Benchmarks for Blaze, A high-performance C++ math library

https://code.google.com/p/blaze-lib/wiki/Benchmarks

by wall_words • 11 years ago

63 30 11 years ago

code.google.com

wall_words4• 11 years ago

I've had great success with Blaze, despite the fact that it has received little publicity compared to alternatives like Eigen, Armadillo, etc. Blaze is consistently the leader of the pack in benchmarks, and even outperforms Intel MKL on the Xeon E5-2660 (the CPU for which the benchmark results are shown).

arcanus3• 11 years ago

For what problems? General statements like this are hard to back up, especially in the wild world of numerical linear algebra.

From my experience, there are currently no good distributed-memory open source sparse-direct solvers.

No good distributed-memory ILU implementation, either. Scalability is almost non-existant beyond 100 cores.

onalark2• 11 years ago

That's because direct solvers can't scale. If you want to solve a large (distributed over hundreds of nodes) sparse linear algebra problem as fast as possible, decades of research have been poured into efficient techniques (Krylov methods, Multigrid, preconditioners) for solving them iteratively.

wall_words4• 11 years ago

I've used Blaze for machine learning applications, where I've relied on the performance of elementwise operations and dense matrix multiplication on a single machine (the results advertised in the benchmark). Eigen has more functionality, but in my experience is not always optimized as well as Blaze. Neither has support for distributed computing, but I believe this is a problem that HPX is trying to address: https://github.com/STEllAR-GROUP/hpx

math_and_stuff2• 11 years ago

I'm working on it...see https://github.com/elemental/Elemental

therobot242• 11 years ago

better link: https://bitbucket.org/blaze-lib/blaze

wall_words4• 11 years ago

Thanks, I tried finding the link to the Bitbucket repository but I had a hard time finding the link via Google.

therobot242• 11 years ago

It actually took me more than a few minutes as well, had to use BitBucket's search since Google (rarely enough) was returning crap

pmelendez2• 11 years ago

Thanks!

Off-topic: I like bitbucket better, so it is nice to see some projects going over there.

jacobolus• 11 years ago

Or the analog of the link in the OP, https://bitbucket.org/blaze-lib/blaze/wiki/Benchmarks

HN mods: could someone change the discussion to point to this link? It has working pictures.

santaclaus2• 11 years ago

It would be interesting to see benchmarks of sparse operations, as well.

east2west• 11 years ago

I am considering converting a C++03 math library to C++14 as a side project to learn C++14 and I examined Eigen and Blaze. Eigen's code size seems to be a fraction of Blaze, even though their functionalities are similar. Eigen also has some design documents while Blaze has papers but not much more. It seems I will try my hands on Eigen library for now. It is amazing that a couple of people could do in a few years; Blaze has hundred of thousands of lines of code.

arcanus3• 11 years ago

Eigen is header only and heavily templated, which certainly keeps the source down.

However, SLOC is a poor metric for the quality of a codebase, especially scientific ones. I've certainly found many instances where longer line counts are more performant, for instance with hand-unrolling loops (very rare edge case, not suggesting doing this as a rule!).

Unless you intend to become involved in development of the library, I see no reason you would care about the lines of code. Even at that point, design philosophy, features, etc. are more likely to be major factors in your choice.

FYI: Computational Scientist here. I am neither affiliated with Blaze nor Eigen.

Profan• 11 years ago

I'd say lines of code does matter if the set of functionality is the same, i'd wager that, if you have the same functionality in less lines of code, generally it's easier to verify that it's correct + avoid daft bugs.

.. Unless it's written in a completely uncomprehensible way of course (such as some meta c++ stuff), but in languages with good metaprogramming.

shepardrtc4• 11 years ago

Take a look at Armadillo as well. I did the same thing about a year ago, and looked at all of them. In the end, Armadillo made writing things very easy. Of course, I was really only focused on matrix multiplication, so you may have different requirements.

jlarocco• 11 years ago

I agree with Arcanus; lines of code isn't a good measurement here. It's not uncommon for high performance math and science libraries to have specialized code to handle a lot of different cases the fastest way possible, or the most accurate way possible, etc. and some libraries are even able to switch between them heuristically based on the data they're being used on.

A common example is matrix multiply. For smaller matrices it's faster to use naive O(n^3) multiply because of the large constant factor with Strassen's algorithm. At some point n^3 will dominate the constant factor, and Strassen's becomes better. To get the best performance in all cases, both algorithms need to be implemented, which increases the code size.

hyperbovine• 11 years ago

If you are interested in C++14 then you are "looking to the future" as it were, in which case I would suggest Eigen. Why? One word: tensors. Eigen has already a quite usable tensor implementation, whereas as far as I can descry Blaze has no plans in that direction. Tensors show up everywhere in scientific computing. They are incredibly useful. For this reason (along with several others, which I can elaborate on if you are interested) I feel like Eigen will become the Numpy of C++ numerical array software in the future.

fizixer• 11 years ago

In the first plot, why do all libraries slow down at the n=1000 mark? something to do with cache?

wall_words4• 11 years ago

I'm guessing that's the point at which the working set exceeds the L1 cache size. You can see a few more subtle dips in the performance graph at later points; these correspond to working set spilling out of the L2 and L3 caches.

acconsta• 11 years ago

Yep. A 32KB L1 cache can hold at most 4000 doubles. 4000/(2 input vectors + 1 result) =1333.

http://danluu.com/3c-conflict/

shepardrtc4• 11 years ago

Does Blaze implement its own BLAS subroutines? Or does it wrap around an existing BLAS library?

shepardrtc4• 11 years ago

Turns out that it does implement its own, but it also has the possibility of wrapping existing libraries:

https://bitbucket.org/blaze-lib/blaze/src/e09d62ee714745b297...

Of course, if you're seriously going to use this library, you're going to use an established BLAS library like OpenBLAS or Intel MKL.

deng• 11 years ago

I remember this library being discussed on the Eigen list in 2012. Here's the thread:

http://thread.gmane.org/gmane.comp.lib.eigen/3423

The main critique at the time was that Blaze always assumes perfectly aligned data, including inside(!) the matrix, and pads the data with zeros if that is not the case. Of course, this makes it impossible to map external data, which is a huge downside. I'm not sure if that is still the case, but from skimming through the docs it doesn't look to me like this has changed.

santaclaus2• 11 years ago

An old thread on the Eigen list also mentioned that the Blaze folks were a little tricky with their benchmarks. Some of the reported performance numbers with Blaze were for calls out to Intel MKL routines. Eigen also supports MKL as a kernel backend, but the Blaze folks failed to enable this feature for the reported comparisons, if I recall.

shepardrtc4• 11 years ago

a little tricky

That's rather generous. If you're going to do serious work with Eigen, or Armadillo, or Blaze, you're going to include a BLAS library like OpenBLAS or Intel MKL (if you can afford it). Not including them is dubious, at best.

Benchmarks for Blaze, A high-performance C++ math library

Related Stories