Recalibrate _AXPY

[brada4]

#1886 #1883

[brada4]

Justification and input.
I basically rigged loop from +=step to <<1
It is approximate, by magnitude bigger to bypass low area for 3rd thread (it just looks more impressive with 4, with 3 it is still < 1/2 of first thread)

_axpy.zip

[martin-frbg]

I have not yet looked at this in detail, but I noticed that (a) the proposed default for everything including "consumer" hardware exceeds the current limit for an IBM mainframe (b) your thresholds look as if you are counting bytes rather than vector elements - obviously the two are related, but I find it surprising that a vector of 512k floats would be processed faster in a single thread.

[brada4]

N is in elements for axpy benchmark threshold is 2MB (cache I have) for S D Z and 1MB for C

The gain from threading at all is not so big, the damage from all 4 threads is quite big. sort of 20% slowdown because of no threading is nothing in place where it becomes eventual 10x problem.

Z13 wikipedia says has 2MB per cpu cache too, so pretty close to my laptop CPU, maybe it can be/should be unified acknowledging memory effect?

512k*4B perfectly fits in cache (just once, not 3x)

[brada4]

Remove all threading gueards in interface/axpy.c
Rig benchmark increment loop into left shift in benchmark/axpy.c
Measurement says better safe (1thr > 2.1MB) than sorry (4thr <1MB)

#!/bin/sh
for a in s d c z ; do
        for b in 1 2 4 ; do
                OPENBLAS_LOOPS=97 OPENBLAS_NUM_THREADS=${b} ./${a}axpy.goto 1 35000000 1 2>&1 | tee ${a}axpy${b}.out
        done
done

[brada4]

Something weird, atom hyperthreads improve speed, when they should get worse in practice.
Could it be l1_thread work splitting should align base for subsequent threads? I will try around idea, do not merge this.

[brada4]

I could not invent much better:
4bytes goes 16 times in maximum practical of today Dcache line, so I round up elements to divisible by 16 , which yields min per-cpu chunk of 64 bytes for S 128 bytes for D C and 256 for Z (and something not so round for X)
It is better than nothing at first sight, presumes arguments aligned. In future can be used to fix alignment and use exact cache lines (at present those are not known at the point, so not so easy)
I will spend some time doing properly.

[brada4]

Lets hold back for upcoming release.