Instantly share code, notes, and snippets.

# volkansalma/atan2_approximation.c

Created June 22, 2012 11:35
Star You must be signed in to star a gist
optimized atan2 approximation
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters. Learn more about bidirectional Unicode characters
 #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; }

### Pflugshaupt commented Aug 26, 2021

approximation1 can be made branchless using std::copysign and std::fabs - which boil down to simple bitwise logic.

``````float atan2_approx(float y, float x) {
float abs_y = std::fabs(y) + 1e-10f;      // kludge to prevent 0/0 condition
float r = (x - std::copysign(abs_y, x)) / (abs_y + std::fabs(x));
float angle = M_PI/2.f - std::copysign(M_PI/4.f, x);

angle += (0.1963f * r * r - 0.9817f) * r;
return std::copysign(angle, y);
}
``````

### 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.