[WIP] Direct to APC trace gen

[qwang98]

Not ready for review.

Depends on OVM branch: powdr-labs/openvm#50
Depends on Stark-Backend branch: powdr-labs/stark-backend#18

[qwang98]

Direct to APC Fibo:

                      filename  num_segments  app_proof_cells  app_proof_cols  total_proof_time_ms  app_proof_time_ms  app_execute_preflight_time_ms  app_execute_metered_time_ms  app_trace_gen_time_ms  leaf_proof_time_ms  inner_recursion_proof_time_ms  normal_instruction_ratio  openvm_precompile_ratio  powdr_ratio  powdr_rows
/home/steve/powdr/metrics.json             1          8009664            1221                   63                 63                              2                            0                    280                   0                              0                   0.00124                 0.986359     0.012401        1024

Direct to APC Keccak:

                      filename  num_segments  app_proof_cells  app_proof_cols  total_proof_time_ms  app_proof_time_ms  app_execute_preflight_time_ms  app_execute_metered_time_ms  app_trace_gen_time_ms  leaf_proof_time_ms  inner_recursion_proof_time_ms  normal_instruction_ratio  openvm_precompile_ratio  powdr_ratio  powdr_rows
/home/steve/powdr/metrics.json             1          8449287            6704                  139                139                              3                            0                    274                   0                              0                   0.01803                 0.961151     0.020819          32

[qwang98]

Using the 10,000 Keccak pass:

• Original: (1608 + 1689 + 1623 + 1653 + 1616 + 1647) / 6 = 1639.33
• Direct to APC: (1583 + 1561 + 1615 + 1579 + 1608 + 1546) / 6 = 1582
• Roughly a savings of 3.5%

Some thoughts:

• Note that the 3.5% savings is only with the ALU chip, which accounts for 318 out of 676 instructions in the sampled APC, so I'd say the actual savings of the current version should be ~7% once all chips are implemented.
• Also note that 7% savings is on the whole trace gen, while the actual savings on APC per se will be greater than that, because non-APC trace gen isn't changed at all. This said, Keccak also represents a "some what special" example, as I'd assume its APC (the compression function) takes a larger portion of all execution traces compared to APCs do in a more "realistic" example like Reth, so the overall savings on a real example on overall trace gen could be smaller than 7% as well.
• Might be larger gain after we imitate the "compile time constants"?
• I'd also raise the fact that trace gen doesn't affect overall proving time that much, at least on the Hetzner machine (it's only about 1/5 of the app proof time), but given its sequential nature, on a beefier machine it might account for a greater percentage of the proving (as the proving parts are more parallelized).

Direct to APC numbers:

                             filename  num_segments  app_proof_cells  app_proof_cols  total_proof_time_ms  app_proof_time_ms  app_execute_preflight_time_ms  app_execute_metered_time_ms  app_trace_gen_time_ms  leaf_proof_time_ms  inner_recursion_proof_time_ms  normal_instruction_ratio  openvm_precompile_ratio  powdr_ratio  powdr_rows
  /home/steve/powdr/keccak_100_1.json             1         40875092            6704                  206                206                             55                            6                    228                   0                              0                  0.250479                 0.198680     0.550842        4096
  /home/steve/powdr/keccak_100_2.json             1         40875092            6704                  205                205                             54                            6                    234                   0                              0                  0.250479                 0.198680     0.550842        4096
  /home/steve/powdr/keccak_100_3.json             1         40875092            6704                  227                227                             53                            6                    233                   0                              0                  0.250479                 0.198680     0.550842        4096
 /home/steve/powdr/keccak_1000_1.json             1        341980884            6704                  685                685                            510                           63                    152                   0                              0                  0.449540                 0.023747     0.526713       32768
 /home/steve/powdr/keccak_1000_2.json             1        341980884            6704                  678                678                            512                           63                    149                   0                              0                  0.449540                 0.023747     0.526713       32768
 /home/steve/powdr/keccak_1000_3.json             1        341980884            6704                  684                684                            511                           64                    151                   0                              0                  0.449540                 0.023747     0.526713       32768
/home/steve/powdr/keccak_10000_1.json             4       2760620370           26534                 5311               5311                           5035                          636                   1583                   0                              0                  0.466226                 0.011788     0.521986      262144
/home/steve/powdr/keccak_10000_2.json             4       2760620370           26534                 5345               5345                           4977                          647                   1561                   0                              0                  0.466226                 0.011788     0.521986      262144
/home/steve/powdr/keccak_10000_3.json             4       2760620370           26534                 5333               5333                           5062                          632                   1615                   0                              0                  0.466226                 0.011788     0.521986      262144
/home/steve/powdr/keccak_10000_4.json             4       2760620370           26534                 5304               5304                           5049                          634                   1579                   0                              0                  0.466226                 0.011788     0.521986      262144
/home/steve/powdr/keccak_10000_5.json             4       2760620370           26534                 5324               5324                           5069                          632                   1608                   0                              0                  0.466226                 0.011788     0.521986      262144
/home/steve/powdr/keccak_10000_6.json             4       2760620370           26534                 5314               5314                           5017                          641                   1546                   0                              0                  0.466226                 0.011788     0.521986      262144

Original numbers:

                                      filename  num_segments  app_proof_cells  app_proof_cols  total_proof_time_ms  app_proof_time_ms  app_execute_preflight_time_ms  app_execute_metered_time_ms  app_trace_gen_time_ms  leaf_proof_time_ms  inner_recursion_proof_time_ms  normal_instruction_ratio  openvm_precompile_ratio  powdr_ratio  powdr_rows
  /home/steve/powdr/keccak_original_100_1.json             1         40875092            6704                  196                196                             56                            6                    230                   0                              0                  0.250479                 0.198680     0.550842        4096
  /home/steve/powdr/keccak_original_100_2.json             1         40875092            6704                  199                199                             55                            6                    246                   0                              0                  0.250479                 0.198680     0.550842        4096
  /home/steve/powdr/keccak_original_100_3.json             1         40875092            6704                  195                195                             54                            6                    243                   0                              0                  0.250479                 0.198680     0.550842        4096
 /home/steve/powdr/keccak_original_1000_1.json             1        341980884            6704                  686                686                            518                           63                    149                   0                              0                  0.449540                 0.023747     0.526713       32768
 /home/steve/powdr/keccak_original_1000_2.json             1        341980884            6704                  675                675                            521                           63                    158                   0                              0                  0.449540                 0.023747     0.526713       32768
 /home/steve/powdr/keccak_original_1000_3.json             1        341980884            6704                  673                673                            520                           64                    153                   0                              0                  0.449540                 0.023747     0.526713       32768
/home/steve/powdr/keccak_original_10000_1.json             4       2760620370           26534                 5336               5336                           5164                          633                   1608                   0                              0                  0.466226                 0.011788     0.521986      262144
/home/steve/powdr/keccak_original_10000_2.json             4       2760620370           26534                 5358               5358                           5181                          643                   1689                   0                              0                  0.466226                 0.011788     0.521986      262144
/home/steve/powdr/keccak_original_10000_3.json             4       2760620370           26534                 5312               5312                           5152                          646                   1623                   0                              0                  0.466226                 0.011788     0.521986      262144
/home/steve/powdr/keccak_original_10000_4.json             4       2760620370           26534                 5314               5314                           5163                          645                   1653                   0                              0                  0.466226                 0.011788     0.521986      262144
/home/steve/powdr/keccak_original_10000_5.json             4       2760620370           26534                 5323               5323                           5185                          648                   1616                   0                              0                  0.466226                 0.011788     0.521986      262144
/home/steve/powdr/keccak_original_10000_6.json             4       2760620370           26534                 5312               5312                           5583                          642                   1647                   0                              0                  0.466226                 0.011788     0.521986      262144

Sample command run: cargo run --bin powdr_openvm -r --features metrics,cuda prove "guest-keccak" --input 10000 --autoprecompiles 1 --skip 0 --metrics "keccak_original_10000_3.json"