Feat/sphere/fft mem opt

[lispc]

we plan to run some tests on this branch, if nothing is broken and mem usage indeed is optimized much, we will make a new `scroll-dev-01XX" branch since this is a big new feature

fyi @spherel

[spherel]

Here is a draft explaining this optimization. Actually there are two points in this draft:

1. partitioning the cosetFFT,
2. exploiting different gate degrees.

By now only the first one has been implemented.

[kunxian-xia]

By running the modified plonk_api test which accepts K as an input (by this branch), we get the following stats on gpu-cluster machine:
K = 25, the running time is 21min15s with peak memory 124GiB.

[2023-02-01T09:32:57Z INFO  plonk_api] [before load params] mem free: 987 GiB, mem available: 986 GiB
[2023-02-01T09:37:13Z INFO  plonk_api] [loaded params] mem free: 981 GiB, mem available: 982 GiB
[2023-02-01T09:37:13Z INFO  halo2_proofs::plonk::keygen] num_fixed_cols: 7
[2023-02-01T09:37:13Z INFO  halo2_proofs::plonk::keygen] permutation: 12 cols
[2023-02-01T09:37:13Z INFO  halo2_proofs::plonk::keygen] num_selectors: 0
[2023-02-01T09:41:13Z INFO  plonk_api] [keygen finished] mem free: 940 GiB, mem available: 941 GiB
[2023-02-01T09:45:36Z INFO  halo2_proofs::plonk::prover] [after phase1] mem free: 926 GiB, mem available: 927 GiB
[2023-02-01T09:46:23Z INFO  halo2_proofs::plonk::prover] [after phase2] mem free: 914 GiB, mem available: 915 GiB
[2023-02-01T09:49:01Z INFO  halo2_proofs::plonk::prover] [after phase3] mem free: 908 GiB, mem available: 909 GiB
[2023-02-01T09:56:24Z INFO  halo2_proofs::plonk::prover] [after quotient h] mem free: 898 GiB, mem available: 899 GiB
[2023-02-01T10:02:28Z INFO  plonk_api] [create proof] mem free: 909 GiB, mem available: 910 GiB
test plonk_api ... ok

test result: ok. 1 passed; 0 failed; 0 ignored; 0 measured; 0 filtered out; finished in 1775.39s

	Command being timed: "cargo test --release --test plonk_api -- --nocapture"
	User time (seconds): 96234.61
	System time (seconds): 353.93
	Percent of CPU this job got: 5383%
	Elapsed (wall clock) time (h:mm:ss or m:ss): 29:53.99
	Average shared text size (kbytes): 0
	Average unshared data size (kbytes): 0
	Average stack size (kbytes): 0
	Average total size (kbytes): 0
	Maximum resident set size (kbytes): 130144868
	Average resident set size (kbytes): 0
	Major (requiring I/O) page faults: 128
	Minor (reclaiming a frame) page faults: 285567295
	Voluntary context switches: 521405
	Involuntary context switches: 89166
	Swaps: 0
	File system inputs: 74872
	File system outputs: 5403512
	Socket messages sent: 0
	Socket messages received: 0
	Signals delivered: 0
	Page size (bytes): 4096
	Exit status: 0

Without this pr, the plonk_api test needs 17min42s but the peak memory is 280GiB.

[2023-02-01T10:17:05Z INFO  plonk_api] [before load params] mem free: 984 GiB, mem available: 986 GiB
[2023-02-01T10:17:30Z INFO  plonk_api] [loaded params] mem free: 980 GiB, mem available: 982 GiB
[2023-02-01T10:17:30Z INFO  halo2_proofs::plonk::keygen] num_fixed_cols: 7
[2023-02-01T10:17:30Z INFO  halo2_proofs::plonk::keygen] permutation: 12 cols
[2023-02-01T10:17:30Z INFO  halo2_proofs::plonk::keygen] num_selectors: 0
[2023-02-01T10:23:33Z INFO  plonk_api] [keygen finished] mem free: 853 GiB, mem available: 856 GiB
[2023-02-01T10:28:01Z INFO  halo2_proofs::plonk::prover] [after phase1] mem free: 839 GiB, mem available: 842 GiB
[2023-02-01T10:28:48Z INFO  halo2_proofs::plonk::prover] [after phase2] mem free: 827 GiB, mem available: 830 GiB
[2023-02-01T10:32:38Z INFO  halo2_proofs::plonk::prover] [after phase3] mem free: 773 GiB, mem available: 775 GiB
[2023-02-01T10:35:02Z INFO  halo2_proofs::plonk::prover] [after quotient h] mem free: 768 GiB, mem available: 770 GiB
[2023-02-01T10:41:15Z INFO  plonk_api] [create proof] mem free: 823 GiB, mem available: 825 GiB
test plonk_api ... ok

test result: ok. 1 passed; 0 failed; 0 ignored; 0 measured; 0 filtered out; finished in 1457.04s

	Command being timed: "cargo test --release --test plonk_api -- --nocapture"
	User time (seconds): 63374.62
	System time (seconds): 288.65
	Percent of CPU this job got: 4327%
	Elapsed (wall clock) time (h:mm:ss or m:ss): 24:31.17
	Average shared text size (kbytes): 0
	Average unshared data size (kbytes): 0
	Average stack size (kbytes): 0
	Average total size (kbytes): 0
	Maximum resident set size (kbytes): 293726392
	Average resident set size (kbytes): 0
	Major (requiring I/O) page faults: 2
	Minor (reclaiming a frame) page faults: 252937119
	Voluntary context switches: 232665
	Involuntary context switches: 61065
	Swaps: 0
	File system inputs: 2008
	File system outputs: 427840
	Socket messages sent: 0
	Socket messages received: 0
	Signals delivered: 0
	Page size (bytes): 4096
	Exit status: 0

[spherel]

It seems domain.coeff_to_extended() and domain.coeff_to_extended_parts have similar running time:
for k = 25, j = 8

domain.coeff_to_extended time: 20.481749943s
domain.coeff_to_extended_parts time: 20.976022433s

[lispc]

OK i will do some final review before merging

[spherel]

Add several features:

• Group constraints in clusters, with degree from 2^0 to 2^(extended_k - k), each only requires a subset of parts to recover the coefficient representation.
• Maintain used fixed, instance and advice columns in the current each cluster and avoid FFT calling for unnecessary columns when computing quotient polynomial h.

[mabbamOG]

Here is a draft explaining this optimization. Actually there are two points in this draft:

1. partitioning the cosetFFT,
2. exploiting different gate degrees.

By now only the first one has been implemented.

draft link is broken?

[spherel]

Here is a draft explaining this optimization. Actually there are two points in this draft:

1. partitioning the cosetFFT,
2. exploiting different gate degrees.

By now only the first one has been implemented.

draft link is broken?

Sorry, I am currently working on revising this blog post to provide a more comprehensive explanation and additional figures for better clarity. The updated version will be published soon.

[lispc]

merged