Speed up mandelbrot

[jackos]

Addresses the improvements @zbosons pointed out.

Changed to using an isolated machine with 8-core CPU, for 960x960 image with 200 max_iters results in:

Pre change

Vectorized: 20.33 ms
Parallelized: 2.76 ms
Parallel speedup: 7.4

After change

Vectorized: 13.54 ms
Parallelized: 1.41 ms
Parallel speedup: 9.59

[zbosons]

The vector version is faster but the parallel version is slower (from 0.96 ms to 1.17 ms). Why is this? What hardware did this run on? It says 32 threads so I assume this is a AVX512 server? Maybe the problem size is too small then?

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[zbosons]

We can calculate the best possible time. I guess this system has 16 physical cores

time = 40120461 * (8.5) /frequency/16/16.

I don't know what the frequency is on this system but lets assume its about 3 GHz. Then the best time is about 0.4 ms. And the best time was 0.96 s. So about 42% of best possible.

We should test with larger sizes. We could increase max_iter to e.g. 1000. I usually try and get something to run for about a second. In this case it runs for less than 1 ms and I am afraid the overhead is large. When I benchmarked I used 4000x4000 and 1000 max iterations.

I think @abduld did not want to do increase the run time default on the server. But 5 * num_cores() still seems too arbitrary to me.

[zbosons]

Turns out the new version is faster on the current system. Can you please report the numbers with the old code and the new code to show the improvement on the current system.