rkepler 0.4.0

/*
Copyright (c) 2022 Peter Hristozov / Петър Христозов

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
*/

//! # References
//! Lainey V., Duriez L.,Vienne A.: 2006, Synthetic representation of the
//! Galilean satellites’ orbital motions from L1 ephemerides, A&A 456, 783–788
//! # Link
//! <https://ftp.imcce.fr/pub/ephem/satel/galilean/L1/L1.2/>

use crate::datetime::mjd;
use crate::frame::constant::GK;
use crate::math::angle::norm_dblpi;
use crate::math::matrix::mat_r::*;
use crate::math::vector::vec_p;
use crate::math::vector::vec_pv;
use crate::pos_eph::equ_orbit::OrbElem;
use crate::BodyId;

const AF1_A: [f64; 37 * 3] = [
    0.0000000762024588,
    0.36392902322306E+01,
    0.35644591656241E+01,
    0.0000000180900324,
    0.99554707056522E+00,
    0.71289183312483E+01,
    0.0000000172337652,
    0.18196487820921E+01,
    0.17822295777568E+01,
    0.0000000101726080,
    0.28150559763861E+01,
    0.89111478635073E+01,
    0.0000000094794086,
    0.34760224933239E+01,
    0.80200331112799E+01,
    0.0000000092196266,
    0.46347004953370E+01,
    0.10693377436209E+02,
    0.0000000058581604,
    0.11586746335276E+01,
    0.26733443704266E+01,
    -0.0000000036218148,
    0.23173675289588E+01,
    0.53466887181044E+01,
    0.0000000034892754,
    0.17122470613669E+00,
    0.12475607079684E+02,
    0.0000000030842852,
    0.36170311370435E+01,
    0.63501320826717E+01,
    0.0000000020794650,
    0.19906655633153E+01,
    0.14257836656755E+02,
    0.0000000013655244,
    0.49369712857369E+01,
    0.13584836518140E-01,
    0.0000000011682572,
    0.57934065580556E+01,
    0.13366721796637E+02,
    -0.0000000008031976,
    0.66879731833041E+00,
    0.16040066232595E+02,
    0.0000000007309510,
    0.56300556878949E+01,
    0.17822295806244E+02,
    0.0000000007014118,
    0.43297377080515E+01,
    0.71002044886497E+01,
    0.0000000006561624,
    0.43188797534991E+01,
    0.13034138433510E-01,
    0.0000000005753088,
    0.54252179509841E+01,
    0.95251981240076E+01,
    0.0000000004359548,
    0.11670110887440E+01,
    0.19604525331797E+02,
    0.0000000003711992,
    0.14936154077537E+01,
    0.12938928912340E-01,
    -0.0000000003412576,
    0.26346374300664E+01,
    0.15571117257960E-01,
    0.0000000003432980,
    0.17994723387341E+01,
    0.31750663461810E+01,
    0.0000000003228344,
    0.29861854159944E+01,
    0.21386754933987E+02,
    0.0000000003014418,
    0.19871924348983E+00,
    0.24675315510310E-01,
    0.0000000001707670,
    0.50718778620273E+01,
    0.35514255456604E+01,
    0.0000000001655832,
    0.29783205832994E+01,
    0.44555739317536E+01,
    0.0000000001612910,
    0.48058392680935E+01,
    0.23168984521460E+02,
    0.0000000001527992,
    0.18275651107267E+01,
    0.18713410599600E+02,
    0.0000000001523312,
    0.46323297275220E+01,
    0.44686092108182E+01,
    0.0000000001449720,
    0.19079860214667E+01,
    0.30506511533200E-02,
    0.0000000001188688,
    0.53321680658912E+01,
    0.70987549449082E+01,
    0.0000000001129258,
    0.95031497804420E+00,
    0.12700264165343E+02,
    0.0000000000986086,
    0.34190944178580E+00,
    0.24951214111224E+02,
    -0.0000000000877720,
    0.36228267942948E+01,
    0.17958145576535E+01,
    0.0000000000857194,
    0.33682834215727E+01,
    0.59736711266730E+01,
    -0.0000000000545492,
    0.19473964103154E+01,
    0.22929425718040E-01,
    0.0000000000326102,
    0.24880420823571E+01,
    0.25119610718870E-01,
];
const AF1_LT: [f64; 2] = [0.1446213296021224E+01, 0.3551552286182400E+01];
const AF1_L: [f64; 32 * 3] = [
    -0.0001925258348666,
    0.49369589722645E+01,
    0.13584836583050E-01,
    -0.0000970803596076,
    0.43188796477322E+01,
    0.13034138432430E-01,
    -0.0000898817416500,
    0.19080016428617E+01,
    0.30506486715800E-02,
    -0.0000553101050262,
    0.14936156681569E+01,
    0.12938928911550E-01,
    -0.0000503584426150,
    0.36410196089987E+01,
    0.35644591049605E+01,
    -0.0000444412770116,
    0.18196478828985E+01,
    0.17822295777568E+01,
    0.0000418078870490,
    0.26346334480977E+01,
    0.15571117221300E-01,
    0.0000372356597388,
    0.21402440902650E+01,
    0.14500977488900E-02,
    -0.0000234440533016,
    0.19871945729267E+00,
    0.24675315507400E-01,
    -0.0000160313164240,
    0.28203470990931E+01,
    0.95196190000000E-04,
    -0.0000119049755698,
    0.99521552502799E+00,
    0.71289183312483E+01,
    -0.0000109014269320,
    0.11586742711973E+01,
    0.26733443704266E+01,
    0.0000087217118104,
    0.22995085327344E+01,
    0.44456805185000E-03,
    0.0000082229455492,
    0.84723690387904E+00,
    0.54980078903000E-03,
    0.0000075365481720,
    0.30644603245150E+01,
    0.64826749624000E-03,
    -0.0000061452803962,
    0.28150499448772E+01,
    0.89111478635073E+01,
    -0.0000057575824778,
    0.34760236756099E+01,
    0.80200331112799E+01,
    -0.0000053196302672,
    0.14952058549171E+01,
    0.29001290992300E-02,
    -0.0000051181206936,
    0.46347077042449E+01,
    0.10693377436209E+02,
    -0.0000047817413326,
    0.49236512419835E+01,
    0.30554833877800E-02,
    0.0000045554015322,
    0.19585097634352E+01,
    0.22928625941210E-01,
    0.0000043204134698,
    0.15842888614383E+01,
    0.15677112478190E-01,
    0.0000037684098282,
    0.23173652780077E+01,
    0.53466887181044E+01,
    -0.0000031403738248,
    0.22184076281042E+01,
    0.25155489165510E-01,
    0.0000024336535428,
    0.85320650238886E+00,
    0.25426968834400E-02,
    -0.0000020289901692,
    0.36168998565188E+01,
    0.63501320826717E+01,
    0.0000018665438704,
    0.48458061649481E+01,
    0.13589674898130E-01,
    -0.0000018552431038,
    0.17086811529922E+00,
    0.12475607079684E+02,
    -0.0000016229875536,
    0.62803206871082E+01,
    0.60414171604000E-03,
    -0.0000013160987604,
    0.14718125754925E+01,
    0.14358460012320E-01,
    0.0000008070729808,
    0.38735416148641E+00,
    0.37658680379100E-02,
    0.0000002602397658,
    0.14337589305551E+01,
    0.45692429208000E-02,
];
const TCH1_L: [f64; 9] = [
    0.826698820334074E-04,
    -0.546986318473484E-05,
    0.594965634346142E-04,
    -0.110076009434021E-04,
    -0.575048718532862E-05,
    0.574994024502453E-05,
    0.178506935927118E-05,
    -0.240677412003469E-05,
    -0.138513209122323E-05,
];
const AF1_Z: [f64; 23 * 3] = [
    0.0041510849668155,
    0.40899396355450E+01,
    -0.12906864146660E-01,
    0.0006260521444113,
    0.14461888986270E+01,
    0.35515522949802E+01,
    0.0000352747346169,
    0.21256287034578E+01,
    0.12727416567000E-03,
    0.0000198194483636,
    0.55835619926762E+01,
    0.32065751140000E-04,
    0.0000146399842989,
    0.44137212696837E+00,
    0.26642533547700E-02,
    0.0000098749504021,
    0.45076118781320E+00,
    -0.35773660260022E+01,
    -0.0000096819265753,
    0.59097266550442E+01,
    0.17693227079462E+01,
    -0.0000083063168209,
    0.28751474873012E+00,
    0.87820791951527E+00,
    0.0000059689735869,
    0.50740752477871E+01,
    0.71160118048918E+01,
    -0.0000052220588690,
    0.27460731023666E+01,
    0.67796100936000E-03,
    0.0000046538995236,
    0.49143203339385E+01,
    -0.53595956184347E+01,
    0.0000045951340101,
    0.42533513770304E+01,
    -0.44684808200578E+01,
    -0.0000037711061757,
    0.54120093562773E+01,
    -0.17951364445825E+01,
    0.0000037405126681,
    0.30946737347297E+01,
    -0.71418251640916E+01,
    0.0000022044764663,
    0.54360702580001E+01,
    -0.26491700241240E-01,
    0.0000018698303790,
    0.41124042914226E+01,
    -0.27985797954589E+01,
    -0.0000015410375360,
    0.27141931505529E+01,
    0.27731236679900E-02,
    0.0000013214613496,
    0.12750177723530E+01,
    -0.89240547799787E+01,
    -0.0000012707585609,
    0.51141075152507E+01,
    0.37654227378982E+00,
    0.0000012193607962,
    0.59977053365953E+01,
    -0.98566169956900E-02,
    -0.0000011886104747,
    0.32658350285168E+01,
    0.53337818460633E+01,
    0.0000008742035177,
    0.23903528311144E+01,
    0.25194921818800E-02,
    -0.0000007689215742,
    0.38308837306225E+01,
    -0.27293225500100E-02,
];
const TCH1_K: [f64; 9] = [
    -0.133581115495368E-06,
    -0.758579668623469E-08,
    -0.173800453537518E-08,
    -0.302381800276162E-08,
    -0.721047445746571E-08,
    -0.392259073275152E-09,
    -0.416879673796892E-08,
    -0.329083173926104E-08,
    0.288537255009037E-08,
];
const TCH1_H: [f64; 9] = [
    -0.447550080805276E-07,
    -0.578177122641661E-09,
    -0.535142525086474E-08,
    0.102942385189608E-09,
    -0.849040607452073E-08,
    -0.252840670456370E-08,
    -0.613405545173217E-08,
    -0.343800069555589E-08,
    -0.359984191898440E-08,
];
const AF1_ZETA: [f64; 15 * 3] = [
    0.0003142172466014,
    0.27964219722923E+01,
    -0.23150960980000E-02,
    0.0000904169207946,
    0.10477061879627E+01,
    -0.56920638196000E-03,
    0.0000175695395780,
    0.24150809680215E+01,
    0.00000000000000E+00,
    0.0000164452324013,
    0.33368861773902E+01,
    -0.12491307197000E-03,
    0.0000055424829091,
    0.59720202381027E+01,
    -0.30561164720000E-04,
    0.0000035856270353,
    0.84898736841329E+00,
    -0.25244521900630E-01,
    0.0000024180760140,
    0.55603770950923E+01,
    0.29003681445800E-02,
    -0.0000008673084930,
    0.28496686106299E+00,
    -0.14500593353200E-02,
    -0.0000003176227277,
    0.53834633036029E+01,
    -0.23498632298700E-01,
    0.0000003152816608,
    0.45569499027478E+01,
    0.43504654304000E-02,
    0.0000002338676726,
    0.17633292120047E+01,
    0.14501339138600E-02,
    0.0000001754553689,
    0.48429319984493E+01,
    -0.25688816532440E-01,
    0.0000001286319583,
    0.57543347143871E+01,
    -0.25813660979740E-01,
    0.0000000967213304,
    0.11503592426900E+01,
    -0.29001471397800E-02,
    0.0000000000692310,
    0.40745966852008E+01,
    -0.32506757319070E-01,
];
const TCH1_Q: [f64; 9] = [
    -0.291234929817703E-06,
    -0.162905002759586E-06,
    -0.368431020234090E-08,
    0.777164290527916E-09,
    0.159932283427177E-08,
    -0.228491296590504E-08,
    0.703033944342130E-09,
    -0.289289190860300E-10,
    0.486451562749639E-09,
];
const TCH1_P: [f64; 9] = [
    -0.317117027043262E-06,
    -0.126321744097649E-06,
    0.651758518535435E-08,
    0.262070675646012E-08,
    0.259238370832140E-08,
    -0.726318061740534E-09,
    -0.118191642174809E-08,
    0.590816038543625E-09,
    0.123053999757825E-08,
];

const AF2_A: [f64; 37 * 3] = [
    0.0000004324367498,
    0.18196456062910E+01,
    0.17822295777568E+01,
    0.0000001603614750,
    0.43002726529577E+01,
    0.26733443704266E+01,
    -0.0000001019146786,
    0.54589480865442E+01,
    0.53466887181044E+01,
    0.0000000924734786,
    0.56222139048906E+01,
    0.89111478887838E+00,
    -0.0000000523665800,
    0.36392846323417E+01,
    0.35644591656241E+01,
    0.0000000511509000,
    0.29783307371014E+01,
    0.44555739317536E+01,
    -0.0000000311907780,
    0.99466557754027E+00,
    0.71289183312483E+01,
    -0.0000000272859938,
    0.28144480309092E+01,
    0.89111478635073E+01,
    0.0000000232225828,
    0.62608434364366E+01,
    0.27856729211550E+01,
    -0.0000000181310770,
    0.43188692380649E+01,
    0.13034138308860E-01,
    0.0000000174960544,
    0.16563941638726E+01,
    0.62378035398422E+01,
    -0.0000000122874072,
    0.46421290370833E+01,
    0.10693377254218E+02,
    -0.0000000095367130,
    0.14936536615312E+01,
    0.12938928820690E-01,
    -0.0000000084863836,
    0.17146854643555E+00,
    0.12475607079684E+02,
    0.0000000071939342,
    0.49376739095661E+01,
    0.13584833017030E-01,
    0.0000000069122354,
    0.62488746138492E+01,
    0.41785094280464E+01,
    0.0000000061377568,
    0.33434976298081E+00,
    0.80200331112799E+01,
    -0.0000000045343054,
    0.19892156959655E+01,
    0.14257836656755E+02,
    0.0000000044574684,
    0.34597804303324E+00,
    0.35357692227539E+01,
    0.0000000042350072,
    0.62719655202169E+01,
    0.13928364636651E+01,
    -0.0000000028783772,
    0.38108811302610E+01,
    0.16040066232595E+02,
    0.0000000024354662,
    0.99587190880214E+00,
    0.90414989297380E+00,
    0.0000000022532940,
    0.52958965893939E+01,
    0.98022627054664E+01,
    0.0000000021573570,
    0.62379050559630E+01,
    0.55713458670107E+01,
    -0.0000000016530062,
    0.56456686036734E+01,
    0.17822294694543E+02,
    0.0000000016464798,
    0.26346435392424E+01,
    0.15571117126760E-01,
    0.0000000011589838,
    0.32732388195745E+01,
    0.17691951440716E+01,
    -0.0000000010251826,
    0.19079858535660E+01,
    0.30506497838200E-02,
    -0.0000000010203510,
    0.11692020351116E+01,
    0.19604525194172E+02,
    0.0000000007614982,
    0.16862812414995E+01,
    0.35342961443230E+01,
    0.0000000007104494,
    0.59112717191092E+01,
    0.24092214574831E+01,
    -0.0000000006957184,
    0.24879412197796E+01,
    0.25119609730670E-01,
    -0.0000000005817914,
    0.19872303312324E+00,
    0.24675315511270E-01,
    -0.0000000003792178,
    0.15765189821595E+01,
    0.25244441830200E-01,
    0.0000000003397378,
    0.58126953372535E+01,
    0.25973067138760E-01,
    0.0000000003159492,
    0.23545476741301E+01,
    0.26068277099550E-01,
    0.0000000002538154,
    0.19471441186087E+01,
    0.22929424919760E-01,
];
const AF2_LT: [f64; 2] = [-0.3735263437471362E+00, 0.1769322711123470E+01];
const AF2_L: [f64; 36 * 3] = [
    0.0008576433172936,
    0.43188693178264E+01,
    0.13034138308050E-01,
    0.0004549582875086,
    0.14936531751079E+01,
    0.12938928819620E-01,
    0.0003248939825174,
    0.18196494533458E+01,
    0.17822295777568E+01,
    -0.0003074250079334,
    0.49377037005911E+01,
    0.13584832867240E-01,
    0.0001982386144784,
    0.19079869054760E+01,
    0.30510121286900E-02,
    0.0001834063551804,
    0.21402853388529E+01,
    0.14500978933800E-02,
    -0.0001434383188452,
    0.56222140366630E+01,
    0.89111478887838E+00,
    -0.0000771939140944,
    0.43002724372350E+01,
    0.26733443704266E+01,
    -0.0000632289777196,
    0.26346392822098E+01,
    0.15571117084700E-01,
    0.0000446766477388,
    0.54589448561143E+01,
    0.53466887181044E+01,
    0.0000436574731410,
    0.36392908617709E+01,
    0.35644591656241E+01,
    0.0000349172750296,
    0.28289867162553E+01,
    0.29885749150000E-04,
    -0.0000325709094646,
    0.53721409780230E+01,
    0.12495233774000E-03,
    0.0000205826473860,
    0.15258464215508E+01,
    0.29001315522200E-02,
    -0.0000192706087556,
    0.29783311531879E+01,
    0.44555739317536E+01,
    0.0000168028316254,
    0.24879414119403E+01,
    0.25119609725650E-01,
    -0.0000141628733606,
    0.29183576504413E+01,
    0.64930403718000E-03,
    0.0000140713155600,
    0.19872319369353E+00,
    0.24675315510310E-01,
    0.0000131946915760,
    0.99584744364935E+00,
    0.71289183312483E+01,
    0.0000106598617620,
    0.53356907396678E+01,
    0.30233219231900E-02,
    -0.0000104011727738,
    0.62608296198866E+01,
    0.27856729211550E+01,
    0.0000100746080234,
    0.44288900030073E+01,
    0.55297871931000E-03,
    0.0000097414019416,
    0.27312462188296E+01,
    0.89111510230745E+01,
    -0.0000094651366640,
    0.25010358163865E+01,
    0.93478322470000E-04,
    0.0000091108073324,
    0.15765182522628E+01,
    0.25244441682120E-01,
    -0.0000087720567668,
    0.15376962386886E+01,
    0.15676393315070E-01,
    -0.0000078429703340,
    0.58128473756772E+01,
    0.25973069246350E-01,
    -0.0000075566039418,
    0.30586251688920E+01,
    0.43252872559000E-03,
    -0.0000066580990752,
    0.19591270593390E+01,
    0.22928567412490E-01,
    -0.0000065854142774,
    0.18617673337640E+01,
    0.26093058384670E-01,
    -0.0000058131135230,
    0.16563893807978E+01,
    0.62378035398422E+01,
    0.0000055720865276,
    0.39565695752204E+01,
    0.25481216339900E-02,
    -0.0000048198508906,
    0.62720230965345E+01,
    0.13928364605775E+01,
    0.0000042728431266,
    0.46220912946918E+01,
    0.10693377982182E+02,
    0.0000042175545304,
    0.13509343368359E+01,
    0.30164435787800E-02,
    0.0000037707624520,
    0.51034507119889E+01,
    0.25219658202250E-01,
];
const TCH2_L: [f64; 9] = [
    -0.234691437046728E-03,
    0.259036121717763E-04,
    -0.173835841495123E-03,
    0.380673357683932E-04,
    -0.103485888270120E-06,
    0.117376776995138E-04,
    0.319509608989603E-05,
    -0.483167496026174E-05,
    0.447094431509368E-06,
];

const AF2_Z: [f64; 41 * 3] = [
    -0.0093589104136341,
    0.40899396509039E+01,
    -0.12906864146660E-01,
    0.0002988994545555,
    0.59097265185595E+01,
    0.17693227079462E+01,
    0.0002139036390350,
    0.21256289300016E+01,
    0.12727418407000E-03,
    0.0001980963564781,
    0.27435168292650E+01,
    0.67797343009000E-03,
    0.0001210388158965,
    0.55839943711203E+01,
    0.32056614900000E-04,
    0.0000837042048393,
    0.16094538368039E+01,
    -0.90402165808846E+00,
    0.0000823525166369,
    0.14461887708689E+01,
    0.35515522949802E+01,
    -0.0000315906532820,
    0.28751224400811E+00,
    0.87820791951527E+00,
    -0.0000294503681314,
    0.45078002968967E+00,
    -0.35773660260022E+01,
    -0.0000278946698536,
    0.22704374310903E+01,
    -0.17951364497113E+01,
    0.0000144958688621,
    0.29313956641719E+01,
    -0.26862512422390E+01,
    0.0000139052321679,
    0.60542576187622E+01,
    -0.25941002404500E-01,
    0.0000108374431350,
    0.59320761116863E+01,
    -0.10163502160128E+01,
    -0.0000082175838585,
    0.49144730088838E+01,
    -0.53595956184347E+01,
    0.0000073925894084,
    0.25962855881215E+01,
    -0.25845792927870E-01,
    0.0000062618381566,
    0.62252936384007E+01,
    -0.71418248393794E+01,
    -0.0000051968296512,
    0.54353355159239E+01,
    -0.26491696725040E-01,
    -0.0000043507065743,
    0.51150292346242E+01,
    0.37654221060604E+00,
    0.0000042081682285,
    0.31202613836361E+01,
    0.44427230757158E+01,
    0.0000041298266970,
    0.42533371370636E+01,
    -0.44684808200578E+01,
    -0.0000036991221930,
    0.52487564172390E+01,
    0.26604375002057E+01,
    -0.0000027357551003,
    0.12734806685602E+01,
    -0.89240546532297E+01,
    -0.0000026854901206,
    0.75596663258784E+00,
    0.15806953180460E-01,
    0.0000023074479953,
    0.19438998534712E+01,
    0.71160114825227E+01,
    0.0000020163445050,
    0.58484195254467E+01,
    -0.24091843401454E+01,
    -0.0000018506530067,
    0.26838225102582E+01,
    0.68236609075000E-03,
    0.0000018159137522,
    0.26048690461733E+01,
    0.62248966818788E+01,
    -0.0000017894118824,
    0.57385537790777E+01,
    -0.10706284328884E+02,
    0.0000016518864520,
    0.32658492478888E+01,
    0.53337818460633E+01,
    -0.0000015660692561,
    0.61789350505156E+01,
    -0.11453588847960E-01,
    0.0000014426949422,
    0.60014075911383E+01,
    -0.17664769149811E+01,
    0.0000013196935928,
    0.55753025652974E+01,
    -0.62507103665413E+01,
    -0.0000011726743714,
    0.50242932747650E+01,
    -0.14351210704140E-01,
    -0.0000009550285338,
    0.28409403047363E+01,
    0.14257595044900E-02,
    -0.0000007569857746,
    0.38098760906143E+01,
    -0.27271627793800E-02,
    -0.0000007495662748,
    0.29896372346394E+01,
    0.20097553243900E-02,
    0.0000007091149133,
    0.27139331814919E+01,
    -0.19924932783300E-02,
    0.0000005646670312,
    0.21683602575236E+01,
    -0.12871803232940E-01,
    -0.0000002004455524,
    0.12893849410519E+01,
    -0.32724923477800E-02,
    -0.0000001623489363,
    0.24189454629613E+00,
    0.44609337678800E-02,
    0.0000001058862562,
    0.45356953407129E+01,
    0.39269908172100E-02,
];
const TCH2_K: [f64; 9] = [
    -0.100355398526925E-05,
    -0.580438343691240E-07,
    0.380875695145265E-07,
    -0.210657418625019E-06,
    0.312238251072476E-06,
    -0.172444072203130E-06,
    0.235985832098386E-06,
    0.613727340553035E-07,
    -0.158131098756712E-06,
];
const TCH2_H: [f64; 9] = [
    -0.261024960215820E-06,
    -0.182656275716032E-06,
    0.278016374834476E-07,
    -0.158858363289506E-06,
    0.231850746815330E-07,
    -0.110691155968765E-06,
    -0.369048459423356E-07,
    0.678631069587260E-08,
    0.190777145516695E-07,
];

const AF2_ZETA: [f64; 25 * 3] = [
    0.0040404917832303,
    0.10477063169425E+01,
    -0.56920640540000E-03,
    0.0002200421034564,
    0.33368857864364E+01,
    -0.12491307307000E-03,
    0.0001662544744719,
    0.24134862374711E+01,
    0.00000000000000E+00,
    0.0000590282470983,
    0.59719930968366E+01,
    -0.30561602250000E-04,
    -0.0000105030331400,
    0.27964978379152E+01,
    -0.23150966123800E-02,
    -0.0000102943248250,
    0.84898796322150E+00,
    -0.25244521901650E-01,
    0.0000072600013020,
    0.55603730312676E+01,
    0.29003676713100E-02,
    0.0000018391258758,
    0.28480515491153E+00,
    -0.14500579196900E-02,
    0.0000014880605763,
    0.48429974929766E+01,
    -0.25688815138710E-01,
    -0.0000008828196274,
    0.65011185407635E+00,
    0.34696170683100E-02,
    0.0000008714042768,
    0.17639430319108E+01,
    0.14501352157600E-02,
    0.0000008536188044,
    0.45568506666427E+01,
    0.43504641410100E-02,
    0.0000006846214331,
    0.57542117253981E+01,
    -0.25813768702630E-01,
    0.0000004471826348,
    0.53834694321520E+01,
    -0.23498632366370E-01,
    0.0000003034392168,
    0.22078201315180E+01,
    -0.25783170906020E-01,
    0.0000001799083735,
    0.31858868501531E+01,
    0.88086056517000E-03,
    -0.0000001792048645,
    0.51949494917342E+01,
    -0.20193236931900E-02,
    -0.0000001098546626,
    0.59286821904995E+01,
    0.49197316579700E-02,
    -0.0000001083128732,
    0.45808061408794E+01,
    -0.59959459406000E-03,
    0.0000001062153531,
    0.38387102863271E+01,
    -0.53795085847000E-03,
    0.0000000768496749,
    0.35553768729770E+01,
    0.58005587812700E-02,
    -0.0000000692273841,
    0.46440611341931E+01,
    0.30253219029200E-02,
    0.0000000676969224,
    0.13621319661456E+00,
    -0.44430413602000E-03,
    -0.0000000621559952,
    0.30093497179950E+01,
    -0.13603287200690E-01,
    0.0000000000608298,
    0.40529569532600E+01,
    -0.32510869900940E-01,
];
const TCH2_Q: [f64; 9] = [
    -0.274704767394256E-05,
    -0.154365304913777E-05,
    -0.349546762061882E-07,
    0.286789414864130E-08,
    0.175452766852069E-07,
    -0.197744662243578E-07,
    0.343169676541053E-08,
    -0.130924950693160E-09,
    0.135338072425105E-07,
];
const TCH2_P: [f64; 9] = [
    -0.298415696654187E-05,
    -0.119708851225481E-05,
    0.567146658521585E-07,
    0.268814727457189E-07,
    0.261897719058852E-07,
    -0.511649608698392E-08,
    -0.127841777400320E-07,
    0.119534263567129E-07,
    0.115749543781328E-07,
];
const AF3_A: [f64; 37 * 3] = [
    0.0000013930299110,
    0.11586745884981E+01,
    0.26733443704266E+01,
    0.0000006449829346,
    0.56222145702102E+01,
    0.89111478887838E+00,
    0.0000002298059520,
    0.12995924044108E+01,
    0.10034433456729E+01,
    -0.0000001221434370,
    0.49612436330515E+01,
    0.17822295777568E+01,
    0.0000001095798176,
    0.19486708778350E+01,
    0.15051650461529E+01,
    0.0000000701435616,
    0.64978508114196E+00,
    0.50172166963138E+00,
    0.0000000547868566,
    0.25992050672074E+01,
    0.20068866945508E+01,
    -0.0000000394635858,
    0.23173535605652E+01,
    0.53466887181044E+01,
    -0.0000000363221428,
    0.36393008632056E+01,
    0.35644591656241E+01,
    0.0000000290949364,
    0.20123392230605E+01,
    0.17535157350384E+01,
    0.0000000281244968,
    0.32490010762048E+01,
    0.25086083721948E+01,
    -0.0000000207924698,
    0.29783308899923E+01,
    0.44555739317536E+01,
    0.0000000146896774,
    0.38988244013504E+01,
    0.30103300418262E+01,
    -0.0000000119930042,
    0.16563968316083E+01,
    0.62378035398422E+01,
    0.0000000112067460,
    0.43188665692819E+01,
    0.13034138285340E-01,
    -0.0000000109535132,
    0.49372826282154E+01,
    0.13584834937940E-01,
    0.0000000099867772,
    0.96700720263958E+00,
    0.62699633776977E+00,
    0.0000000077668260,
    0.45486373016444E+01,
    0.35120517182683E+01,
    0.0000000074143972,
    0.16140449852661E+00,
    0.12531361661566E+00,
    0.0000000066346638,
    0.33441073536010E+00,
    0.80200331112799E+01,
    0.0000000057842684,
    0.14936630646671E+01,
    0.12938928799370E-01,
    -0.0000000055768352,
    0.44651777597613E+01,
    0.11287386144710E+01,
    -0.0000000049395106,
    0.61563894598809E+01,
    0.17520662093793E+01,
    0.0000000041439704,
    0.51984558307998E+01,
    0.40137734147421E+01,
    -0.0000000040765630,
    0.99543742426922E+00,
    0.71289183312483E+01,
    -0.0000000036862062,
    0.46386836178626E+01,
    0.10693377254218E+02,
    0.0000000033617538,
    0.37493658441448E+01,
    0.87808669180168E+00,
    0.0000000033348284,
    0.22668196818990E+01,
    0.16304394485673E+01,
    -0.0000000025754698,
    0.33293196902303E+00,
    0.17952648120307E+01,
    0.0000000024363084,
    0.19604838407749E+01,
    0.11232854513197E+00,
    0.0000000022265432,
    0.58482745704418E+01,
    0.45154950951905E+01,
    0.0000000020032676,
    0.29166648062069E+01,
    0.21321610765333E+01,
    -0.0000000018115706,
    0.99782757414001E+00,
    0.90414978368384E+00,
    0.0000000014535006,
    0.18748212041600E+01,
    0.89112137093506E+01,
    -0.0000000006819260,
    0.19871670124324E+00,
    0.24675315493830E-01,
    0.0000000004433776,
    0.24880003003965E+01,
    0.25119610196650E-01,
    -0.0000000002836658,
    0.58126277034761E+01,
    0.25973068607520E-01,
];
const AF3_LT: [f64; 2] = [0.2874089391143348E+00, 0.8782079235893280E+00];
const AF3_L: [f64; 31 * 3] = [
    0.0002310797886226,
    0.21402987195942E+01,
    0.14500978438400E-02,
    -0.0001828635964118,
    0.43188672736968E+01,
    0.13034138282630E-01,
    0.0001512378778204,
    0.49373102372298E+01,
    0.13584834812520E-01,
    -0.0001163720969778,
    0.43002659861490E+01,
    0.26733443704266E+01,
    -0.0000955478069846,
    0.14936612842567E+01,
    0.12938928798570E-01,
    0.0000815246854464,
    0.56222137132535E+01,
    0.89111478887838E+00,
    -0.0000801219679602,
    0.12995922951532E+01,
    0.10034433456729E+01,
    -0.0000607017260182,
    0.64978769669238E+00,
    0.50172167043264E+00,
    0.0000543922473002,
    0.27927547440639E+01,
    0.29880873700000E-04,
    -0.0000489253646474,
    0.53711728089803E+01,
    0.12495278292000E-03,
    -0.0000427574981536,
    0.18196513407448E+01,
    0.17822295777568E+01,
    -0.0000307360417826,
    0.19498372703786E+01,
    0.15051650064903E+01,
    -0.0000169767346458,
    0.19078637281659E+01,
    0.30507678226700E-02,
    0.0000154725890508,
    0.56912713028984E+01,
    0.65164073556000E-03,
    -0.0000145268863648,
    0.18863875475387E+00,
    0.12530827181195E+00,
    -0.0000135654458738,
    0.27930238268852E+01,
    0.55663681407000E-03,
    -0.0000134648621904,
    0.25991972928128E+01,
    0.20068866945508E+01,
    0.0000095524017320,
    0.23173520454449E+01,
    0.53466887181044E+01,
    0.0000087955125170,
    0.36393024031096E+01,
    0.35644591656241E+01,
    0.0000075462003630,
    0.53560617584395E+01,
    0.92426977490000E-04,
    -0.0000071146195958,
    0.20120561622463E+01,
    0.17535157644008E+01,
    0.0000064153141218,
    0.15526366820734E+01,
    0.29001309732400E-02,
    -0.0000063221625942,
    0.32490122452649E+01,
    0.25086083721948E+01,
    -0.0000056564973024,
    0.24862139082596E+01,
    0.44834622386000E-03,
    0.0000052570245720,
    0.19871532348033E+00,
    0.24675315501580E-01,
    0.0000047020767994,
    0.29783317790630E+01,
    0.44555739317536E+01,
    -0.0000047004229470,
    0.96617050453708E+00,
    0.62699712737505E+00,
    -0.0000046565198820,
    0.36125113449716E+01,
    0.43633231340000E-03,
    -0.0000042349322008,
    0.19604744669606E+01,
    0.11232854282257E+00,
    -0.0000038755741918,
    0.22619624763183E+01,
    0.25146663939730E-01,
    -0.0000032577733688,
    0.56861827246039E+01,
    0.17074576501600E-02,
];
const TCH3_L: [f64; 9] = [
    -0.402499890223698E-03,
    0.422870514937427E-04,
    -0.288258753042082E-03,
    0.623338370193608E-04,
    0.178692873660163E-05,
    0.144147643545141E-04,
    0.658944353306297E-05,
    -0.619139500170464E-05,
    0.782954615405540E-06,
];
const AF3_Z: [f64; 50 * 3] = [
    0.0014289811307319,
    0.21256295942739E+01,
    0.12727413029000E-03,
    0.0007710931226760,
    0.55836330003496E+01,
    0.32064341100000E-04,
    0.0005925911780766,
    0.40899396636448E+01,
    -0.12906864146660E-01,
    0.0002045597496146,
    0.52713683670372E+01,
    -0.12523544076106E+00,
    0.0001785118648258,
    0.28743156721063E+00,
    0.87820792442520E+00,
    0.0001131999784893,
    0.14462127277818E+01,
    0.35515522949802E+01,
    -0.0000658778169210,
    0.22702423990985E+01,
    -0.17951364394537E+01,
    0.0000497058888328,
    0.59096792204858E+01,
    0.17693227129285E+01,
    -0.0000316384926978,
    0.16093054939404E+01,
    -0.90402165028424E+00,
    0.0000287801237327,
    0.46217321268757E+01,
    -0.62695712341840E+00,
    -0.0000181744317896,
    0.59210641379360E+01,
    0.37648623991673E+00,
    0.0000105558175161,
    0.39720191398746E+01,
    -0.11286788041058E+01,
    -0.0000070808673396,
    0.60542548894164E+01,
    -0.25941002415210E-01,
    -0.0000070804404020,
    0.27978433776854E+01,
    0.67774258703000E-03,
    -0.0000061046181888,
    0.14151685760988E+01,
    -0.87530769416913E+00,
    -0.0000057610853129,
    0.42530537622646E+01,
    -0.44684807882788E+01,
    -0.0000057310334964,
    0.29311803223072E+01,
    -0.26862512192699E+01,
    0.0000048299146941,
    0.27138294508149E+01,
    0.27731329671900E-02,
    0.0000046610005483,
    0.33222980229554E+01,
    -0.16304004832039E+01,
    -0.0000038142769361,
    0.25962943627643E+01,
    -0.25845792955510E-01,
    0.0000034982417330,
    0.15866568011217E+01,
    0.18816512920593E+01,
    -0.0000030091617315,
    0.35921173988567E+01,
    -0.35773660056343E+01,
    -0.0000024732926446,
    0.53461730094807E+01,
    0.25122576835111E+00,
    0.0000024416432533,
    0.47049477027963E+01,
    -0.25049613834712E+00,
    0.0000024171568015,
    0.34508032389167E+01,
    0.00000000000000E+00,
    0.0000023143850535,
    0.55385759257808E+01,
    0.28683339028800E-02,
    0.0000022651772374,
    0.55608006706192E+01,
    0.14501892967800E-02,
    0.0000022247695560,
    0.26725424635341E+01,
    -0.21321221654766E+01,
    0.0000020947921969,
    0.22350374116258E+01,
    0.23833730192673E+01,
    -0.0000014042712722,
    0.93718044411525E+00,
    0.13799296041822E+01,
    0.0000011932531874,
    0.28861941414418E+01,
    0.28850946416201E+01,
    -0.0000011180389240,
    0.49139919849718E+01,
    -0.53595955727170E+01,
    0.0000011076384510,
    0.20227538540345E+01,
    -0.26338438454332E+01,
    -0.0000010371714944,
    0.40722739402948E+00,
    -0.87385759089274E+00,
    -0.0000008993128501,
    0.30942691883530E+01,
    -0.71418251640916E+01,
    0.0000007268381420,
    0.54334774230433E+01,
    -0.26491687896550E-01,
    -0.0000007178049665,
    0.52487423493616E+01,
    0.26604375002057E+01,
    0.0000006908412319,
    0.40596134184175E+01,
    -0.75221793556997E+00,
    -0.0000006784151570,
    0.38846818226669E+01,
    0.42496535534400E-02,
    0.0000006772314920,
    0.23013479896873E+01,
    0.26317235358158E+01,
    0.0000006659820028,
    0.35359530295550E+01,
    0.33868163258510E+01,
    -0.0000006339665249,
    0.39268665697903E+01,
    0.44426670658559E+01,
    -0.0000006286307601,
    0.19440608894162E+01,
    0.71160114019304E+01,
    -0.0000006128705113,
    0.25027415074658E+01,
    0.62249001971556E+01,
    0.0000005660807396,
    0.13729316457251E+01,
    -0.31355655165873E+01,
    -0.0000005206551413,
    0.55749300982469E+01,
    -0.62507103665413E+01,
    -0.0000004718481418,
    0.45366605084874E+01,
    0.16786677353000E-03,
    -0.0000004583970422,
    0.19351070248496E+01,
    -0.98151695574500E+01,
    -0.0000004577854173,
    0.62350780976534E+01,
    0.17563373058434E+01,
    0.0000003466029660,
    0.75412427489767E+00,
    0.15807097495700E-01,
];
const TCH3_K: [f64; 9] = [
    -0.111797459279082E-06,
    -0.278967292638245E-06,
    -0.704645336679784E-07,
    -0.238693040681653E-06,
    0.122869992713930E-07,
    -0.153370399783488E-06,
    0.447318789843126E-07,
    -0.165802124252890E-07,
    -0.828946056921499E-07,
];
const TCH3_H: [f64; 9] = [
    -0.107044201697345E-06,
    -0.223668695371038E-06,
    -0.218527598721759E-06,
    -0.200040954734845E-06,
    -0.319586844323525E-06,
    -0.222086683443490E-06,
    -0.298609138042077E-06,
    -0.129217448782639E-06,
    -0.150654590880644E-06,
];
const AF3_ZETA: [f64; 18 * 3] = [
    0.0015932721570848,
    0.33368862796665E+01,
    -0.12491307058000E-03,
    0.0008533093128905,
    0.24133881688166E+01,
    0.00000000000000E+00,
    0.0003513347911037,
    0.59720789850127E+01,
    -0.30561017710000E-04,
    -0.0001441929255483,
    0.10477061764435E+01,
    -0.56920632124000E-03,
    0.0000157303527750,
    0.55604041197704E+01,
    0.29003665011200E-02,
    0.0000025161319881,
    0.28477653709685E+00,
    -0.14500554486800E-02,
    0.0000020438305183,
    0.17652628559998E+01,
    0.14501383926500E-02,
    0.0000017939612784,
    0.45568977341583E+01,
    0.43504621590400E-02,
    0.0000013614276895,
    0.84898872627945E+00,
    -0.25244521900630E-01,
    -0.0000008996109017,
    0.46441156003340E+01,
    0.30253214588300E-02,
    -0.0000008702078430,
    0.27972000093551E+01,
    -0.23150965645100E-02,
    -0.0000004371144064,
    0.48429530385679E+01,
    -0.25688816011500E-01,
    -0.0000002174259374,
    0.57543785603741E+01,
    -0.25813642993310E-01,
    -0.0000001926397869,
    0.20118539705648E+01,
    0.29330596864500E-02,
    0.0000001589279656,
    0.35554727018503E+01,
    0.58005577768400E-02,
    -0.0000001432228753,
    0.11966574544002E+01,
    -0.15750124983800E-02,
    -0.0000000926213408,
    0.22052538606469E+01,
    -0.25782797426020E-01,
    0.0000000000106902,
    0.45764213311755E+01,
    -0.32611614716800E-01,
];
const TCH3_Q: [f64; 9] = [
    -0.141968295962213E-04,
    -0.793995493982020E-05,
    -0.208882224662785E-06,
    0.209762683478441E-07,
    0.835070484335148E-07,
    -0.107729670354460E-06,
    0.306301230195125E-07,
    0.112449433356374E-07,
    0.708786417409988E-08,
];
const TCH3_P: [f64; 9] = [
    -0.153976109321613E-04,
    -0.612022141299496E-05,
    0.315217558237908E-06,
    0.148179418616661E-06,
    0.141150094231365E-06,
    -0.224063936978287E-07,
    -0.333311708439601E-07,
    0.107863442857316E-07,
    0.662499119729457E-07,
];

const AF4_A: [f64; 21 * 3] = [
    0.0000035952049470,
    0.64965776007116E+00,
    0.50172168165034E+00,
    0.0000027580210652,
    0.18084235781510E+01,
    0.31750660413359E+01,
    0.0000012874896172,
    0.62718908285025E+01,
    0.13928364698403E+01,
    -0.0000004173729106,
    0.12990650292663E+01,
    0.10034433697108E+01,
    0.0000002790757718,
    0.71428870045577E+00,
    0.75007225869130E+00,
    -0.0000001998252258,
    0.19489881012004E+01,
    0.15051650461529E+01,
    -0.0000001001149838,
    0.25987168731338E+01,
    0.20068867266014E+01,
    -0.0000000513967092,
    0.32484798706247E+01,
    0.25086084022422E+01,
    -0.0000000475687992,
    0.48635521917696E+01,
    0.74862216593606E+00,
    0.0000000348242240,
    0.15082713497295E+00,
    0.37645917070525E+00,
    0.0000000283840630,
    0.51672973364888E+01,
    0.12530678073049E+00,
    -0.0000000263234638,
    0.33499822210495E+01,
    0.30103491232578E+01,
    0.0000000239106346,
    0.43573519442736E+01,
    0.62698238798737E+00,
    0.0000000219977422,
    0.15075404808879E+01,
    0.27986109086768E+01,
    -0.0000000171144478,
    0.62607361864777E+01,
    0.27856729335053E+01,
    -0.0000000141956834,
    0.45481077718910E+01,
    0.35120517575303E+01,
    -0.0000000120003630,
    0.18583887479127E+01,
    0.11287042579152E+01,
    0.0000000108418904,
    0.54873138800427E+01,
    0.67395238593127E+01,
    0.0000000108218254,
    0.59772630516669E+01,
    0.10163811590412E+01,
    0.0000000002477642,
    0.56894071957878E+01,
    0.65165021654000E-03,
    -0.0000000001874576,
    0.28598333265121E+01,
    0.55639542661000E-03,
];
const AF4_LT: [f64; 2] = [-0.3620341291375704E+00, 0.3764862334338280E+00];
const AF4_L: [f64; 19 * 3] = [
    0.0005586040123824,
    0.21404207189815E+01,
    0.14500979323100E-02,
    -0.0003805813868176,
    0.27358844897853E+01,
    0.29729650620000E-04,
    0.0002205152863262,
    0.64979652596400E+00,
    0.50172167243580E+00,
    0.0001877895151158,
    0.18084787604005E+01,
    0.31750660413359E+01,
    0.0000766916975242,
    0.62720114319755E+01,
    0.13928364636651E+01,
    0.0000747056855106,
    0.12995916202344E+01,
    0.10034433456729E+01,
    -0.0000388323297366,
    0.71289234751879E+00,
    0.75007236972328E+00,
    0.0000335036484314,
    0.53712641184981E+01,
    0.12494011725000E-03,
    0.0000293032677938,
    0.19493939340593E+01,
    0.15051650209131E+01,
    0.0000185940935472,
    0.14630998372377E+01,
    0.29001339405200E-02,
    -0.0000170438022886,
    0.56893382353856E+01,
    0.65165044781000E-03,
    0.0000151393833114,
    0.28749516044614E+01,
    0.55646069067000E-03,
    -0.0000148825637256,
    0.33321074618840E+01,
    0.12530790075011E+00,
    0.0000129927896682,
    0.25991973549465E+01,
    0.20068866945508E+01,
    -0.0000116117398772,
    0.56192268627131E+01,
    0.93166256720000E-04,
    0.0000066211702894,
    0.48564958193206E+01,
    0.74862286166569E+00,
    0.0000065387442486,
    0.35580120361824E+01,
    0.16550513741900E-02,
    0.0000061580798140,
    0.32490037889701E+01,
    0.25086083721948E+01,
    0.0000046797140778,
    0.96612169919707E+00,
    0.62699716616712E+00,
];
const TCH4_L: [f64; 9] = [
    0.306204347064615E-03,
    -0.168321429486551E-03,
    0.202182016979082E-03,
    -0.137641833741129E-03,
    -0.530404402536766E-04,
    -0.110474926063654E-04,
    -0.105634674903822E-04,
    0.311526543050599E-04,
    0.466495863544146E-05,
];
const AF4_Z: [f64; 46 * 3] = [
    0.0073755808467977,
    0.55836071576084E+01,
    0.32065099140000E-04,
    0.0002065924169942,
    0.59209831565786E+01,
    0.37648624194703E+00,
    0.0001589869764021,
    0.28744006242623E+00,
    0.87820792442520E+00,
    -0.0001561131605348,
    0.21257397865089E+01,
    0.12727441285000E-03,
    0.0001486043380971,
    0.14462134301023E+01,
    0.35515522949802E+01,
    0.0000635073108731,
    0.59096803285954E+01,
    0.17693227129285E+01,
    0.0000599351698525,
    0.41125517584798E+01,
    -0.27985797954589E+01,
    0.0000540660842731,
    0.55390350845569E+01,
    0.28683408228300E-02,
    -0.0000489596900866,
    0.46218149483338E+01,
    -0.62695712529519E+00,
    0.0000333682283528,
    0.52066975238880E+01,
    -0.37358601734497E+00,
    0.0000295832427279,
    0.59322697896516E+01,
    -0.10163502275209E+01,
    0.0000292325461337,
    0.52707623402008E+01,
    -0.12523542448602E+00,
    0.0000197588369441,
    0.33317768022759E+01,
    0.00000000000000E+00,
    -0.0000183551029746,
    0.39720443249757E+01,
    -0.11286788041058E+01,
    0.0000090411191759,
    0.55606719963947E+01,
    0.14501837490800E-02,
    -0.0000081987970452,
    0.33223313720086E+01,
    -0.16304004832039E+01,
    -0.0000060406575087,
    0.13970265485562E+01,
    0.43191832032300E-02,
    0.0000056895636122,
    0.41990956668120E+01,
    -0.37213592656720E+00,
    -0.0000040434854859,
    0.47008406172134E+01,
    -0.25049602889288E+00,
    -0.0000039403527376,
    0.26725832255243E+01,
    -0.21321221654766E+01,
    0.0000036901291978,
    0.35207772267753E+00,
    0.11265585018525E+01,
    -0.0000028551622596,
    0.55601265129356E+01,
    -0.31584886140000E-04,
    -0.0000026588026505,
    0.25969882784477E+00,
    0.14182025553300E-02,
    -0.0000019711212463,
    0.20228019680496E+01,
    -0.26338438454332E+01,
    0.0000019322089806,
    0.51418595457408E+01,
    0.25123117908847E+00,
    -0.0000018673159813,
    0.93674892088247E+00,
    0.13799296163047E+01,
    0.0000016838424078,
    0.60796033426941E+01,
    0.75294520843775E+00,
    -0.0000016695689644,
    0.15867810488422E+01,
    0.18816512864243E+01,
    0.0000016317841395,
    0.45789534393209E+01,
    0.14822429153000E-02,
    -0.0000016159095087,
    0.30157253757329E+00,
    -0.14180284447900E-02,
    -0.0000014034621874,
    0.59433512039442E+01,
    -0.24091866865037E+01,
    -0.0000012029942283,
    0.27137754880270E+01,
    0.27731373092900E-02,
    -0.0000011758260607,
    0.40581098970285E+01,
    -0.75221789504525E+00,
    -0.0000010798624964,
    0.22364861319452E+01,
    0.23833729650229E+01,
    -0.0000010108880552,
    0.13729872033949E+01,
    -0.31355655165873E+01,
    -0.0000008876681807,
    0.50534107615010E+01,
    -0.50169281575682E+00,
    0.0000008869382117,
    0.50147420853991E+01,
    0.68353864231000E-03,
    -0.0000008194699011,
    0.62190878357566E+01,
    -0.37503615934219E+00,
    0.0000007093782158,
    0.44118312641559E+01,
    -0.24221246131672E+01,
    0.0000006728737059,
    0.31910016062920E+01,
    -0.37068584881726E+00,
    0.0000006297345982,
    0.13595719733984E+01,
    0.11251084135564E+01,
    0.0000006128899757,
    0.51402161299290E+01,
    0.71160095483087E+01,
    -0.0000005580987049,
    0.34117733109010E+01,
    -0.12539396666771E+01,
    0.0000005321318002,
    0.35377046967957E+01,
    0.57685340271300E-02,
    -0.0000004739086661,
    0.21645217929478E+01,
    0.58845474482000E-03,
    0.0000004518928658,
    0.44963664372727E+01,
    0.29023325111200E-02,
];
const TCH4_K: [f64; 9] = [
    -0.181310025984216E-06,
    -0.126014618556329E-05,
    -0.382306332383069E-06,
    -0.667102945644653E-06,
    -0.505214970641581E-07,
    0.153918794369926E-06,
    0.928279781805284E-07,
    0.366048038576706E-06,
    0.568038769950531E-07,
];
const TCH4_H: [f64; 9] = [
    -0.140782617429892E-05,
    -0.135394137498700E-05,
    -0.320084097458594E-06,
    -0.620618627039507E-06,
    -0.611742588608485E-06,
    -0.276537195728238E-06,
    -0.133810977431205E-06,
    0.289677483700145E-06,
    0.470713328715423E-07,
];
const AF4_ZETA: [f64; 18 * 3] = [
    0.0038422977898495,
    0.24133922085557E+01,
    0.00000000000000E+00,
    0.0022453891791894,
    0.59721736773277E+01,
    -0.30561255250000E-04,
    -0.0002604479450559,
    0.33368746306409E+01,
    -0.12491309972000E-03,
    0.0000332112143230,
    0.55604137742337E+01,
    0.29003768850700E-02,
    0.0000049727136261,
    0.28488229706820E+00,
    -0.14500571761900E-02,
    -0.0000049416729114,
    0.10476908456459E+01,
    -0.56920298857000E-03,
    0.0000043945193428,
    0.17684273746003E+01,
    0.14501344524700E-02,
    0.0000037630501589,
    0.45567680530533E+01,
    0.43504645407000E-02,
    -0.0000030823418750,
    0.20094360655956E+01,
    0.29313051376700E-02,
    0.0000004719790711,
    0.18055417618741E+01,
    0.14195445432000E-02,
    -0.0000004637177865,
    0.38277528822158E+01,
    -0.14808731001600E-02,
    0.0000003497224175,
    0.46444360330108E+01,
    0.30253130162300E-02,
    -0.0000003467132626,
    0.10120757927163E+01,
    0.43816126822900E-02,
    0.0000003324412570,
    0.35549391686606E+01,
    0.58005379032100E-02,
    0.0000001945374351,
    0.61251687150860E+01,
    0.28808264872800E-02,
    0.0000001727743329,
    0.11900773236610E+01,
    -0.29001068524700E-02,
    -0.0000001485176585,
    0.62335834706368E+01,
    0.14807679092700E-02,
    0.0000000000666922,
    0.40616225761771E+01,
    -0.32724923474890E-01,
];
const TCH4_Q: [f64; 9] = [
    -0.640936655172450E-04,
    -0.357948862513955E-04,
    -0.887261624128964E-06,
    0.164506004407617E-06,
    0.477415826267116E-06,
    -0.359030239515192E-06,
    0.117406290303369E-06,
    0.895051737231057E-07,
    0.971875658565188E-08,
];
const TCH4_P: [f64; 9] = [
    -0.696069435911693E-04,
    -0.276636397672750E-04,
    0.138328020437413E-05,
    0.651631405812798E-06,
    0.620307849865976E-06,
    -0.266081185506962E-06,
    -0.209003718083271E-06,
    -0.146372661194868E-06,
    -0.122390974721364E-06,
];

const MU: [f64; 4] = [
    0.2824894284338140E-06,
    0.2824832743928930E-06,
    0.2824981841847230E-06,
    0.2824921448899090E-06,
];

const A0: [f64; 4] = [
    0.0028210960212903,
    0.0044871037804314,
    0.0071566594572575,
    0.0125879701715314,
];

const TO_ICRS: MatR = MatR {
    r00: 0.9994327653386544,
    r01: 0.030395942890628476,
    r02: -0.014499455966335291,
    r10: -0.03367710746976414,
    r11: 0.902057912352809,
    r12: -0.43029916940910073,
    r20: 0.0,
    r21: 0.43054338854229507,
    r22: 0.902569881273754,
};

///
/// # Arguments
/// # Returns
///
pub fn get_orb_elem(mjd_tdb: f64, body: &BodyId) -> OrbElem {
    let dt = mjd_tdb - mjd::J1950;
    let gk2 = GK * GK;
    match body {
        BodyId::IO => {
            let tch = calc_tcheb(dt, &TCH1_L, &TCH1_K, &TCH1_H, &TCH1_Q, &TCH1_P);
            OrbElem {
                mu: MU[0] / gk2,
                mjd0: mjd_tdb,
                a: A0[0] + calc_cos_ser(dt, &AF1_A),
                l: norm_dblpi(AF1_LT[0] + AF1_LT[1] * dt + calc_sin_ser(dt, &AF1_L) + tch.0),
                k: calc_cos_ser(dt, &AF1_Z) + tch.1,
                h: calc_sin_ser(dt, &AF1_Z) + tch.2,
                q: calc_cos_ser(dt, &AF1_ZETA) + tch.3,
                p: calc_sin_ser(dt, &AF1_ZETA) + tch.4,
            }
        }
        BodyId::EUROPA => {
            let tch = calc_tcheb(dt, &TCH2_L, &TCH2_K, &TCH2_H, &TCH2_Q, &TCH2_P);
            OrbElem {
                mu: MU[1] / gk2,
                mjd0: mjd_tdb,
                a: A0[1] + calc_cos_ser(dt, &AF2_A),
                l: norm_dblpi(AF2_LT[0] + AF2_LT[1] * dt + calc_sin_ser(dt, &AF2_L) + tch.0),
                k: calc_cos_ser(dt, &AF2_Z) + tch.1,
                h: calc_sin_ser(dt, &AF2_Z) + tch.2,
                q: calc_cos_ser(dt, &AF2_ZETA) + tch.3,
                p: calc_sin_ser(dt, &AF2_ZETA) + tch.4,
            }
        }
        BodyId::GANYMEDE => {
            let tch = calc_tcheb(dt, &TCH3_L, &TCH3_K, &TCH3_H, &TCH3_Q, &TCH3_P);
            OrbElem {
                mu: MU[2] / gk2,
                mjd0: mjd_tdb,
                a: A0[2] + calc_cos_ser(dt, &AF3_A),
                l: norm_dblpi(AF3_LT[0] + AF3_LT[1] * dt + calc_sin_ser(dt, &AF3_L) + tch.0),
                k: calc_cos_ser(dt, &AF3_Z) + tch.1,
                h: calc_sin_ser(dt, &AF3_Z) + tch.2,
                q: calc_cos_ser(dt, &AF3_ZETA) + tch.3,
                p: calc_sin_ser(dt, &AF3_ZETA) + tch.4,
            }
        }
        BodyId::CALLISTO => {
            let tch = calc_tcheb(dt, &TCH4_L, &TCH4_K, &TCH4_H, &TCH4_Q, &TCH4_P);
            OrbElem {
                mu: MU[3] / gk2,
                mjd0: mjd_tdb,
                a: A0[3] + calc_cos_ser(dt, &AF4_A),
                l: norm_dblpi(AF4_LT[0] + AF4_LT[1] * dt + calc_sin_ser(dt, &AF4_L) + tch.0),
                k: calc_cos_ser(dt, &AF4_Z) + tch.1,
                h: calc_sin_ser(dt, &AF4_Z) + tch.2,
                q: calc_cos_ser(dt, &AF4_ZETA) + tch.3,
                p: calc_sin_ser(dt, &AF4_ZETA) + tch.4,
            }
        }
        _ => OrbElem {
            mu: f64::NAN,
            mjd0: f64::NAN,
            a: f64::NAN,
            l: f64::NAN,
            k: f64::NAN,
            h: f64::NAN,
            q: f64::NAN,
            p: f64::NAN,
        },
    }
}

///
/// # Arguments
/// # Returns
///
pub fn get_icrs_p(mjd_tdb: f64, body: &BodyId) -> vec_p::VecP {
    let orb_el = get_orb_elem(mjd_tdb, body);
    let out = orb_el.get_p();
    mul_p(&TO_ICRS, &out)
}

///
/// # Arguments
/// # Returns
///
pub fn get_icrs_pv(mjd_tdb: f64, body: &BodyId) -> vec_pv::VecPv {
    let orb_el = get_orb_elem(mjd_tdb, body);
    let out = orb_el.get_pv();
    mul_pv(&TO_ICRS, &out)
}

fn calc_sin_ser(dt: f64, coeffs: &[f64]) -> f64 {
    let nt = coeffs.len() / 3;
    let mut out = 0.0;
    for j in 0..nt {
        let ampl = coeffs[j * 3];
        let phase = coeffs[j * 3 + 1];
        let frec = coeffs[j * 3 + 2];
        out += ampl * (phase + frec * dt).sin();
    }
    out
}

fn calc_cos_ser(dt: f64, coeffs: &[f64]) -> f64 {
    let nt = coeffs.len() / 3;
    let mut out = 0.0;
    for j in 0..nt {
        let ampl = coeffs[j * 3];
        let phase = coeffs[j * 3 + 1];
        let frec = coeffs[j * 3 + 2];
        out += ampl * (phase + frec * dt).cos();
    }
    out
}

fn calc_tcheb(
    dt: f64,
    tch_l: &[f64],
    tch_k: &[f64],
    tch_h: &[f64],
    tch_q: &[f64],
    tch_p: &[f64],
) -> (f64, f64, f64, f64, f64) {
    let mut tl = 0.0;
    let mut th = 0.0;
    let mut tk = 0.0;
    let mut tq = 0.0;
    let mut tp = 0.0;
    let ach = -819.727638594856;
    let bch = 812.721806990360;
    let x = (dt / 365.25 - 0.5 * (bch + ach)) / (0.5 * (bch - ach));
    if x.abs() <= 1.0 {
        let mut tn: [f64; 9] = [1.0, x, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0];
        for j in 2..9 {
            tn[j] = 2.0 * x * tn[j - 1] - tn[j - 2];
        }
        for j in 0..9 {
            tl += tch_l[j] * tn[j];
            tk += tch_k[j] * tn[j];
            th += tch_h[j] * tn[j];
            tq += tch_q[j] * tn[j];
            tp += tch_p[j] * tn[j];
        }
        tl += -0.5 * tch_l[0];
        tk += -0.5 * tch_k[0];
        th += -0.5 * tch_h[0];
        tq += -0.5 * tch_q[0];
        tp += -0.5 * tch_p[0];
    }
    (tl, tk, th, tq, tp)
}