Skip to content

Instantly share code, notes, and snippets.

Embed
What would you like to do?
optimized atan2 approximation
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
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

This comment has been minimized.

Copy link

commented May 10, 2014

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

@mpaperno

This comment has been minimized.

Copy link

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!

Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
You can’t perform that action at this time.