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I am looking for a website/database of computer hardware (CPUs/GPUs) benchmarked with common scientific tools, e.g. *GEMM (see comment below for more info on this tool).

Currently, I am quite frustrated looking for this information, as it seems scattered across blogs, embedded in manufacturing marketing materials, or shadowed by the plethora of enthusiast gamers posting FPS results.

Are there any good databases out there? Or even some good peer-reviewed journals to look out for?

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I don't know if there is one source. Mostly just blogs and manufacturers show this kind of thing. You may want to start a blog on this! The Puget Systems HPC Blog is probably the most complete source, featuring a lot of benchmarks on Xeon processors, NVIDIA GPUs, and Xeon Phi acceleration cards. It doesn't only focus on BLAS, but the applications are all scientific computing and so it's a good indicator of performance for many people's algorithms (i.e. it uses a lot of BLAS).

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There's two recent papers you should check:

GPU Performance Modeling and Optimization: https://pure.tue.nl/ws/files/39759895/20161018_Li.pdf

Accelerating BLAS on Custom Architecture thru Algo/Arch codesign https://arxiv.org/abs/1610.06385

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