nim-libp2p/libp2p/crypto/ed25519/constants.nim

# Nim-Libp2p
# Copyright (c) 2023 Status Research & Development GmbH
# Licensed under either of
#  * Apache License, version 2.0, ([LICENSE-APACHE](LICENSE-APACHE))
#  * MIT license ([LICENSE-MIT](LICENSE-MIT))
# at your option.
# This file may not be copied, modified, or distributed except according to
# those terms.

## This module implements ED25519.
## This is pure nim implementation of ED25519 ref10.

type
  Fe* = array[10, int32]

  GeP2* = object
    x*, y*, z*: Fe

  GeP3* = object
    x*, y*, z*, t*: Fe

  GeP1P1* = object
    x*, y*, z*, t*: Fe

  GePrecomp* = object
    yplusx*, yminusx*, xy2d*: Fe

  GeCached* = object
    yplusx*, yminusx*, z*, t2d*: Fe

const
  CurveOrder* = [
    0xED'u8, 0xD3'u8, 0xF5'u8, 0x5C'u8, 0x1A'u8, 0x63'u8, 0x12'u8, 0x58'u8, 0xD6'u8,
    0x9C'u8, 0xF7'u8, 0xA2'u8, 0xDE'u8, 0xF9'u8, 0xDE'u8, 0x14'u8, 0x00'u8, 0x00'u8,
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8,
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x10'u8,
  ]

  ZeroFe* = [
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8,
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8,
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8,
    0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8, 0x00'u8,
  ]

  BasePrecomp* = [
    [
      GePrecomp(
        yplusx: [
          25967493'i32, -14356035, 29566456, 3660896, -12694345, 4014787, 27544626,
          -11754271, -6079156, 2047605,
        ],
        yminusx: [
          -12545711'i32, 934262, -2722910, 3049990, -727428, 9406986, 12720692, 5043384,
          19500929, -15469378,
        ],
        xy2d: [
          -8738181'i32, 4489570, 9688441, -14785194, 10184609, -12363380, 29287919,
          11864899, -24514362, -4438546,
        ],
      ),
      GePrecomp(
        yplusx: [
          -12815894'i32, -12976347, -21581243, 11784320, -25355658, -2750717, -11717903,
          -3814571, -358445, -10211303,
        ],
        yminusx: [
          -21703237'i32, 6903825, 27185491, 6451973, -29577724, -9554005, -15616551,
          11189268, -26829678, -5319081,
        ],
        xy2d: [
          26966642'i32, 11152617, 32442495, 15396054, 14353839, -12752335, -3128826,
          -9541118, -15472047, -4166697,
        ],
      ),
      GePrecomp(
        yplusx: [
          15636291'i32, -9688557, 24204773, -7912398, 616977, -16685262, 27787600,
          -14772189, 28944400, -1550024,
        ],
        yminusx: [
          16568933'i32, 4717097, -11556148, -1102322, 15682896, -11807043, 16354577,
          -11775962, 7689662, 11199574,
        ],
        xy2d: [
          30464156'i32, -5976125, -11779434, -15670865, 23220365, 15915852, 7512774,
          10017326, -17749093, -9920357,
        ],
      ),
      GePrecomp(
        yplusx: [
          -17036878'i32, 13921892, 10945806, -6033431, 27105052, -16084379, -28926210,
          15006023, 3284568, -6276540,
        ],
        yminusx: [
          23599295'i32, -8306047, -11193664, -7687416, 13236774, 10506355, 7464579,
          9656445, 13059162, 10374397,
        ],
        xy2d: [
          7798556'i32, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664,
          -3839045, -641708, -101325,
        ],
      ),
      GePrecomp(
        yplusx: [
          10861363'i32, 11473154, 27284546, 1981175, -30064349, 12577861, 32867885,
          14515107, -15438304, 10819380,
        ],
        yminusx: [
          4708026'i32, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668,
          12483688, -12668491, 5581306,
        ],
        xy2d: [
          19563160'i32, 16186464, -29386857, 4097519, 10237984, -4348115, 28542350,
          13850243, -23678021, -15815942,
        ],
      ),
      GePrecomp(
        yplusx: [
          -15371964'i32, -12862754, 32573250, 4720197, -26436522, 5875511, -19188627,
          -15224819, -9818940, -12085777,
        ],
        yminusx: [
          -8549212'i32, 109983, 15149363, 2178705, 22900618, 4543417, 3044240,
          -15689887, 1762328, 14866737,
        ],
        xy2d: [
          -18199695'i32, -15951423, -10473290, 1707278, -17185920, 3916101, -28236412,
          3959421, 27914454, 4383652,
        ],
      ),
      GePrecomp(
        yplusx: [
          5153746'i32, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, 5230134,
          -23952439, -15175766,
        ],
        yminusx: [
          -30269007'i32, -3463509, 7665486, 10083793, 28475525, 1649722, 20654025,
          16520125, 30598449, 7715701,
        ],
        xy2d: [
          28881845'i32, 14381568, 9657904, 3680757, -20181635, 7843316, -31400660,
          1370708, 29794553, -1409300,
        ],
      ),
      GePrecomp(
        yplusx: [
          14499471'i32, -2729599, -33191113, -4254652, 28494862, 14271267, 30290735,
          10876454, -33154098, 2381726,
        ],
        yminusx: [
          -7195431'i32, -2655363, -14730155, 462251, -27724326, 3941372, -6236617,
          3696005, -32300832, 15351955,
        ],
        xy2d: [
          27431194'i32, 8222322, 16448760, -3907995, -18707002, 11938355, -32961401,
          -2970515, 29551813, 10109425,
        ],
      ),
    ],
    [
      GePrecomp(
        yplusx: [
          -13657040'i32, -13155431, -31283750, 11777098, 21447386, 6519384, -2378284,
          -1627556, 10092783, -4764171,
        ],
        yminusx: [
          27939166'i32, 14210322, 4677035, 16277044, -22964462, -12398139, -32508754,
          12005538, -17810127, 12803510,
        ],
        xy2d: [
          17228999'i32, -15661624, -1233527, 300140, -1224870, -11714777, 30364213,
          -9038194, 18016357, 4397660,
        ],
      ),
      GePrecomp(
        yplusx: [
          -10958843'i32, -7690207, 4776341, -14954238, 27850028, -15602212, -26619106,
          14544525, -17477504, 982639,
        ],
        yminusx: [
          29253598'i32, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899,
          -4120128, -21047696, 9934963,
        ],
        xy2d: [
          5793303'i32, 16271923, -24131614, -10116404, 29188560, 1206517, -14747930,
          4559895, -30123922, -10897950,
        ],
      ),
      GePrecomp(
        yplusx: [
          -27643952'i32, -11493006, 16282657, -11036493, 28414021, -15012264, 24191034,
          4541697, -13338309, 5500568,
        ],
        yminusx: [
          12650548'i32, -1497113, 9052871, 11355358, -17680037, -8400164, -17430592,
          12264343, 10874051, 13524335,
        ],
        xy2d: [
          25556948'i32, -3045990, 714651, 2510400, 23394682, -10415330, 33119038,
          5080568, -22528059, 5376628,
        ],
      ),
      GePrecomp(
        yplusx: [
          -26088264'i32, -4011052, -17013699, -3537628, -6726793, 1920897, -22321305,
          -9447443, 4535768, 1569007,
        ],
        yminusx: [
          -2255422'i32, 14606630, -21692440, -8039818, 28430649, 8775819, -30494562,
          3044290, 31848280, 12543772,
        ],
        xy2d: [
          -22028579'i32, 2943893, -31857513, 6777306, 13784462, -4292203, -27377195,
          -2062731, 7718482, 14474653,
        ],
      ),
      GePrecomp(
        yplusx: [
          2385315'i32, 2454213, -22631320, 46603, -4437935, -15680415, 656965, -7236665,
          24316168, -5253567,
        ],
        yminusx: [
          13741529'i32, 10911568, -33233417, -8603737, -20177830, -1033297, 33040651,
          -13424532, -20729456, 8321686,
        ],
        xy2d: [
          21060490'i32, -2212744, 15712757, -4336099, 1639040, 10656336, 23845965,
          -11874838, -9984458, 608372,
        ],
      ),
      GePrecomp(
        yplusx: [
          -13672732'i32, -15087586, -10889693, -7557059, -6036909, 11305547, 1123968,
          -6780577, 27229399, 23887,
        ],
        yminusx: [
          -23244140'i32, -294205, -11744728, 14712571, -29465699, -2029617, 12797024,
          -6440308, -1633405, 16678954,
        ],
        xy2d: [
          -29500620'i32, 4770662, -16054387, 14001338, 7830047, 9564805, -1508144,
          -4795045, -17169265, 4904953,
        ],
      ),
      GePrecomp(
        yplusx: [
          24059557'i32, 14617003, 19037157, -15039908, 19766093, -14906429, 5169211,
          16191880, 2128236, -4326833,
        ],
        yminusx: [
          -16981152'i32, 4124966, -8540610, -10653797, 30336522, -14105247, -29806336,
          916033, -6882542, -2986532,
        ],
        xy2d: [
          -22630907'i32, 12419372, -7134229, -7473371, -16478904, 16739175, 285431,
          2763829, 15736322, 4143876,
        ],
      ),
      GePrecomp(
        yplusx: [
          2379352'i32, 11839345, -4110402, -5988665, 11274298, 794957, 212801,
          -14594663, 23527084, -16458268,
        ],
        yminusx: [
          33431127'i32, -11130478, -17838966, -15626900, 8909499, 8376530, -32625340,
          4087881, -15188911, -14416214,
        ],
        xy2d: [
          1767683'i32, 7197987, -13205226, -2022635, -13091350, 448826, 5799055,
          4357868, -4774191, -16323038,
        ],
      ),
    ],
    [
      GePrecomp(
        yplusx: [
          6721966'i32, 13833823, -23523388, -1551314, 26354293, -11863321, 23365147,
          -3949732, 7390890, 2759800,
        ],
        yminusx: [
          4409041'i32, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353,
          -4264057, 1244380, -12919645,
        ],
        xy2d: [
          -4421239'i32, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413,
          9208236, 15886429, 16489664,
        ],
      ),
      GePrecomp(
        yplusx: [
          1996075'i32, 10375649, 14346367, 13311202, -6874135, -16438411, -13693198,
          398369, -30606455, -712933,
        ],
        yminusx: [
          -25307465'i32, 9795880, -2777414, 14878809, -33531835, 14780363, 13348553,
          12076947, -30836462, 5113182,
        ],
        xy2d: [
          -17770784'i32, 11797796, 31950843, 13929123, -25888302, 12288344, -30341101,
          -7336386, 13847711, 5387222,
        ],
      ),
      GePrecomp(
        yplusx: [
          -18582163'i32, -3416217, 17824843, -2340966, 22744343, -10442611, 8763061,
          3617786, -19600662, 10370991,
        ],
        yminusx: [
          20246567'i32, -14369378, 22358229, -543712, 18507283, -10413996, 14554437,
          -8746092, 32232924, 16763880,
        ],
        xy2d: [
          9648505'i32, 10094563, 26416693, 14745928, -30374318, -6472621, 11094161,
          15689506, 3140038, -16510092,
        ],
      ),
      GePrecomp(
        yplusx: [
          -16160072'i32, 5472695, 31895588, 4744994, 8823515, 10365685, -27224800,
          9448613, -28774454, 366295,
        ],
        yminusx: [
          19153450'i32, 11523972, -11096490, -6503142, -24647631, 5420647, 28344573,
          8041113, 719605, 11671788,
        ],
        xy2d: [
          8678025'i32, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916,
          -15266516, 27000813, -10195553,
        ],
      ),
      GePrecomp(
        yplusx: [
          -15157904'i32, 7134312, 8639287, -2814877, -7235688, 10421742, 564065,
          5336097, 6750977, -14521026,
        ],
        yminusx: [
          11836410'i32, -3979488, 26297894, 16080799, 23455045, 15735944, 1695823,
          -8819122, 8169720, 16220347,
        ],
        xy2d: [
          -18115838'i32, 8653647, 17578566, -6092619, -8025777, -16012763, -11144307,
          -2627664, -5990708, -14166033,
        ],
      ),
      GePrecomp(
        yplusx: [
          -23308498'i32, -10968312, 15213228, -10081214, -30853605, -11050004, 27884329,
          2847284, 2655861, 1738395,
        ],
        yminusx: [
          -27537433'i32, -14253021, -25336301, -8002780, -9370762, 8129821, 21651608,
          -3239336, -19087449, -11005278,
        ],
        xy2d: [
          1533110'i32, 3437855, 23735889, 459276, 29970501, 11335377, 26030092, 5821408,
          10478196, 8544890,
        ],
      ),
      GePrecomp(
        yplusx: [
          32173121'i32, -16129311, 24896207, 3921497, 22579056, -3410854, 19270449,
          12217473, 17789017, -3395995,
        ],
        yminusx: [
          -30552961'i32, -2228401, -15578829, -10147201, 13243889, 517024, 15479401,
          -3853233, 30460520, 1052596,
        ],
        xy2d: [
          -11614875'i32, 13323618, 32618793, 8175907, -15230173, 12596687, 27491595,
          -4612359, 3179268, -9478891,
        ],
      ),
      GePrecomp(
        yplusx: [
          31947069'i32, -14366651, -4640583, -15339921, -15125977, -6039709, -14756777,
          -16411740, 19072640, -9511060,
        ],
        yminusx: [
          11685058'i32, 11822410, 3158003, -13952594, 33402194, -4165066, 5977896,
          -5215017, 473099, 5040608,
        ],
        xy2d: [
          -20290863'i32, 8198642, -27410132, 11602123, 1290375, -2799760, 28326862,
          1721092, -19558642, -3131606,
        ],
      ),
    ],
    [
      GePrecomp(
        yplusx: [
          7881532'i32, 10687937, 7578723, 7738378, -18951012, -2553952, 21820786,
          8076149, -27868496, 11538389,
        ],
        yminusx: [
          -19935666'i32, 3899861, 18283497, -6801568, -15728660, -11249211, 8754525,
          7446702, -5676054, 5797016,
        ],
        xy2d: [
          -11295600'i32, -3793569, -15782110, -7964573, 12708869, -8456199, 2014099,
          -9050574, -2369172, -5877341,
        ],
      ),
      GePrecomp(
        yplusx: [
          -22472376'i32, -11568741, -27682020, 1146375, 18956691, 16640559, 1192730,
          -3714199, 15123619, 10811505,
        ],
        yminusx: [
          14352098'i32, -3419715, -18942044, 10822655, 32750596, 4699007, -70363,
          15776356, -28886779, -11974553,
        ],
        xy2d: [
          -28241164'i32, -8072475, -4978962, -5315317, 29416931, 1847569, -20654173,
          -16484855, 4714547, -9600655,
        ],
      ),
      GePrecomp(
        yplusx: [
          15200332'i32, 8368572, 19679101, 15970074, -31872674, 1959451, 24611599,
          -4543832, -11745876, 12340220,
        ],
        yminusx: [
          12876937'i32, -10480056, 33134381, 6590940, -6307776, 14872440, 9613953,
          8241152, 15370987, 9608631,
        ],
        xy2d: [
          -4143277'i32, -12014408, 8446281, -391603, 4407738, 13629032, -7724868,
          15866074, -28210621, -8814099,
        ],
      ),
      GePrecomp(
        yplusx: [
          26660628'i32, -15677655, 8393734, 358047, -7401291, 992988, -23904233, 858697,
          20571223, 8420556,
        ],
        yminusx: [
          14620715'i32, 13067227, -15447274, 8264467, 14106269, 15080814, 33531827,
          12516406, -21574435, -12476749,
        ],
        xy2d: [
          236881'i32, 10476226, 57258, -14677024, 6472998, 2466984, 17258519, 7256740,
          8791136, 15069930,
        ],
      ),
      GePrecomp(
        yplusx: [
          1276410'i32, -9371918, 22949635, -16322807, -23493039, -5702186, 14711875,
          4874229, -30663140, -2331391,
        ],
        yminusx: [
          5855666'i32, 4990204, -13711848, 7294284, -7804282, 1924647, -1423175,
          -7912378, -33069337, 9234253,
        ],
        xy2d: [
          20590503'i32, -9018988, 31529744, -7352666, -2706834, 10650548, 31559055,
          -11609587, 18979186, 13396066,
        ],
      ),
      GePrecomp(
        yplusx: [
          24474287'i32, 4968103, 22267082, 4407354, 24063882, -8325180, -18816887,
          13594782, 33514650, 7021958,
        ],
        yminusx: [
          -11566906'i32, -6565505, -21365085, 15928892, -26158305, 4315421, -25948728,
          -3916677, -21480480, 12868082,
        ],
        xy2d: [
          -28635013'i32, 13504661, 19988037, -2132761, 21078225, 6443208, -21446107,
          2244500, -12455797, -8089383,
        ],
      ),
      GePrecomp(
        yplusx: [
          -30595528'i32, 13793479, -5852820, 319136, -25723172, -6263899, 33086546,
          8957937, -15233648, 5540521,
        ],
        yminusx: [
          -11630176'i32, -11503902, -8119500, -7643073, 2620056, 1022908, -23710744,
          -1568984, -16128528, -14962807,
        ],
        xy2d: [
          23152971'i32, 775386, 27395463, 14006635, -9701118, 4649512, 1689819, 892185,
          -11513277, -15205948,
        ],
      ),
      GePrecomp(
        yplusx: [
          9770129'i32, 9586738, 26496094, 4324120, 1556511, -3550024, 27453819, 4763127,
          -19179614, 5867134,
        ],
        yminusx: [
          -32765025'i32, 1927590, 31726409, -4753295, 23962434, -16019500, 27846559,
          5931263, -29749703, -16108455,
        ],
        xy2d: [
          27461885'i32, -2977536, 22380810, 1815854, -23033753, -3031938, 7283490,
          -15148073, -19526700, 7734629,
        ],
      ),
    ],
    [
      GePrecomp(
        yplusx: [
          -8010264'i32, -9590817, -11120403, 6196038, 29344158, -13430885, 7585295,
          -3176626, 18549497, 15302069,
        ],
        yminusx: [
          -32658337'i32, -6171222, -7672793, -11051681, 6258878, 13504381, 10458790,
          -6418461, -8872242, 8424746,
        ],
        xy2d: [
          24687205'i32, 8613276, -30667046, -3233545, 1863892, -1830544, 19206234,
          7134917, -11284482, -828919,
        ],
      ),
      GePrecomp(
        yplusx: [
          11334899'i32, -9218022, 8025293, 12707519, 17523892, -10476071, 10243738,
          -14685461, -5066034, 16498837,
        ],
        yminusx: [
          8911542'i32, 6887158, -9584260, -6958590, 11145641, -9543680, 17303925,
          -14124238, 6536641, 10543906,
        ],
        xy2d: [
          -28946384'i32, 15479763, -17466835, 568876, -1497683, 11223454, -2669190,
          -16625574, -27235709, 8876771,
        ],
      ),
      GePrecomp(
        yplusx: [
          -25742899'i32, -12566864, -15649966, -846607, -33026686, -796288, -33481822,
          15824474, -604426, -9039817,
        ],
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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    [
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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      GePrecomp(
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  BiPrecomp* = [
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      xy2d: [
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    GePrecomp(
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    GePrecomp(
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    GePrecomp(
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      xy2d: [
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    GePrecomp(
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      yminusx: [
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      ],
      xy2d: [
        4566830'i32, -12963868, -28974889, -12240689, -7602672, -2830569, -8514358,
        -10431137, 2207753, -3209784,
      ],
    ),
    GePrecomp(
      yplusx: [
        -25154831'i32, -4185821, 29681144, 7868801, -6854661, -9423865, -12437364,
        -663000, -31111463, -16132436,
      ],
      yminusx: [
        25576264'i32, -2703214, 7349804, -11814844, 16472782, 9300885, 3844789,
        15725684, 171356, 6466918,
      ],
      xy2d: [
        23103977'i32, 13316479, 9739013, -16149481, 817875, -15038942, 8965339,
        -14088058, -30714912, 16193877,
      ],
    ),
    GePrecomp(
      yplusx: [
        -33521811'i32, 3180713, -2394130, 14003687, -16903474, -16270840, 17238398,
        4729455, -18074513, 9256800,
      ],
      yminusx: [
        -25182317'i32, -4174131, 32336398, 5036987, -21236817, 11360617, 22616405,
        9761698, -19827198, 630305,
      ],
      xy2d: [
        -13720693'i32, 2639453, -24237460, -7406481, 9494427, -5774029, -6554551,
        -15960994, -2449256, -14291300,
      ],
    ),
    GePrecomp(
      yplusx: [
        -3151181'i32, -5046075, 9282714, 6866145, -31907062, -863023, -18940575,
        15033784, 25105118, -7894876,
      ],
      yminusx: [
        -24326370'i32, 15950226, -31801215, -14592823, -11662737, -5090925, 1573892,
        -2625887, 2198790, -15804619,
      ],
      xy2d: [
        -3099351'i32, 10324967, -2241613, 7453183, -5446979, -2735503, -13812022,
        -16236442, -32461234, -12290683,
      ],
    ),
  ]

  DConst* = [
    -10913610'i32, 13857413, -15372611, 6949391, 114729, -8787816, -6275908, -3247719,
    -18696448, -12055116,
  ]

  D2Const* = [
    -21827239'i32, -5839606, -30745221, 13898782, 229458, 15978800, -12551817, -6495438,
    29715968, 9444199,
  ]

  SqrTm1* = [
    -32595792'i32, -7943725, 9377950, 3500415, 12389472, -272473, -25146209, -2005654,
    326686, 11406482,
  ]