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# volkansalma/atan2_approximation.c

Created June 22, 2012 11:35
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optimized atan2 approximation
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 #include #include #include float atan2_approximation1(float y, float x); float atan2_approximation2(float y, float x); int main() { float x = 1; float y = 0; for( y = 0; y < 2*M_PI; y+= 0.1 ) { for(x = 0; x < 2*M_PI; x+= 0.1) { printf("atan2 for %f,%f: %f \n", y, x, atan2(y, x)); printf("approx1 for %f,%f: %f \n", y, x, atan2_approximation1(y, x)); printf("approx2 for %f,%f: %f \n \n", y, x, atan2_approximation2(y, x)); getch(); } } return 0; } float atan2_approximation1(float y, float x) { //http://pubs.opengroup.org/onlinepubs/009695399/functions/atan2.html //Volkan SALMA const float ONEQTR_PI = M_PI / 4.0; const float THRQTR_PI = 3.0 * M_PI / 4.0; float r, angle; float abs_y = fabs(y) + 1e-10f; // kludge to prevent 0/0 condition if ( x < 0.0f ) { r = (x + abs_y) / (abs_y - x); angle = THRQTR_PI; } else { r = (x - abs_y) / (x + abs_y); angle = ONEQTR_PI; } angle += (0.1963f * r * r - 0.9817f) * r; if ( y < 0.0f ) return( -angle ); // negate if in quad III or IV else return( angle ); } #define PI_FLOAT 3.14159265f #define PIBY2_FLOAT 1.5707963f // |error| < 0.005 float atan2_approximation2( float y, float x ) { if ( x == 0.0f ) { if ( y > 0.0f ) return PIBY2_FLOAT; if ( y == 0.0f ) return 0.0f; return -PIBY2_FLOAT; } float atan; float z = y/x; if ( fabs( z ) < 1.0f ) { atan = z/(1.0f + 0.28f*z*z); if ( x < 0.0f ) { if ( y < 0.0f ) return atan - PI_FLOAT; return atan + PI_FLOAT; } } else { atan = PIBY2_FLOAT - z/(z*z + 0.28f); if ( y < 0.0f ) return atan - PI_FLOAT; } return atan; }

### pswiatki commented Sep 7, 2021 • edited

I was pointing out the fact they used a compare operation to 0.0 float. That will be true very seldom (to put it mildly) and - according to my knowledge - shall be avoided. Let me think about your code snippet above (interesting kludge of 1e-10f ;)

### Pflugshaupt commented Sep 7, 2021 • edited

the kludge line comes from approximation1, you were pointing out the comparisons in approximation2. Sorry, I didn't mean to answer your question, but wanted to comment on the original code because it inspired me to get to a branchless version.
The beauty of a branchless atan2 is that it can easily be performed using SIMD instructions.

### pswiatki commented Sep 7, 2021

very nice, indeed.

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