The accuracy and speed of function approximations – part 3

In part 2 we had a look at the accuracy of the approximated functions. In this part we will take a look at the speed of the same approximated functions.

There is no reason to use approximation unless you gain something from it. Usually the gain will be in the form of a speed improvement over the real function. Embedded devices with low memory and low frequency CPU can benefit greatly from approximation – even new computers can benefit from it. Lets test it out:

ApproxSineTable

The timing depends a lot on the platform and settings. This is compiled under .Net 3.5 SP1 x64 in release mode. Timing is based on 1000000 iterations.

The results are clear – the quadratic curve equation is a lot faster than both the Taylor series and real sine function. The quadratic curve equation is also more accurate than the Taylor series.

Conclusion

If you are programming for embedded devices such as mobile phones, PDAs or barcode readers, you can gain a lot of function approximations. In this article series we tested the accuracy (true across all platforms – small but consistent variations can occur) and the speed on the PC platform. Using a quadratic curve approximation with added accuracy can give you 10 times better performance for a small sacrifice in accuracy.

You can get the code to the approximation library (written in C#) here: Approx.net

Update: I managed to improve the performance of the LowSin() function. It now runs at 3 ms on my computer.

Comments

Post a Comment

Popular posts from this blog

.NET Compression Libraries Benchmark

Image
I often find myself needing a compression library in a software development project, and after a few tests with disappointing results I usually fall back to spawning 7Zip as an external process. This time however, the application specification prohibits any data written to disk, which 7Zip needs to do in order to work correctly. I needed to do everything in memory, and so I had to test some of the C# libraries available for compression as well as the different compression algorithms. Here is a full list of the tested libraries: .NET DeflateStream ICSharpCode SharpZip Zlib.NET DotNetZip Managed LZMA LZMA SDK QuickLZ    Compression 101 Before I get to the results of the benchmark, I think it is important to understand the different archive formats and compression algorithms in order to compare the results with other benchmarks/and or tests. Lets get to it! A compression algorithm can be compared to a small machine that takes in some data, do some math on it and transfor
Read more

Reducing the size of self-contained .NET Core applications

Just for note keeping, I've written down some methods of reducing the size of a .NET Core application. I thought others could use it as well, so here you go. Original Size First off, let's see how much disk space a self-contained 'hello world' application takes up. > dotnet new console > dotnet publish -r win-x86 -c release Size: 53.9 MB -  yuck! Trimming Microsoft has built a tool that finds unused assemblies and removes them from the distribution package. This is much needed since the 'netcoreapp2.0' profile is basically .NET Framework all over again, and it contains a truckload of assemblies our little 'hello world' application don't use. > dotnet new console > dotnet add package Microsoft.Packaging.Tools.Trimming -v 1.1.0-preview1-25818-01 > dotnet publish -r win-x86 -c release /p:TrimUnusedDependencies=true Size: 15.8 MB Much better! Although, we have only removed unused assemblies - what about unused
Read more

Convex polygon based collision detection

Image
A lot of people have asked me: Why use a convex polygon only engine like Box2D? In this post I will provide some info on why convex polygons is the optimal polygon type to use. What does convex mean? Convex polygons needs to satisfy the following requirements: All internal angles must be below 180 degrees Every line segment between two vertices can be contained fully inside or at the edge the polygon A non-convex polygon is called a concave polygon and it must have an internal angle measuring greater than 180 degrees. As you might have thought about yourself; concave polygons can be quite handy. Convex-only engines can’t represent a simple player polygon like Pac-Man . Why use convex-only? There are really only one big juicy reason: performance Physics engines are able to take quite a few shortcuts and use cheap algorithms to determine the closest vertex, shortest distance and a lot more. An algorithm like Separating Axis Theorem and the Gilbert – Johnson –
Read more