While searching for a fast arctan approximation I came across this paper:

“**Efficient approximations for the arctangent function”, **Rajan, S. Sichun Wang Inkol, R. Joyal, A., May 2006

Unfortunately I no longer have access to the IEEE papers (despite paying for yearly membership, what a joke …), but fortunately the paper appeared in a book that Google has for preview (for selected pages), **“Streamlining digital signal processing: a tricks of the trade guidebook”**. Even luckier, Google had the important pages on preview. The paper presents 7 different approximation, each with varying degree of accuracy and complexity.

Here is one algorithm I tried, which has a reported maximum error 0.0015 radians (0.085944 degrees), lowest error in the paper.

double FastArcTan(double x) { return M_PI_4*x - x*(fabs(x) - 1)*(0.2447 + 0.0663*fabs(x)); }

The valid range for x is between -1 and 1. Comparing the above with the standard C atan function for 1,000,000 calls using GCC gives:

Time ms | |

FastArcTan | 17.315 |

Standard C atan | 60.708 |

About 3x times faster, pretty good!

Hi, thanks for sharing this. Helped me to find out that atan function is correct on my GPU in OpenCL. I tested this because another function, tan, turned out to be buggy on this GPU.

Glad you found it useful ðŸ™‚

Thanks for posting this, it’s very useful if you don’t have time for the standard C function but can deal with a small accuracy loss!

What is M_PI_4?

Thanks for the resource!

PI/4

Ahh makes sense. I figured, just didn’t want to assume.

Thanks once more, will use this in some sand dune simulations!

Oh and one more thing, as far as speed is concerned, if you make this a macro (using #DEFINE in C/C++) it’ll theoretically be even faster than your standard function (or making it inline should have similar effect).

Depends. The compiler may be smart enough to inline such a small function. But doesn’t hurt to be explicit I guess.