pub(crate) const LN_LUT_SEGMENTS: usize = 1024;
pub(crate) const LN_LUT_STEP: u128 = 976562500;
pub(crate) const LN_LUT_HALF_STEP: u128 = 488281250;
pub(crate) const LN_LUT_MID_LOG: [i64; LN_LUT_SEGMENTS] = [
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684072930679,
684565541527,
685057909828,
685550035823,
686041919748,
686533561842,
687024962344,
687516121489,
688007039516,
688497716660,
688988153158,
689478349246,
689968305160,
690458021135,
690947497405,
691436734205,
691925731770,
692414490333,
692903010128,
];
pub(crate) const LN_Q42_RECIP_G32: [i64; LN_LUT_SEGMENTS] = [
18880247061,
18861836288,
18843461387,
18825122252,
18806818779,
18788550863,
18770318403,
18752121293,
18733959432,
18715832718,
18697741048,
18679684320,
18661662435,
18643675290,
18625722787,
18607804823,
18589921301,
18572072121,
18554257184,
18536476391,
18518729645,
18501016847,
18483337901,
18465692710,
18448081177,
18430503205,
18412958700,
18395447564,
18377969704,
18360525025,
18343113432,
18325734831,
18308389128,
18291076231,
18273796045,
18256548479,
18239333441,
18222150837,
18205000578,
18187882571,
18170796725,
18153742951,
18136721157,
18119731254,
18102773153,
18085846764,
18068951998,
18052088767,
18035256983,
18018456557,
18001687402,
17984949432,
17968242558,
17951566695,
17934921756,
17918307655,
17901724307,
17885171626,
17868649528,
17852157927,
17835696739,
17819265881,
17802865268,
17786494817,
17770154445,
17753844070,
17737563607,
17721312976,
17705092095,
17688900881,
17672739254,
17656607133,
17640504436,
17624431083,
17608386995,
17592372091,
17576386292,
17560429518,
17544501691,
17528602731,
17512732561,
17496891103,
17481078277,
17465294008,
17449538217,
17433810828,
17418111764,
17402440948,
17386798305,
17371183757,
17355597231,
17340038650,
17324507939,
17309005024,
17293529829,
17278082281,
17262662306,
17247269830,
17231904778,
17216567080,
17201256660,
17185973446,
17170717367,
17155488349,
17140286322,
17125111212,
17109962949,
17094841462,
17079746679,
17064678530,
17049636945,
17034621853,
17019633184,
17004670869,
16989734839,
16974825023,
16959941354,
16945083762,
16930252178,
16915446536,
16900666766,
16885912801,
16871184574,
16856482016,
16841805062,
16827153644,
16812527696,
16797927151,
16783351943,
16768802006,
16754277275,
16739777684,
16725303168,
16710853662,
16696429101,
16682029421,
16667654557,
16653304446,
16638979023,
16624678224,
16610401987,
16596150248,
16581922944,
16567720012,
16553541390,
16539387015,
16525256825,
16511150759,
16497068754,
16483010749,
16468976683,
16454966494,
16440980122,
16427017506,
16413078586,
16399163301,
16385271592,
16371403397,
16357558659,
16343737316,
16329939311,
16316164584,
16302413075,
16288684727,
16274979482,
16261297279,
16247638063,
16234001774,
16220388355,
16206797749,
16193229899,
16179684746,
16166162235,
16152662308,
16139184909,
16125729982,
16112297471,
16098887319,
16085499471,
16072133871,
16058790464,
16045469194,
16032170007,
16018892848,
16005637661,
15992404393,
15979192990,
15966003396,
15952835558,
15939689422,
15926564935,
15913462043,
15900380694,
15887320833,
15874282408,
15861265366,
15848269655,
15835295222,
15822342015,
15809409983,
15796499072,
15783609232,
15770740411,
15757892557,
15745065620,
15732259548,
15719474290,
15706709796,
15693966015,
15681242897,
15668540392,
15655858449,
15643197019,
15630556052,
15617935498,
15605335308,
15592755432,
15580195823,
15567656430,
15555137205,
15542638099,
15530159064,
15517700051,
15505261013,
15492841901,
15480442668,
15468063266,
15455703647,
15443363764,
15431043569,
15418743016,
15406462058,
15394200648,
15381958739,
15369736284,
15357533238,
15345349555,
15333185187,
15321040090,
15308914218,
15296807524,
15284719964,
15272651491,
15260602062,
15248571631,
15236560153,
15224567583,
15212593876,
15200638989,
15188702877,
15176785495,
15164886800,
15153006748,
15141145295,
15129302396,
15117478010,
15105672092,
15093884599,
15082115488,
15070364717,
15058632241,
15046918019,
15035222008,
15023544166,
15011884450,
15000242818,
14988619228,
14977013638,
14965426007,
14953856292,
14942304453,
14930770447,
14919254234,
14907755772,
14896275020,
14884811938,
14873366485,
14861938620,
14850528302,
14839135492,
14827760149,
14816402232,
14805061702,
14793738519,
14782432643,
14771144035,
14759872655,
14748618463,
14737381420,
14726161488,
14714958626,
14703772797,
14692603960,
14681452079,
14670317113,
14659199025,
14648097776,
14637013329,
14625945644,
14614894684,
14603860411,
14592842787,
14581841774,
14570857336,
14559889435,
14548938032,
14538003092,
14527084577,
14516182449,
14505296673,
14494427212,
14483574028,
14472737085,
14461916347,
14451111777,
14440323340,
14429550999,
14418794718,
14408054461,
14397330193,
14386621877,
14375929479,
14365252962,
14354592292,
14343947433,
14333318350,
14322705008,
14312107372,
14301525408,
14290959079,
14280408353,
14269873194,
14259353567,
14248849439,
14238360776,
14227887542,
14217429705,
14206987230,
14196560084,
14186148232,
14175751641,
14165370277,
14155004108,
14144653100,
14134317219,
14123996432,
14113690707,
14103400010,
14093124309,
14082863570,
14072617762,
14062386851,
14052170806,
14041969593,
14031783180,
14021611536,
14011454628,
14001312424,
13991184892,
13981072001,
13970973719,
13960890014,
13950820854,
13940766208,
13930726045,
13920700334,
13910689043,
13900692141,
13890709597,
13880741381,
13870787461,
13860847806,
13850922387,
13841011173,
13831114132,
13821231235,
13811362452,
13801507752,
13791667104,
13781840480,
13772027849,
13762229181,
13752444446,
13742673616,
13732916659,
13723173547,
13713444249,
13703728738,
13694026983,
13684338956,
13674664626,
13665003966,
13655356946,
13645723537,
13636103711,
13626497438,
13616904691,
13607325441,
13597759658,
13588207316,
13578668385,
13569142837,
13559630644,
13550131779,
13540646212,
13531173917,
13521714865,
13512269028,
13502836380,
13493416891,
13484010536,
13474617286,
13465237114,
13455869992,
13446515894,
13437174793,
13427846660,
13418531470,
13409229195,
13399939809,
13390663284,
13381399594,
13372148713,
13362910614,
13353685270,
13344472655,
13335272743,
13326085507,
13316910922,
13307748960,
13298599597,
13289462806,
13280338561,
13271226836,
13262127606,
13253040845,
13243966528,
13234904628,
13225855121,
13216817980,
13207793181,
13198780699,
13189780507,
13180792582,
13171816897,
13162853429,
13153902152,
13144963040,
13136036071,
13127121217,
13118218456,
13109327763,
13100449112,
13091582480,
13082727842,
13073885173,
13065054450,
13056235649,
13047428745,
13038633713,
13029850531,
13021079175,
13012319619,
13003571841,
12994835817,
12986111523,
12977398936,
12968698031,
12960008786,
12951331178,
12942665182,
12934010775,
12925367934,
12916736637,
12908116859,
12899508579,
12890911772,
12882326416,
12873752488,
12865189966,
12856638826,
12848099046,
12839570603,
12831053475,
12822547639,
12814053073,
12805569754,
12797097660,
12788636769,
12780187059,
12771748507,
12763321091,
12754904790,
12746499581,
12738105442,
12729722352,
12721350289,
12712989230,
12704639155,
12696300042,
12687971869,
12679654614,
12671348257,
12663052775,
12654768148,
12646494354,
12638231371,
12629979180,
12621737758,
12613507084,
12605287138,
12597077899,
12588879345,
12580691456,
12572514211,
12564347589,
12556191570,
12548046133,
12539911257,
12531786922,
12523673107,
12515569792,
12507476957,
12499394581,
12491322644,
12483261125,
12475210006,
12467169264,
12459138882,
12451118837,
12443109112,
12435109684,
12427120536,
12419141646,
12411172996,
12403214565,
12395266334,
12387328283,
12379400393,
12371482644,
12363575017,
12355677492,
12347790050,
12339912672,
12332045339,
12324188030,
12316340728,
12308503413,
12300676066,
12292858668,
12285051200,
12277253643,
12269465978,
12261688186,
12253920249,
12246162149,
12238413865,
12230675380,
12222946675,
12215227732,
12207518532,
12199819056,
12192129287,
12184449206,
12176778794,
12169118033,
12161466906,
12153825394,
12146193478,
12138571141,
12130958366,
12123355132,
12115761424,
12108177223,
12100602511,
12093037270,
12085481483,
12077935132,
12070398199,
12062870667,
12055352517,
12047843733,
12040344297,
12032854192,
12025373400,
12017901904,
12010439686,
12002986729,
11995543016,
11988108530,
11980683254,
11973267170,
11965860262,
11958462512,
11951073904,
11943694420,
11936324044,
11928962759,
11921610548,
11914267394,
11906933280,
11899608191,
11892292108,
11884985016,
11877686898,
11870397738,
11863117518,
11855846224,
11848583837,
11841330342,
11834085723,
11826849963,
11819623045,
11812404955,
11805195675,
11797995190,
11790803483,
11783620538,
11776446340,
11769280872,
11762124119,
11754976064,
11747836692,
11740705987,
11733583933,
11726470515,
11719365716,
11712269521,
11705181915,
11698102881,
11691032405,
11683970470,
11676917062,
11669872165,
11662835764,
11655807842,
11648788385,
11641777378,
11634774805,
11627780652,
11620794902,
11613817541,
11606848553,
11599887924,
11592935639,
11585991682,
11579056039,
11572128695,
11565209635,
11558298843,
11551396306,
11544502008,
11537615934,
11530738071,
11523868403,
11517006915,
11510153593,
11503308423,
11496471390,
11489642479,
11482821676,
11476008967,
11469204337,
11462407771,
11455619256,
11448838777,
11442066320,
11435301870,
11428545414,
11421796938,
11415056426,
11408323865,
11401599242,
11394882541,
11388173750,
11381472853,
11374779838,
11368094689,
11361417394,
11354747939,
11348086309,
11341432491,
11334786472,
11328148237,
11321517772,
11314895065,
11308280102,
11301672868,
11295073351,
11288481537,
11281897413,
11275320964,
11268752178,
11262191042,
11255637541,
11249091663,
11242553394,
11236022721,
11229499631,
11222984110,
11216476146,
11209975725,
11203482835,
11196997461,
11190519591,
11184049213,
11177586313,
11171130877,
11164682894,
11158242350,
11151809233,
11145383529,
11138965225,
11132554310,
11126150770,
11119754593,
11113365765,
11106984274,
11100610108,
11094243254,
11087883700,
11081531432,
11075186438,
11068848706,
11062518224,
11056194978,
11049878957,
11043570148,
11037268539,
11030974117,
11024686870,
11018406787,
11012133854,
11005868059,
10999609391,
10993357837,
10987113385,
10980876023,
10974645738,
10968422520,
10962206355,
10955997232,
10949795139,
10943600064,
10937411995,
10931230921,
10925056828,
10918889706,
10912729542,
10906576326,
10900430044,
10894290686,
10888158240,
10882032694,
10875914036,
10869802256,
10863697340,
10857599278,
10851508058,
10845423669,
10839346099,
10833275337,
10827211371,
10821154190,
10815103782,
10809060136,
10803023241,
10796993086,
10790969659,
10784952949,
10778942944,
10772939635,
10766943008,
10760953054,
10754969760,
10748993117,
10743023112,
10737059736,
10731102976,
10725152822,
10719209262,
10713272287,
10707341884,
10701418044,
10695500754,
10689590005,
10683685785,
10677788084,
10671896890,
10666012194,
10660133984,
10654262249,
10648396980,
10642538164,
10636685793,
10630839854,
10625000337,
10619167232,
10613340529,
10607520216,
10601706283,
10595898720,
10590097516,
10584302661,
10578514145,
10572731956,
10566956085,
10561186521,
10555423254,
10549666274,
10543915570,
10538171133,
10532432951,
10526701014,
10520975313,
10515255838,
10509542577,
10503835522,
10498134662,
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10486751485,
10481069149,
10475392967,
10469722930,
10464059028,
10458401251,
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10447104031,
10441464569,
10435831192,
10430203890,
10424582654,
10418967473,
10413358339,
10407755240,
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10396567113,
10390982065,
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10363146592,
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10340985359,
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10318918706,
10313416750,
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10280527831,
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10264161907,
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10247848007,
10242421559,
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10220773112,
10215375291,
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10167050257,
10161709017,
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10087516617,
10082258595,
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10071758976,
10066517363,
10061281204,
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10045605356,
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10029978280,
10024780054,
10019587213,
10014399748,
10009217653,
10004040917,
9998869534,
9993703495,
9988542791,
9983387414,
9978237356,
9973092608,
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9962819013,
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9952566562,
9947448246,
9942335191,
9937227390,
9932124834,
9927027515,
9921935426,
9916848559,
9911766904,
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9901619203,
9896553141,
9891492260,
9886436552,
9881386010,
9876340625,
9871300390,
9866265297,
9861235337,
9856210504,
9851190789,
9846176184,
9841166682,
9836162275,
9831162955,
9826168714,
9821179545,
9816195440,
9811216390,
9806242390,
9801273430,
9796309503,
9791350602,
9786396718,
9781447845,
9776503975,
9771565099,
9766631211,
9761702303,
9756778368,
9751859397,
9746945384,
9742036320,
9737132199,
9732233013,
9727338755,
9722449416,
9717564991,
9712685470,
9707810848,
9702941116,
9698076267,
9693216294,
9688361189,
9683510946,
9678665556,
9673825013,
9668989310,
9664158438,
9659332391,
9654511162,
9649694744,
9644883128,
9640076309,
9635274278,
9630477030,
9625684555,
9620896848,
9616113902,
9611335709,
9606562262,
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9597029578,
9592270327,
9587515794,
9582765972,
9578020854,
9573280432,
9568544701,
9563813653,
9559087281,
9554365579,
9549648538,
9544936153,
9540228416,
9535525321,
9530826861,
9526133028,
9521443817,
9516759220,
9512079230,
9507403841,
9502733045,
9498066837,
9493405209,
9488748155,
9484095667,
9479447740,
9474804366,
9470165539,
9465531252,
9460901499,
9456276272,
9451655565,
9447039372,
];