path: root/src/crypto/crypto_ops_builder/crypto-ops-data.c

// Copyright (c) 2014-2020, The Monero Project
// 
// All rights reserved.
// 
// Redistribution and use in source and binary forms, with or without modification, are
// permitted provided that the following conditions are met:
// 
// 1. Redistributions of source code must retain the above copyright notice, this list of
//    conditions and the following disclaimer.
// 
// 2. Redistributions in binary form must reproduce the above copyright notice, this list
//    of conditions and the following disclaimer in the documentation and/or other
//    materials provided with the distribution.
// 
// 3. Neither the name of the copyright holder nor the names of its contributors may be
//    used to endorse or promote products derived from this software without specific
//    prior written permission.
// 
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
// EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
// MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL
// THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT,
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// THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
// 
// Parts of this file are originally copyright (c) 2012-2013 The Cryptonote developers

#include <stdint.h>

#include "crypto-ops.h"

/* sqrt(x) is such an integer y that 0 <= y <= p - 1, y % 2 = 0, and y^2 = x (mod p). */
/* d = -121665 / 121666 */
const fe fe_d = {-10913610, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719, -18696448, -12055116}; /* d */
const fe fe_sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654, 326686, 11406482}; /* sqrt(-1) */
const fe fe_d2 = {-21827239, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438, 29715968, 9444199}; /* 2 * d */

/* base[i][j] = (j+1)*256^i*B */
const ge_precomp ge_base[32][8] = {
  {
    {{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605},
     {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378},
     {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546}},
    {{-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903, -3814571, -358445, -10211303},
     {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551, 11189268, -26829678, -5319081},
     {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826, -9541118, -15472047, -4166697}},
    {{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024},
     {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574},
     {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357}},
    {{-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210, 15006023, 3284568, -6276540},
     {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579, 9656445, 13059162, 10374397},
     {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, -3839045, -641708, -101325}},
    {{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380},
     {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306},
     {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942}},
    {{-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627, -15224819, -9818940, -12085777},
     {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, -15689887, 1762328, 14866737},
     {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412, 3959421, 27914454, 4383652}},
    {{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766},
     {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701},
     {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300}},
    {{14499471, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735, 10876454, -33154098, 2381726},
     {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, -6236617, 3696005, -32300832, 15351955},
     {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401, -2970515, 29551813, 10109425}}
  }, {
    {{-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284, -1627556, 10092783, -4764171},
     {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754, 12005538, -17810127, 12803510},
     {17228999, -15661624, -1233527, 300140, -1224870, -11714777, 30364213, -9038194, 18016357, 4397660}},
    {{-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106, 14544525, -17477504, 982639},
     {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, -4120128, -21047696, 9934963},
     {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930, 4559895, -30123922, -10897950}},
    {{-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034, 4541697, -13338309, 5500568},
     {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592, 12264343, 10874051, 13524335},
     {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, 5080568, -22528059, 5376628}},
    {{-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305, -9447443, 4535768, 1569007},
     {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562, 3044290, 31848280, 12543772},
     {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195, -2062731, 7718482, 14474653}},
    {{2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665, 24316168, -5253567},
     {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651, -13424532, -20729456, 8321686},
     {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965, -11874838, -9984458, 608372}},
    {{-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968, -6780577, 27229399, 23887},
     {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, 12797024, -6440308, -1633405, 16678954},
     {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144, -4795045, -17169265, 4904953}},
    {{24059557, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211, 16191880, 2128236, -4326833},
     {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336, 916033, -6882542, -2986532},
     {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, 285431, 2763829, 15736322, 4143876}},
    {{2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, -14594663, 23527084, -16458268},
     {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340, 4087881, -15188911, -14416214},
     {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, 4357868, -4774191, -16323038}}
  }, {
    {{6721966, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147, -3949732, 7390890, 2759800},
     {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, -4264057, 1244380, -12919645},
     {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, 9208236, 15886429, 16489664}},
    {{1996075, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198, 398369, -30606455, -712933},
     {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553, 12076947, -30836462, 5113182},
     {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101, -7336386, 13847711, 5387222}},
    {{-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061, 3617786, -19600662, 10370991},
     {20246567, -14369378, 22358229, -543712, 18507283, -10413996, 14554437, -8746092, 32232924, 16763880},
     {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161, 15689506, 3140038, -16510092}},
    {{-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800, 9448613, -28774454, 366295},
     {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573, 8041113, 719605, 11671788},
     {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, -15266516, 27000813, -10195553}},
    {{-15157904, 7134312, 8639287, -2814877, -7235688, 10421742, 564065, 5336097, 6750977, -14521026},
     {11836410, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823, -8819122, 8169720, 16220347},
     {-18115838, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307, -2627664, -5990708, -14166033}},
    {{-23308498, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329, 2847284, 2655861, 1738395},
     {-27537433, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608, -3239336, -19087449, -11005278},
     {1533110, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408, 10478196, 8544890}},
    {{32173121, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449, 12217473, 17789017, -3395995},
     {-30552961, -2228401, -15578829, -10147201, 13243889, 517024, 15479401, -3853233, 30460520, 1052596},
     {-11614875, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595, -4612359, 3179268, -9478891}},
    {{31947069, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777, -16411740, 19072640, -9511060},
     {11685058, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896, -5215017, 473099, 5040608},
     {-20290863, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862, 1721092, -19558642, -3131606}}
  }, {
    {{7881532, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786, 8076149, -27868496, 11538389},
     {-19935666, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525, 7446702, -5676054, 5797016},
     {-11295600, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099, -9050574, -2369172, -5877341}},
    {{-22472376, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730, -3714199, 15123619, 10811505},
     {14352098, -3419715, -18942044, 10822655, 32750596, 4699007, -70363, 15776356, -28886779, -11974553},
     {-28241164, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173, -16484855, 4714547, -9600655}},
    {{15200332, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599, -4543832, -11745876, 12340220},
     {12876937, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953, 8241152, 15370987, 9608631},
     {-4143277, -12014408, 8446281, -391603, 4407738, 13629032, -7724868, 15866074, -28210621, -8814099}},
    {{26660628, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697, 20571223, 8420556},
     {14620715, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827, 12516406, -21574435, -12476749},
     {236881, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740, 8791136, 15069930}},
    {{1276410, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875, 4874229, -30663140, -2331391},
     {5855666, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175, -7912378, -33069337, 9234253},
     {20590503, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055, -11609587, 18979186, 13396066}},
    {{24474287, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887, 13594782, 33514650, 7021958},
     {-11566906, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728, -3916677, -21480480, 12868082},
     {-28635013, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107, 2244500, -12455797, -8089383}},
    {{-30595528, 13793479, -5852820, 319136, -25723172, -6263899, 33086546, 8957937, -15233648, 5540521},
     {-11630176, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744, -1568984, -16128528, -14962807},
     {23152971, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185, -11513277, -15205948}},
    {{9770129, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127, -19179614, 5867134},
     {-32765025, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559, 5931263, -29749703, -16108455},
     {27461885, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490, -15148073, -19526700, 7734629}}
  }, {
    {{-8010264, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295, -3176626, 18549497, 15302069},
     {-32658337, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790, -6418461, -8872242, 8424746},
     {24687205, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234, 7134917, -11284482, -828919}},
    {{11334899, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738, -14685461, -5066034, 16498837},
     {8911542, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925, -14124238, 6536641, 10543906},
     {-28946384, 15479763, -17466835, 568876, -1497683, 11223454, -2669190, -16625574, -27235709, 8876771}},
    {{-25742899, -12566864, -15649966, -846607, -33026686, -796288, -33481822, 15824474, -604426, -9039817},
     {10330056, 70051, 7957388, -9002667, 9764902, 15609756, 27698697, -4890037, 1657394, 3084098},
     {10477963, -7470260, 12119566, -13250805, 29016247, -5365589, 31280319, 14396151, -30233575, 15272409}},
    {{-12288309, 3169463, 28813183, 16658753, 25116432, -5630466, -25173957, -12636138, -25014757, 1950504},
     {-26180358, 9489187, 11053416, -14746161, -31053720, 5825630, -8384306, -8767532, 15341279, 8373727},
     {28685821, 7759505, -14378516, -12002860, -31971820, 4079242, 298136, -10232602, -2878207, 15190420}},
    {{-32932876, 13806336, -14337485, -15794431, -24004620, 10940928, 8669718, 2742393, -26033313, -6875003},
     {-1580388, -11729417, -25979658, -11445023, -17411874, -10912854, 9291594, -16247779, -12154742, 6048605},
     {-30305315, 14843444, 1539301, 11864366, 20201677, 1900163, 13934231, 5128323, 11213262, 9168384}},
    {{-26280513, 11007847, 19408960, -940758, -18592965, -4328580, -5088060, -11105150, 20470157, -16398701},
     {-23136053, 9282192, 14855179, -15390078, -7362815, -14408560, -22783952, 14461608, 14042978, 5230683},
     {29969567, -2741594, -16711867, -8552442, 9175486, -2468974, 21556951, 3506042, -5933891, -12449708}},
    {{-3144746, 8744661, 19704003, 4581278, -20430686, 6830683, -21284170, 8971513, -28539189, 15326563},
     {-19464629, 10110288, -17262528, -3503892, -23500387, 1355669, -15523050, 15300988, -20514118, 9168260},
     {-5353335, 4488613, -23803248, 16314347, 7780487, -15638939, -28948358, 9601605, 33087103, -9011387}},
    {{-19443170, -15512900, -20797467, -12445323, -29824447, 10229461, -27444329, -15000531, -5996870, 15664672},
     {23294591, -16632613, -22650781, -8470978, 27844204, 11461195, 13099750, -2460356, 18151676, 13417686},
     {-24722913, -4176517, -31150679, 5988919, -26858785, 6685065, 1661597, -12551441, 15271676, -15452665}}
  }, {
    {{11433042, -13228665, 8239631, -5279517, -1985436, -725718, -18698764, 2167544, -6921301, -13440182},
     {-31436171, 15575146, 30436815, 12192228, -22463353, 9395379, -9917708, -8638997, 12215110, 12028277},
     {14098400, 6555944, 23007258, 5757252, -15427832, -12950502, 30123440, 4617780, -16900089, -655628}},
    {{-4026201, -15240835, 11893168, 13718664, -14809462, 1847385, -15819999, 10154009, 23973261, -12684474},
     {-26531820, -3695990, -1908898, 2534301, -31870557, -16550355, 18341390, -11419951, 32013174, -10103539},
     {-25479301, 10876443, -11771086, -14625140, -12369567, 1838104, 21911214, 6354752, 4425632, -837822}},
    {{-10433389, -14612966, 22229858, -3091047, -13191166, 776729, -17415375, -12020462, 4725005, 14044970},
     {19268650, -7304421, 1555349, 8692754, -21474059, -9910664, 6347390, -1411784, -19522291, -16109756},
     {-24864089, 12986008, -10898878, -5558584, -11312371, -148526, 19541418, 8180106, 9282262, 10282508}},
    {{-26205082, 4428547, -8661196, -13194263, 4098402, -14165257, 15522535, 8372215, 5542595, -10702683},
     {-10562541, 14895633, 26814552, -16673850, -17480754, -2489360, -2781891, 6993761, -18093885, 10114655},
     {-20107055, -929418, 31422704, 10427861, -7110749, 6150669, -29091755, -11529146, 25953725, -106158}},
    {{-4234397, -8039292, -9119125, 3046000, 2101609, -12607294, 19390020, 6094296, -3315279, 12831125},
     {-15998678, 7578152, 5310217, 14408357, -33548620, -224739, 31575954, 6326196, 7381791, -2421839},
     {-20902779, 3296811, 24736065, -16328389, 18374254, 7318640, 6295303, 8082724, -15362489, 12339664}},
    {{27724736, 2291157, 6088201, -14184798, 1792727, 5857634, 13848414, 15768922, 25091167, 14856294},
     {-18866652, 8331043, 24373479, 8541013, -701998, -9269457, 12927300, -12695493, -22182473, -9012899},
     {-11423429, -5421590, 11632845, 3405020, 30536730, -11674039, -27260765, 13866390, 30146206, 9142070}},
    {{3924129, -15307516, -13817122, -10054960, 12291820, -668366, -27702774, 9326384, -8237858, 4171294},
     {-15921940, 16037937, 6713787, 16606682, -21612135, 2790944, 26396185, 3731949, 345228, -5462949},
     {-21327538, 13448259, 25284571, 1143661, 20614966, -8849387, 2031539, -12391231, -16253183, -13582083}},
    {{31016211, -16722429, 26371392, -14451233, -5027349, 14854137, 17477601, 3842657, 28012650, -16405420},
     {-5075835, 9368966, -8562079, -4600902, -15249953, 6970560, -9189873, 16292057, -8867157, 3507940},
     {29439664, 3537914, 23333589, 6997794, -17555561, -11018068, -15209202, -15051267, -9164929, 6580396}}
  }, {
    {{-12185861, -7679788, 16438269, 10826160, -8696817, -6235611, 17860444, -9273846, -2095802, 9304567},
     {20714564, -4336911, 29088195, 7406487, 11426967, -5095705, 14792667, -14608617, 5289421, -477127},
     {-16665533, -10650790, -6160345, -13305760, 9192020, -1802462, 17271490, 12349094, 26939669, -3752294}},
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    {{-4839289, -3535444, 9744961, 2871048, 25113978, 3187018, -25110813, -849066, 17258084, -7977739},
     {18164541, -10595176, -17154882, -1542417, 19237078, -9745295, 23357533, -15217008, 26908270, 12150756},
     {-30264870, -7647865, 5112249, -7036672, -1499807, -6974257, 43168, -5537701, -32302074, 16215819}}
  }, {
    {{-6898905, 9824394, -12304779, -4401089, -31397141, -6276835, 32574489, 12532905, -7503072, -8675347},
     {-27343522, -16515468, -27151524, -10722951, 946346, 16291093, 254968, 7168080, 21676107, -1943028},
     {21260961, -8424752, -16831886, -11920822, -23677961, 3968121, -3651949, -6215466, -3556191, -7913075}},
    {{16544754, 13250366, -16804428, 15546242, -4583003, 12757258, -2462308, -8680336, -18907032, -9662799},
     {-2415239, -15577728, 18312303, 4964443, -15272530, -12653564, 26820651, 16690659, 25459437, -4564609},
     {-25144690, 11425020, 28423002, -11020557, -6144921, -15826224, 9142795, -2391602, -6432418, -1644817}},
    {{-23104652, 6253476, 16964147, -3768872, -25113972, -12296437, -27457225, -16344658, 6335692, 7249989},
     {-30333227, 13979675, 7503222, -12368314, -11956721, -4621693, -30272269, 2682242, 25993170, -12478523},
     {4364628, 5930691, 32304656, -10044554, -8054781, 15091131, 22857016, -10598955, 31820368, 15075278}},
    {{31879134, -8918693, 17258761, 90626, -8041836, -4917709, 24162788, -9650886, -17970238, 12833045},
     {19073683, 14851414, -24403169, -11860168, 7625278, 11091125, -19619190, 2074449, -9413939, 14905377},
     {24483667, -11935567, -2518866, -11547418, -1553130, 15355506, -25282080, 9253129, 27628530, -7555480}},
    {{17597607, 8340603, 19355617, 552187, 26198470, -3176583, 4593324, -9157582, -14110875, 15297016},
     {510886, 14337390, -31785257, 16638632, 6328095, 2713355, -20217417, -11864220, 8683221, 2921426},
     {18606791, 11874196, 27155355, -5281482, -24031742, 6265446, -25178240, -1278924, 4674690, 13890525}},
    {{13609624, 13069022, -27372361, -13055908, 24360586, 9592974, 14977157, 9835105, 4389687, 288396},
     {9922506, -519394, 13613107, 5883594, -18758345, -434263, -12304062, 8317628, 23388070, 16052080},
     {12720016, 11937594, -31970060, -5028689, 26900120, 8561328, -20155687, -11632979, -14754271, -10812892}},
    {{15961858, 14150409, 26716931, -665832, -22794328, 13603569, 11829573, 7467844, -28822128, 929275},
     {11038231, -11582396, -27310482, -7316562, -10498527, -16307831, -23479533, -9371869, -21393143, 2465074},
     {20017163, -4323226, 27915242, 1529148, 12396362, 15675764, 13817261, -9658066, 2463391, -4622140}},
    {{-16358878, -12663911, -12065183, 4996454, -1256422, 1073572, 9583558, 12851107, 4003896, 12673717},
     {-1731589, -15155870, -3262930, 16143082, 19294135, 13385325, 14741514, -9103726, 7903886, 2348101},
     {24536016, -16515207, 12715592, -3862155, 1511293, 10047386, -3842346, -7129159, -28377538, 10048127}}
  }, {
    {{-12622226, -6204820, 30718825, 2591312, -10617028, 12192840, 18873298, -7297090, -32297756, 15221632},
     {-26478122, -11103864, 11546244, -1852483, 9180880, 7656409, -21343950, 2095755, 29769758, 6593415},
     {-31994208, -2907461, 4176912, 3264766, 12538965, -868111, 26312345, -6118678, 30958054, 8292160}},
    {{31429822, -13959116, 29173532, 15632448, 12174511, -2760094, 32808831, 3977186, 26143136, -3148876},
     {22648901, 1402143, -22799984, 13746059, 7936347, 365344, -8668633, -1674433, -3758243, -2304625},
     {-15491917, 8012313, -2514730, -12702462, -23965846, -10254029, -1612713, -1535569, -16664475, 8194478}},
    {{27338066, -7507420, -7414224, 10140405, -19026427, -6589889, 27277191, 8855376, 28572286, 3005164},
     {26287124, 4821776, 25476601, -4145903, -3764513, -15788984, -18008582, 1182479, -26094821, -13079595},
     {-7171154, 3178080, 23970071, 6201893, -17195577, -4489192, -21876275, -13982627, 32208683, -1198248}},
    {{-16657702, 2817643, -10286362, 14811298, 6024667, 13349505, -27315504, -10497842, -27672585, -11539858},
     {15941029, -9405932, -21367050, 8062055, 31876073, -238629, -15278393, -1444429, 15397331, -4130193},
     {8934485, -13485467, -23286397, -13423241, -32446090, 14047986, 31170398, -1441021, -27505566, 15087184}},
    {{-18357243, -2156491, 24524913, -16677868, 15520427, -6360776, -15502406, 11461896, 16788528, -5868942},
     {-1947386, 16013773, 21750665, 3714552, -17401782, -16055433, -3770287, -10323320, 31322514, -11615635},
     {21426655, -5650218, -13648287, -5347537, -28812189, -4920970, -18275391, -14621414, 13040862, -12112948}},
    {{11293895, 12478086, -27136401, 15083750, -29307421, 14748872, 14555558, -13417103, 1613711, 4896935},
     {-25894883, 15323294, -8489791, -8057900, 25967126, -13425460, 2825960, -4897045, -23971776, -11267415},
     {-15924766, -5229880, -17443532, 6410664, 3622847, 10243618, 20615400, 12405433, -23753030, -8436416}},
    {{-7091295, 12556208, -20191352, 9025187, -17072479, 4333801, 4378436, 2432030, 23097949, -566018},
     {4565804, -16025654, 20084412, -7842817, 1724999, 189254, 24767264, 10103221, -18512313, 2424778},
     {366633, -11976806, 8173090, -6890119, 30788634, 5745705, -7168678, 1344109, -3642553, 12412659}},
    {{-24001791, 7690286, 14929416, -168257, -32210835, -13412986, 24162697, -15326504, -3141501, 11179385},
     {18289522, -14724954, 8056945, 16430056, -21729724, 7842514, -6001441, -1486897, -18684645, -11443503},
     {476239, 6601091, -6152790, -9723375, 17503545, -4863900, 27672959, 13403813, 11052904, 5219329}}
  }, {
    {{20678546, -8375738, -32671898, 8849123, -5009758, 14574752, 31186971, -3973730, 9014762, -8579056},
     {-13644050, -10350239, -15962508, 5075808, -1514661, -11534600, -33102500, 9160280, 8473550, -3256838},
     {24900749, 14435722, 17209120, -15292541, -22592275, 9878983, -7689309, -16335821, -24568481, 11788948}},
    {{-3118155, -11395194, -13802089, 14797441, 9652448, -6845904, -20037437, 10410733, -24568470, -1458691},
     {-15659161, 16736706, -22467150, 10215878, -9097177, 7563911, 11871841, -12505194, -18513325, 8464118},
     {-23400612, 8348507, -14585951, -861714, -3950205, -6373419, 14325289, 8628612, 33313881, -8370517}},
    {{-20186973, -4967935, 22367356, 5271547, -1097117, -4788838, -24805667, -10236854, -8940735, -5818269},
     {-6948785, -1795212, -32625683, -16021179, 32635414, -7374245, 15989197, -12838188, 28358192, -4253904},
     {-23561781, -2799059, -32351682, -1661963, -9147719, 10429267, -16637684, 4072016, -5351664, 5596589}},
    {{-28236598, -3390048, 12312896, 6213178, 3117142, 16078565, 29266239, 2557221, 1768301, 15373193},
     {-7243358, -3246960, -4593467, -7553353, -127927, -912245, -1090902, -4504991, -24660491, 3442910},
     {-30210571, 5124043, 14181784, 8197961, 18964734, -11939093, 22597931, 7176455, -18585478, 13365930}},
    {{-7877390, -1499958, 8324673, 4690079, 6261860, 890446, 24538107, -8570186, -9689599, -3031667},
     {25008904, -10771599, -4305031, -9638010, 16265036, 15721635, 683793, -11823784, 15723479, -15163481},
     {-9660625, 12374379, -27006999, -7026148, -7724114, -12314514, 11879682, 5400171, 519526, -1235876}},
    {{22258397, -16332233, -7869817, 14613016, -22520255, -2950923, -20353881, 7315967, 16648397, 7605640},
     {-8081308, -8464597, -8223311, 9719710, 19259459, -15348212, 23994942, -5281555, -9468848, 4763278},
     {-21699244, 9220969, -15730624, 1084137, -25476107, -2852390, 31088447, -7764523, -11356529, 728112}},
    {{26047220, -11751471, -6900323, -16521798, 24092068, 9158119, -4273545, -12555558, -29365436, -5498272},
     {17510331, -322857, 5854289, 8403524, 17133918, -3112612, -28111007, 12327945, 10750447, 10014012},
     {-10312768, 3936952, 9156313, -8897683, 16498692, -994647, -27481051, -666732, 3424691, 7540221}},
    {{30322361, -6964110, 11361005, -4143317, 7433304, 4989748, -7071422, -16317219, -9244265, 15258046},
     {13054562, -2779497, 19155474, 469045, -12482797, 4566042, 5631406, 2711395, 1062915, -5136345},
     {-19240248, -11254599, -29509029, -7499965, -5835763, 13005411, -6066489, 12194497, 32960380, 1459310}}
  }, {
    {{19852034, 7027924, 23669353, 10020366, 8586503, -6657907, 394197, -6101885, 18638003, -11174937},
     {31395534, 15098109, 26581030, 8030562, -16527914, -5007134, 9012486, -7584354, -6643087, -5442636},
     {-9192165, -2347377, -1997099, 4529534, 25766844, 607986, -13222, 9677543, -32294889, -6456008}},
    {{-2444496, -149937, 29348902, 8186665, 1873760, 12489863, -30934579, -7839692, -7852844, -8138429},
     {-15236356, -15433509, 7766470, 746860, 26346930, -10221762, -27333451, 10754588, -9431476, 5203576},
     {31834314, 14135496, -770007, 5159118, 20917671, -16768096, -7467973, -7337524, 31809243, 7347066}},
    {{-9606723, -11874240, 20414459, 13033986, 13716524, -11691881, 19797970, -12211255, 15192876, -2087490},
     {-12663563, -2181719, 1168162, -3804809, 26747877, -14138091, 10609330, 12694420, 33473243, -13382104},
     {33184999, 11180355, 15832085, -11385430, -1633671, 225884, 15089336, -11023903, -6135662, 14480053}},
    {{31308717, -5619998, 31030840, -1897099, 15674547, -6582883, 5496208, 13685227, 27595050, 8737275},
     {-20318852, -15150239, 10933843, -16178022, 8335352, -7546022, -31008351, -12610604, 26498114, 66511},
     {22644454, -8761729, -16671776, 4884562, -3105614, -13559366, 30540766, -4286747, -13327787, -7515095}},
    {{-28017847, 9834845, 18617207, -2681312, -3401956, -13307506, 8205540, 13585437, -17127465, 15115439},
     {23711543, -672915, 31206561, -8362711, 6164647, -9709987, -33535882, -1426096, 8236921, 16492939},
     {-23910559, -13515526, -26299483, -4503841, 25005590, -7687270, 19574902, 10071562, 6708380, -6222424}},
    {{2101391, -4930054, 19702731, 2367575, -15427167, 1047675, 5301017, 9328700, 29955601, -11678310},
     {3096359, 9271816, -21620864, -15521844, -14847996, -7592937, -25892142, -12635595, -9917575, 6216608},
     {-32615849, 338663, -25195611, 2510422, -29213566, -13820213, 24822830, -6146567, -26767480, 7525079}},
    {{-23066649, -13985623, 16133487, -7896178, -3389565, 778788, -910336, -2782495, -19386633, 11994101},
     {21691500, -13624626, -641331, -14367021, 3285881, -3483596, -25064666, 9718258, -7477437, 13381418},
     {18445390, -4202236, 14979846, 11622458, -1727110, -3582980, 23111648, -6375247, 28535282, 15779576}},
    {{30098053, 3089662, -9234387, 16662135, -21306940, 11308411, -14068454, 12021730, 9955285, -16303356},
     {9734894, -14576830, -7473633, -9138735, 2060392, 11313496, -18426029, 9924399, 20194861, 13380996},
     {-26378102, -7965207, -22167821, 15789297, -18055342, -6168792, -1984914, 15707771, 26342023, 10146099}}
  }, {
    {{-26016874, -219943, 21339191, -41388, 19745256, -2878700, -29637280, 2227040, 21612326, -545728},
     {-13077387, 1184228, 23562814, -5970442, -20351244, -6348714, 25764461, 12243797, -20856566, 11649658},
     {-10031494, 11262626, 27384172, 2271902, 26947504, -15997771, 39944, 6114064, 33514190, 2333242}},
    {{-21433588, -12421821, 8119782, 7219913, -21830522, -9016134, -6679750, -12670638, 24350578, -13450001},
     {-4116307, -11271533, -23886186, 4843615, -30088339, 690623, -31536088, -10406836, 8317860, 12352766},
     {18200138, -14475911, -33087759, -2696619, -23702521, -9102511, -23552096, -2287550, 20712163, 6719373}},
    {{26656208, 6075253, -7858556, 1886072, -28344043, 4262326, 11117530, -3763210, 26224235, -3297458},
     {-17168938, -14854097, -3395676, -16369877, -19954045, 14050420, 21728352, 9493610, 18620611, -16428628},
     {-13323321, 13325349, 11432106, 5964811, 18609221, 6062965, -5269471, -9725556, -30701573, -16479657}},
    {{-23860538, -11233159, 26961357, 1640861, -32413112, -16737940, 12248509, -5240639, 13735342, 1934062},
     {25089769, 6742589, 17081145, -13406266, 21909293, -16067981, -15136294, -3765346, -21277997, 5473616},
     {31883677, -7961101, 1083432, -11572403, 22828471, 13290673, -7125085, 12469656, 29111212, -5451014}},
    {{24244947, -15050407, -26262976, 2791540, -14997599, 16666678, 24367466, 6388839, -10295587, 452383},
     {-25640782, -3417841, 5217916, 16224624, 19987036, -4082269, -24236251, -5915248, 15766062, 8407814},
     {-20406999, 13990231, 15495425, 16395525, 5377168, 15166495, -8917023, -4388953, -8067909, 2276718}},
    {{30157918, 12924066, -17712050, 9245753, 19895028, 3368142, -23827587, 5096219, 22740376, -7303417},
     {2041139, -14256350, 7783687, 13876377, -25946985, -13352459, 24051124, 13742383, -15637599, 13295222},
     {33338237, -8505733, 12532113, 7977527, 9106186, -1715251, -17720195, -4612972, -4451357, -14669444}},
    {{-20045281, 5454097, -14346548, 6447146, 28862071, 1883651, -2469266, -4141880, 7770569, 9620597},
     {23208068, 7979712, 33071466, 8149229, 1758231, -10834995, 30945528, -1694323, -33502340, -14767970},
     {1439958, -16270480, -1079989, -793782, 4625402, 10647766, -5043801, 1220118, 30494170, -11440799}},
    {{-5037580, -13028295, -2970559, -3061767, 15640974, -6701666, -26739026, 926050, -1684339, -13333647},
     {13908495, -3549272, 30919928, -6273825, -21521863, 7989039, 9021034, 9078865, 3353509, 4033511},
     {-29663431, -15113610, 32259991, -344482, 24295849, -12912123, 23161163, 8839127, 27485041, 7356032}}
  }, {
    {{9661027, 705443, 11980065, -5370154, -1628543, 14661173, -6346142, 2625015, 28431036, -16771834},
     {-23839233, -8311415, -25945511, 7480958, -17681669, -8354183, -22545972, 14150565, 15970762, 4099461},
     {29262576, 16756590, 26350592, -8793563, 8529671, -11208050, 13617293, -9937143, 11465739, 8317062}},
    {{-25493081, -6962928, 32500200, -9419051, -23038724, -2302222, 14898637, 3848455, 20969334, -5157516},
     {-20384450, -14347713, -18336405, 13884722, -33039454, 2842114, -21610826, -3649888, 11177095, 14989547},
     {-24496721, -11716016, 16959896, 2278463, 12066309, 10137771, 13515641, 2581286, -28487508, 9930240}},
    {{-17751622, -2097826, 16544300, -13009300, -15914807, -14949081, 18345767, -13403753, 16291481, -5314038},
     {-33229194, 2553288, 32678213, 9875984, 8534129, 6889387, -9676774, 6957617, 4368891, 9788741},
     {16660756, 7281060, -10830758, 12911820, 20108584, -8101676, -21722536, -8613148, 16250552, -11111103}},
    {{-19765507, 2390526, -16551031, 14161980, 1905286, 6414907, 4689584, 10604807, -30190403, 4782747},
     {-1354539, 14736941, -7367442, -13292886, 7710542, -14155590, -9981571, 4383045, 22546403, 437323},
     {31665577, -12180464, -16186830, 1491339, -18368625, 3294682, 27343084, 2786261, -30633590, -14097016}},
    {{-14467279, -683715, -33374107, 7448552, 19294360, 14334329, -19690631, 2355319, -19284671, -6114373},
     {15121312, -15796162, 6377020, -6031361, -10798111, -12957845, 18952177, 15496498, -29380133, 11754228},
     {-2637277, -13483075, 8488727, -14303896, 12728761, -1622493, 7141596, 11724556, 22761615, -10134141}},
    {{16918416, 11729663, -18083579, 3022987, -31015732, -13339659, -28741185, -12227393, 32851222, 11717399},
     {11166634, 7338049, -6722523, 4531520, -29468672, -7302055, 31474879, 3483633, -1193175, -4030831},
     {-185635, 9921305, 31456609, -13536438, -12013818, 13348923, 33142652, 6546660, -19985279, -3948376}},
    {{-32460596, 11266712, -11197107, -7899103, 31703694, 3855903, -8537131, -12833048, -30772034, -15486313},
     {-18006477, 12709068, 3991746, -6479188, -21491523, -10550425, -31135347, -16049879, 10928917, 3011958},
     {-6957757, -15594337, 31696059, 334240, 29576716, 14796075, -30831056, -12805180, 18008031, 10258577}},
    {{-22448644, 15655569, 7018479, -4410003, -30314266, -1201591, -1853465, 1367120, 25127874, 6671743},
     {29701166, -14373934, -10878120, 9279288, -17568, 13127210, 21382910, 11042292, 25838796, 4642684},
     {-20430234, 14955537, -24126347, 8124619, -5369288, -5990470, 30468147, -13900640, 18423289, 4177476}}
  }
};

const ge_precomp ge_Bi[8] = {
  {{25967493, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626, -11754271, -6079156, 2047605},
   {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384, 19500929, -15469378},
   {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919, 11864899, -24514362, -4438546}}, {{15636291, -9688557, 24204773, -7912398, 616977, -16685262, 27787600, -14772189, 28944400, -1550024},
   {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577, -11775962, 7689662, 11199574},
   {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774, 10017326, -17749093, -9920357}}, {{10861363, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885, 14515107, -15438304, 10819380},
   {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, 12483688, -12668491, 5581306},
   {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350, 13850243, -23678021, -15815942}}, {{5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134, -23952439, -15175766},
   {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025, 16520125, 30598449, 7715701},
   {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660, 1370708, 29794553, -1409300}}, {{-22518993, -6692182, 14201702, -8745502, -23510406, 8844726, 18474211, -1361450, -13062696, 13821877},
   {-6455177, -7839871, 3374702, -4740862, -27098617, -10571707, 31655028, -7212327, 18853322, -14220951},
   {4566830, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358, -10431137, 2207753, -3209784}}, {{-25154831, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364, -663000, -31111463, -16132436},
   {25576264, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789, 15725684, 171356, 6466918},
   {23103977, 13316479, 9739013, -16149481, 817875, -15038942, 8965339, -14088058, -30714912, 16193877}}, {{-33521811, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398, 4729455, -18074513, 9256800},
   {-25182317, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405, 9761698, -19827198, 630305},
   {-13720693, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551, -15960994, -2449256, -14291300}}, {{-3151181, -5046075, 9282714, 6866145, -31907062, -863023, -18940575, 15033784, 25105118, -7894876},
   {-24326370, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892, -2625887, 2198790, -15804619},
   {-3099351, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022, -16236442, -32461234, -12290683}}
};

/* A = 2 * (1 - d) / (1 + d) = 486662 */
const fe fe_ma2 = {-12721188, -3529, 0, 0, 0, 0, 0, 0, 0, 0}; /* -A^2 */
const fe fe_ma = {-486662, 0, 0, 0, 0, 0, 0, 0, 0, 0}; /* -A */
const fe fe_fffb1 = {-31702527, -2466483, -26106795, -12203692, -12169197, -321052, 14850977, -10296299, -16929438, -407568}; /* sqrt(-2 * A * (A + 2)) */
const fe fe_fffb2 = {8166131, -6741800, -17040804, 3154616, 21461005, 1466302, -30876704, -6368709, 10503587, -13363080}; /* sqrt(2 * A * (A + 2)) */
const fe fe_fffb3 = {-13620103, 14639558, 4532995, 7679154, 16815101, -15883539, -22863840, -14813421, 13716513, -6477756}; /* sqrt(-sqrt(-1) * A * (A + 2)) */
const fe fe_fffb4 = {-21786234, -12173074, 21573800, 4524538, -4645904, 16204591, 8012863, -8444712, 3212926, 6885324}; /* sqrt(sqrt(-1) * A * (A + 2)) */