compute fft on multiple cores

[kwanCCC]

benchmark for making proof

64 cores
AMD EPYC 7542 32-Core Processor
Linux AMD-10-10-17-3 5.4.0-26-generic Ubuntu SMP x86_64 GNU/Linux

num of gate	serial	parallel
32	[35.099 ms 35.177 ms 35.261 ms]	[79.786 ms 79.922 ms 80.079 ms]
64	[44.420 ms 44.566 ms 44.709 ms]	[135.46 ms 135.71 ms 135.87 ms]
128	[72.038 ms 72.250 ms 72.458 ms]	[162.33 ms 162.57 ms 162.90 ms]
256	[120.19 ms 120.50 ms 120.80 ms]	[207.36 ms 207.65 ms 207.90 ms]
512	[177.21 ms 177.69 ms 178.04 ms]	[255.12 ms 255.95 ms 256.74 ms]
1024	[318.83 ms 319.37 ms 319.88 ms]	[373.69 ms 374.70 ms 375.35 ms]
2048	[561.37 ms 563.03 ms 565.32 ms]	[564.12 ms 565.35 ms 566.25 ms]
4096	[939.41 ms 941.26 ms 944.20 ms]	[840.42 ms 842.35 ms 843.70 ms]
8192	[1.8037 s 1.8067 s 1.8101 s]	[1.4302 s 1.4327 s 1.4344 s]
32768	[7.4818 s 7.4935 s 7.5064 s]	[5.2018 s 5.2176 s 5.2342 s]
65536	[16.076 s 16.151 s 16.219 s]	[10.904 s 10.976 s 11.045 s]
131072	[38.577 s 38.758 s 38.927 s]	[27.012 s 27.167 s 27.336 s]

summary:

1. when the number of gate is lower than 2048, the serial version is faster than the parallel version. Because there are too many create and destroy of thread pool
2. when the number of gates is increasing, the performance of parallels is about 1.5 times that of serials.

[keyvank]

Beautifully written. Thank you! Though the speedup is much lower from what I expected. Only 1.5 times for a 64 core CPU? :( Feel free to merge yourself. LGTM 👍

[keyvank]

Ah, this is for whole proof. I thought its only for fft! That’s a good speedup for the start :)

[kwanCCC]

Thanks man. Yep, this is used as a universally adapted optimization for the whole proof. As I know, there are three implementations of PLONKish, dusk-network, bellman and the newest halo2, respectively. There are differences not only in implementation, but also in performance. For current repo, I think there are some further optimizations
including the GPU version like you said and making a gadget about aggregation of proofs. I would keep on doing this :)

[keyvank]

@kwanCCC Great job! Thanks man. Can you also check if different parts of the proof generation process can be done in parallel with each other? This also helps: dusk-network#680
Feel free to merge this yourself. Also, can you keep it rebased with original dusk-plonk repo?