iOS - GPU Accelerated Matrix Transpose, Multiplication and Eigen-Decomposition Dilemma

Question

I'm working on a library that requires the use of vectors and matrices on the iOS platform. I decided to look into OpenGLES because the matrix and vector manipulations I plan on doing (mainly, transposing, matrix multiplication, and eigendecomposition) could definitely benefit from GPU acceleration.

The issue is that I'm not that familiar with OpenGLES and honestly might not be the best option. If I were to utilize OpenGLES, would I have to manually write the algorithms that do the matrix transposition, multiplication and eigendecomposition? Or is there another Apple or 3rd party framework that can help me with these tasks.

The main dividing issue however is that I want these operations to be GPU accelerated.

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I'm going to implement my program using the Accelerate Framework and vectorized arithmetic and then test to see if its fast enough for my purposes and, if it isn't, then try the GPU implementation.

Answer 1

As combinatorial states, Accelerate uses SIMD to accelerate many of its functions, but it is CPU-based. For smaller data sets, it's definitely the way to go, but operating on the GPU can significantly outclass it for large enough data sets with easily parallelized operations.

To avoid having to write all of the OpenGL ES interaction code yourself, you could take a look at my GPUImage framework, which encapsulates fragment shader operations within Objective-C. In particular, you can use the GPUImageRawDataInput and GPUImageRawDataOutput classes to feed raw byte data into the GPU, then operate over that using a custom fragment shader.

A matrix transpose operation would be quick to implement, since all of the matrix elements are independent of one another. Matrix multiplication by a constant or small matrix would also be reasonably easy to do, but I'm not sure how to scale the multiplication of two large matrices properly. Likewise, I don't have a good implementation of eigendecomposition that I could point to off of the top of my head.

The downside to dealing with fragment shader processing is the fact that by default OpenGL ES takes in and outputs 4-byte RGBA values at each pixel. You can change that to half floats on newer devices, and I know that others have done this with this framework, but I haven't attempted that myself. You can pack individual float values into RGBA bytes and unpack at the end, as another approach to get this data in and out of the GPU.

The OpenGL ES 3.0 support on the very latest A7 devices provides some other opportunities for working with float data. You can use vertex data instead of texture input, which lets you supply four floats per vertex and extract those floats in the end. Bartosz Ciechanowski has a very detailed writeup of this on his blog. That might be a better general approach for GPGPU operations, but if you can get your operations to run against texture data in a fragment shader, you'll see huge speedups on the latest hardware (the iPhone 5S can be ~100-1000X faster than the iPhone 4 in this regard, where vertex processing and CPU speeds haven't advanced nearly as rapidly).

Answer 2

The accelerate framework is not accelerated on the GPU, but it is very well optimized and uses SIMD on Neon where appropriate.