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The most famous bitwise hack in gaming history — the fast inverse square root, specifically designed to accelerate 1 / sqrt(x) in vector normalization:

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float Q_rsqrt(float number)
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{
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    long i;
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    float x2, y;
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    const float threehalfs = 1.5f;
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    x2 = number * 0.5f;
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    y  = number;
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    i  = *(long *)&y;            // evil floating point bit level hacking
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    i  = 0x5f3759df - (i >> 1);  // what the fuck?
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    y  = *(float *)&i;
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    y  = y * (threehalfs - (x2 * y * y));   // 1st iteration
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    return y;
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}

Combined with vector length, you can directly compute normalized normals, and back in the day it was much faster than the standard library.

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