xtensor VS blis

I use xtensor: https://github.com/xtensor-stack/xtensor

Currently, one of my current favorites is xtensor.

xTensor natively supports tensors and multidimensional arrays - not just vectors and matrices. Is fast, but not always as fast as Eigen and Blaze - and compiles very slow. Has a nice syntax.

I wonder how Eigen compares to xtensor, which was inspired by Numpy and has support for views, slicing, and broadcasting?

https://github.com/xtensor-stack/xtensor

You can try eigen (http://eigen.tuxfamily.org/), armadillo (http://arma.sourceforge.net/) which is based on LAPACK which is what numpy is based on and xtensor (https://github.com/QuantStack/xtensor) which I think is the closest thing to numpy you’re gonna find in c++

There is a recent update to the blis alternative to BLAS that includes a number of RISC-V performance optimizations.

https://github.com/flame/blis/pull/737

https://github.com/flame/blis/blob/master/docs/Performance.m...

It seems that the selling point is that BLIS does multi-core quite well. I am especially impressed that it does as well as the highly optimized Intel's MKL on Intel's CPUs.

I do not see the selling point of BLIS-specific APIs, though. The whole point of having an open BLAS API standard is that numerical libraries should be drop-in replaceable, so when a new library (such as BLIS here) comes along, one could just re-link the library and reap the performance gain immediately.

What is interesting is that numerical algebra work, by nature, is mostly embarrassingly parallel, so it should not be too difficult to write multi-core implementations. And yet, BLIS here performs so much better than some other industry-leading implementations on multi-core configurations. So the question is not why BLIS does so well; the question is why some other implementations do so poorly.

First we can use Laser, which was my initial BLAS experiment in 2019. At the time in particular, OpenBLAS didn't properly use the AVX512 VPUs. (See thread in BLIS https://github.com/flame/blis/issues/352 ), It has made progress since then, still, on my current laptop perf is in the same range

Reproduction:

https://github.com/flame/blis/

Field et al, recent winners of the James H. Wilkinson Prize for Numerical Software.

Field and Goto both worked with Robert van de Geijn. Lots of TACC interaction in that broader team.

BLIS is fine too~ https://github.com/flame/blis

Here's BLIS's object API:

https://github.com/flame/blis/blob/master/docs/BLISObjectAPI...

Searching "object" in BLIS's README (https://github.com/flame/blis) to see what they think of it:

"Objects are relatively lightweight structs and passed by address, which helps tame function calling overhead."

"This is API abstracts away properties of vectors and matrices within obj_t structs that can be queried with accessor functions. Many developers and experts prefer this API over the typed API."

In my opinion, this API is a strict improvement over BLAS. I do not think there is any reason to prefer the old BLAS-style API over an improvement like this.

Regarding your own experience, it's great that using BLAS proved to be a valuable learning experience for you. But your argument that the BLAS API is somehow uniquely helpful in terms of learning how to program numerical algorithms efficiently, or that it will help you avoid performance problems, is not true. It is possible to replace the BLAS API with a more modern and intuitive API with the same benefits. To be clear, the benefits here are direct memory management and control of striding and matrix layout, which create opportunities for optimization. There is nothing unique about BLAS in this regard---it's possible to learn these lessons using any of the other listed options if you're paying attention and being systematic.

The article asks "Which Micro-optimizations matter for BLAS3?", implying small dimensions, but doesn't actually tell me. The problem is well-studied, depending on what you consider "small". The most important thing is to avoid the packing step below an appropriate threshold. Implementations include libxsmm, blasfeo, and the "sup" version in blis (with papers on libxsmm and blasfeo). Eigen might also be relevant.

https://libxsmm.readthedocs.io/

https://blasfeo.syscop.de/

https://github.com/flame/blis