Fast Arctan2

/*

Written by Marco Pennekamp.


arctan2 results:

1e6 iterations.

Fast arctan2:
14763917 ns
13036519 ns
13084908 ns
12826451 ns
12405162 ns
12806097 ns
12592956 ns
12683205 ns
12366759 ns
12316065 ns

Math atan2:
127117003 ns
124614619 ns
122801197 ns
126679586 ns
123187922 ns
124409927 ns
122724773 ns
121995871 ns
122014689 ns
122691362 ns

So, about 10x faster and 12 - 14ns per arctan2 call.


Accuracy: (randomly taken values)

        Fast            Java

x<0;y>0     -1.215991       -1.2179305185113805
x<0;y<0     -2.1207047      -2.1160234823321717
x>0;y>0     1.5273854       1.5273896081693032
x>0;y<0     2.3276424       2.3288875696242464

Conclusion: Not a very good accuracy, but enough for most games, especially when the yaw is calculated each update.
*/


public static float arctan (float x) {
    if (x > 1) {
        return 1.57079632675f - x / (x * x + 0.28f);
    }else if (x < -1) {
        return -1.57079632675f - x / (x * x + 0.28f);
    }else {
        return x / (1f + 0.28f * x * x);
    }
}

public static float arctan2 (float y, float x) {
    if (x > 0) {
        return arctan (y / x);
    }else if (x < 0) {
        if (y >= 0) {
            return arctan(y / x) + 3.1415926535f;
        }
        return arctan(y / x) - 3.1415926535f;
    }

    if (y > 0) {
        return 1.57079632675f;
    }
    if (y < 0) {
        return -1.57079632675f;
    }

    return 0;
}