/************************************************************************ The PLANETARY SOLUTION VSOP87 by Bretagnon P. and Francou G. can be found at ftp://ftp.imcce.fr/pub/ephem/planets/vsop87 I (Johannes Gajdosik) have just taken the data obtained from above (VSOP87.mer,...,VSOP87.nep) and rearranged it into this piece of software. I can neigther allow nor forbid the usage of VSOP87. The copyright notice below covers not the work of Bretagnon P. and Francou G. but just my work, that is the compilation of the VSOP87 data into the software supplied in this file. Copyright (c) 2006 Johannes Gajdosik 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. This is my implementation of the VSOP87 planetary solution. I tried to optimize for speed by rearranging the terms so that for a given touple of (a[0],a[1],...,a[11]) the values (cos,sin)(a[0]*lambda[0](T)+...a[11]*lambda[11](T)) have only to be calculated once. Furthermore I used the addition formulas (cos,sin)(x+y) = ... so that for given T the functions cos and sin have only to be called 12 times. ****************************************************************/ #include "vsop87.h" #include "calc_interpolated_elements.h" #include "elliptic_to_rectangular.h" #include #include static const int vsop87_max_lambda_factor[12] = { 16, 27, 27, 32, 22, 26, 24, 23, 2, 1, 2, 1, }; static const double lambda_0[12] = { 4.40260884240, 3.17614669689, 1.75347045953, 6.20347611291, 0.59954649739, 0.87401675650, 5.48129387159, 5.31188628676, 5.19846674103, 1.62790523337, 2.35555589827, 3.81034454697, }; static const double lambda_1[12] = { 26087.9031415742, 10213.2855462110, 6283.0758499914, 3340.6124266998, 529.6909650946, 213.2990954380, 74.7815985673, 38.1330356378, 77713.7714681205, 84334.6615813083, 83286.9142695536, 83997.0911355954, }; /* taken out from vsop87_constants: */ static const double vsop87_l[8] = { 26087.90314157420, 10213.28554621100, 6283.07584999140, 3340.61242669981, 529.69096509460, 213.29909543800, 74.78159856730, 38.13303563780, }; static const double vsop87_constants[253] = { 0.38709830982, 0.00000000000, 0.00000000000, 4.40260884240, 0.0, -0.00000934669, 0.00000003100, 0.04466059760, -0.00552114624, -0.00001860568, 0.00000079123, 0.00000000590, -0.00000000016, 0.20072331368, 0.00143750118, -0.00007974120, -0.00000030459, 0.00000000812, -0.00000000008, 0.04061563384, 0.00065433117, -0.00001071215, 0.00000022459, -0.00000000377, -0.00000000003, 0.04563550461, -0.00127633657, -0.00000913350, 0.00000018993, -0.00000000640, -0.00000000002, 0.72332981996, 0.00000000000, 0.00000000000, 3.17614669689, 0.0, 0.00000287889, -0.00000003038, -0.00449282133, 0.00031259019, 0.00000604065, -0.00000068351, 0.00000000494, 0.00000000060, 0.00506684726, -0.00036121239, 0.00001846764, 0.00000003281, -0.00000000614, -0.00000000017, 0.00682410142, 0.00138133826, -0.00001090942, -0.00000186418, 0.00000000602, 0.00000000075, 0.02882285775, -0.00040384791, -0.00006232891, 0.00000024731, 0.00000004229, -0.00000000006, 1.00000101778, 0.00000000000, 0.00000000000, 1.75347045953, 0.0, -0.00000991013, -0.00000002537, 0.00000000000, 0.00000000000, -0.00374081650, -0.00082267418, 0.00002762465, 0.00000116955, -0.00000002696, -0.00000000071, 0.01628447663, -0.00062029655, -0.00003382631, 0.00000085101, 0.00000002770, -0.00000000047, 0.00000000000, -0.00113468869, 0.00001237314, 0.00000126542, -0.00000001372, -0.00000000032, 0.00000000000, 0.00010180375, 0.00004701998, -0.00000054174, -0.00000002508, 0.00000000046, 1.52367934191, 0.00000000000, 0.00000000000, 6.20347611291, 0.0, 0.00000457003, -0.00000005057, 0.00000000000, 0.00000000000, 0.08536560252, 0.00376330152, -0.00024657776, -0.00000367305, 0.00000011112, 0.00000000026, -0.03789973236, 0.00624657465, 0.00015529482, -0.00000634879, -0.00000006593, 0.00000000073, 0.01047042574, 0.00017138526, -0.00004077491, -0.00000138835, 0.00000000916, 0.00000000176, 0.01228449307, -0.00108020083, -0.00001922224, 0.00000087186, 0.00000003090, 5.20260319132, 0.00000191323, 0.00000000000, 0.00000000000, 0.00000000000, 0.00000000000, 0.59954649739, 0.0, -0.00014837133, 0.00000007482, 0.00000000000, 0.00000000000, 0.04698572124, 0.00113010377, -0.00010930126, -0.00000428748, 0.00000020539, 0.01200385748, 0.00217149360, 0.00009858539, -0.00000513109, -0.00000009007, -0.00206561098, -0.00031340156, -0.00001667392, 0.00000076926, 0.01118377157, -0.00023427562, 0.00002086760, 0.00000050721, 9.55490959574, -0.00002138957, 0.00000000000, 0.00000000000, 0.00000000000, 0.00000000000, 0.87401675650, 0.0, 0.00036659741, -0.00000033330, 0.00000000217, 0.00000000000, -0.00296003595, -0.00529602626, 0.00030928405, 0.00001296215, -0.00000059959, 0.00000000000, 0.05542964254, -0.00375593887, -0.00031990236, 0.00001598633, 0.00000032451, 0.00000000000, -0.00871747436, 0.00080171499, 0.00004142282, -0.00000196049, -0.00000009439, 0.01989147301, 0.00059439766, -0.00005235117, -0.00000127219, 0.00000008295, 19.21844606178, -0.00000037163, 0.00000009791, 0.00000000000, 0.00000000000, 0.00000000000, 5.48129387159, 0.0, -0.00000848828, 0.00000010450, 0.00000000000, 0.00000000000, -0.04595132376, 0.00018344115, -0.00000080849, -0.00000045396, 0.00000002185, 0.00563791307, -0.00074964350, 0.00001210200, -0.00000042088, -0.00000001714, 0.00185915075, -0.00012449382, -0.00000207373, 0.00000007621, 0.00648617008, -0.00011744733, 0.00000317799, 0.00000007317, 30.11038686942, -0.00000166346, 0.00000006857, 0.00000000000, 0.00000000000, 0.00000000000, 5.31188628676, 0.0, 0.00000102311, -0.00000004340, 0.00000000000, 0.00000000000, 0.00599977571, 0.00000871304, -0.00000119902, -0.00000004034, 0.00000000000, 0.00000000000, 0.00669242413, 0.00007824336, 0.00000080801, -0.00000003955, 0.00000000000, 0.00000000000, -0.01029147819, -0.00000072727, -0.00000006568, 0.00000001668, 0.01151683985, 0.00002575536, 0.00000019377, 0.00000001331, }; static const double vsop87_coefficients[61126*2] = { -0.00000002893, -0.00000011799, 0.00000000332, -0.00000000078, 0.00000000001, 0.00000000003, -0.00000091933, 0.00000023240, -0.00000000656, -0.00000002636, 0.00000000033, -0.00000000009, -0.00000063987, 0.00000001677, 0.00000000006, -0.00000000055, 0.00000001754, -0.00000064219, -0.00000000058, -0.00000000056, -0.00000001018, 0.00000001921, 0.00000000087, 0.00000000151, -0.00000004656, -0.00000001902, -0.00000000125, 0.00000000062, 0.00000002356, -0.00000000340, 0.00000034105, -0.00000000214, -0.00000000097, 0.00000033741, 0.00000000025, -0.00000000050, 0.00000000125, 0.00000000028, 0.00000001423, 0.00000000081, -0.00000000035, 0.00000000059, 0.00000039352, -0.00000000242, -0.00000000244, 0.00000038921, -0.00000002629, -0.00000006147, 0.00000000453, -0.00000000270, 0.00000048318, -0.00000000210, -0.00000000203, 0.00000047817, -0.00000000124, -0.00000000139, 0.00000000059, 0.00000000064, 0.00000001642, -0.00000006257, 0.00000000289, -0.00000000150, 0.00000089329, -0.00000000565, -0.00000000372, 0.00000088559, -0.00000000180, -0.00000000143, 0.00000010075, 0.00000000464, -0.00000000678, 0.00000000954, 0.00000120906, -0.00000000875, -0.00000000297, 0.00000120136, -0.00000000332, -0.00000000171, 0.00000001393, 0.00000011733, -0.00000000173, -0.00000000044, 0.00000171894, -0.00000000976, -0.00000000859, 0.00000170186, 0.00000000307, 0.00000000307, 0.00000002168, -0.00000001934, 0.00000214912, -0.00000001640, -0.00000000844, 0.00000213398, -0.00000000066, -0.00000000043, -0.00000000073, -0.00000000049, -0.00000000005, -0.00000000003, -0.00000000003, 0.00000000005, -0.00000000007, 0.00000000009, -0.00000000007, 0.00000000027, 0.00000000005, 0.00000000001, 0.00000000028, 0.00000000006, 0.00000000001, -0.00000000005, 0.00000000002, 0.00000000004, 0.00000000005, 0.00000000003, -0.00000000001, 0.00000000004, 0.00000000054, 0.00000000015, 0.00000000002, -0.00000000011, 0.00000000142, -0.00000000013, -0.00000000002, -0.00000000022, -0.00000000014, -0.00000000143, -0.00000000023, 0.00000000002, 0.00000000011, 0.00000000010, 0.00000000013, -0.00000000012, 0.00000000020, 0.00000000001, 0.00000000023, -0.00000000002, 0.00000000000, -0.00000000004, -0.00000000020, -0.00000000285, -0.00000000045, 0.00000000005, -0.00000000297, -0.00000000677, -0.00000000091, 0.00000000040, 0.00000000002, 0.00000000004, -0.00000000686, 0.00000000303, 0.00000000040, 0.00000000092, 0.00000000004, -0.00000000002, 0.00000000026, -0.00000000060, -0.00000000005, -0.00000000001, -0.00000000070, -0.00000000042, -0.00000000003, 0.00000000007, 0.00000000024, 0.00000000056, 0.00000000057, -0.00000000024, 0.00000000002, -0.00000000008, -0.00000000008, -0.00000000002, -0.00000000005, 0.00000000000, 0.00000000000, 0.00000000005, 0.00000000006, -0.00000000032, 0.00000000000, 0.00000000005, 0.00000000005, 0.00000000000, 0.00000000014, 0.00000000000, -0.00000000063, -0.00000000146, -0.00000000018, 0.00000000008, -0.00000001283, 0.00000000552, 0.00000000078, 0.00000000171, 0.00000000007, -0.00000000003, -0.00000003012, 0.00000002660, 0.00000000258, 0.00000000304, 0.00000000012, -0.00000000011, 0.00000002703, 0.00000003054, 0.00000000309, -0.00000000262, -0.00000000011, -0.00000000013, -0.00000000283, -0.00000000033, 0.00000000005, 0.00000000013, -0.00000000099, 0.00000000359, 0.00000000023, 0.00000000001, 0.00000000029, 0.00000000068, 0.00000000072, -0.00000000031, 0.00000000250, -0.00000000219, -0.00000000221, -0.00000000259, -0.00000000003, 0.00000000011, 0.00000000011, 0.00000000003, 0.00000000001, -0.00000000005, 0.00000000048, 0.00000000012, -0.00000000033, -0.00000000001, -0.00000000001, 0.00000000034, 0.00000000026, 0.00000000003, 0.00000002208, -0.00000017037, 0.00000000500, 0.00000000347, 0.00000000001, -0.00000000093, -0.00000000091, 0.00000000002, 0.00000000001, -0.00000000009, -0.00000000224, 0.00000001642, -0.00000000048, -0.00000000042, 0.00000000084, -0.00000000576, -0.00000000969, 0.00000000846, 0.00000000083, 0.00000000098, 0.00000000004, -0.00000000004, 0.00000003239, 0.00000003521, 0.00000000345, -0.00000000319, -0.00000000012, -0.00000000012, 0.00000020786, 0.00000012709, 0.00000000881, -0.00000001318, -0.00000000038, -0.00000000023, 0.00000012949, -0.00000021142, -0.00000001346, -0.00000000909, -0.00000000025, 0.00000000039, 0.00000000221, 0.00000001231, 0.00000000006, -0.00000000030, 0.00000001794, 0.00000000034, -0.00000000018, -0.00000000061, 0.00000000359, -0.00000000314, -0.00000000029, -0.00000000034, -0.00000000185, -0.00000000203, -0.00000001743, -0.00000001067, -0.00000000069, 0.00000000104, -0.00000001115, 0.00000001770, 0.00000000107, 0.00000000074, -0.00000000003, -0.00000000068, -0.00000000083, -0.00000000006, -0.00000000004, 0.00000000017, -0.00000000696, -0.00000000163, 0.00000000000, 0.00000000018, 0.00000000109, 0.00000000000, 0.00000000000, -0.00000000112, 0.00000000005, 0.00000000000, 0.00000000015, -0.00000000159, 0.00000000003, 0.00000000002, 0.00000000001, -0.00000000015, -0.00000000011, 0.00000000002, 0.00000000007, -0.00000000004, 0.00000016706, 0.00000010365, 0.00000000718, -0.00000001078, -0.00000000031, -0.00000000019, -0.00000146974, 0.00000231921, 0.00000015141, 0.00000010270, 0.00000000280, -0.00000000452, 0.00000064161, -0.00000238769, -0.00000007418, -0.00000002531, -0.00000000018, 0.00000000119, -0.00000243967, -0.00000066559, -0.00000002771, 0.00000007730, 0.00000000132, 0.00000000035, 0.00000006138, -0.00000003078, -0.00000000053, 0.00000000274, -0.00000000003, -0.00000000007, -0.00000002102, -0.00000012748, -0.00000000093, 0.00000000113, -0.00000000014, 0.00000000009, -0.00000004647, -0.00000002879, -0.00000000200, 0.00000000299, 0.00000000009, 0.00000000005, 0.00000007314, -0.00000011549, -0.00000000753, -0.00000000511, -0.00000004963, 0.00000020844, 0.00000000598, 0.00000000171, 0.00000021294, 0.00000005391, 0.00000000212, -0.00000000638, -0.00000000412, 0.00000000085, 0.00000000044, 0.00000000587, -0.00000000002, 0.00000000000, 0.00000000000, 0.00000000044, -0.00000000010, -0.00000000002, -0.00000000009, 0.00000000004, -0.00000016521, 0.00000071340, 0.00000002014, 0.00000000574, 0.00000000005, -0.00000000027, 0.00001686982, 0.00000394035, 0.00000013916, -0.00000047867, -0.00000000613, -0.00000000132, 0.00000445156, -0.00000003021, 0.00000000012, 0.00000000363, 0.00000000011, 0.00000000015, 0.00000001223, -0.00000463407, -0.00000000322, -0.00000000275, 0.00000000003, 0.00000000013, -0.00000001112, -0.00000001817, -0.00000000122, 0.00000000203, -0.00000000006, -0.00000000010, 0.00000013525, -0.00000000665, -0.00000000081, -0.00000000152, -0.00000000012, -0.00000000007, 0.00000002806, -0.00000013517, -0.00000000356, -0.00000000086, -0.00000081288, -0.00000019014, -0.00000000674, 0.00000002308, 0.00000012697, 0.00000000229, -0.00000000427, -0.00000011417, 0.00000000043, 0.00000000029, 0.00000000123, -0.00000000225, -0.00000000624, -0.00000000122, 0.00000013008, 0.00000000057, 0.00000000017, -0.00000000006, 0.00000000449, -0.00000201760, -0.00000000058, -0.00000000289, 0.00000000004, 0.00000000005, -0.00000000260, -0.00000018158, 0.00000000039, -0.00000000170, -0.00000000001, 0.00000000007, -0.00000002130, 0.00000005242, 0.00000000042, -0.00000000584, -0.00000000654, 0.00000001479, -0.00000000021, -0.00000000047, 0.00000000001, 0.00000000007, 0.00000000357, -0.00000005883, -0.00000000031, 0.00000000044, 0.00000043444, -0.00000000082, 0.00000000015, 0.00000044908, 0.00000000376, 0.00000000274, -0.00000000039, 0.00000000018, 0.00000001221, -0.00000000294, 0.00000000528, 0.00000000186, 0.00000000226, -0.00000000238, 0.00000000016, 0.00000000010, -0.00000000010, -0.00000000003, -0.00000000003, 0.00000000010, -0.00000000018, 0.00000000032, -0.00000000003, 0.00000000012, 0.00000000011, 0.00000000003, 0.00000000020, 0.00000000005, 0.00000000005, 0.00000000000, 0.00000000000, -0.00000000005, 0.00000000004, 0.00000000007, 0.00000000070, 0.00000000041, -0.00000000005, 0.00000000006, 0.00000000421, -0.00000000815, 0.00000000081, 0.00000000065, 0.00000001241, -0.00000000892, 0.00000000057, 0.00000000089, 0.00000000838, 0.00000001262, -0.00000000087, 0.00000000049, 0.00000000069, -0.00000000415, 0.00000000005, 0.00000000010, 0.00000000468, 0.00000000042, -0.00000000009, 0.00000000010, -0.00000000021, 0.00000000043, -0.00000000046, 0.00000000041, -0.00000000040, -0.00000000046, 0.00000000001, -0.00000000011, 0.00000000002, 0.00000000000, -0.00000000156, -0.00000000006, 0.00000000006, -0.00000000021, -0.00000000245, -0.00000000153, 0.00000000018, -0.00000000023, 0.00000000160, -0.00000000239, 0.00000000022, 0.00000000019, -0.00000000082, 0.00000000014, 0.00000000001, -0.00000000004, -0.00000000023, -0.00000000089, 0.00000000006, 0.00000000000, -0.00000000032, -0.00000000098, -0.00000000002, 0.00000000000, 0.00000000011, 0.00000000026, -0.00000000005, 0.00000000001, -0.00000000009, 0.00000000055, -0.00000000007, -0.00000000002, -0.00000000054, -0.00000000011, 0.00000000003, -0.00000000007, 0.00000000008, 0.00000000015, -0.00000000016, 0.00000000010, 0.00000000004, -0.00000000004, 0.00000000011, -0.00000000002, 0.00000000002, 0.00000000011, 0.00000000003, 0.00000000002, 0.00000000002, 0.00000000005, -0.00000000003, -0.00000000004, -0.00000000004, 0.00000000003, 0.00000000016, -0.00000000016, 0.00000000003, -0.00000000005, -0.00000000005, -0.00000000003, 0.00000000005, 0.00000000000, 0.00000000001, 0.00000000001, 0.00000037671, -0.00000029029, 0.00000007389, 0.00000010232, 0.00000000021, -0.00000000019, -0.00000000020, -0.00000000021, -0.00000003026, 0.00000002275, -0.00000000612, -0.00000000742, 0.00000013396, -0.00000010090, 0.00000002593, 0.00000003165, 0.00000000008, 0.00000000001, 0.00000000003, 0.00000000002, 0.00000000004, 0.00000000003, 0.00000000016, 0.00000000004, 0.00000000004, -0.00000000016, 0.00000000005, 0.00000000001, 0.00000000004, -0.00000000030, -0.00000000023, -0.00000000153, -0.00000000012, -0.00000000001, -0.00000000154, 0.00000000023, -0.00000000001, 0.00000000012, 0.00000000003, -0.00000000015, -0.00000000017, -0.00000000006, -0.00000000010, -0.00000000073, -0.00000000005, 0.00000000000, 0.00000000457, -0.00000000010, 0.00000000012, -0.00000000039, -0.00000001699, 0.00000000989, 0.00000000042, 0.00000000124, 0.00000001001, 0.00000001720, 0.00000000128, -0.00000000042, -0.00000000166, 0.00000000028, 0.00000000005, 0.00000000207, 0.00000000001, 0.00000000005, 0.00000000136, -0.00000000078, -0.00000000078, -0.00000000138, 0.00000002569, -0.00000001468, -0.00000000060, -0.00000000180, -0.00000000008, -0.00000000003, -0.00000171761, -0.00000297696, -0.00000020815, 0.00000007247, -0.00000000284, 0.00000000933, -0.00000047216, -0.00000037766, -0.00000002269, 0.00000001739, -0.00000000007, 0.00000000093, -0.00000038482, 0.00000047909, 0.00000001759, 0.00000002397, 0.00000000098, 0.00000000008, -0.00000002101, -0.00000003442, 0.00000000055, -0.00000000091, 0.00000000001, 0.00000000004, -0.00000004920, 0.00000001886, -0.00000000122, -0.00000000015, -0.00000000902, 0.00000000516, 0.00000000021, 0.00000000063, 0.00000005863, 0.00000010166, 0.00000000733, -0.00000000238, 0.00000003610, 0.00000003135, 0.00000000185, -0.00000000104, 0.00000003208, -0.00000003629, -0.00000000105, -0.00000000191, 0.00000000051, 0.00000000128, 0.00000000142, -0.00000000047, -0.00000002090, -0.00000001846, -0.00000000118, 0.00000000069, -0.00000000001, 0.00000000005, -0.00000039197, 0.00000046999, 0.00000001701, 0.00000002406, 0.00000000110, 0.00000000007, -0.00000012312, 0.00000037424, 0.00000000836, 0.00000000583, 0.00000000018, 0.00000000004, 0.00000038180, 0.00000012845, 0.00000000677, -0.00000000874, 0.00000000001, -0.00000000020, -0.00000000936, 0.00000001288, -0.00000000068, -0.00000000053, 0.00000001496, 0.00000001958, -0.00000000044, 0.00000000083, 0.00000000525, 0.00000000498, 0.00000000032, -0.00000000013, 0.00000001330, -0.00000001591, -0.00000000049, -0.00000000076, 0.00000000728, 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0.00000000268, 0.00000001123, 0.00000000123, -0.00000000010, -0.00000000128, -0.00000000125, 0.00000001124, 0.00000000128, -0.00000000010, -0.00000000232, 0.00000000057, -0.00000000055, -0.00000000227, 0.00000000124, -0.00000000002, 0.00000000002, 0.00000000124, -0.00000000949, 0.00000000000, 0.00000000000, 0.00000001474, 0.00000000096, 0.00000000000, 0.00000000000, -0.00000000088, 0.00000000339, 0.00000000000, 0.00000000000, -0.00000000571, 0.00000000000, 0.00000000052, 0.00000000061, 0.00000000000, 0.00000000000, -0.00000000188, }; static const unsigned char vsop87_instructions[] = { 0,0,49, 0, 1, 2, 3, 4, 5, 7, 8, 13, 14, 19, 20, 25, 26, 34, 38, 44, 50, 56, 65, 66, 71, 77, 98, 99, 104, 110, 116, 122, 133, 134, 139, 144, 149, 163, 164, 169, 175, 186, 197, 198, 203, 208, 213, 227, 233, 239, 245, 249, 0,49,2, 7, 13, 0xFE, 0,47,6, 3, 7, 8, 13, 14, 25, 0,102,1, 3, 0xFE, 0xFE, 0,45,9, 0, 3, 4, 7, 8, 13, 14, 19, 25, 0,98,1, 3, 0xFE, 0xFE, 0,43,16, 0, 1, 3, 4, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 38, 44, 0,90,2, 7, 13, 0xFE, 0,92,2, 7, 13, 0xFE, 0,94,3, 3, 7, 13, 0xFE, 0,96,1, 3, 0xFE, 0xFE, 0,41,19, 0, 1, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 31, 34, 38, 44, 0,88,2, 7, 13, 0xFE, 0,90,4, 0, 3, 7, 13, 0xFE, 0,92,9, 0, 3, 4, 7, 13, 25, 34, 35, 65, 0xFE, 0xFE, 0,39,25, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 31, 32, 34, 38, 39, 44, 45, 50, 56, 0,88,5, 0, 3, 4, 7, 13, 0xFE, 0,90,5, 0, 3, 4, 7, 13, 0xFE, 0,144,1, 3, 0xFE, 0xFE, 0,37,29, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 21, 25, 26, 27, 31, 32, 33, 34, 35, 38, 39, 44, 45, 50, 56, 0,88,2, 0, 3, 0xFE, 0,140,1, 3, 0xFE, 0,144,1, 3, 0xFE, 0xFE, 0,35,27, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 21, 25, 26, 27, 31, 32, 34, 35, 38, 44, 45, 50, 56, 0xFE, 0,33,22, 0, 1, 3, 4, 5, 7, 8, 9, 13, 14, 19, 20, 21, 25, 26, 31, 34, 38, 39, 44, 50, 56, 0,91,3, 3, 7, 13, 0xFE, 0,89,3, 3, 7, 13, 0xFE, 0,87,3, 3, 7, 13, 0xFE, 0,145,1, 3, 0xFE, 0xFE, 0,34,15, 0, 1, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 34, 38, 44, 0xFE, 0,36,12, 0, 1, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 0,103,1, 3, 0xFE, 0xFE, 0,38,9, 0, 3, 4, 7, 8, 13, 14, 19, 25, 0xFE, 0,40,4, 3, 7, 13, 25, 0,111,3, 3, 7, 13, 0xFE, 0xFE, 0,42,0, 0,111,3, 3, 7, 13, 0xFE, 0xFE, 0,46,0, 0,119,1, 3, 0xFE, 0xFE, 0,105,0, 0,160,9, 0, 3, 4, 7, 13, 65, 66, 98, 99, 0xFE, 0xFE, 0,103,0, 0,156,1, 3, 0xFE, 0xFE, 0,101,0, 0,152,1, 3, 0xFE, 0xFE, 0,99,3, 3, 7, 13, 0xFE, 0,97,8, 0, 3, 7, 8, 13, 14, 19, 25, 0xFE, 0,95,13, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 26, 71, 77, 0xFE, 0,93,27, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 21, 25, 26, 62, 63, 65, 66, 71, 72, 77, 78, 83, 89, 0xFE, 0,91,26, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 62, 63, 65, 66, 71, 72, 77, 78, 83, 89, 0,143,1, 3, 0xFE, 0xFE, 0,89,23, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 19, 20, 25, 26, 62, 63, 65, 66, 71, 77, 83, 89, 0,147,2, 3, 4, 0xFE, 0xFE, 0,87,20, 0, 1, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 62, 65, 71, 77, 83, 84, 89, 90, 0,35,4, 3, 4, 7, 13, 0xFE, 0,151,1, 3, 0xFE, 0xFE, 0,88,11, 0, 3, 4, 7, 8, 13, 14, 19, 25, 71, 77, 0xFE, 0,90,6, 0, 3, 7, 13, 19, 25, 0xFE, 0,92,3, 3, 7, 13, 0xFE, 0,110,0, 0,53,3, 3, 7, 13, 0xFE, 0,51,3, 3, 7, 13, 0xFE, 0xFE, 0,155,7, 3, 4, 5, 7, 8, 13, 14, 0xFE, 0,153,6, 3, 4, 7, 8, 13, 14, 0xFE, 0,151,9, 0, 3, 4, 7, 8, 13, 14, 104, 110, 0xFE, 0,149,14, 0, 1, 3, 4, 5, 7, 8, 13, 14, 25, 95, 98, 104, 110, 0xFE, 0,147,17, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 95, 96, 98, 104, 105, 110, 111, 0xFE, 0,145,19, 0, 1, 3, 4, 5, 7, 8, 13, 14, 19, 25, 95, 96, 97, 98, 104, 105, 110, 111, 0xFE, 0,143,18, 0, 1, 3, 4, 7, 13, 14, 19, 25, 95, 96, 97, 98, 99, 104, 110, 116, 122, 0xFE, 0,141,15, 0, 3, 7, 13, 14, 19, 25, 95, 98, 104, 105, 110, 111, 116, 122, 0xFE, 0,140,15, 0, 3, 4, 7, 13, 19, 25, 95, 98, 104, 105, 110, 111, 116, 122, 0xFE, 0,142,7, 3, 7, 13, 19, 25, 104, 110, 0,95,3, 3, 7, 13, 0xFE, 0,93,1, 3, 0xFE, 0xFE, 0,144,2, 7, 13, 0xFE, 0,215,4, 0, 3, 7, 13, 1,10,2, 3, 13, 0xFE, 0xFE, 0,213,10, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 0xFE, 0,211,16, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 25, 139, 144, 0xFE, 0,209,21, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 127, 139, 140, 144, 145, 0,154,0, 0,101,3, 3, 7, 13, 0xFE, 0,97,1, 3, 0xFE, 0xFE, 0xFE, 0,207,23, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 127, 128, 133, 134, 139, 144, 221, 0,93,2, 3, 4, 0xFE, 1,1,6, 0, 3, 4, 7, 13, 14, 0xFE, 0,251,4, 0, 3, 7, 13, 0xFE, 0,249,3, 3, 7, 13, 0xFE, 0xFE, 0,205,24, 0, 1, 3, 4, 7, 8, 9, 13, 14, 15, 19, 25, 26, 127, 133, 139, 140, 144, 145, 149, 153, 157, 191, 221, 0,35,1, 3, 0xFE, 0,33,1, 3, 0xFE, 0,93,1, 3, 0xFE, 1,1,8, 0, 1, 3, 4, 7, 8, 13, 14, 0xFE, 0,251,7, 0, 3, 4, 7, 8, 13, 14, 0xFE, 0,249,4, 0, 3, 7, 13, 0xFE, 1,45,2, 203, 208, 0xFE, 1,44,2, 203, 208, 0xFE, 1,93,2, 233, 239, 0xFE, 1,92,2, 233, 239, 0xFE, 0xFE, 1,3,0, 1,48,2, 3, 13, 0xFE, 0xFE, 1,1,11, 0, 1, 3, 4, 7, 8, 13, 14, 25, 139, 144, 0xFE, 0,255,10, 0, 1, 3, 4, 7, 8, 13, 14, 169, 175, 0xFE, 0,253,19, 0, 1, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 25, 157, 158, 169, 170, 175, 176, 0xFE, 0,251,16, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 157, 158, 163, 164, 169, 175, 0xFE, 0,249,19, 0, 3, 4, 7, 8, 13, 14, 19, 25, 157, 163, 169, 170, 175, 176, 181, 186, 191, 221, 0xFE, 1,51,2, 203, 208, 0xFE, 1,49,7, 0, 3, 7, 13, 191, 203, 208, 0,211,0, 1,2,2, 3, 13, 0xFE, 0xFE, 1,94,4, 191, 197, 203, 208, 0xFE, 0xFE, 1,47,11, 0, 3, 7, 13, 191, 192, 197, 203, 208, 213, 217, 1,94,2, 191, 197, 0xFE, 0xFE, 1,45,12, 3, 191, 197, 203, 208, 213, 214, 217, 218, 221, 233, 239, 1,95,3, 191, 203, 208, 0xFE, 1,92,2, 221, 227, 0xFE, 0xFE, 1,44,8, 191, 197, 203, 208, 213, 214, 217, 218, 1,99,2, 233, 239, 0xFE, 1,97,2, 221, 227, 0xFE, 1,95,2, 197, 227, 0xFE, 0xFE, 1,46,4, 203, 208, 213, 217, 0xFE, 1,97,2, 233, 239, 0xFE, 1,95,12, 0, 3, 7, 13, 191, 197, 203, 208, 221, 227, 233, 239, 0xFE, 1,93,8, 221, 227, 233, 239, 245, 246, 249, 250, 0xFE, 1,92,10, 221, 222, 227, 228, 233, 239, 245, 246, 249, 250, 0xFE, 1,94,2, 233, 239, 0xFE, 0xFE, 0,2,55, 0, 1, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 34, 38, 39, 44, 45, 50, 56, 65, 71, 72, 77, 78, 98, 99, 104, 105, 110, 111, 116, 133, 134, 139, 140, 144, 145, 163, 164, 169, 170, 175, 176, 197, 198, 203, 204, 208, 209, 213, 227, 233, 234, 239, 240, 0,53,0, 0,104,1, 3, 0xFE, 0xFE, 0,51,3, 3, 7, 13, 0,100,6, 0, 3, 4, 7, 13, 34, 0xFE, 0xFE, 0,49,9, 0, 3, 4, 7, 8, 13, 14, 19, 25, 0,94,1, 3, 0xFE, 0,96,3, 3, 7, 13, 0xFE, 0xFE, 0,47,11, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 26, 0,90,2, 7, 13, 0xFE, 0,92,3, 3, 7, 13, 0xFE, 0,94,5, 0, 3, 4, 7, 13, 0,207,1, 3, 0xFE, 0xFE, 0,98,0, 0,147,1, 3, 0xFE, 0xFE, 0xFE, 0,45,17, 0, 1, 3, 4, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 31, 38, 44, 0,88,3, 3, 7, 13, 0xFE, 0,90,13, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 34, 35, 65, 0xFE, 0,92,3, 3, 7, 13, 0xFE, 0,94,1, 3, 0xFE, 0,150,1, 3, 0xFE, 0xFE, 0,43,24, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 31, 32, 34, 38, 39, 44, 45, 56, 0,88,5, 0, 3, 4, 7, 13, 0xFE, 0,90,4, 0, 3, 7, 13, 0xFE, 0,92,1, 3, 0xFE, 0,142,1, 3, 0xFE, 0,144,5, 0, 3, 4, 7, 13, 0xFE, 0xFE, 0,41,32, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 21, 25, 26, 27, 31, 32, 33, 34, 35, 36, 38, 39, 40, 44, 45, 46, 50, 56, 0,88,4, 0, 3, 7, 13, 0xFE, 0,90,2, 0, 3, 0xFE, 0,207,5, 3, 4, 7, 13, 34, 0xFE, 0,205,5, 0, 3, 4, 7, 13, 0xFE, 1,1,1, 3, 0xFE, 0,249,1, 3, 0xFE, 0xFE, 0,39,27, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 27, 31, 32, 34, 35, 38, 39, 44, 45, 50, 56, 0,89,4, 3, 4, 7, 13, 0xFE, 0,87,3, 3, 7, 13, 0xFE, 0,88,2, 0, 3, 0xFE, 0,145,2, 3, 4, 0xFE, 0xFE, 0,37,24, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 31, 32, 34, 35, 38, 44, 50, 56, 0,91,3, 3, 7, 13, 0xFE, 0,89,1, 3, 0xFE, 0,87,1, 3, 0xFE, 0xFE, 0,35,22, 0, 1, 3, 4, 5, 7, 8, 9, 13, 14, 19, 20, 25, 26, 31, 34, 38, 39, 44, 45, 50, 56, 0,99,0, 0,146,1, 3, 0xFE, 0xFE, 0,95,5, 0, 3, 4, 7, 13, 0xFE, 0,91,1, 3, 0xFE, 0,87,1, 3, 0xFE, 0xFE, 0,33,20, 0, 1, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 31, 32, 34, 35, 38, 44, 50, 56, 0,91,1, 3, 0xFE, 0xFE, 0,34,6, 0, 3, 7, 13, 19, 25, 0xFE, 0,36,5, 3, 7, 13, 19, 25, 0xFE, 0,125,0, 0,182,2, 98, 99, 0xFE, 0xFE, 0,111,0, 0,36,4, 3, 4, 7, 13, 0xFE, 0,38,1, 3, 0xFE, 0,40,1, 3, 0xFE, 0xFE, 0,103,3, 3, 7, 13, 0xFE, 0,101,9, 0, 3, 4, 7, 8, 13, 14, 19, 25, 0xFE, 0,99,9, 0, 3, 4, 7, 8, 13, 14, 19, 25, 0xFE, 0,97,12, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 71, 77, 0xFE, 0,95,14, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 62, 65, 71, 77, 0xFE, 0,93,17, 0, 1, 3, 4, 5, 7, 8, 13, 14, 19, 20, 25, 26, 62, 65, 71, 77, 0xFE, 0,91,17, 0, 1, 2, 3, 4, 5, 7, 8, 13, 14, 19, 25, 26, 62, 65, 71, 77, 0xFE, 0,89,18, 0, 1, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 62, 65, 71, 72, 77, 78, 0xFE, 0,87,19, 0, 1, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 62, 63, 65, 66, 77, 83, 89, 0xFE, 0,88,5, 3, 7, 13, 19, 25, 0xFE, 0,110,0, 0,57,4, 3, 4, 7, 13, 0xFE, 0,55,1, 3, 0xFE, 0,53,1, 3, 0xFE, 0xFE, 0,153,3, 3, 7, 13, 0xFE, 0,151,7, 0, 3, 4, 7, 8, 13, 14, 0xFE, 0,149,10, 0, 1, 3, 4, 7, 8, 13, 14, 104, 110, 0xFE, 0,147,12, 0, 1, 3, 4, 7, 8, 13, 14, 95, 98, 104, 110, 0xFE, 0,145,15, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 95, 96, 98, 104, 110, 0xFE, 0,143,14, 0, 3, 7, 13, 14, 19, 25, 95, 96, 98, 104, 105, 110, 111, 0xFE, 0,141,16, 0, 3, 4, 7, 13, 25, 95, 96, 98, 99, 104, 105, 110, 111, 116, 122, 0xFE, 0,140,6, 95, 98, 104, 110, 116, 122, 0xFE, 0,215,4, 0, 3, 7, 13, 1,10,1, 3, 0xFE, 0xFE, 0,213,8, 0, 1, 3, 4, 7, 8, 13, 14, 0xFE, 0,211,12, 0, 1, 2, 3, 4, 5, 7, 8, 13, 14, 19, 25, 0xFE, 0,209,16, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 19, 20, 25, 139, 144, 0xFE, 0,207,20, 0, 1, 3, 4, 5, 7, 8, 9, 13, 14, 19, 20, 25, 26, 127, 133, 139, 140, 144, 145, 1,1,5, 0, 3, 4, 7, 13, 0xFE, 0,251,4, 0, 3, 7, 13, 0xFE, 0,249,2, 0, 3, 0xFE, 0xFE, 0,205,24, 0, 1, 3, 4, 5, 7, 8, 13, 14, 19, 20, 25, 26, 127, 128, 133, 134, 139, 144, 149, 153, 157, 191, 221, 1,1,8, 0, 1, 3, 4, 7, 8, 13, 14, 0xFE, 0,251,5, 0, 3, 4, 7, 13, 0xFE, 0,249,2, 0, 3, 0xFE, 0xFE, 1,3,0, 1,48,1, 3, 0xFE, 0xFE, 1,1,10, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 0xFE, 0,255,7, 0, 1, 3, 4, 7, 8, 13, 0xFE, 0,253,14, 0, 1, 3, 4, 5, 7, 8, 13, 14, 19, 25, 157, 169, 175, 0xFE, 0,251,15, 0, 3, 7, 8, 13, 14, 19, 25, 157, 158, 163, 169, 170, 175, 176, 0xFE, 0,249,16, 0, 1, 3, 4, 7, 13, 157, 158, 163, 164, 169, 170, 175, 181, 186, 221, 0xFE, 1,49,5, 0, 3, 191, 203, 208, 0,211,0, 1,2,1, 3, 0xFE, 0xFE, 1,94,2, 203, 208, 0xFE, 0xFE, 1,47,10, 0, 3, 7, 13, 191, 197, 203, 204, 208, 209, 1,94,2, 191, 197, 0xFE, 0xFE, 1,45,10, 191, 192, 197, 198, 203, 208, 213, 217, 233, 239, 1,95,2, 203, 208, 0xFE, 1,92,2, 221, 227, 0xFE, 0xFE, 1,44,6, 191, 197, 203, 208, 213, 217, 1,99,2, 233, 239, 0xFE, 1,97,2, 221, 227, 0xFE, 1,95,1, 197, 0xFE, 0xFE, 1,97,2, 233, 239, 0xFE, 1,95,10, 0, 3, 191, 197, 221, 227, 233, 234, 239, 240, 0xFE, 1,93,8, 221, 222, 227, 228, 233, 239, 245, 249, 0xFE, 1,92,4, 221, 227, 245, 249, 0xFE, 0xFE, 0,4,45, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 38, 39, 44, 45, 65, 71, 72, 77, 78, 98, 99, 104, 105, 110, 111, 133, 139, 140, 144, 145, 163, 169, 170, 175, 176, 197, 203, 204, 208, 209, 227, 233, 234, 239, 240, 0,61,0, 0,108,1, 3, 0xFE, 0xFE, 0,57,0, 0,100,1, 3, 0xFE, 0xFE, 0,55,2, 7, 13, 0,98,2, 3, 4, 0xFE, 0,100,1, 3, 0xFE, 0xFE, 0,53,6, 0, 3, 7, 8, 13, 14, 0,94,1, 3, 0xFE, 0xFE, 0,51,10, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 0,90,3, 3, 7, 13, 0xFE, 0,92,5, 0, 3, 4, 7, 13, 0xFE, 0,94,1, 3, 0xFE, 0xFE, 0,49,15, 0, 1, 3, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 38, 44, 0,88,5, 0, 3, 4, 7, 13, 0xFE, 0,90,4, 0, 3, 7, 13, 0xFE, 0,92,1, 3, 0xFE, 0,146,1, 3, 0xFE, 0xFE, 0,47,25, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 31, 32, 34, 35, 38, 39, 44, 45, 56, 0,88,3, 3, 7, 13, 0xFE, 0,90,4, 0, 3, 7, 13, 0xFE, 0xFE, 0,45,26, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 31, 32, 34, 35, 38, 39, 44, 45, 50, 56, 0,87,4, 3, 4, 7, 13, 0xFE, 0,88,4, 0, 3, 7, 13, 0xFE, 0,90,3, 0, 3, 13, 0xFE, 0,143,2, 3, 4, 0xFE, 0xFE, 0,43,25, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 31, 32, 34, 35, 38, 39, 44, 45, 56, 0,91,1, 3, 0xFE, 0,88,3, 0, 3, 13, 0xFE, 0,90,2, 0, 3, 0xFE, 0xFE, 0,41,25, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 31, 32, 34, 35, 38, 39, 44, 45, 56, 0,88,1, 3, 0xFE, 0xFE, 0,39,23, 0, 1, 2, 3, 4, 5, 7, 8, 9, 13, 14, 15, 19, 20, 25, 26, 31, 32, 34, 35, 38, 44, 56, 0,97,1, 3, 0xFE, 0xFE, 0,37,18, 0, 1, 3, 4, 7, 8, 9, 13, 14, 19, 20, 25, 26, 31, 34, 38, 44, 56, 0xFE, 0,35,18, 0, 1, 2, 3, 4, 5, 7, 8, 13, 14, 19, 20, 25, 26, 31, 34, 38, 44, 0xFE, 0,33,18, 0, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 31, 32, 34, 35, 38, 44, 50, 0xFE, 0,105,1, 13, 0xFE, 0,103,3, 3, 7, 13, 0xFE, 0,101,7, 0, 3, 4, 7, 13, 14, 25, 0xFE, 0,99,10, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 0xFE, 0,97,12, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 71, 77, 0xFE, 0,95,14, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 62, 65, 71, 77, 0xFE, 0,93,15, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 26, 62, 65, 71, 77, 0xFE, 0,91,16, 0, 1, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 62, 65, 71, 77, 0xFE, 0,89,18, 0, 1, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 62, 65, 71, 72, 77, 78, 0xFE, 0,87,17, 0, 1, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 62, 63, 65, 66, 83, 0xFE, 0,153,4, 0, 3, 7, 13, 0xFE, 0,151,5, 0, 3, 4, 7, 13, 0xFE, 0,149,6, 0, 1, 3, 4, 7, 13, 0xFE, 0,147,10, 0, 1, 3, 4, 7, 13, 95, 98, 104, 110, 0xFE, 0,145,9, 0, 3, 7, 13, 14, 95, 98, 104, 110, 0xFE, 0,143,11, 0, 3, 4, 7, 13, 95, 98, 104, 105, 110, 111, 0xFE, 0,141,10, 0, 3, 7, 13, 95, 96, 98, 99, 104, 110, 0xFE, 0,215,4, 0, 3, 7, 13, 0xFE, 0,213,7, 0, 1, 3, 4, 7, 8, 13, 0xFE, 0,211,10, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 0xFE, 0,209,13, 0, 1, 3, 4, 5, 7, 8, 13, 14, 19, 25, 139, 144, 0xFE, 0,207,16, 0, 1, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 127, 133, 139, 144, 1,1,3, 0, 3, 7, 0xFE, 0,251,2, 0, 3, 0xFE, 0xFE, 0,205,16, 0, 1, 3, 4, 7, 8, 13, 14, 19, 25, 127, 128, 133, 134, 144, 221, 1,1,7, 0, 1, 3, 4, 7, 8, 13, 0xFE, 0,251,3, 0, 3, 13, 0xFE, 0xFE, 1,1,8, 0, 1, 3, 4, 7, 8, 13, 14, 0xFE, 0,255,5, 0, 1, 3, 4, 13, 0xFE, 0,253,10, 0, 1, 3, 4, 7, 8, 13, 14, 169, 175, 0xFE, 0,251,14, 0, 1, 3, 4, 7, 13, 19, 25, 157, 163, 169, 170, 175, 176, 0xFE, 0,249,12, 0, 3, 7, 13, 157, 158, 163, 164, 169, 175, 181, 186, 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0xFE, 1,67,3, 191, 197, 203, 0xFE, 1,65,3, 191, 197, 208, 0xFE, 1,63,2, 191, 197, 0xFE, 0xFE, 1,16,0, 1,71,1, 203, 0xFE, 1,69,2, 191, 197, 0xFE, 0xFE, 1,44,58, 3, 7, 34, 38, 44, 65, 71, 77, 98, 99, 104, 110, 133, 134, 139, 144, 157, 163, 164, 169, 175, 181, 186, 191, 192, 193, 194, 197, 198, 199, 200, 203, 204, 205, 208, 209, 210, 213, 214, 217, 218, 221, 222, 223, 224, 227, 228, 229, 230, 233, 234, 239, 240, 241, 245, 246, 249, 250, 0xFE, 1,46,47, 3, 7, 34, 65, 98, 104, 133, 139, 144, 163, 164, 169, 170, 175, 176, 181, 186, 191, 192, 193, 197, 198, 199, 203, 204, 205, 208, 209, 210, 213, 214, 217, 218, 221, 222, 227, 228, 229, 233, 234, 239, 240, 241, 245, 246, 249, 250, 0xFE, 1,50,28, 7, 13, 104, 110, 139, 144, 163, 169, 175, 191, 197, 198, 203, 204, 208, 209, 213, 214, 217, 218, 221, 227, 228, 233, 239, 240, 245, 249, 0xFE, 1,52,10, 169, 175, 191, 197, 203, 204, 208, 209, 233, 239, 0xFE, 1,54,2, 203, 208, 0xFE, 0xFE, 1,92,62, 3, 4, 7, 13, 19, 25, 34, 38, 44, 65, 71, 77, 98, 99, 104, 110, 133, 134, 139, 144, 157, 163, 164, 165, 169, 170, 175, 181, 186, 191, 192, 197, 198, 199, 203, 204, 205, 208, 209, 210, 213, 214, 217, 218, 221, 222, 223, 224, 227, 228, 229, 230, 233, 234, 235, 239, 240, 241, 245, 246, 249, 250, 0xFE, 1,94,91, 3, 4, 7, 8, 13, 14, 19, 20, 25, 26, 34, 38, 44, 50, 56, 65, 71, 72, 77, 78, 83, 89, 98, 99, 104, 105, 110, 111, 116, 122, 133, 134, 139, 140, 141, 144, 145, 146, 149, 153, 157, 163, 164, 165, 169, 170, 171, 175, 176, 177, 181, 182, 186, 187, 191, 192, 193, 197, 198, 199, 203, 204, 205, 208, 209, 210, 213, 214, 217, 218, 221, 222, 223, 224, 227, 228, 229, 233, 234, 235, 236, 239, 240, 241, 242, 245, 246, 247, 249, 250, 251, 1,4,0, 1,69,2, 203, 208, 0xFE, 1,67,4, 191, 197, 203, 208, 0xFE, 1,65,10, 157, 163, 169, 175, 191, 197, 203, 204, 208, 209, 0xFE, 1,63,12, 157, 163, 169, 175, 191, 192, 197, 198, 203, 204, 208, 209, 0xFE, 1,61,13, 157, 163, 164, 169, 175, 191, 192, 197, 198, 203, 204, 208, 209, 0xFE, 1,59,11, 157, 163, 169, 191, 192, 197, 198, 203, 204, 208, 209, 0xFE, 1,57,10, 157, 163, 169, 175, 191, 192, 197, 198, 203, 208, 0xFE, 1,55,6, 169, 175, 191, 197, 203, 208, 0xFE, 0xFE, 1,6,0, 1,71,2, 203, 208, 0xFE, 1,69,4, 191, 197, 203, 208, 0xFE, 1,67,5, 191, 197, 203, 208, 209, 0xFE, 1,65,12, 157, 163, 169, 175, 191, 192, 197, 198, 203, 204, 208, 209, 0xFE, 1,63,11, 157, 163, 169, 175, 191, 192, 197, 198, 203, 204, 208, 0xFE, 1,61,11, 157, 163, 169, 191, 192, 197, 198, 203, 204, 208, 209, 0xFE, 1,59,10, 157, 163, 169, 175, 191, 192, 197, 198, 203, 208, 0xFE, 1,57,4, 191, 197, 203, 208, 0xFE, 0xFE, 1,8,0, 1,71,2, 203, 208, 0xFE, 1,69,4, 191, 197, 203, 208, 0xFE, 1,67,6, 163, 175, 191, 197, 203, 208, 0xFE, 1,65,10, 157, 163, 169, 175, 191, 192, 197, 198, 203, 208, 0xFE, 1,63,6, 157, 163, 191, 197, 203, 208, 0xFE, 1,61,8, 157, 163, 169, 175, 191, 197, 203, 208, 0xFE, 1,59,3, 191, 197, 208, 0xFE, 0xFE, 1,10,0, 1,71,4, 191, 197, 203, 208, 0xFE, 1,69,4, 191, 197, 203, 208, 0xFE, 1,67,6, 157, 163, 191, 197, 203, 208, 0xFE, 1,65,6, 157, 163, 191, 197, 203, 208, 0xFE, 1,63,5, 163, 191, 197, 203, 208, 0xFE, 0xFE, 1,12,0, 1,73,2, 203, 208, 0xFE, 1,71,4, 191, 197, 203, 208, 0xFE, 1,69,4, 191, 197, 203, 208, 0xFE, 1,67,4, 191, 197, 203, 208, 0xFE, 1,65,3, 191, 197, 208, 0xFE, 0xFE, 1,14,0, 1,73,2, 203, 208, 0xFE, 1,71,4, 191, 197, 203, 208, 0xFE, 1,69,3, 191, 197, 203, 0xFE, 1,67,2, 191, 197, 0xFE, 0xFE, 1,44,36, 3, 7, 13, 19, 25, 98, 104, 110, 133, 139, 144, 163, 169, 170, 175, 176, 181, 186, 191, 192, 197, 198, 203, 204, 205, 208, 209, 210, 213, 217, 221, 227, 233, 239, 245, 249, 0xFE, 1,46,20, 7, 13, 104, 110, 139, 144, 169, 170, 175, 176, 191, 197, 203, 204, 208, 209, 213, 217, 233, 239, 0xFE, 1,50,1, 203, 0xFE, 0xFE, 1,96,37, 3, 7, 13, 104, 110, 139, 144, 163, 169, 170, 171, 175, 176, 177, 181, 186, 191, 197, 198, 203, 204, 208, 209, 213, 217, 221, 222, 227, 228, 233, 234, 235, 239, 240, 241, 245, 249, 0xFE, 1,98,18, 169, 175, 191, 197, 203, 204, 208, 209, 213, 217, 221, 227, 233, 234, 239, 240, 245, 249, 0xFE, 1,100,2, 233, 239, 0xFE, 1,140,2, 62, 65, 1,147,2, 62, 65, 0xFE, 1,145,2, 62, 65, 0xFE, 1,144,1, 65, 0xFE, 0xFE, 1,144,2, 62, 65, 0xFE, 0xFF }; static const int vsop87_index_translation_table[8*6*6] = { 0, 1, 2, -1, -1, -1, 3, 4, 5, 6, -1, -1, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, -1, -1, -1, 34, 35, 36, 37, -1, -1, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, -1, -1, -1, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, -1, -1, -1, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, -1, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, -1, 144, 145, 146, 147, 148, -1, 149, 150, 151, 152, -1, -1, 153, 154, 155, 156, -1, -1, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, -1, 186, 187, 188, 189, 190, -1, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, -1, 208, 209, 210, 211, 212, -1, 213, 214, 215, 216, -1, -1, 217, 218, 219, 220, -1, -1, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, -1, -1, 249, 250, 251, 252, -1, -1, }; /* Original VSOP87 values come from IAU 1976 constants. Thanks to Jean-Louis Simon for this information. */ #define GAUSS_GRAV_CONST (0.01720209895*0.01720209895) static const double vsop87_mu[8] = { (1.0+1.0/6023600)*GAUSS_GRAV_CONST, (1.0+1.0/408523.5)*GAUSS_GRAV_CONST, (1.0+1.0/328900.5)*GAUSS_GRAV_CONST, (1.0+1.0/3098710)*GAUSS_GRAV_CONST, (1.0+1.0/1047.355)*GAUSS_GRAV_CONST, (1.0+1.0/3498.5)*GAUSS_GRAV_CONST, (1.0+1.0/22869)*GAUSS_GRAV_CONST, (1.0+1.0/19314)*GAUSS_GRAV_CONST }; static void PrepareLambdaArray(int nr_of_lambdas, const int max_lambda_factor[], const double lambda[], double cos_sin_lambda[]) { /* initialize cos_sin_lambda: (cos,sin)(1*lambda[0]),(cos,sin)(-1*lambda[0]),(cos,sin)(2*lambda[0]),... (cos,sin)(1*lambda[1]),(cos,sin)(-1*lambda[1]),(cos,sin)(2*lambda[1]),... */ int i,m; for (i=0;i>1)-1)<<2); const double *m1 = cos_sin_lambda + ((((m+1)>>1)-1)<<2); cslp += 4; cslp[0] = m0[0] * m1[0] - m0[1] * m1[1]; cslp[1] = m0[0] * m1[1] + m0[1] * m1[0]; cslp[2] = cslp[0]; cslp[3] = -cslp[1]; } cos_sin_lambda += (max_factor<<2); } } static void AccumulateVsop87Terms(const unsigned char *instructions, const double *coefficients, const double cos_sin_lambda[], double accu[], double *sp) { /* Accumulates the series given in instructions/coefficients. The argument of the series is cos_sin_lambda which has been initialized using PrepareLambdaArray(). accu is the output accumulator. sp must point to a memory area holding 2*nr_of_lambdas double. area must be supplied by the caller, it will be destroyed during the calculation. */ sp[0] = 1.0; sp[1] = 0.0; for (;;) { int lambda_index = *instructions++; if (lambda_index < 0xFE) { lambda_index = (lambda_index<<8)|(*instructions++); { int term_count = (*instructions++); /* calculate new argument and push it on the stack */ const double *const cos_sin = cos_sin_lambda + (lambda_index<<1); sp[2] = cos_sin[0]*sp[0] - cos_sin[1]*sp[1]; sp[3] = cos_sin[0]*sp[1] + cos_sin[1]*sp[0]; sp += 2; while (--term_count >= 0) { accu[*instructions++] += (coefficients[0]*sp[0] + coefficients[1]*sp[1]); coefficients += 2; } } } else { if (lambda_index == 0xFF) break; /* pop argument from the stack */ sp -= 2; } } } static void CalcVsop87Elem(const double t,double elem[8*6]) { unsigned int i; double lambda[12]; double cos_sin_lambda[203*4]; double accu[sizeof(vsop87_constants)/sizeof(vsop87_constants[0])]; double stack[12*2]; double use_polynomials; for (i=0;i<12;i++) lambda[i] = lambda_0[i] + lambda_1[i] * t; PrepareLambdaArray(12,vsop87_max_lambda_factor,lambda,cos_sin_lambda); for (i=0;i<(sizeof(vsop87_constants)/sizeof(vsop87_constants[0]));++i) { accu[i] = 0.0; } AccumulateVsop87Terms(vsop87_instructions,vsop87_coefficients,cos_sin_lambda, accu,stack); for (i=0;i<8*6;i++) { elem[i] = 0.0; } /* terms of order t^alpha: */ use_polynomials = (6.1 - fabs(t)) / 0.1; if (use_polynomials > 0) { if (use_polynomials > 1.0) use_polynomials = 1.0; for (i=0;i<8*6;i++) { int alpha; for (alpha=5;alpha>0;alpha--) { const int j = vsop87_index_translation_table[i*6+alpha]; if (j >= 0) { elem[i] += accu[j] + vsop87_constants[j]; elem[i] *= t; } } elem[i] *= use_polynomials; } } /* terms of order t^0: */ for (i=0;i<8*6;i++) { const int j = vsop87_index_translation_table[i*6]; elem[i] += accu[j] + vsop87_constants[j]; } /* longitudes: */ for (i=0;i<8;i++) { elem[i*6+1] += t*vsop87_l[i]; } /* for (i=0;i<8;i++) { printf("%f %d %15.10f %15.10f %15.10f %15.10f %15.10f %15.10f\n", 2451545.0+t*365250.0,i, elem[i*6+0],elem[i*6+1],elem[i*6+2], elem[i*6+3],elem[i*6+3],elem[i*6+4]); } */ } /* dirty caching in static variables */ #define VSOP87_DIM (8*6) static double t_0 = -1e100; static double t_1 = -1e100; static double t_2 = -1e100; static double vsop87_elem_0[VSOP87_DIM]; static double vsop87_elem_1[VSOP87_DIM]; static double vsop87_elem_2[VSOP87_DIM]; /* 10 days: */ #define DELTA_T (10.0/365250.0) static double vsop87_jd0 = -1e100; static double vsop87_elem[VSOP87_DIM]; void GetVsop87Coor(double jd,int body,double *xyz) { GetVsop87OsculatingCoor(jd,jd,body,xyz); } void GetVsop87OsculatingCoor(const double jd0,const double jd, const int body,double *xyz) { if (jd0 != vsop87_jd0) { const double t0 = (jd0 - 2451545.0) / 365250.0; vsop87_jd0 = jd0; CalcInterpolatedElements(t0,vsop87_elem, VSOP87_DIM, &CalcVsop87Elem,DELTA_T, &t_0,vsop87_elem_0, &t_1,vsop87_elem_1, &t_2,vsop87_elem_2); } EllipticToRectangularA(vsop87_mu[body],vsop87_elem+(body*6),jd-jd0,xyz); }