Fast Inverse Square Root

#include <cstdint>

float FastInverseSqrt(float x) {
    float xhalf = 0.5f * x;
    int32_t i = (int32_t)&x;    // reinterpret bits of x as an integer
    i = 0x5f3759df - (i >> 1);    // initial guess for the inverse square root
    x = (float)&i;              // convert bits back to float
    x = x  (1.5f - xhalf  x * x); // Newton-Raphson iteration to improve accuracy
    return x;
}

Explanation:

1. float xhalf = 0.5f * x;: Compute half of the input value.

2. int32_t i = (int32_t)&x;: Interpret the bits of the floating-point number x as an integer.

3. i = 0x5f3759df - (i >> 1);: Apply a magic number and some bit manipulation to make an initial guess for the inverse square root using integer operations.

4. x = (float)&i;: Convert the bits back to a floating-point number.

5. x = x (1.5f - xhalf x * x);: Perform one iteration of the Newton-Raphson method to refine the estimate of the inverse square root.

6. Return the computed value x.