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# volkansalma/atan2_approximation.c

Created Jun 22, 2012
optimized atan2 approximation
 #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; }

### karussell commented May 10, 2014

 Can I use and publish this under Apache 2 license with proper attribution? It would be for graphhopper

### mpaperno commented Feb 2, 2018

 In my (somewhat limited but concise) testing on both a very fast Gen 7 Xeon and an STM32F4 (w/FPU) ARM micro show `atan2_approximation1` to be faster (and much more accurate) than the 2nd version. On STM32F4 `a1` is ~2.3 times faster than stdlib (with gcc-arm 4.7.4)., while `a2` is ~2.1 times faster than stdlib. On the Xeon under Windows with MSVC `a1` shows maybe a very slight improvement in speed over std (within margin of error, really), while with MinGW-w64 on same system the std version is a whopping 12 times slower! Thanks for this snip, very handy!

### mooman219 commented Sep 6, 2020 • edited

 For anyone looking at this in the future, this function was first referenced on an Apple mailing list in 2005 that's not in their current archives (but it is on the wayback machine!). It was a derivative of a similar function form 1999 which can be found here. That function was in the `public domain` if anyone is concerned about licensing.