feat(avm)!: optimised poseidon2 permutation

Implements the "quad-gate" approach (although our K=56 for the avm) for the poseidon2 for lots of committed column savings!

the bb-pilcom changes are claude heavy but arent really used in the end because of the optimized file

Author: IlyasRidhuan

barretenberg/.gitignore

@@ -20,3 +20,4 @@ ts/src/cbind/generated/
 !cpp/src/barretenberg/flavor/generated/
 !cpp/src/barretenberg/vm2/generated/
 !cpp/src/barretenberg/honk/execution_trace/generated/
+!cpp/src/barretenberg/vm2/generated/

barretenberg/cpp/pil/vm2/poseidon2_params.pil

@@ -1,4 +1,5 @@
 // Values taken from barretenberg/crypto/poseidon2/poseidon2_params.hpp
+// More information can also be found at barretenberg/crypto/poseidon2/poseidon2_quad_params.hpp
 
 // Note: These constants are solely used in poseidon2_perm.pil but the latter
 //       is not re-generated when we run `bb_pil`. We manually optimized the
@@ -18,6 +19,21 @@ namespace poseidon2_params;
     pol MU_2 = 148936322117705719734052984176402258788283488576388928671173547788498414613;
     pol MU_3 = 15456385653678559339152734484033356164266089951521103188900320352052358038155;
 
+    // Closed-form constants for the K_BRIDGE=56 partial-round chain in
+    // poseidon2_perm.pil.
+    //
+    // Algebraic source:  M_3 = diag(MU_1, MU_2, MU_3) + 1·1^T  acts on the 3 linear
+    // lanes of one Poseidon2 internal round. M3_ii is the diagonal entry on lane i;
+    // off-diagonal entries are all 1 and inlined at use site.
+    //   M3_ii = MU_i + 1
+    //
+    // Soundness precondition: MU_1, MU_2, MU_3 must be pairwise distinct so the
+    // linear-lane evolution is uniquely solvable. Holds on BN254 with the
+    // parameters above.
+    pol M3_11 = MU_1 + 1;
+    pol M3_22 = MU_2 + 1;
+    pol M3_33 = MU_3 + 1;
+
     // Round constants
     // Naming scheme is c_{round_count}_{input_count} where the counts are zero-indexed
     // So the round constant applied in the 5th round to the 3rd input is c_4_2
@@ -44,284 +60,116 @@ namespace poseidon2_params;
     pol C_3_3 = 4573768376486344895797915946239137669624900197544620153250805961657870918727;
     // Round 5 constants
     pol C_4_0 = 5624865188680173294191042415227598609140934495743721047183803859030618890703;
-    pol C_4_1 = 0;
-    pol C_4_2 = 0;
-    pol C_4_3 = 0;
     // Round 6 constants
     pol C_5_0 = 8228252753786907198149068514193371173033070694924002912950645971088002709521;
-    pol C_5_1 = 0;
-    pol C_5_2 = 0;
-    pol C_5_3 = 0;
     // Round 7 constants
     pol C_6_0 = 17586714789554691446538331362711502394998837215506284064347036653995353304693;
-    pol C_6_1 = 0;
-    pol C_6_2 = 0;
-    pol C_6_3 = 0;
     // Round 8 constants
     pol C_7_0 = 12985198716830497423350597750558817467658937953000235442251074063454897365701;
-    pol C_7_1 = 0;
-    pol C_7_2 = 0;
-    pol C_7_3 = 0;
     // Round 9 constants
     pol C_8_0 = 13480076116139680784838493959937969792577589073830107110893279354229821035984;
-    pol C_8_1 = 0;
-    pol C_8_2 = 0;
-    pol C_8_3 = 0;
     // Round 10 constants
     pol C_9_0 = 480609231761423388761863647137314056373740727639536352979673303078459561332;
-    pol C_9_1 = 0;
-    pol C_9_2 = 0;
-    pol C_9_3 = 0;
     // Round 11 constants
     pol C_10_0 = 19503345496799249258956440299354839375920540225688429628121751361906635419276;
-    pol C_10_1 = 0;
-    pol C_10_2 = 0;
-    pol C_10_3 = 0;
     // Round 12 constants
     pol C_11_0 = 16837818502122887883669221005435922946567532037624537243846974433811447595173;
-    pol C_11_1 = 0;
-    pol C_11_2 = 0;
-    pol C_11_3 = 0;
     // Round 13 constants
     pol C_12_0 = 5492108497278641078569490709794391352213168666744080628008171695469579703581;
-    pol C_12_1 = 0;
-    pol C_12_2 = 0;
-    pol C_12_3 = 0;
     // Round 14 constants
     pol C_13_0 = 11365311159988448419785032079155356000691294261495515880484003277443744617083;
-    pol C_13_1 = 0;
-    pol C_13_2 = 0;
-    pol C_13_3 = 0;
     // Round 15 constants
     pol C_14_0 = 13876891705632851072613751905778242936713392247975808888614530203269491723653;
-    pol C_14_1 = 0;
-    pol C_14_2 = 0;
-    pol C_14_3 = 0;
     // Round 16 constants
     pol C_15_0 = 10660388389107698747692475159023710744797290186015856503629656779989214850043;
-    pol C_15_1 = 0;
-    pol C_15_2 = 0;
-    pol C_15_3 = 0;
     // Round 17 constants
     pol C_16_0 = 18876318870401623474401728758498150977988613254023317877612912724282285739292;
-    pol C_16_1 = 0;
-    pol C_16_2 = 0;
-    pol C_16_3 = 0;
     // Round 18 constants
     pol C_17_0 = 15543349138237018307536452195922365893694804703361435879256942490123776892424;
-    pol C_17_1 = 0;
-    pol C_17_2 = 0;
-    pol C_17_3 = 0;
     // Round 19 constants
     pol C_18_0 = 2839988449157209999638903652853828318645773519300826410959678570041742458201;
-    pol C_18_1 = 0;
-    pol C_18_2 = 0;
-    pol C_18_3 = 0;
     // Round 20 constants
     pol C_19_0 = 7566039810305694135184226097163626060317478635973510706368412858136696413063;
-    pol C_19_1 = 0;
-    pol C_19_2 = 0;
-    pol C_19_3 = 0;
     // Round 21 constants
     pol C_20_0 = 6344830340705033582410486810600848473125256338903726340728639711688240744220;
-    pol C_20_1 = 0;
-    pol C_20_2 = 0;
-    pol C_20_3 = 0;
     // Round 22 constants
     pol C_21_0 = 12475357769019880256619207099578191648078162511547701737481203260317463892731;
-    pol C_21_1 = 0;
-    pol C_21_2 = 0;
-    pol C_21_3 = 0;
     // Round 23 constants
     pol C_22_0 = 13337401254840718303633782478677852514218549070508887338718446132574012311307;
-    pol C_22_1 = 0;
-    pol C_22_2 = 0;
-    pol C_22_3 = 0;
     // Round 24 constants
     pol C_23_0 = 21161869193849404954234950798647336336709035097706159414187214758702055364571;
-    pol C_23_1 = 0;
-    pol C_23_2 = 0;
-    pol C_23_3 = 0;
     // Round 25 constants
     pol C_24_0 = 20671052961616073313397254362345395594858011165315285344464242404604146448678;
-    pol C_24_1 = 0;
-    pol C_24_2 = 0;
-    pol C_24_3 = 0;
     // Round 26 constants
     pol C_25_0 = 2772189387845778213446441819361180378678387127454165972767013098872140927416;
-    pol C_25_1 = 0;
-    pol C_25_2 = 0;
-    pol C_25_3 = 0;
     // Round 27 constants
     pol C_26_0 = 3339032002224218054945450150550795352855387702520990006196627537441898997147;
-    pol C_26_1 = 0;
-    pol C_26_2 = 0;
-    pol C_26_3 = 0;
     // Round 28 constants
     pol C_27_0 = 14919705931281848425960108279746818433850049439186607267862213649460469542157;
-    pol C_27_1 = 0;
-    pol C_27_2 = 0;
-    pol C_27_3 = 0;
     // Round 29 constants
     pol C_28_0 = 17056699976793486403099510941807022658662936611123286147276760381688934087770;
-    pol C_28_1 = 0;
-    pol C_28_2 = 0;
-    pol C_28_3 = 0;
     // Round 30 constants
     pol C_29_0 = 16144580075268719403964467603213740327573316872987042261854346306108421013323;
-    pol C_29_1 = 0;
-    pol C_29_2 = 0;
-    pol C_29_3 = 0;
     // Round 31 constants
     pol C_30_0 = 15582343953927413680541644067712456296539774919658221087452235772880573393376;
-    pol C_30_1 = 0;
-    pol C_30_2 = 0;
-    pol C_30_3 = 0;
     // Round 32 constants
     pol C_31_0 = 17528510080741946423534916423363640132610906812668323263058626230135522155749;
-    pol C_31_1 = 0;
-    pol C_31_2 = 0;
-    pol C_31_3 = 0;
     // Round 33 constants
     pol C_32_0 = 3190600034239022251529646836642735752388641846393941612827022280601486805721;
-    pol C_32_1 = 0;
-    pol C_32_2 = 0;
-    pol C_32_3 = 0;
     // Round 34 constants
     pol C_33_0 = 8463814172152682468446984305780323150741498069701538916468821815030498611418;
-    pol C_33_1 = 0;
-    pol C_33_2 = 0;
-    pol C_33_3 = 0;
     // Round 35 constants
     pol C_34_0 = 16533435971270903741871235576178437313873873358463959658178441562520661055273;
-    pol C_34_1 = 0;
-    pol C_34_2 = 0;
-    pol C_34_3 = 0;
     // Round 36 constants
     pol C_35_0 = 11845696835505436397913764735273748291716405946246049903478361223369666046634;
-    pol C_35_1 = 0;
-    pol C_35_2 = 0;
-    pol C_35_3 = 0;
     // Round 37 constants
     pol C_36_0 = 18391057370973634202531308463652130631065370546571735004701144829951670507215;
-    pol C_36_1 = 0;
-    pol C_36_2 = 0;
-    pol C_36_3 = 0;
     // Round 38 constants
     pol C_37_0 = 262537877325812689820791215463881982531707709719292538608229687240243203710;
-    pol C_37_1 = 0;
-    pol C_37_2 = 0;
-    pol C_37_3 = 0;
     // Round 39 constants
     pol C_38_0 = 2187234489894387585309965540987639130975753519805550941279098789852422770021;
-    pol C_38_1 = 0;
-    pol C_38_2 = 0;
-    pol C_38_3 = 0;
     // Round 40 constants
     pol C_39_0 = 19189656350920455659006418422409390013967064310525314160026356916172976152967;
-    pol C_39_1 = 0;
-    pol C_39_2 = 0;
-    pol C_39_3 = 0;
     // Round 41 constants
     pol C_40_0 = 15839474183930359560478122372067744245080413846070743460407578046890458719219;
-    pol C_40_1 = 0;
-    pol C_40_2 = 0;
-    pol C_40_3 = 0;
     // Round 42 constants
     pol C_41_0 = 1805019124769763805045852541831585930225376844141668951787801647576910524592;
-    pol C_41_1 = 0;
-    pol C_41_2 = 0;
-    pol C_41_3 = 0;
     // Round 43 constants
     pol C_42_0 = 323592203814803486950280155834638828455175703393817797003361354810251742052;
-    pol C_42_1 = 0;
-    pol C_42_2 = 0;
-    pol C_42_3 = 0;
     // Round 44 constants
     pol C_43_0 = 9780393509796825017346015868945480913627956475147371732521398519483580624282;
-    pol C_43_1 = 0;
-    pol C_43_2 = 0;
-    pol C_43_3 = 0;
     // Round 45 constants
     pol C_44_0 = 14009429785059642386335012561867511048847749030947687313594053997432177705759;
-    pol C_44_1 = 0;
-    pol C_44_2 = 0;
-    pol C_44_3 = 0;
     // Round 46 constants
     pol C_45_0 = 13749550162460745037234826077137388777330401847577727796245150843898019635981;
-    pol C_45_1 = 0;
-    pol C_45_2 = 0;
-    pol C_45_3 = 0;
     // Round 47 constants
     pol C_46_0 = 19497187499283431845443758879472819384797584633472792651343926414232528405311;
-    pol C_46_1 = 0;
-    pol C_46_2 = 0;
-    pol C_46_3 = 0;
     // Round 48 constants
     pol C_47_0 = 3708428802547661961864524194762556064568867603968214870300574294082023305587;
-    pol C_47_1 = 0;
-    pol C_47_2 = 0;
-    pol C_47_3 = 0;
     // Round 49 constants
     pol C_48_0 = 1339414413482882567499652761996854155383863472782829777976929310155400981782;
-    pol C_48_1 = 0;
-    pol C_48_2 = 0;
-    pol C_48_3 = 0;
     // Round 50 constants
     pol C_49_0 = 6396261245879814100794661157306877072718690153118140891315137894471052482309;
-    pol C_49_1 = 0;
-    pol C_49_2 = 0;
-    pol C_49_3 = 0;
     // Round 51 constants
     pol C_50_0 = 2069661495404347929962833138824526893650803079024564477269192079629046031674;
-    pol C_50_1 = 0;
-    pol C_50_2 = 0;
-    pol C_50_3 = 0;
     // Round 52 constants
     pol C_51_0 = 15793521554502133342917616035884588152451122589545915605459159078589855944361;
-    pol C_51_1 = 0;
-    pol C_51_2 = 0;
-    pol C_51_3 = 0;
     // Round 53 constants
     pol C_52_0 = 17053424498357819626596285492499512504457128907932827007302385782133229252374;
-    pol C_52_1 = 0;
-    pol C_52_2 = 0;
-    pol C_52_3 = 0;
     // Round 54 constants
     pol C_53_0 = 13658536470391360399708067455536748955260723760813498481671323619545320978896;
-    pol C_53_1 = 0;
-    pol C_53_2 = 0;
-    pol C_53_3 = 0;
     // Round 55 constants
     pol C_54_0 = 21546095668130239633971575351786704948662094117932406102037724221634677838565;
-    pol C_54_1 = 0;
-    pol C_54_2 = 0;
-    pol C_54_3 = 0;
     // Round 56 constants
     pol C_55_0 = 21411726238386979516934941789127061362496195649331822900487557574597304399109;
-    pol C_55_1 = 0;
-    pol C_55_2 = 0;
-    pol C_55_3 = 0;
     // Round 57 constants
     pol C_56_0 = 1944776378988765673004063363506638781964264107780425928778257145151172817981;
-    pol C_56_1 = 0;
-    pol C_56_2 = 0;
-    pol C_56_3 = 0;
     // Round 58 constants
     pol C_57_0 = 15590719714223718537172639598316570285163081746016049278954513732528516468773;
-    pol C_57_1 = 0;
-    pol C_57_2 = 0;
-    pol C_57_3 = 0;
     // Round 59 constants
     pol C_58_0 = 1351266421179051765004709939353170430290500926943038391678843253157009556309;
-    pol C_58_1 = 0;
-    pol C_58_2 = 0;
-    pol C_58_3 = 0;
     // Round 60 constants
     pol C_59_0 = 6772476224477167317130064764757502335545080109882028900432703947986275397548;
-    pol C_59_1 = 0;
-    pol C_59_2 = 0;
-    pol C_59_3 = 0;
     // Round 61 constants
     pol C_60_0 = 10670120969725161535937685539136065944959698664551200616467222887025111751992;
     pol C_60_1 = 4731853626374224678749618809759140702342195350742653173378450474772131006181;