cross_reference.h

/* Generated by tools/make_cross_reference.py -- do not edit.
 *
 * Truth rows from independent COMPUTED implementations,
 * consumed by `sight_reduction --cross-check`. Two lineages:
 *
 *   PyEphem/libastro 4.2.1 (the XEphem lineage):
 *   cross_sun_rows, cross_moon_rows, cross_star_rows,
 *   cross_aries_rows. Geocentric apparent equinox-of-date
 *   RA/dec + apparent GAST -> GHA -> ITRS Q2.30. Each row
 *   carries libastro's own delta_t as tt_minus_ut1_ms.
 *   Independence scope: the Sun (Bretagnon) and Moon
 *   (ELP-derived) rows are code AND data disjoint from both
 *   Skyfield/DE421 (ephemeris_reference.h) and printed
 *   pages (external_reference.h). The STAR rows are not
 *   data-independent: PyEphem's catalog is the same
 *   Hipparcos data, epoch-shifted with Skyfield (per
 *   ephem/stars.py), so they validate libastro's own
 *   precession/nutation/aberration/sidereal chain, not
 *   independent star positions.
 *
 *   github.com/alinnman/celestial-navigation
 *   revision b3ab049a291ac4da0a0431e798a2125f549bcd8d
 *   (independent spherical-geometry engine, MIT):
 *   cross_reduce_rows (Hc/Zn from its vector primitives),
 *   cross_fix_rows (two-body fix by direct circle-of-
 *   position intersection -- a different algorithm from
 *   this library's iterated least-squares).
 *
 * Angles: Q2.30 unit vectors or milli-arcmin; positions in
 * rows are centidegrees (inputs) and milli-arcmin (oracle
 * outputs); time is UT1 ms since J2000.0. */

typedef struct {
    int64_t ut1_ms;          /* UT1 ms since J2000.0 */
    int32_t tt_minus_ut1_ms; /* libastro's delta_t */
    int32_t x, y, z;         /* ITRS apparent direction, Q2.30 */
    int32_t dist_uau;        /* apparent distance, micro-AU */
    int32_t sd_marcmin;      /* libastro apparent SD */
    int32_t hp_marcmin;      /* asin(6378.137 km / dist) */
} cross_sun_row_t;

static const cross_sun_row_t cross_sun_rows[] = {
    {        9876543LL,  63831,   753486702,  -639393776,  -419946297,  983327, 16265, 149 },
    {    27279876543LL,  64059,     2018193,  1022456349,  -327872607,  989680, 16161, 148 },
    {    54549876543LL,  64247,  -733645678,  -783991139,    -6589198, 1003231, 15942, 146 },
    {    81819876543LL,  64408,  1022657602,    95692381,   312947124, 1014403, 15767, 144 },
    {   109089876543LL,  64520,  -744221893,   646322378,   425819988, 1015895, 15744, 144 },
    {   136359876543LL,  64606,    58739304, -1039690670,   261752765, 1006786, 15886, 146 },
    {   163629876543LL,  64713,   666711708,   837632284,   -82396353,  992987, 16107, 148 },
    {   190899876543LL,  64862,  -999877583,  -113689578,  -374487653,  983897, 16256, 149 },
    {   218169876543LL,  65122,   717913780,  -692909219,  -396734324,  986175, 16218, 149 },
    {   245439876543LL,  65391,    -9404247,  1065090806,  -135700549,  998171, 16023, 147 },
    {   272709876543LL,  65667,  -683285519,  -800456905,   212864154, 1011244, 15816, 145 },
    {   299979876543LL,  65932,   985858063,    85541890,   416758885, 1016666, 15732, 144 },
    {   327249876543LL,  66164,  -753466904,   679970676,   350498230, 1011041, 15819, 145 },
    {   354519876543LL,  66383,    97134651, -1068174384,    49898396,  997833, 16029, 147 },
    {   381789876543LL,  66629,   631253712,   818214781,  -291487268,  986012, 16221, 149 },
    {   409059876543LL,  66897,  -984177432,   -51387562,  -426234213,  983992, 16254, 149 },
    {   436329876543LL,  67215,   734909060,  -740802843,  -253063878,  993208, 16103, 148 },
    {   463599876543LL,  67523,   -58228434,  1068142561,    92749254, 1006996, 15883, 146 },
    {   490869876543LL,  67885,  -641439142,  -777154866,   370820234, 1015994, 15742, 144 },
    {   518139876543LL,  68308,   991927167,    58232544,   406953278, 1014318, 15768, 145 },
    {   545409876543LL,  68697,  -798496336,   695937635,   176056567, 1002943, 15947, 146 },
    {   572679876543LL,  69022,   132198466, -1050244084,  -180090074,  989527, 16163, 148 },
    {   599949876543LL,  69358,   635041879,   760941790,  -413050734,  983310, 16265, 149 },
    {   627219876543LL,  69742, -1016171497,     -748380,  -346866593,  988836, 16174, 148 },
    {   654489876543LL,  70172,   778958678,  -738096815,   -36850717, 1002133, 15960, 146 },
    {   681759876543LL,  70649,   -94145349,  1028985876,   291969562, 1013856, 15775, 145 },
    {   709029876543LL,  71172,  -642839132,  -746520069,   427068075, 1016192, 15739, 144 },
    {   736299876543LL,  71740,  1033758999,    56036214,   284822365, 1007680, 15872, 145 },
    {   763569876543LL,  72353,  -835869226,   671972135,   -51938341,  993979, 16091, 147 },
    {   790839876543LL,  73008,   119276026, -1005119778,  -358369874,  984259, 16250, 149 },
    {   818109876543LL,  73708,   685084701,   719556705,  -407208307,  985604, 16227, 149 },
    {   845379876543LL,  74451, -1061071763,    -4941633,  -164389166,  997077, 16041, 147 },
    {   872649876543LL,  75236,   800924776,  -690426842,   186418306, 1010413, 15829, 145 },
    {   899919876543LL,  76061,   -88840144,   988700983,   409266783, 1016647, 15732, 144 },
    {   927189876543LL,  76927,  -675582094,  -749730440,   366625976, 1011845, 15807, 145 },
    {   954459876543LL,  77834,  1066864871,    91141130,    80088368,  998983, 16010, 147 },
    {   981729876543LL,  78781,  -823705296,   634576942,  -267849202,  986648, 16210, 149 },
    {  1008999876543LL,  79767,    59970011,  -983370347,  -426975248,  983651, 16260, 149 },
    {  1036269876543LL,  80788,   736953183,   730051342,  -277212099,  992230, 16119, 148 },
    {  1063539876543LL,  81849, -1070642160,   -51560557,    63153613, 1006009, 15898, 146 },
    {  1090809876543LL,  82947,   781814447,  -644602165,   355212224, 1015617, 15748, 144 },
    {   820731600000LL,  73778,   275328538,  -951002424,  -415584036,  983302, 16265, 149 },
    {   836629200000LL,  74208,   276590623,  -951668511,   413214444, 1016644, 15732, 144 },
    {  1104670800000LL,  83519,  -960260439,   238720914,  -416933712,  983325, 16265, 149 },
    {  1120636800000LL,  84190,  -477191280,  -868609271,   413192354, 1016737, 15731, 144 },
};
#define CROSS_SUN_ROW_COUNT (sizeof cross_sun_rows / sizeof cross_sun_rows[0])

typedef struct {
    int64_t ut1_ms;
    int32_t tt_minus_ut1_ms;
    int32_t x, y, z;         /* ITRS apparent direction, Q2.30 */
    int32_t dist_km;
    int32_t sd_marcmin;      /* libastro apparent SD */
    int32_t hp_marcmin;      /* asin(6378.137 km / dist) */
} cross_moon_row_t;

static const cross_moon_row_t cross_moon_rows[] = {
    {        7654321LL,  63830,    19168061, -1053021957,  -209042694, 402692, 14854, 54452 },
    {    27877654321LL,  64063,   778831444,   694548918,   252873262, 373318, 16023, 58737 },
    {    55747654321LL,  64254,  -905209743,   428885364,   386748201, 385147, 15531, 56933 },
    {    83617654321LL,  64418,   363278394, -1010416419,    -2995725, 405604, 14748, 54061 },
    {   111487654321LL,  64527,   410753068,   896029578,  -425833791, 374687, 15965, 58522 },
    {   139357654321LL,  64617, -1023633753,    55614509,  -319378256, 361476, 16548, 60661 },
    {   167227654321LL,  64728,   681460500,  -797844617,   227984779, 397991, 15030, 55095 },
    {   195097654321LL,  64897,    68273312,   941533513,   511639428, 397483, 15049, 55165 },
    {   222967654321LL,  65170,  -949537981,  -446434255,   228025398, 369856, 16173, 59287 },
    {   250837654321LL,  65444,   873485855,  -496515875,  -378702985, 391511, 15278, 56007 },
    {   278707654321LL,  65727,  -155724069,   955873822,  -463655859, 404028, 14805, 54272 },
    {   306577654321LL,  65992,  -678423626,  -830621009,   -52264976, 368418, 16236, 59518 },
    {   334447654321LL,  66220,   969408632,  -166952827,   430459245, 367602, 16272, 59650 },
    {   362317654321LL,  66451,  -471176594,   919034954,   293749682, 402231, 14871, 54514 },
    {   390187654321LL,  66707,  -230942799, -1042164547,  -116103338, 390769, 15308, 56114 },
    {   418057654321LL,  66999,   965495108,   289504400,  -370037704, 367912, 16258, 59600 },
    {   445927654321LL,  67325,  -806571054,   707716791,   -38750261, 396738, 15077, 55269 },
    {   473797654321LL,  67646,   113830164, -1026607589,   293327558, 400213, 14946, 54789 },
    {   501667654321LL,  68050,   796585622,   676256862,   247081985, 363566, 16453, 60312 },
    {   529537654321LL,  68485, -1001388139,   330243540,  -202688193, 375046, 15949, 58466 },
    {   557407654321LL,  68842,   415735000,  -927137784,  -347133178, 404150, 14801, 54255 },
    {   585277654321LL,  69172,   376872882,  1002226698,   -80187163, 383514, 15597, 57175 },
    {   613147654321LL,  69538,  -989657077,  -175808508,   377613220, 368791, 16220, 59458 },
    {   641017654321LL,  69954,   677128371,  -783296737,   284367537, 401344, 14904, 54635 },
    {   668887654321LL,  70418,   -10772500,  1062735235,  -152968223, 395574, 15122, 55432 },
    {   696757654321LL,  70931,  -821504348,  -500988558,  -476510835, 362421, 16505, 60503 },
    {   724627654321LL,  71491,   928310014,  -527791573,  -112241162, 384125, 15572, 57084 },
    {   752497654321LL,  72099,  -380280338,   938819918,   356266097, 403994, 14806, 54276 },
    {   780367654321LL,  72751,  -494093751,  -813842858,   496439998, 376099, 15905, 58302 },
    {   808237654321LL,  73450,  1072601589,   -42873066,   -24682696, 371719, 16092, 58989 },
    {   836107654321LL,  74194,  -587714016,   765453077,  -470739129, 404332, 14794, 54231 },
    {   863977654321LL,  74982,  -241998225,  -974665619,  -379980650, 389775, 15347, 56257 },
    {   891847654321LL,  75813,   984179343,   381196521,   197488576, 363903, 16438, 60257 },
    {   919717654321LL,  76686,  -760215643,   609415596,   451227561, 392516, 15239, 55864 },
    {   947587654321LL,  77602,   152390784, -1046386913,   186475149, 400887, 14921, 54697 },
    {   975457654321LL,  78560,   639422385,   820718496,  -265483839, 368626, 16227, 59484 },
    {  1003327654321LL,  79559,  -994365317,   257160090,  -313093930, 376558, 15885, 58231 },
    {  1031197654321LL,  80595,   521203809,  -935766757,    74891062, 406328, 14721, 53965 },
    {  1059067654321LL,  81672,   310559344,   970796816,   337680233, 384109, 15573, 57086 },
    {  1086937654321LL,  82789, -1056745598,  -164038775,    96444420, 367500, 16277, 59667 },
    {  1114807654321LL,  83944,   763438267,  -696274328,  -292036945, 398730, 15002, 54993 },
    {   850244400000LL,  74588,  -172204406,   950590427,  -468662979, 406419, 14718, 53952 },
    {   851374800000LL,  74620,  -616185008,  -733590883,   484852510, 356651, 16772, 61482 },
    {   794635200000LL,  73103,   676596446,   654963628,   515908325, 379143, 15777, 57834 },
    {   795898800000LL,  73135,   908139568,  -248779801,  -516054882, 394809, 15151, 55539 },
    {   836424000000LL,  74203,   368470399,  -986774795,  -208390437, 394585, 15159, 55571 },
    {   835164000000LL,  74168,   963271448,  -429740806,   200879220, 375451, 15932, 58403 },
};
#define CROSS_MOON_ROW_COUNT (sizeof cross_moon_rows / sizeof cross_moon_rows[0])

typedef struct {
    int32_t star;    /* index into astro_nav_stars[] */
    int64_t ut1_ms;
    int32_t x, y, z; /* ITRS apparent direction, Q2.30 */
} cross_star_row_t;

static const cross_star_row_t cross_star_rows[] = {
    {  0,       12345678LL,  -650673572,   796332244,  -308869493 },
    {  1,       12345678LL,  -363474678,   539731342,  -854106399 },
    {  2,       12345678LL,  -478119006,  -894343510,   352807888 },
    {  3,       12345678LL,   505891861,  -666799741,   672586823 },
    {  4,       12345678LL,  -219790435,   712804022,   772349723 },
    {  5,       12345678LL,  -303584329,  1018469525,  -153224953 },
    {  6,       12345678LL,  -851591691,   646650335,    97757051 },
    {  7,       12345678LL,  -479367948,   950776720,   138388963 },
    {  8,       12345678LL,   354569444,   460220416,  -902994564 },
    {  9,       12345678LL,   875877417,  -598628262,   165542921 },
    { 10,       12345678LL,  -124449758,  1021934202,   305097113 },
    { 11,       12345678LL,  -687568611,  -798117328,  -207797115 },
    { 12,       12345678LL,    88889613,  -957404252,  -477909238 },
    { 13,       12345678LL,  -769653308,   553210253,   504493515 },
    { 14,       12345678LL,   911712453,   199902574,  -530792679 },
    { 15,       12345678LL,   702015342,  -279202903,   762982112 },
    { 16,       12345678LL, -1050407961,     -994997,   222628907 },
    { 17,       12345678LL,     5555468,    12564712,  1073653934 },
    {  0,    81252345678LL, -1027394882,   -44616304,  -308853763 },
    {  1,    81252345678LL,  -649981938,    32104159,  -854057555 },
    {  2,    81252345678LL,   430551545,  -918253158,   352644310 },
    {  3,    81252345678LL,   836925642,     6428629,   672633367 },
    {  4,    81252345678LL,  -702630259,   250354518,   772369626 },
    {  5,    81252345678LL,  -997646852,   366316513,  -153083230 },
    {  6,    81252345678LL, -1027713111,  -295264437,    97704549 },
    {  7,    81252345678LL, -1048597647,   184914945,   138459176 },
    {  8,    81252345678LL,  -156649891,   559841153,  -902751461 },
    {  9,    81252345678LL,  1003634724,   343794542,   165662785 },
    { 10,    81252345678LL,  -893224459,   511775803,   305216476 },
    { 11,    81252345678LL,   228113242, -1028394891,  -208062015 },
    { 12,    81252345678LL,   820376615,  -501354063,  -478066751 },
    { 13,    81252345678LL,  -903808415,  -285617428,   504454694 },
    { 14,    81252345678LL,   385220047,   850359016,  -530487100 },
    { 15,    81252345678LL,   643652811,   395429028,   763065166 },
    { 16,    81252345678LL,  -627798774,  -842195925,   222477476 },
    { 17,    81252345678LL,    -6790415,    11898888,  1073654419 },
    {  0,   162492345678LL,  -578879292,  -849911252,  -308984033 },
    {  1,   162492345678LL,  -414611275,  -501456014,  -854143349 },
    {  2,   162492345678LL,   993494852,  -204457160,   352259498 },
    {  3,   162492345678LL,   495902992,   674300873,   672547440 },
    {  4,   162492345678LL,  -620731984,  -413387026,   772479433 },
    {  5,   162492345678LL,  -890389689,  -580253083,  -153081895 },
    {  6,   162492345678LL,  -378134123, -1000210640,    97543662 },
    {  7,   162492345678LL,  -775444160,  -729683696,   138454192 },
    {  8,   162492345678LL,  -542318978,   209614621,  -902703352 },
    {  9,   162492345678LL,   325228294,  1009798040,   165698458 },
    { 10,   162492345678LL,  -944406627,  -409620234,   305334066 },
    { 11,   162492345678LL,   960483830,  -432407381,  -208365479 },
    { 12,   162492345678LL,   892493618,   357393164,  -478170233 },
    { 13,   162492345678LL,  -311641075,  -895228655,   504348095 },
    { 14,   162492345678LL,  -450811844,   817574777,  -530341088 },
    { 15,   162492345678LL,    68624721,   752223021,   763133461 },
    { 16,   162492345678LL,   299428360, -1006927718,   222172753 },
    { 17,   162492345678LL,   -13175471,     1504824,  1073659931 },
    {  0,   243732345678LL,   334491681,  -972418230,  -308933012 },
    {  1,   243732345678LL,   153470292,  -632436215,  -854044968 },
    {  2,   243732345678LL,   758414580,   673603610,   352117886 },
    {  3,   243732345678LL,  -243442583,   800688524,   672722158 },
    {  4,   243732345678LL,   -39963325,  -744737448,   772457488 },
    {  5,   243732345678LL,   -67849383, -1060629085,  -152917981 },
    {  6,   243732345678LL,   575102158,  -901486574,    97472914 },
    {  7,   243732345678LL,   120703782, -1057906129,   138516151 },
    {  8,   243732345678LL,  -492700191,  -309349359,  -902480471 },
    {  9,   243732345678LL,  -614576839,   864685411,   165939608 },
    { 10,   243732345678LL,  -236730366, -1001786883,   305455854 },
    { 11,   243732345678LL,   921172284,   510742328,  -208579486 },
    { 12,   243732345678LL,   247524381,   928923127,  -478283398 },
    { 13,   243732345678LL,   530880709,  -785388616,   504233973 },
    { 14,   243732345678LL,  -925021281,   127740050,  -530037370 },
    { 15,   243732345678LL,  -561490712,   504900963,   763364070 },
    { 16,   243732345678LL,   985946392,  -362703596,   221984949 },
    { 17,   243732345678LL,    -8814589,    -9806790,  1073660856 },
    {  0,   324972345678LL,   979196889,  -313872632,  -309158420 },
    {  1,   324972345678LL,   598279541,  -255580161,  -854202480 },
    {  2,   324972345678LL,   -86076152,  1010817807,   351795056 },
    {  3,   324972345678LL,  -787223865,   284165869,   672643925 },
    {  4,   324972345678LL,   572850155,  -477475792,   772516066 },
    {  5,   324972345678LL,   809153950,  -689045489,  -152995765 },
    {  6,   324972345678LL,  1066441847,   -78524327,    97248243 },
    {  7,   324972345678LL,   919877716,  -536266888,   138435248 },
    {  8,   324972345678LL,   -47243799,  -579993939,  -902383820 },
    {  9,   324972345678LL, -1060538499,    24988413,   165997520 },
    { 10,   324972345678LL,   661020266,  -789080882,   305491529 },
    { 11,   324972345678LL,   141691100,  1043649669,  -208903100 },
    { 12,   324972345678LL,  -596377578,   753941251,  -478359571 },
    { 13,   324972345678LL,   947006764,   -44398026,   504111604 },
    { 14,   324972345678LL,  -655995761,  -664749753,  -529810186 },
    { 15,   324972345678LL,  -740528276,  -147589677,   763385004 },
    { 16,   324972345678LL,   880496207,   573157055,   221673011 },
    { 17,   324972345678LL,     2565348,   -12651883,  1073664218 },
    {  0,   406212345678LL,   837346594,   596818191,  -309160530 },
    {  1,   406212345678LL,   562852242,   326425079,  -854146080 },
    {  2,   406212345678LL,  -861334909,   536077450,   351631407 },
    {  3,   406212345678LL,  -698720953,  -460445035,   672830517 },
    {  4,   406212345678LL,   725272801,   173671514,   772488883 },
    {  5,   406212345678LL,  1036218918,   236200412,  -152909198 },
    {  6,   406212345678LL,   700938482,   807571961,    97130210 },
    {  7,   406212345678LL,   979997975,   416364618,   138441249 },
    {  8,   406212345678LL,   436628623,  -384937263,  -902275043 },
    {  9,   406212345678LL,  -654596827,  -834736565,   166250910 },
    { 10,   406212345678LL,  1027719204,    57782425,   305574758 },
    { 11,   406212345678LL,  -751327563,   738054592,  -209054579 },
    { 12,   406212345678LL,  -960908517,   -26693161,  -478397117 },
    { 13,   406212345678LL,   602122747,   732400403,   503943799 },
    { 14,   406212345678LL,   140282218,  -923449175,  -529607425 },
    { 15,   406212345678LL,  -324813776,  -681355159,   763657425 },
    { 16,   406212345678LL,    67618352,  1048479993,   221447435 },
    { 17,   406212345678LL,    11678812,    -5072678,  1073666325 },
    {  0,   487452345678LL,    23038421,  1027970118,  -309302720 },
    {  1,   487452345678LL,    75571137,   646142344,  -854230987 },
    {  2,   487452345678LL,  -944913754,  -369529966,   351435779 },
    {  3,   487452345678LL,   -49087608,  -835364437,   672813621 },
    {  4,   487452345678LL,   294802620,   685019776,   772502962 },
    {  5,   487452345678LL,   430943653,   971506399,  -152919550 },
    {  6,   487452345678LL,  -227565455,  1044859483,    96974892 },
    {  7,   487452345678LL,   252889055,  1034318025,   138401060 },
    {  8,   487452345678LL,   569988755,   119352688,  -902102688 },
    {  9,   487452345678LL,   277291326, -1023896246,   166335514 },
    { 10,   487452345678LL,   568710048,   857959921,   305606215 },
    { 11,   487452345678LL, -1040826850,  -160568404,  -209329310 },
    { 12,   487452345678LL,  -553257881,  -786050128,  -478489726 },
    { 13,   487452345678LL,  -226545575,   920715613,   503866417 },
    { 14,   487452345678LL,   823996823,  -440177139,  -529334324 },
    { 15,   487452345678LL,   351573910,  -667918785,   763676494 },
    { 16,   487452345678LL,  -799676321,   681537832,   221236231 },
    { 17,   487452345678LL,    10990450,     6287633,  1073667165 },
    {  0,   568692345678LL,  -809956204,   633399402,  -309350367 },
    {  1,   568692345678LL,  -472517335,   447132651,  -854237242 },
    {  2,   568692345678LL,  -269445461,  -978270477,   351151708 },
    {  3,   568692345678LL,   639728754,  -539400669,   672841396 },
    {  4,   568692345678LL,  -372785078,   645832637,   772562616 },
    {  5,   568692345678LL,  -520738095,   926489570,  -152873860 },
    {  6,   568692345678LL,  -973455149,   442634198,    96858378 },
    {  7,   568692345678LL,  -677633550,   821325476,   138415097 },
    {  8,   568692345678LL,   245421858,   528164274,  -902071015 },
    {  9,   568692345678LL,   986219313,  -390625851,   166446434 },
    { 10,   568692345678LL,  -347407583,   968899800,   305716624 },
    { 11,   568692345678LL,  -494109093,  -929987756,  -209524418 },
    { 12,   568692345678LL,   298714855,  -913607384,  -478552491 },
    { 13,   568692345678LL,  -873451383,   369116191,   503743411 },
    { 14,   568692345678LL,   845774144,   396873190,  -529225162 },
    { 15,   568692345678LL,   745320490,  -118199558,   763837506 },
    { 16,   568692345678LL, -1024569127,  -233115126,   220990830 },
    { 17,   568692345678LL,     1214870,    12254249,  1073671208 },
    {  0,   649932345678LL,  -992208241,  -269749431,  -309321120 },
    {  1,   649932345678LL,  -641131942,  -110708195,  -854175060 },
    {  2,   649932345678LL,   622640909,  -801271784,   351003321 },
    {  3,   649932345678LL,   814902477,   189874600,   672906453 },
    {  4,   649932345678LL,  -740513723,    87689060,   772574630 },
    {  5,   649932345678LL, -1053922138,   137276600,  -152724480 },
    {  6,   649932345678LL,  -937193363,  -514992601,    96812841 },
    {  7,   649932345678LL, -1063531690,   -51407632,   138488641 },
    {  8,   649932345678LL,  -276498163,   513004886,  -901829395 },
    {  9,   649932345678LL,   902955319,   556636835,   166579205 },
    { 10,   649932345678LL,  -984148063,   301394843,   305835319 },
    { 11,   649932345678LL,   449493467,  -952298520,  -209772867 },
    { 12,   649932345678LL,   910764420,  -307038674,  -478703382 },
    { 13,   649932345678LL,  -818424279,  -478944478,   503701689 },
    { 14,   649932345678LL,   187878949,   915348136,  -528924186 },
    { 15,   649932345678LL,   540545591,   526435006,   763935962 },
    { 16,   649932345678LL,  -426370893,  -960393417,   220848027 },
    { 17,   649932345678LL,    -9145974,     8218945,  1073671414 },
    {  0,   731172345678LL,  -377451737,  -956392856,  -309458228 },
    {  1,   731172345678LL,  -294926692,  -579797324,  -854268584 },
    {  2,   731172345678LL,  1014695837,    19503598,   350618700 },
    {  3,   731172345678LL,   335746135,   766504665,   672805051 },
    {  4,   731172345678LL,  -513043233,  -540983119,   772687137 },
    {  5,   731172345678LL,  -740544554,  -762357656,  -152728756 },
    {  6,   731172345678LL,  -147914811, -1059103873,    96652472 },
    {  7,   731172345678LL,  -595017800,  -883005142,   138481918 },
    {  8,   731172345678LL,  -576536334,    85572290,  -901778655 },
    {  9,   731172345678LL,    94446116,  1056525337,   166600266 },
    { 10,   731172345678LL,  -830229958,  -608304805,   305949318 },
    { 11,   731172345678LL,  1031942697,  -209479851,  -210080860 },
    { 12,   731172345678LL,   790858343,   546081851,  -478810191 },
    { 13,   731172345678LL,  -105635620,  -942415106,   503603404 },
    { 14,   731172345678LL,  -620982544,   698352766,  -528777457 },
    { 15,   731172345678LL,   -98033601,   748089958,   763984511 },
    { 16,   731172345678LL,   514648110,  -916197167,   220548360 },
    { 17,   731172345678LL,   -11621684,    -2458422,  1073676114 },
    {  0,   812412345678LL,   540369891,  -874754478,  -309396977 },
    {  1,   812412345678LL,   287928383,  -583459979,  -854162282 },
    {  2,   812412345678LL,   591683913,   824622503,   350470226 },
    {  3,   812412345678LL,  -413104797,   727574559,   672979340 },
    {  4,   812412345678LL,   126731048,  -734739111,   772670165 },
    {  5,   812412345678LL,   167750183, -1049527277,  -152557781 },
    {  6,   812412345678LL,   760064777,  -752259074,    96588436 },
    {  7,   812412345678LL,   351527887, -1005063804,   138551072 },
    {  8,   812412345678LL,  -413702577,  -411039554,  -901564289 },
    {  9,   812412345678LL,  -790063168,   707733253,   166839254 },
    { 10,   812412345678LL,    -9199750, -1029151396,   306078868 },
    { 11,   812412345678LL,   785344510,   701379883,  -210289716 },
    { 12,   812412345678LL,    35562355,   960358663,  -478923859 },
    { 13,   812412345678LL,   691971056,  -648533373,   503489848 },
    { 14,   812412345678LL,  -931250227,   -79981050,  -528486093 },
    { 15,   812412345678LL,  -657848350,   368948247,   764221332 },
    { 16,   812412345678LL,  1042054079,  -135961926,   220361420 },
    { 17,   812412345678LL,    -4661130,   -10858049,  1073676805 },
    {  0,   893652345678LL,  1024141381,   -90523269,  -309615041 },
    {  1,   893652345678LL,   639528634,  -118631401,  -854313304 },
    {  2,   893652345678LL,  -306866981,   967547230,   350152135 },
    {  3,   893652345678LL,  -830190173,   104448093,   672901462 },
    {  4,   893652345678LL,   664535928,  -337942614,   772727827 },
    {  5,   893652345678LL,   941234021,  -493665446,  -152625193 },
    {  6,   893652345678LL,  1057530811,   158943338,    96369614 },
    {  7,   893652345678LL,  1015639381,  -319722173,   138477015 },
    {  8,   893652345678LL,    81539664,  -577631549,  -901451375 },
    {  9,   893652345678LL, -1039785788,  -209552580,   166897382 },
    { 10,   893652345678LL,   819072483,  -623163740,   306118807 },
    { 11,   893652345678LL,   -92316202,  1048827089,  -210620421 },
    { 12,   893652345678LL,  -748352128,   602860839,  -479008774 },
    { 13,   893652345678LL,   933701140,   166549469,   503373579 },
    { 14,   893652345678LL,  -493270054,  -794080613,  -528244392 },
    { 15,   893652345678LL,  -689290997,  -306169970,   764237774 },
    { 16,   893652345678LL,   732361617,   753753251,   220054544 },
    { 17,   893652345678LL,     5828592,    -9984423,  1073679581 },
    {  0,   974892345678LL,   685254964,   766470275,  -309629547 },
    {  1,   974892345678LL,   477784990,   441440713,  -854267584 },
    {  2,   974892345678LL,  -958832735,   333291084,   349969062 },
    {  3,   974892345678LL,  -580518080,  -602400533,   673077901 },
    {  4,   974892345678LL,   668236200,   330614791,   772706766 },
    {  5,   974892345678LL,   958659736,   458935723,  -152548409 },
    {  6,   974892345678LL,   505300921,   942512655,    96241258 },
    {  7,   974892345678LL,   863740655,   622653770,   138476959 },
    {  8,   974892345678LL,   511780022,  -280297554,  -901352315 },
    {  9,   974892345678LL,  -454291590,  -958437664,   167146342 },
    { 10,   974892345678LL,   989282652,   283692379,   306202503 },
    { 11,   974892345678LL,  -895513187,   553668929,  -210780343 },
    { 12,   974892345678LL,  -930800060,  -238848912,  -479044830 },
    { 13,   974892345678LL,   425080403,   847949696,   503199233 },
    { 14,   974892345678LL,   341268478,  -870415907,  -528046853 },
    { 15,   974892345678LL,  -167189034,  -735183684,   764509177 },
    { 16,   974892345678LL,  -165752805,  1037848418,   219813952 },
    { 17,   974892345678LL,    11368337,     -860815,  1073681296 },
    {  0,  1056132345678LL,  -203877809,  1007671355,  -309764077 },
    {  1,  1056132345678LL,   -67445700,   646893996,  -854342285 },
    {  2,  1056132345678LL,  -840741506,  -568966724,   349788639 },
    {  3,  1056132345678LL,   135387412,  -825560672,   673083449 },
    {  4,  1056132345678LL,   134931452,   733236155,   772709356 },
    {  5,  1056132345678LL,   206091081,  1042677338,  -152551435 },
    {  6,  1056132345678LL,  -452737350,   968874532,    96086098 },
    {  7,  1056132345678LL,    18050462,  1064627136,   138436799 },
    {  8,  1056132345678LL,   531154132,   242265872,  -901168153 },
    {  9,  1056132345678LL,   496255607,  -937378687,   167251529 },
    { 10,  1056132345678LL,   364714397,   962354959,   306231685 },
    { 11,  1056132345678LL,  -979330180,  -386383036,  -211049882 },
    { 12,  1056132345678LL,  -365226204,  -888797913,  -479134213 },
    { 13,  1056132345678LL,  -425055807,   848011814,   503115323 },
    { 14,  1056132345678LL,   901780079,  -247353472,  -527759845 },
    { 15,  1056132345678LL,   489018502,  -573806193,   764544872 },
    { 16,  1056132345678LL,  -930782013,   488201017,   219604451 },
    { 17,  1056132345678LL,     7442980,     8575987,  1073681777 },
    {  0,  1137372345678LL,  -929427303,   439417731,  -309836167 },
    {  1,  1137372345678LL,  -558662052,   332973646,  -854369222 },
    {  2,  1137372345678LL,   -47280334, -1014168411,   349497509 },
    {  3,  1137372345678LL,   742319414,  -385772811,   673099347 },
    {  4,  1137372345678LL,  -507007086,   546529206,   772768495 },
    {  5,  1137372345678LL,  -712269021,   788878641,  -152528148 },
    {  6,  1137372345678LL, -1047255317,   216727307,    95953531 },
    {  7,  1137372345678LL,  -842387695,   651260603,   138434470 },
    {  8,  1137372345678LL,   123716551,   570573030,  -901144904 },
    {  9,  1137372345678LL,  1047951333,  -163436591,   167355874 },
    { 10,  1137372345678LL,  -553070775,   867868899,   306329556 },
    { 11,  1137372345678LL,  -276364985, -1015833393,  -211249656 },
    { 12,  1137372345678LL,   493560853,  -824437215,  -479189385 },
    { 13,  1137372345678LL,  -933914687,   166521068,   502986676 },
    { 14,  1137372345678LL,   737823642,   574560805,  -527652973 },
    { 15,  1137372345678LL,   752224526,    48192264,   764694235 },
    { 16,  1137372345678LL,  -948060763,  -453859465,   219348765 },
    { 17,  1137372345678LL,    -2649162,    10712554,  1073685116 },
};
#define CROSS_STAR_ROW_COUNT (sizeof cross_star_rows / sizeof cross_star_rows[0])

typedef struct {
    int64_t ut1_ms;
    int32_t gha_marcmin; /* apparent GAST as GHA Aries */
} cross_aries_row_t;

static const cross_aries_row_t cross_aries_rows[] = {
    {       12345678LL, 19922294 },
    {    81252345678LL, 16729210 },
    {   162492345678LL, 13536294 },
    {   243732345678LL, 10343431 },
    {   324972345678LL,  7150500 },
    {   406212345678LL,  3957400 },
    {   487452345678LL,   764163 },
    {   568692345678LL, 19170909 },
    {   649932345678LL, 15977779 },
    {   731172345678LL, 12784820 },
    {   812412345678LL,  9591947 },
    {   893652345678LL,  6399047 },
    {   974892345678LL,  3205998 },
    {  1056132345678LL,    12797 },
    {  1137372345678LL, 18419533 },
    {   820731600000LL, 21499911 },
    {   836629200000LL, 10781494 },
    {  1104670800000LL,  7049719 },
    {  1120636800000LL, 13478047 },
};
#define CROSS_ARIES_ROW_COUNT (sizeof cross_aries_rows / sizeof cross_aries_rows[0])

typedef struct {
    int32_t lat_cdeg, lon_east_cdeg; /* observer */
    int32_t gha_cdeg, dec_cdeg;      /* body GP */
    int32_t hc_marcmin;              /* oracle Hc */
    int32_t zn_marcmin;              /* oracle Zn */
} cross_reduce_row_t;

static const cross_reduce_row_t cross_reduce_rows[] = {
    {   4500,  -3000,  4500,  2000,  3725274, 12678128 },
    {      0,      0, 33000,     0,  3600000,  5400000 },
    {      0,  17950, 21000, -1200,  3501439, 14799142 },
    {  -3356,  15123, 20200, -1650,  4313018,  1278918 },
    {   7800,   -500, 12000,  6215,  3328048, 18700729 },
    {   8900,   4500, 20000,  8000,  4772307,  3604913 },
    {   2312, -15801, 16000, -2800,  2330638, 10935365 },
    {   5150,     -1,     0,  2326,  3705600, 10798835 },
    {   5150,     -1, 35999,  2326,  3705600, 10797670 },
    {   4500,  -3000,  3100,  4480,  5355838, 15275177 },
    {   4500,  -3000, 15000, -2000, -2102098, 16580265 },
    {   6912,   1033, 27000,  1512,  1066970,  5648508 },
    {  -5601,  -6754,  8000, -5000,  4824904, 18216105 },
    {   1500,  12000, 29500,  2100,  2255310, 17111113 },
    {   3333, -17999, 15000,   333,  2938110,  7831465 },
    {   2000,   5999, 26000,  -100,  2732020,  6804674 },
};
#define CROSS_REDUCE_ROW_COUNT (sizeof cross_reduce_rows / sizeof cross_reduce_rows[0])

typedef struct {
    int32_t dr_lat_cdeg, dr_lon_cdeg;
    int32_t gha1_cdeg, dec1_cdeg;
    int32_t ho1_marcmin;
    int32_t gha2_cdeg, dec2_cdeg;
    int32_t ho2_marcmin;
    int32_t lat_marcmin, lon_marcmin; /* oracle fix */
} cross_fix_row_t;

static const cross_fix_row_t cross_fix_rows[] = {
    {   4450,  -3100,  4500,  2000, 3731200,  1000,  1000, 3040817,  2707404,  -1834069 },
    {   3700,  -2500,  4000,  1500, 3874219,  3000,   500, 3471223,  2212199,  -1524598 },
    {   1000,  14000, 22500,  3000, 4169944, 20500, -2500, 3128370,   612001,   8442002 },
    {      0,      0, 33000,  1200, 3515567,  3000, -1500, 3360956,    50997,     24002 },
    {   7800,   1500, 33000,  6000, 4265474, 12000,  7000, 3633754,  4700699,    940189 },
    {  -4200,  14800, 20000, -2000, 3905065, 25000, -6000, 3686426, -2550002,   8838003 },
    {   1200, -17950, 17000,   500, 4654444, 19500,  2500, 4266331,   740397,  10790997 },
    {   2100, -15800, 15850,  2050, 5340076, 16400,  1800, 5000605,  1278000,  -9471600 },
    {   5000,   -200,  6000,  1500, 1872886, 32000, -1000, 1160245,  3054000,    -84000 },
    {   3400, -11700, 12500,  1400, 4197593, 10000,  2800, 4423798,  1980000,  -7080000 },
    {   -100,  17900, 15500,  1000, 3735769, 18200, -1200, 4706311,   -30000,  10752000 },
    {   5900, -15200, 17500,  2300, 3050468, 13000,  4000, 3989725,  3522600,  -9146401 },
    {   2400,   5500, 33500,  1200, 3570117, 30800,  2600, 5244642,  1473600,   3262800 },
    {  -3400,   1800, 34500, -1800, 4427340, 35500,  -800, 3676722, -2035200,   1105199 },
};
#define CROSS_FIX_ROW_COUNT (sizeof cross_fix_rows / sizeof cross_fix_rows[0])