[perf] Optimize FriReducedOpeningChip

[nyunyunyunyu]

closes INT-3055

Reduced # of columns of FriReducedOpeningChip from 64 to 26. A side effect is that we use a more efficient way to compute alpha_pow.

Notes for reviewers:

• All meaningful changes are in extensions/native/circuit/src/fri/mod.rs. I rewrite everything so diff view is not helpful.
• The rows of the new implementation has 3 variants: WorkloadCols/ Instruction1Cols/ Instruction2Cols. I use lots of static assertions in order to guarantee that some columns in these variants are aligned.

WorkloadCols:

• 1 instruction has length rows of WorkloadCols.
• Each row reads a/b from memory and write local.result * local.alpha + b - a into next.result

Instruction1Cols:

• 1 instruction has only 1 row of Instruction1Cols after all WorkloadCols.
• This rows reads a_ptr/b_ptr/length/alpha and write local.result into local.result_ptr.
• We constraint a_ptr/b_ptr/alpha in WorkloadCols above are from this row.
• This rows also handle the PC interaction of the instruction.

Instruction2Cols:

• 1 instruction has only 1 row of Instruction2Cols after Instruction1Cols.
• This is just for some memory aux columns to reduce the overall width.

fib_e2e before this PR(ref):

Summary	Proof Time (s)	Parallel Proof Time (s)
Total	455.70	316.94
fib_e2e	41.24	6.33
leaf	55.94	8.36
internal.0	56.76	16.20
internal.1	31.91	16.20
internal.2	16.26	16.26
root	39.22	39.22
halo2_outer	168.55	168.55
halo2_wrapper	45.82	45.82

fib_e2e after this PR(ref):

Summary	Proof Time (s)	Parallel Proof Time (s)
Total	433.68	298.21
fib_e2e	40.31	6.25
leaf	54.28	8.29
internal.0	55.42	15.67
internal.1	31.41	15.73
internal.2	15.91	15.91
root	39.70	39.70
halo2_outer	155.79	155.79
halo2_wrapper	40.86	40.86

Proof time of some verifier drops ~30% but others keep same. I'm surprised halo2_outer proof time increases because the number column decreases.

[yi-sun]

Can you also update the ISA documentation?

[github-actions]

group	app.proof_time_ms	app.cycles	app.cells_used	leaf.proof_time_ms	leaf.cycles	leaf.cells_used
verify_fibair	(+113 [+5.0%]) 2,361	513,309	(-28071 [-0.1%]) 19,357,682	-	-	-
fibonacci_program	(+38 [+0.6%]) 6,109	1,500,137	51,487,838	(-94 [-1.2%]) 7,966	(-16002 [-0.9%]) 1,817,697	(-5225391 [-6.9%]) 70,261,826
regex_program	(-703 [-3.8%]) 17,821	4,190,904	165,010,909	(-2029 [-10.6%]) 17,127	(-21360 [-0.7%]) 3,007,473	(-21669219 [-13.3%]) 141,617,522
fib_e2e	40,273	12,000,137	410,699,582	54,976	11,373,351	435,143,222
ecrecover_program	(+5 [+0.2%]) 2,616	285,401	15,075,033	(-1145 [-5.1%]) 21,260	(-28047 [-0.7%]) 4,138,626	(-38606313 [-16.0%]) 202,803,516

Commit: 0ff18c5

Benchmark Workflow