: https://cs.uwaterloo.ca/~m32rober/rsqrt.pdf

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