[performance] monomial term arithmetics common term factorized

[hero78119]

Extract common factor in monomial arithmetics to improve gpu performance

benchmark

Only modify prove_main_constraint
Below shows in 23817600 first 3 shards keccak prove_main_constraint data

name	Before (ms)	After (ms)	Improvement
e2e	161s	158s
Shard 0th keccak prove_main_constraint	115.0	73.4	36.17%
Shard 1th keccak prove_main_constraint	119.0	76.8	35.46%
Shard 2th keccak prove_main_constraint	119.0	74.2	37.65%

circuit stats

Layer	Total Terms	Total Factors	Min	Max	Avg Factors	Groups	Factored %	Naive Mul	Factored Mul
ADD_main	25	51	1	3	2.04	3	88.00%	51	27
SUB_main	25	51	1	3	2.04	3	88.00%	51	27
AND_main	29	57	1	2	1.97	1	96.55%	57	29
OR_main	29	57	1	2	1.97	1	96.55%	57	29
XOR_main	29	57	1	2	1.97	1	96.55%	57	29
SLL_main	108	286	1	4	2.65	23	78.70%	286	134
SRL_main	117	317	1	4	2.71	24	79.49%	317	145
SRA_main	117	317	1	4	2.71	24	79.49%	317	145
SLT_main	57	149	1	4	2.61	13	77.19%	149	73
SLTU_main	57	149	1	4	2.61	13	77.19%	149	73
MUL_main	26	54	1	3	2.08	3	88.46%	54	28
MULH_main	37	83	1	3	2.24	5	86.49%	83	41
MULHSU_main	37	83	1	3	2.24	5	86.49%	83	41
MULHU_main	37	83	1	3	2.24	5	86.49%	83	41
DIVU_main	151	450	1	4	2.98	43	71.52%	450	218
REMU_main	151	450	1	4	2.98	43	71.52%	450	218
DIV_main	151	450	1	4	2.98	43	71.52%	450	218
REM_main	151	450	1	4	2.98	43	71.52%	450	218
ADDI_main	21	43	1	3	2.05	3	85.71%	43	23
ANDI_main	25	49	1	2	1.96	1	96.00%	49	25
ORI_main	25	49	1	2	1.96	1	96.00%	49	25
XORI_main	25	49	1	2	1.96	1	96.00%	49	25
SLLI_main	101	272	1	4	2.69	23	77.23%	272	127
SRLI_main	110	303	1	4	2.75	24	78.18%	303	138
SRAI_main	110	303	1	4	2.75	24	78.18%	303	138
SLTI_main	53	141	1	4	2.66	13	75.47%	141	69
SLTIU_main	53	141	1	4	2.66	13	75.47%	141	69
LUI_main	17	33	1	2	1.94	1	94.12%	33	17
AUIPC_main	69	184	1	3	2.67	11	84.06%	184	79
BEQ_main	30	69	1	3	2.30	5	83.33%	69	34
BNE_main	30	69	1	3	2.30	5	83.33%	69	34
BLT_main	54	144	1	4	2.67	14	74.07%	144	71
BLTU_main	54	144	1	4	2.67	14	74.07%	144	71
BGE_main	54	144	1	4	2.67	14	74.07%	144	71
BGEU_main	54	144	1	4	2.67	14	74.07%	144	71
JAL_main	14	27	1	2	1.93	1	92.86%	27	14
JALR_main	46	114	1	3	2.48	9	80.43%	114	54
LW_main	45	110	1	3	2.44	7	84.44%	110	51
LHU_main	50	123	1	3	2.46	8	84.00%	123	57
LH_main	52	128	1	3	2.46	9	82.69%	128	60
LBU_main	56	138	1	3	2.46	11	80.36%	138	66
LB_main	58	143	1	3	2.47	12	79.31%	143	69
SW_main	45	110	1	3	2.44	7	84.44%	110	51
SH_main	50	124	1	3	2.48	8	84.00%	124	57
SB_main	59	146	1	3	2.47	13	77.97%	146	71
ECALL_HALT_main	9	17	1	2	1.89	1	88.89%	17	9
Ecall_Keccak	2785	5595	1	3	2.01	34	98.89%	5595	2816
weierstrass_add	4512	11599	1	3	2.57	65	98.56%	11599	4576
weierstrass_double	5297	13697	1	3	2.59	97	98.17%	13697	5393
fp_add	3192	10242	1	4	3.21	1156	63.78%	10242	5371
fp_mul	3192	10242	1	4	3.21	1156	63.78%	10242	5371
fp2_add	1938	5124	1	3	2.64	194	89.99%	5124	2131
fp2_mul	6656	18527	1	3	2.78	129	98.06%	18527	6784
weierstrass_decompress	5332	14681	1	4	2.75	291	94.54%	14681	5686
secp256k1_scalar_invert	1877	5337	1	3	2.84	65	96.54%	5337	1941
secp256r1_scalar_invert	1877	5337	1	3	2.84	65	96.54%	5337	1941
uint256_mul	5298	17558	1	4	3.31	726	86.30%	17558	6615
DYNAMIC_RANGE_18	4	7	1	2	1.75	1	75.00%	7	4
DOUBLE_RANGE_DoubleU8	4	7	1	2	1.75	1	75.00%	7	4
And_OPS_ROM_TABLE	5	9	1	2	1.80	1	80.00%	9	5
Or_OPS_ROM_TABLE	5	9	1	2	1.80	1	80.00%	9	5
Xor_OPS_ROM_TABLE	5	9	1	2	1.80	1	80.00%	9	5
Ltu_OPS_ROM_TABLE	5	9	1	2	1.80	1	80.00%	9	5
RAM_Register_RegTable	4	7	1	2	1.75	1	75.00%	7	4
RAM_Memory_StaticMemTable	4	7	1	2	1.75	1	75.00%	7	4
RAM_Memory_PubIOTable	4	7	1	2	1.75	1	75.00%	7	4
HintsTable_Memory_RAM	4	7	1	2	1.75	1	75.00%	7	4
StackTable_Memory_RAM	2	3	1	2	1.50	1	50.00%	3	2
HeapTable_Memory_RAM	2	3	1	2	1.50	1	50.00%	3	2
LocalRAMTableFinal	6	11	1	2	1.83	1	83.33%	11	6
ShardRamCircuit_main	957	2778	1	4	2.90	542	43.36%	2778	1778
SHA256_EXTEND_main	530	1059	1	2	2.00	1	99.81%	1059	530
LOG_PC_CYCLE_main	26	51	1	2	1.96	1	96.15%	51	26
PROGRAM	9	17	1	2	1.89	1	88.89%	17	9