Re: GNAT can't vectorize Real_Matrix multiplication from Ada.Numerics.Real_Arrays. What a surprise!

[Robert Eachus <rieachus@comcast.net>]

On Sunday, February 18, 2018 at 4:48:42 PM UTC-5, Nasser M. Abbasi wrote:
> On 2/18/2018 1:38 PM, Bojan Bozovic wrote:
> 
> If you are doing A*B by hand, then you are doing something
> wrong. Almost all languages end up calling Blas
> Fortran libraries for these operations. Your code and
> the Ada code can't be faster.
> 
> http://www.netlib.org/blas/
> 
> Intel Math Kernel Library has all these.
> 
> https://en.wikipedia.org/wiki/Math_Kernel_Library

For multiplying two small matrices, blas is overkill and will be slower.  If you have say, 1000x1000 matrices, then you should be using blas.  But which BLAS?  Intel and AMD both have math libraries optimized for their CPUs.  However, I tend to use ATLAS.  ATLAS will build a blas targeted at your specific hardware.  This is not just about instruction set additions like SIMD2.  It will tailor the implementation to your number of cores and supported threads, cache sizes, and memory speeds.  I've also used the goto blas, but ATLAS even though not perfect, builds all of blas3 using matrix multiplication and blas2, such that all operations slower than O(n^2) have their speed determined by matrix multiplication.  (Then use multiple matrix multiplication codes with different parameters to find the fastest.)

Usually hardware vendor libraries catch up to and surpass ATLAS, but by then the hardware is obsolete. :-(   The other problem right now is that blas libraries are pretty dumb when it comes to multiprocessor systems.  I'm working on fixing that. ;-)