clmul_8bytes.cpp

Go to the documentation of this file.

/**********************************************************************
 * Copyright (c) 2018 Pieter Wuille, Greg Maxwell, Gleb Naumenko      *
 * Distributed under the MIT software license, see the accompanying   *
 * file LICENSE or http://www.opensource.org/licenses/mit-license.php.*
 **********************************************************************/
 
/* This file was substantially auto-generated by doc/gen_params.sage. */
#include "../fielddefines.h"
 
#if defined(ENABLE_FIELD_BYTES_INT_8)
 
#include "clmul_common_impl.h"
 
#include "../int_utils.h"
#include "../lintrans.h"
#include "../sketch_impl.h"
 
#endif
 
#include "../sketch.h"
 
namespace {
#ifdef ENABLE_FIELD_INT_57
// 57 bit field
typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5> StatTable57;
constexpr StatTable57 SQR_TABLE_57({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x22, 0x88, 0x220, 0x880, 0x2200, 0x8800, 0x22000, 0x88000, 0x220000, 0x880000, 0x2200000, 0x8800000, 0x22000000, 0x88000000, 0x220000000, 0x880000000, 0x2200000000, 0x8800000000, 0x22000000000, 0x88000000000, 0x220000000000, 0x880000000000, 0x2200000000000, 0x8800000000000, 0x22000000000000, 0x88000000000000, 0x20000000000011, 0x80000000000044});
constexpr StatTable57 SQR2_TABLE_57({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x88, 0x880, 0x8800, 0x88000, 0x880000, 0x8800000, 0x88000000, 0x880000000, 0x8800000000, 0x88000000000, 0x880000000000, 0x8800000000000, 0x88000000000000, 0x80000000000044, 0x404, 0x4040, 0x40400, 0x404000, 0x4040000, 0x40400000, 0x404000000, 0x4040000000, 0x40400000000, 0x404000000000, 0x4040000000000, 0x40400000000000, 0x4000000000022, 0x40000000000220, 0x2222, 0x22220, 0x222200, 0x2222000, 0x22220000, 0x222200000, 0x2222000000, 0x22220000000, 0x222200000000, 0x2222000000000, 0x22220000000000, 0x22200000000011, 0x22000000000101, 0x20000000001001});
constexpr StatTable57 SQR4_TABLE_57({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x880, 0x8800000, 0x88000000000, 0x80000000000044, 0x404000, 0x4040000000, 0x40400000000000, 0x22220, 0x222200000, 0x2222000000000, 0x20000000001001, 0x10001000, 0x100010000000, 0x100000000088, 0x880088, 0x8800880000, 0x88008800000000, 0x88000000040400, 0x404040400, 0x4040404000000, 0x4040000002222, 0x22222222, 0x222222220000, 0x22222200000101, 0x22000001000001, 0x10000000100, 0x100000001000000, 0x10000088000, 0x100000880000000, 0x8800000088000, 0x880004040, 0x8800040400000, 0x404000004040, 0x40000040400220, 0x404002222000, 0x40022220000220, 0x22200002222011, 0x22220100010, 0x22201000100011, 0x10001000100010, 0x10001000108800, 0x10001088008800, 0x10880088008800, 0x880088008c04, 0x88008c040404, 0x8c0404040404, 0x4040404040426, 0x4040404262222, 0x4042622222222, 0x26222222222222, 0x22222222232201, 0x22222322000001, 0x23220000000001});
constexpr StatTable57 SQR8_TABLE_57({0x1, 0x100010000000, 0x100000880000000, 0x88008c040404, 0x80000000022264, 0x26262604000101, 0x50023220100230, 0x222aa222000001, 0x20000404041401, 0x100404003222000, 0x32aa22aa23aa01, 0x2326048800088, 0x808100222ea722, 0x508e36ec548e34, 0x26222000022223, 0x22000223200001, 0x32001001108801, 0x91001000108844, 0x85048c04880044, 0x4c86ae64c80220, 0x6ea40546662003, 0x66662726ae22ab, 0x40622aa2aa40c8, 0x26063ea6364477, 0x2406744c950437, 0x8a33606aa727aa, 0xd09332ca7e2d9a, 0x7e2c14ce3e6c17, 0x22aa2626260405, 0x22200002626011, 0x27260000002223, 0x22208812aa3011, 0x2ba30040488001, 0x48c8c9caebe26, 0x28898040489001, 0x1048c008922aa26, 0x30c0c08a22b801, 0x12222666fa72601, 0x9afa60a8048eaa, 0x6aa1400afba131, 0xbc9c168c00800d, 0xc083aa60588bb0, 0xbeeefeae26e6e7, 0x8c44ee22226ae2, 0x8c44ee32205042, 0x2667443228d143, 0x36af14ba381d17, 0x72eb33981a3f35, 0x72c911aab20d9d, 0x72ca2b2aaacccd, 0x66463fae3f44ff, 0xac345eee3b4077, 0xe4977caefbe1fd, 0xf01b70a0dd0f9a, 0xf40f74bc580bbd, 0x17e2d1c6c5c0f35, 0x3624140232aa33});
constexpr StatTable57 SQR16_TABLE_57({0x1, 0xaeeec814065447, 0x110889c99ba3004, 0x1c59ed582798e0e, 0x1c9c766272a2a74, 0x1422928a5250a00, 0x2c97eb48f402a1, 0x10c6d916b128dea, 0x3f2e6ca66ebf67, 0x93ac75fcd63ec8, 0x19263128e42246, 0x1fd1ca54b556091, 0x60ff38200c4e09, 0x1381808ede9982b, 0xc7a9ace2f9dc2a, 0x6c2ee414271c57, 0x3c16f4cffdbe17, 0xc627ec6fe179ee, 0x178f994adf6525b, 0x18be0b635ca1650, 0x4afcb2ae2e98b6, 0x6f81f53a7688dd, 0x45319b3e02c15c, 0x1044be090058910, 0xaa02d012fca063, 0x11fba4c5b80dbfa, 0xf9f44be142268b, 0x1e351a44eb480bf, 0xacf5c17bd0aedf, 0x6f2d74bab851eb, 0x1b8ac3589da9915, 0x1afeb885d3fdd67, 0x7d7d596dd60bbd, 0x1329567316f5723, 0xfdfe23b549fcef, 0xc985ed1e7a009e, 0x71f794bbac1b03, 0xc740582125f7d0, 0x1b3584e031e3b77, 0x29978a3c559ed3, 0xde04d46b4ae516, 0x2f6d6e1c749405, 0x1ec95b44a4251f3, 0xb95b0a5f451f2d, 0x1dc80aedaab9bf2, 0xd0354d3ff74808, 0x180889b484b0364, 0x196895708367d90, 0x104575064a09414, 0x19e88f14fc111ec, 0x1cf4088d3cffd88, 0x1e6c28b9a76c6d5, 0x81ba060c9e485e, 0x12b811107188d68, 0x5e6f10ca82cd88, 0x120882748af043d, 0x145fb82467c596e});
constexpr StatTable57 QRT_TABLE_57({0xd0c3a82c902426, 0x232aa54103915e, 0x232aa54103915c, 0x1763e291e61699c, 0x232aa541039158, 0x1f424d678bb15e, 0x1763e291e616994, 0x26fd8122f10d36, 0x232aa541039148, 0x1e0a0206002000, 0x1f424d678bb17e, 0x5d72563f39d7e, 0x1763e291e6169d4, 0x1519beb9d597df4, 0x26fd8122f10db6, 0x150c3a87c90e4aa, 0x232aa541039048, 0x15514891f6179d4, 0x1e0a0206002200, 0x14ec9ba7a94c6aa, 0x1f424d678bb57e, 0x1e0f4286382420, 0x5d72563f3957e, 0x4000080000, 0x1763e291e6179d4, 0x1ac0e804882000, 0x1519beb9d595df4, 0x1f430d6793b57e, 0x26fd8122f14db6, 0x3c68e806882000, 0x150c3a87c9064aa, 0x1484fe18b915e, 0x232aa541029048, 0x14f91eb9b595df4, 0x15514891f6379d4, 0x48f6a82380420, 0x1e0a0206042200, 0x14b1beb99595df4, 0x14ec9ba7a9cc6aa, 0x4cf2a82b00420, 0x1f424d679bb57e, 0x26aa0002000000, 0x1e0f4286182420, 0x173f1039dd17df4, 0x5d72563b3957e, 0x4aa0002000000, 0x4000880000, 0x16d31eb9b595df4, 0x1763e291f6179d4, 0x20000000000000, 0x1ac0e806882000, 0x2caa0002000000, 0x1519beb99595df4, 0, 0x1f430d6f93b57e, 0x73e90d6d93b57e, 0x26fd8132f14db6});
typedef Field<uint64_t, 57, 17, StatTable57, &SQR_TABLE_57, &SQR2_TABLE_57, &SQR4_TABLE_57, &SQR8_TABLE_57, &SQR16_TABLE_57, &QRT_TABLE_57, IdTrans, &ID_TRANS, &ID_TRANS> Field57;
typedef FieldTri<uint64_t, 57, 4, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5>, &SQR_TABLE_57, &SQR2_TABLE_57, &SQR4_TABLE_57, &SQR8_TABLE_57, &SQR16_TABLE_57, &QRT_TABLE_57, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri57;
#endif
 
#ifdef ENABLE_FIELD_INT_58
// 58 bit field
typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5> StatTable58;
constexpr StatTable58 LOAD_TABLE_58({0x1, 0x77dd188d5d600, 0x41a7213270def0, 0x10921661867b40a, 0x880b92a6f74da3, 0x143e72cde8f4484, 0x1863cb65c3eee0e, 0x2a1aa4a82154057, 0x22265135db9e135, 0x1446f023770d6d0, 0x183c4be7b4fae6, 0x1cc8a1187e99bd4, 0x3a1ea282e1e2ff1, 0x2700aae9dbcd275, 0x1571f84428a416e, 0xc8eb0b234b8a57, 0x23227afc0d9ba75, 0x1de9497779018c7, 0x5898e896d43329, 0x1501bd1b83bb55f, 0xbb56c28ce180b, 0x188e087d2dbf7e0, 0x36eee77125d8ec9, 0xde4235cbe95166, 0x1c71e4d57306163, 0x2a7e1b1ae5d87ee, 0x3a685560450c909, 0x1cd0545bc185c4b, 0x151779b11f09892, 0x2ab069803c4d787, 0x3bf279c0b825ad5, 0x15edc1ef3d2513c, 0x37bf223b4d0d045, 0x262a786b0324cd3, 0x27658294b696713, 0x33771167b0137e8, 0x86a73ef2dc3271, 0xc64453d2ff05, 0x14c55bc975ce8c, 0x3581164b1e4826e, 0x461dde5468bc26, 0x3f31528346e9451, 0x3f2669a5324a555, 0xd0b1c042854400, 0x32cc9899ea263e3, 0x2a423a8a96f4e95, 0x3e64acd727b470b, 0x2f1f1c1de9c997d, 0x268f2df0a8ab060, 0x14fd82231712442, 0x106e14e5e9e8f8c, 0x2686a15d911a24c, 0x182f831c5142b40, 0x36ca3e60fc7c678, 0x22ba581841d83ff, 0x11539696ce13d17, 0x558c3670aecb8e, 0x2b9b2d828d6d864});
constexpr StatTable58 SAVE_TABLE_58({0x1, 0xde56167ca60c8e, 0x166391328282dfb, 0x2c6ed660535e701, 0xf83470e499e0e, 0x3686f752cff05fd, 0x1ada23d28022d0b, 0x2a2ac069b41ffd4, 0x2d40f316b40053e, 0x3fb69372877a1f3, 0x13def6e665e9b30, 0x23eb4222bc98b90, 0x2991c5ab618f62c, 0x1c4b63ee1e37a86, 0xdcb10179c77602, 0x708837c2f0ee59, 0x151fe1b533a6d99, 0x44613653cb9d83, 0x33dc64f2b5abae6, 0x27d704726f1f9ba, 0x2fdef2de96892ad, 0x3fd032a21834dbe, 0x1ce2548191e42ab, 0x431410a40ab44b, 0x206f1338c9a75e1, 0x130035675a32179, 0xdf781bb8adbd09, 0x1aaaf085ea624e0, 0x1df0605123c28e9, 0x28d3b3631320c9c, 0x81951a3af55e95, 0x388c776adc88ca1, 0x3ebed178f719885, 0x3c4546b19b0fe51, 0x129564a29700d09, 0x3f642277d82c520, 0x3a46d24ff0ac3fd, 0x1e75e367d627740, 0x33b01746a0f4aad, 0x2af930ca2fa61f, 0x3fcea0ca3af7aac, 0x230722de56e3f4a, 0x3541e58cc5afefd, 0x32cf711ae15ba7e, 0x11d3670d510fc6f, 0x6ddd78eec82112, 0x216210641885856, 0x87535f37c08809, 0x1fa464b5f82155b, 0xdbd43e91708494, 0x1500e23396dd2c4, 0x16cf4098632235f, 0x37e9117da8979ba, 0x6f8bfa04f66a7, 0x18dff008060e626, 0x196286fd9dbad1c, 0x35078156610f8ab, 0x7a669ff8398fea});
constexpr StatTable58 SQR_TABLE_58({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x63, 0x18c, 0x630, 0x18c0, 0x6300, 0x18c00, 0x63000, 0x18c000, 0x630000, 0x18c0000, 0x6300000, 0x18c00000, 0x63000000, 0x18c000000, 0x630000000, 0x18c0000000, 0x6300000000, 0x18c00000000, 0x63000000000, 0x18c000000000, 0x630000000000, 0x18c0000000000, 0x6300000000000, 0x18c00000000000, 0x63000000000000, 0x18c000000000000, 0x230000000000063, 0xc000000000014a, 0x300000000000528});
constexpr StatTable58 SQR2_TABLE_58({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x18c, 0x18c0, 0x18c00, 0x18c000, 0x18c0000, 0x18c00000, 0x18c000000, 0x18c0000000, 0x18c00000000, 0x18c000000000, 0x18c0000000000, 0x18c00000000000, 0x18c000000000000, 0xc000000000014a, 0x1405, 0x14050, 0x140500, 0x1405000, 0x14050000, 0x140500000, 0x1405000000, 0x14050000000, 0x140500000000, 0x1405000000000, 0x14050000000000, 0x140500000000000, 0x50000000001ef, 0x50000000001ef0, 0x10000000001ef63, 0x1ef7bc, 0x1ef7bc0, 0x1ef7bc00, 0x1ef7bc000, 0x1ef7bc0000, 0x1ef7bc00000, 0x1ef7bc000000, 0x1ef7bc0000000, 0x1ef7bc00000000, 0x1ef7bc000000000, 0x2f7bc0000000129, 0x37bc0000000112d, 0x3bc000000011027, 0x3c0000000110022});
constexpr StatTable58 SQR4_TABLE_58({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x18c0, 0x18c00000, 0x18c000000000, 0xc000000000014a, 0x1405000, 0x14050000000, 0x140500000000000, 0x1ef7bc, 0x1ef7bc0000, 0x1ef7bc00000000, 0x3bc000000011027, 0x110001100, 0x1100011000000, 0x11000000194c, 0x1000000194c018c, 0x194c0194c000, 0x14c0194c000014a, 0x194c00001545500, 0x15455154550, 0x154551545500000, 0x1154550001f18df, 0x150001f18c63193, 0x1f18c6318c7c00, 0xc6318c7c01010a, 0x18c7c0101000014, 0x1010000000101, 0x1000000010118c0, 0x10118d8c000, 0x10118d8c0000000, 0xd8c0000018d98a, 0x18d9811050, 0x18d98110500000, 0x18110500001411a, 0x500001410eb94c, 0x1410eb94bbc00, 0x10eb94bbc001ef0, 0x14bbc001ee85ab2, 0x1ee85aac1111, 0x2e85aac11110129, 0x2ac11110111097a, 0x111011109445c8c, 0x11109445c9554c0, 0x1445c9554d95406, 0x9554d954189419, 0xd954189414901f, 0x1894149014051f, 0x149014051e478f, 0x14051e478ee2ec, 0x11e478ee2edef63, 0x38ee2edef7aded3, 0x2edef7adef6bdc8, 0x37adef6bdf07c2d, 0x2f6bdf07c0018f9, 0x1f07c0018c018d1});
constexpr StatTable58 SQR8_TABLE_58({0x1, 0x1100011000000, 0x10118d8c0000000, 0xd954189414901f, 0xc018def7a2f6f6, 0x1e19cc6d44444e, 0x2b2e8450d1ef706, 0x196294c624791e5, 0x2a9441aa2b74da8, 0x1c6810fa7a2fe66, 0x4e0f0eff6badbb, 0x26faf3a76e59127, 0x11aa58d6498919f, 0x3b3ce4e04f23b30, 0x2ed3f70684ae8d7, 0x8d64c737fc5014, 0x1516c589c4fd458, 0x5ba5cee14ea182, 0x368ad344d93d4ae, 0x15e2547ea25ba2a, 0xdecb4283969d9a, 0x2f2a95e5c791149, 0x3fc958586bc93d2, 0x3216bfeab663783, 0xced412d3f6e530, 0x85fb7bcb26d797, 0x19be97fdbcede01, 0x192a5409529ebf4, 0x98b4f8527795b1, 0x192e8188bbc9aac, 0x322f07e9abdf6d0, 0x2a4a5cd6239de91, 0x4c97dec82e63a, 0x37d6397e1d26aee, 0x1939dc6d77a98db, 0x2e23b8e5b0a982a, 0x2787751f5aa0dba, 0x3f81252033f3cc8, 0x1171b73d009f511, 0x8811f0328040bb, 0x3a659ae0b1d2417, 0xc8b454d91baa72, 0x197b01428520b86, 0x1872c8c17f7fe81, 0x143f7913f4c7f5, 0x3a71b7542e7ec68, 0x3e60d3d49155d34, 0x11d5f10402402c8, 0x2be8db11809a1df, 0x3667129f17b1d6a, 0x2749715db24cd0a, 0x185d6130cdfee96, 0x3abdc4d78640154, 0x39bd5ea2e22f89a, 0x3f9a113c1095209, 0xdb4c8bd4f72f4e, 0x32ae35f0ad0b4ee, 0x2f3770997f16cc});
constexpr StatTable58 SQR16_TABLE_58({0x1, 0x2fcd2228a7c16ab, 0x846ef4a277243e, 0x1d2bf9061084cfb, 0x23598fddcd64f64, 0xcc36f3a7174e2a, 0x365a50c11b89583, 0x611bed1afae48, 0x22a03fae7957244, 0x45e6546308ff3e, 0x3aebd6f3893b9b4, 0x2bf4a9d5586f8db, 0x32fd7d2d5d6f867, 0x14819feeb813a6f, 0x100ab4d9ad808fc, 0x11c0fd674209c71, 0x3701211690581e7, 0x5c33087013a39a, 0x188935ebbc048bb, 0x10787f930a52538, 0xd49849206986b2, 0x17d1298ba5b565, 0x5d465e006f3142, 0x569a5ce90e9bff, 0x2b591716524b4cb, 0x32f7d39faa352cf, 0x10f701fea440dc0, 0x11c5f10a9d3c9d5, 0x18457154a0bf6ea, 0x15516f140726673, 0x1cf780781353aa4, 0x2a7d7e0e83c4bbc, 0x276c009e3198958, 0x220b8531adc2c11, 0x937d7effc370ab, 0x27632fc1b91dac1, 0x3b36628aa135d3f, 0x37230eddd77f21a, 0x1c1b5e0f410eca9, 0x3200c9c78a9127f, 0x3a55e6fb19e6dc4, 0x150cb064eb271f7, 0x5c74759db43ae1, 0x37046240fba02a9, 0x1937118eb920f04, 0x2795ad9a663a0c9, 0x1d4297ad3d62e8a, 0x3b927d82816e04d, 0x15b56f89c278c21, 0x2b8e4ef675619d6, 0x2e0823575b9bb28, 0xdeb4b405ed7e9c, 0x83d627c04e5155, 0x391134c52f7ae67, 0x9e2c9657999608, 0x3b1e574e9a4eb3a, 0x2b58dd062cd0021, 0x38d1fb86f1978ab});
constexpr StatTable58 QRT_TABLE_58({0x21b9dfe73454bc2, 0x351ca3a13788360, 0x351ca3a13788362, 0x1ad5a042934094, 0x351ca3a13788366, 0x48f62c33f34cc, 0x1ad5a04293409c, 0x14b1f9a41eb8342, 0x351ca3a13788376, 0x3682437996f7786, 0x48f62c33f34ec, 0x21ad5a152920174, 0x1ad5a0429340dc, 0x3766ef998858a86, 0x14b1f9a41eb83c2, 0x151ca3a437843c2, 0x351ca3a13788276, 0x1e5ac7c1aff42c, 0x3682437996f7586, 0x3767ee558c7856a, 0x48f62c33f30ec, 0x39fb408a690330, 0x21ad5a152920974, 0x372f1d7dbf4255a, 0x1ad5a0429350dc, 0x39bb888af33330, 0x3766ef99885aa86, 0x27b58e0ba2df00, 0x14b1f9a41ebc3c2, 0x1540d06c191bcf2, 0x151ca3a4378c3c2, 0x39ee0d0a17f4c0, 0x351ca3a13798276, 0x2049f6c5379fdb4, 0x1e5ac7c1adf42c, 0x1ac5a182d64bf0, 0x3682437996b7586, 0x16cbe3c0a2c7c1e, 0x3767ee558cf856a, 0x372a1d35b20aa6a, 0x48f62c32f30ec, 0x26ab144a891cdc, 0x39fb408a490330, 0x205df3712ae76a8, 0x21ad5a152d20974, 0x34fb58f12e386b6, 0x372f1d7db74255a, 0x21b4a5f53871674, 0x1ad5a0439350dc, 0x1d602e40318fdc, 0x39bb8888f33330, 0x179bb8888f3332e, 0x3766ef99c85aa86, 0x2cec9eb2f5d0aa8, 0x27b58e03a2df00, 0x6caa1452491cdc, 0x14b1f9a51ebc3c2, 0});
typedef Field<uint64_t, 58, 99, StatTable58, &SQR_TABLE_58, &SQR2_TABLE_58, &SQR4_TABLE_58, &SQR8_TABLE_58, &SQR16_TABLE_58, &QRT_TABLE_58, StatTable58, &LOAD_TABLE_58, &SAVE_TABLE_58> Field58;
typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5> StatTableTRI58;
constexpr StatTableTRI58 SQR_TABLE_TRI58({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x80001, 0x200004, 0x800010, 0x2000040, 0x8000100, 0x20000400, 0x80001000, 0x200004000, 0x800010000, 0x2000040000, 0x8000100000, 0x20000400000, 0x80001000000, 0x200004000000, 0x800010000000, 0x2000040000000, 0x8000100000000, 0x20000400000000, 0x80001000000000, 0x200004000000000, 0x10000100002, 0x40000400008, 0x100001000020, 0x400004000080, 0x1000010000200, 0x4000040000800, 0x10000100002000, 0x40000400008000, 0x100001000020000});
constexpr StatTableTRI58 SQR2_TABLE_TRI58({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x200004, 0x2000040, 0x20000400, 0x200004000, 0x2000040000, 0x20000400000, 0x200004000000, 0x2000040000000, 0x20000400000000, 0x200004000000000, 0x40000400008, 0x400004000080, 0x4000040000800, 0x40000400008000, 0x4000000001, 0x40000000010, 0x400000000100, 0x4000000001000, 0x40000000010000, 0x180001, 0x1800010, 0x18000100, 0x180001000, 0x1800010000, 0x18000100000, 0x180001000000, 0x1800010000000, 0x18000100000000, 0x180001000000000, 0x10000300006, 0x100003000060, 0x1000030000600, 0x10000300006000, 0x100003000060000, 0x30000400004, 0x300004000040, 0x3000040000400, 0x30000400004000, 0x300004000040000, 0x4000020000c, 0x4000020000c0, 0x4000020000c00, 0x4000020000c000});
constexpr StatTableTRI58 SQR4_TABLE_TRI58({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x2000040, 0x20000400000, 0x200004000000000, 0x40000400008000, 0x4000000001000, 0x18000100, 0x180001000000, 0x10000300006, 0x100003000060000, 0x30000400004000, 0x4000020000c00, 0x200004000100, 0x40001400008, 0x14000000001, 0x140000000010000, 0x380005000, 0x3800050000000, 0x5000070000e0, 0x70000400014, 0x3000040001c0001, 0x40001a0001c000, 0x1a000140001000, 0x1400024000680, 0x240004000050, 0x40000180009, 0x1800010001, 0x18000100010000, 0x1000130000600, 0x1300004000040, 0x4000220004c, 0x22000440001, 0x220004400010000, 0x44000540008800, 0x5400000001100, 0x1b800150, 0x1b8001500000, 0x380015000300006, 0x15000370006e000, 0x37000440005400, 0x440003a000dc0, 0x3a0005400110, 0x20005400160000e, 0x140016400068001, 0x164000400015000, 0x4000398005900, 0x3980051000100, 0x5100063000e6, 0x100063000460014, 0x2300044001c4001, 0x44001820018c00, 0x18200104001100, 0x1040021400608, 0x214004000041, 0x140040000010008});
constexpr StatTableTRI58 SQR8_TABLE_TRI58({0x1, 0x40001400008, 0x1300004000040, 0x4000398005900, 0x21a004140001000, 0x15007370046e014, 0x14004001b810158, 0x18022100441001, 0x1005130063600e6, 0x4200004181059, 0x447a1a3f41ccd0, 0x383d151573100e6, 0x101600544019940, 0x270027c0059c000, 0x4818070100e1, 0x20545402560168e, 0x76071e40419414, 0x38001501bb00157, 0x18054101401149, 0x104343116260a0c, 0x17b9c06c9180809, 0x35b793b6107d791, 0x2e706624276b452, 0x3a543cf805118, 0x278004063619444, 0x22aae45555d4155, 0x105597ba5075e80, 0x364504676052ce, 0x35800790000401, 0x264044141418809, 0x3313274051a405d, 0x52c1b85195848, 0x57f03b8205e9e, 0x22c5044070044e0, 0x1547370047f115, 0x10402383a848d51, 0x16220024510a1, 0x4050579e30c9e7, 0x15e201b4605c018, 0x297e7fd6e672cc2, 0x286f01429f08ff7, 0x31c56646279854c, 0x36fd34ece6e98e6, 0x31e6939431f00b9, 0x311386d18673a0a, 0x2b6524f5cf195aa, 0x2dd63711ff50016, 0x1585649073391ae, 0x1004431143e1ab5, 0x13be61cf659d4d9, 0x98a87036371777, 0x66673706472d14, 0x273867fcbd99159, 0x27c4c58464098e9, 0x347304213c56db, 0x721f05c140cc15, 0x38144503ed007d9, 0x2e054541404549});
constexpr StatTableTRI58 SQR16_TABLE_TRI58({0x1, 0x3f4d56f7779e1f0, 0xe27368ee2eeacd, 0x135c653e9699a2f, 0x6b0f78c5b96a46, 0x25fa3044c7e0248, 0x2a078335aa8c788, 0x2b2fb5e8ec09222, 0x214fe2bd0b14a22, 0x10b6f34977f0f41, 0x3dc4a1564361cee, 0xa2ae7c793a9fcf, 0x7fc45e1a362304, 0x3ec19729047ce58, 0x1ef9b26acd27396, 0x225a72a9b2db21a, 0xaaa90ccba715d8, 0x2da6362d54cd62, 0x37dae1e3484d433, 0x1ced37972ce3594, 0x164d907773ab8b9, 0xbeaf6f3fc883a1, 0x1d8ac7ee4682652, 0x102fa1481f0470a, 0x3e17062fd515fba, 0x21652276c35fe65, 0x57862a59d3fa78, 0x36b077a8057cde3, 0x287ce593d9cee2f, 0x290b965ae5d215a, 0x2cc2a18d887125c, 0xc46c603fd8423b, 0xdcd705a0e16776, 0x3307e00c6585a3f, 0x2d82d4b6c18532d, 0x28efe74f174d530, 0x2ddbc57b95adaac, 0x31d41679a107eb4, 0x1f24f6f872cb97f, 0x32718f9b0a03ff6, 0x1f283546f68ca0c, 0x158f309c150c885, 0x1ccaf78ea1873ea, 0x30e3b732bf1875f, 0xcce47efdb9ecb1, 0xcf3954987b5601, 0xebdc136185c456, 0x388046727963e11, 0x22e117909faee51, 0x3215b67613a2a60, 0x172480d3a2f11de, 0x382552280610b4d, 0x3c53c5d9c350cce, 0x6edc0d3330295e, 0x3452a6b8c868f37, 0x398cd7e93017ecc, 0x2e1ec37c30a741e, 0xb00d11006ffa14});
constexpr StatTableTRI58 QRT_TABLE_TRI58({0x2450096792a5c5c, 0x610014271011c, 0x610014271011e, 0x1f0cb811314ea88, 0x610014271011a, 0x8000000420, 0x1f0cb811314ea80, 0x265407ad8a20bcc, 0x610014271010a, 0x3d18be98392ebd0, 0x8000000400, 0xc29b930e407056, 0x1f0cb811314eac0, 0x1fcef001154dee8, 0x265407ad8a20b4c, 0xc69b924c61f94a, 0x610014271000a, 0x211006895845190, 0x3d18be98392e9d0, 0x54007accac09cc, 0x8000000000, 0xc08b934e107854, 0xc29b930e407856, 0x275407adc220bcc, 0x1f0cb811314fac0, 0x1f6db815164ea8a, 0x1fcef001154fee8, 0x1b2db801945e396, 0x265407ad8a24b4c, 0x21100ec95865590, 0xc69b924c61794a, 0x273507b1e530ad6, 0x610014270000a, 0x1b4cb835b34e29c, 0x211006895865190, 0x3839bf20d47e016, 0x3d18be98396e9d0, 0x3858bd34f36e01c, 0x54007acca409cc, 0, 0x8000100000, 0xc29a130e507856, 0xc08b934e307854, 0x13253921d448296, 0xc29b930e007856, 0x13c60935f6486bc, 0x275407adca20bcc, 0x3571be8c5e6c9da, 0x1f0cb811214fac0, 0x410014261011c, 0x1f6db815364ea8a, 0x13a50921d1486b6, 0x1fcef001554fee8, 0x64001249245a5c, 0x1b2db801145e396, 0x8610014670200a, 0x265407ac8a24b4c, 0x1a5cbfbdeb0f30c});
typedef FieldTri<uint64_t, 58, 19, StatTableTRI58, &SQR_TABLE_TRI58, &SQR2_TABLE_TRI58, &SQR4_TABLE_TRI58, &SQR8_TABLE_TRI58, &SQR16_TABLE_TRI58, &QRT_TABLE_TRI58, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri58;
#endif
 
#ifdef ENABLE_FIELD_INT_59
// 59 bit field
typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5> StatTable59;
constexpr StatTable59 SQR_TABLE_59({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x12a, 0x4a8, 0x12a0, 0x4a80, 0x12a00, 0x4a800, 0x12a000, 0x4a8000, 0x12a0000, 0x4a80000, 0x12a00000, 0x4a800000, 0x12a000000, 0x4a8000000, 0x12a0000000, 0x4a80000000, 0x12a00000000, 0x4a800000000, 0x12a000000000, 0x4a8000000000, 0x12a0000000000, 0x4a80000000000, 0x12a00000000000, 0x4a800000000000, 0x12a000000000000, 0x4a8000000000000, 0x2a000000000012a, 0x28000000000043d, 0x200000000001061});
constexpr StatTable59 SQR2_TABLE_59({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x12a, 0x12a0, 0x12a00, 0x12a000, 0x12a0000, 0x12a00000, 0x12a000000, 0x12a0000000, 0x12a00000000, 0x12a000000000, 0x12a0000000000, 0x12a00000000000, 0x12a000000000000, 0x2a000000000012a, 0x200000000001061, 0x10444, 0x104440, 0x1044400, 0x10444000, 0x104440000, 0x1044400000, 0x10444000000, 0x104440000000, 0x1044400000000, 0x10444000000000, 0x104440000000000, 0x4440000000012a, 0x4440000000012a0, 0x440000000012ea8, 0x40000000012ee28, 0x12ee628, 0x12ee6280, 0x12ee62800, 0x12ee628000, 0x12ee6280000, 0x12ee62800000, 0x12ee628000000, 0x12ee6280000000, 0x12ee62800000000, 0x2ee62800000012a, 0x6e6280000001061, 0x662800000010079, 0x62800000010016c, 0x28000000100103c});
constexpr StatTable59 SQR4_TABLE_59({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x12a0, 0x12a00000, 0x12a000000000, 0x2a000000000012a, 0x1044400, 0x10444000000, 0x104440000000000, 0x40000000012ee28, 0x12ee628000, 0x12ee6280000000, 0x662800000010079, 0x100101010, 0x1001010100000, 0x101010000012a0, 0x10000012a12b2a, 0x12a12b2b2a00, 0x2a12b2b2a00012a, 0x32b2a0001045461, 0x200010454541421, 0x104545414044000, 0x45414044012ef02, 0x4044012ef4d49aa, 0x12ef4d49e0ce28, 0x74d49e0ce290079, 0x1e0ce290000011d, 0x62900000100016d, 0x100010013a0, 0x100010013a00000, 0x10013a00012a000, 0x3a00012a012a12a, 0x12a012a116e400, 0x12a116e4010444, 0x116e40104450444, 0x40104450457ea6c, 0x4450457ea2692a0, 0x457ea2692ee7020, 0x22692ee706f7059, 0x2ee706f707e73ba, 0x6f707e73901116, 0x7e7390111013b6, 0x390111013b12b16, 0x11013b12b299b2a, 0x3b12b299b398b2a, 0x3299b398b17de61, 0x3398b17de543b4f, 0x317de543b7b1065, 0x6543b7b1053bb27, 0x37b1053bb4d0b6b, 0x53bb4d0b5b95ca, 0x34d0b5b95cfbf5b, 0x35b95cfbf6885b5, 0x5cfbf688587c89a, 0x7688587c8cf3adb, 0x587c8cf3aa00050, 0xcf3aa00001000d});
constexpr StatTable59 SQR8_TABLE_59({0x1, 0x1001010100000, 0x10013a00012a000, 0x3398b17de543b4f, 0x2a00116b8c2812a, 0x7cbf06ffa4d5cd6, 0x1288f1cf576c2e0, 0x3047cfc394d3391, 0x322d00452b2c451, 0x226dcb1999949d1, 0x2e2e5ab30351bc0, 0x10b2afcfca2edc6, 0x7ff39b98a3372a8, 0x2d7b439441ae332, 0x5603b26a2dae616, 0x3a13899c470338a, 0x16e8a14f0113f3c, 0x754f4aa46d3bb2, 0x38aa45436b16334, 0x634468d6b3f47b5, 0x248ca58bd03241d, 0x255d1fbddf51ae7, 0x7f4b46a330ef6bc, 0x3b3159b37b1a654, 0x7bbff798b50cf3e, 0x568afef7a72512a, 0x701d7955e599ab3, 0x3e7aed5ec2e2c82, 0x5c4d118847ff477, 0x21264d599c12421, 0x4d287fc89bb5a71, 0x6d1f30202fff956, 0x6c54d2de7c68bf8, 0x350c930ed65aed3, 0x5630ddede4ba32c, 0x7c18282af602d36, 0x198a362bf3c8a07, 0x40dde880541e01c, 0x49c0e7e7438c0c7, 0x3ade2abe6845a50, 0x6ffad83e7ac09c4, 0x52185a0d23e667a, 0x2e8c821b63a858a, 0x770e59a57577b23, 0x2fe0ea55e7032a6, 0x23cf0c9a1565a09, 0x1c53d32d80a4427, 0x23164f78db9fa8b, 0x691c4ffab038e2a, 0x33fc91a8a831d85, 0x48039e34eec4e05, 0x2581dbb898c10b5, 0x374067097dfc9f9, 0x241611fdbd3f8e7, 0x1b9f2934941d831, 0x1940c046b9b4a62, 0x5333ac5e7a608f6, 0xe9fa1f11b06830, 0x3d3bbe0ab819c34});
constexpr StatTable59 SQR16_TABLE_59({0x1, 0x857cdd2d43d447, 0xf829d2f68520b5, 0x19fe843a13f84fd, 0xcac85f3b30aa13, 0x5c7d9cd6997e169, 0x21e7ab9693a08f3, 0xe5cda6478df23f, 0xc3e206ed797b25, 0x755908ad7cca1c1, 0x16236a14b269480, 0x5fedfd73877a5e3, 0x6d66cb2c634cab2, 0x1b60fade310cb41, 0x5dcfd76c147e4ff, 0x2e686c220dcdc6a, 0x1d348a9dfc46113, 0x4e97ec4ce1b1081, 0x20ccc4ae0ada275, 0x5ec224932d09f73, 0x385cecd0572d2a0, 0x520f6a5162503d4, 0x3ff8003ba0976e, 0x5a314f7726ffcb7, 0x505c4f556b43e5a, 0x259ddd3f8c27783, 0x25441858e820409, 0x2714ab44ef6c58b, 0x53437cae5c3011c, 0x122c6454cb53ac0, 0x349b57934525af9, 0x394e01a9ab9a786, 0x665a91eb8e73f0d, 0x4c4e86cc5c98631, 0x7983a92ec037fe2, 0x67919ad3e0a3d69, 0x685c3d6c72af62e, 0x4eafca0e4b49fd7, 0x69534a8afbbeee, 0x720f8307d28c8cb, 0x49828239c03d1b7, 0x4c7e6edd9907a53, 0x1fe81ca4466f8fb, 0x19a865c194c7a23, 0x518bbfec9151454, 0x5b7bfbc756a7e4d, 0x146cc66da8b0754, 0x58e7cba08f0b29b, 0x1b578332a8f1985, 0x72d1c4f9eacac25, 0x6fc4f312025b99a, 0x199f6741974302b, 0x3edcb2e16193874, 0x38b45862414392c, 0x3a6669ab6604f52, 0x227da450a65496e, 0x4e85a5c57a7f719, 0x36b5dbf304b88be, 0x2ba8a1264ef68a0});
constexpr StatTable59 QRT_TABLE_59({0x38d905ab028567a, 0x789fa6ed3b44d72, 0x789fa6ed3b44d70, 0x74ec857e93d828c, 0x789fa6ed3b44d74, 0x116b3c1203c96, 0x74ec857e93d8284, 0xc25ebc3871e280, 0x789fa6ed3b44d64, 0x47a37c3d910b6, 0x116b3c1203cb6, 0xc7322d7a8f48de, 0x74ec857e93d82c4, 0xb509a0ea52e496, 0xc25ebc3871e200, 0x74fdee4681d3e0c, 0x789fa6ed3b44c64, 0x7ffbbd080b2f09a, 0x47a37c3d912b6, 0xd5c937bae506c8, 0x116b3c12038b6, 0xb173c76987625e, 0xc7322d7a8f40de, 0x7591ff36b3a682c, 0x74ec857e93d92c4, 0x72b253bfbfc90c4, 0xb509a0ea52c496, 0x79f2e7b10e6d452, 0xc25ebc3871a200, 0x78c86e951086aac, 0x74fdee4681dbe0c, 0x78c96eb514c602c, 0x789fa6ed3b54c64, 0xc34818b95658e8, 0x7ffbbd080b0f09a, 0x7399f563b1980f2, 0x47a37c3dd12b6, 0xa29e0e28c58880, 0xd5c937baed06c8, 0x788ac23520ac82c, 0x116b3c13038b6, 0xa2c857e83d92b6, 0xb173c769a7625e, 0x608da990122e48, 0xc7322d7acf40de, 0xa3a89269eebefe, 0x7591ff36bba682c, 0xa25ebc2871a200, 0x74ec857e83d92c4, 0x11f62e419f1cfe, 0x72b253bf9fc90c4, 0x7425ebc2871a272, 0xb509a0ee52c496, 0x4ed8555979c8de, 0x79f2e7b18e6d452, 0x6c3580d5915d4d2, 0xc25ebc2871a200, 0, 0x78c86e971086aac});
typedef Field<uint64_t, 59, 149, StatTable59, &SQR_TABLE_59, &SQR2_TABLE_59, &SQR4_TABLE_59, &SQR8_TABLE_59, &SQR16_TABLE_59, &QRT_TABLE_59, IdTrans, &ID_TRANS, &ID_TRANS> Field59;
#endif
 
#ifdef ENABLE_FIELD_INT_60
// 60 bit field
typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6> StatTableTRI60;
constexpr StatTableTRI60 SQR_TABLE_TRI60({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x3, 0xc, 0x30, 0xc0, 0x300, 0xc00, 0x3000, 0xc000, 0x30000, 0xc0000, 0x300000, 0xc00000, 0x3000000, 0xc000000, 0x30000000, 0xc0000000, 0x300000000, 0xc00000000, 0x3000000000, 0xc000000000, 0x30000000000, 0xc0000000000, 0x300000000000, 0xc00000000000, 0x3000000000000, 0xc000000000000, 0x30000000000000, 0xc0000000000000, 0x300000000000000, 0xc00000000000000});
constexpr StatTableTRI60 SQR2_TABLE_TRI60({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x3, 0x30, 0x300, 0x3000, 0x30000, 0x300000, 0x3000000, 0x30000000, 0x300000000, 0x3000000000, 0x30000000000, 0x300000000000, 0x3000000000000, 0x30000000000000, 0x300000000000000, 0x5, 0x50, 0x500, 0x5000, 0x50000, 0x500000, 0x5000000, 0x50000000, 0x500000000, 0x5000000000, 0x50000000000, 0x500000000000, 0x5000000000000, 0x50000000000000, 0x500000000000000, 0xf, 0xf0, 0xf00, 0xf000, 0xf0000, 0xf00000, 0xf000000, 0xf0000000, 0xf00000000, 0xf000000000, 0xf0000000000, 0xf00000000000, 0xf000000000000, 0xf0000000000000, 0xf00000000000000});
constexpr StatTableTRI60 SQR4_TABLE_TRI60({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x30, 0x300000, 0x3000000000, 0x30000000000000, 0x500, 0x5000000, 0x50000000000, 0x500000000000000, 0xf000, 0xf0000000, 0xf00000000000, 0x11, 0x110000, 0x1100000000, 0x11000000000000, 0x330, 0x3300000, 0x33000000000, 0x330000000000000, 0x5500, 0x55000000, 0x550000000000, 0x50000000000000f, 0xff000, 0xff0000000, 0xff00000000000, 0x101, 0x1010000, 0x10100000000, 0x101000000000000, 0x3030, 0x30300000, 0x303000000000, 0x30000000000005, 0x50500, 0x505000000, 0x5050000000000, 0x5000000000000f0, 0xf0f000, 0xf0f0000000, 0xf0f00000000000, 0x1111, 0x11110000, 0x111100000000, 0x111000000000003, 0x33330, 0x333300000, 0x3333000000000, 0x330000000000055, 0x555500, 0x5555000000, 0x55550000000000, 0x500000000000fff, 0xffff000, 0xffff0000000, 0xffff00000000000});
constexpr StatTableTRI60 SQR8_TABLE_TRI60({0x1, 0x110000, 0x10100000000, 0x111000000000003, 0x300030, 0x33003300000, 0x30303000000005, 0x330000000555555, 0x50000000500, 0x50000005500000f, 0x5050000f0f000, 0x5000ffff0000fff, 0xf000f000f011, 0xff00ff1010101, 0xf0e11111111111, 0x31, 0x3210000, 0x313100000000, 0x221000000000056, 0x5300530, 0x563056300000, 0x5353530000000f5, 0x63000000faaaaaa, 0xf5000000f500, 0x500000fa500010e, 0xf5f50011e1f000, 0x5010ffef0010ffe, 0x11f011f011f321, 0x10ef10ec1313131, 0x1e2d22222222222, 0x501, 0x55110000, 0x5040100000000, 0x411000000000ffc, 0xf030f030, 0xff33ff3300000, 0xc0c03000001114, 0x330000100555554, 0x11050000110500, 0x50001015500303f, 0x114050333c0f003, 0x5300fcff0300fcf, 0x330f330f330a511, 0x3fc03af4040404, 0x395b44444444444, 0xf531, 0xfa6210000, 0xf5c43100000000, 0x721000000010fa8, 0x11f521f530, 0x10ea73ea6300000, 0x4d4c530000322d7, 0x63000310faaaa9b, 0x321f5000321f500, 0x500313ea505343e, 0x2d4f55677d1f056, 0x310acef5310ace, 0x621a621a62e562e, 0x43bc4cb34c4c4c4, 0x878788888888888});
constexpr StatTableTRI60 SQR16_TABLE_TRI60({0x1, 0x563055110000, 0x111010233c0f003, 0x1200afffa8baffc, 0x5356030553000c5, 0x7145cf221744a77, 0x5748045489aaaaf, 0x7d52fcee4febdb3, 0x221f633c000a012, 0x41431fb55d4f4c8, 0x7f126132f4be5d5, 0x323da1f43c3a7e0, 0x373b24844474766, 0x6cc378a25584eb, 0x7ef66648aae4aca, 0x33003000031, 0xc0c03fb7c0f1fb, 0x174757777d10536, 0x2116210a52facb3, 0x5316fc100c1fb35, 0x7aae07597d161e1, 0x6752c4decfb6b7f, 0xf590fa78d56bf3, 0x1be67573275f157, 0xe3e0e9e0d61817, 0x25ac0012251ff6c, 0x407de1e40e3a849, 0x7a7264848fdf67e, 0x3bb8ba7d3879348, 0x498941f57060c6c, 0x5000000f0f501, 0x10fa8cfc1213ac0, 0x51a500f5501aab9, 0x73ef9049dcace64, 0x526a202f322f6e7, 0x2789a852500ca93, 0x4d1346684907509, 0x7d02bcfe4febdb2, 0x330a0329aba0521, 0x50a33c66415f5eb, 0x2e99dced402a73d, 0xf78f2f1a2dbcfe, 0x793a675db461a6a, 0x73848cd4c2f25d2, 0x54fa22d244aa9c6, 0xfae22e13e01501, 0x538ead296f222e5, 0x4da65592d2a750a, 0x40f91ebc14fcd2a, 0x5e73ff2f3c21c03, 0x4c72dce55551460, 0x3ffa59f8e5aef0a, 0x30057fa7b802f82, 0x36efe87d58aa6e4, 0x3bc96a196d71957, 0x5a82cfde2ad602f, 0x1f9bce94df9d3bf, 0x43c91d9b6bcabba, 0x2193c1833502ba3, 0xd28f516c1311d3d});
constexpr StatTableTRI60 QRT_TABLE_TRI60({0x6983c00fe00104a, 0x804570322e054e6, 0x804570322e054e4, 0x15673387e0a4e4, 0x804570322e054e0, 0x100010110, 0x15673387e0a4ec, 0x920d01f34442a70, 0x804570322e054f0, 0x7a8dc0f2e4058f0, 0x100010130, 0x120c01f140462f0, 0x15673387e0a4ac, 0x7bdbb2ca9a4fe5c, 0x920d01f34442af0, 0xe9c6b039ce0c4ac, 0x804570322e055f0, 0xfac8b080ca20c00, 0x7a8dc0f2e405af0, 0x7a8dc4b2e4a59f0, 0x100010530, 0x10000100000, 0x120c01f14046af0, 0x131a02d91c5db6c, 0x15673387e0b4ac, 0x15623387d0b4ac, 0x7bdbb2ca9a4de5c, 0x7ffbbbca0a8ee5c, 0x920d01f34446af0, 0x800000020000000, 0xe9c6b039ce044ac, 0x81130302500f000, 0x804570322e155f0, 0x935b72eb3a48e9c, 0xfac8b080ca00c00, 0x120c016140563c0, 0x7a8dc0f2e445af0, 0x7bcbb3ca8a4ee5c, 0x7a8dc4b2e4259f0, 0xc4000a0300, 0x100110530, 0x11623285c1b19c, 0x10000300000, 0x420890090c3000, 0x120c01f14446af0, 0x68d7b33b9e0b4ac, 0x131a02d9145db6c, 0xe8ccb1e18a56fc0, 0x15673386e0b4ac, 0x7aadc8f2e485af0, 0x15623385d0b4ac, 0x4a0990093c3000, 0x7bdbb2cada4de5c, 0xf9d6b3389e0b4ac, 0x7ffbbbca8a8ee5c, 0xdf6ba38cec84ac, 0x920d01f24446af0, 0x520d01f24446af0, 0x800000000000000, 0});
typedef FieldTri<uint64_t, 60, 1, StatTableTRI60, &SQR_TABLE_TRI60, &SQR2_TABLE_TRI60, &SQR4_TABLE_TRI60, &SQR8_TABLE_TRI60, &SQR16_TABLE_TRI60, &QRT_TABLE_TRI60, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri60;
#endif
 
#ifdef ENABLE_FIELD_INT_61
// 61 bit field
typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5, 5> StatTable61;
constexpr StatTable61 SQR_TABLE_61({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x4e, 0x138, 0x4e0, 0x1380, 0x4e00, 0x13800, 0x4e000, 0x138000, 0x4e0000, 0x1380000, 0x4e00000, 0x13800000, 0x4e000000, 0x138000000, 0x4e0000000, 0x1380000000, 0x4e00000000, 0x13800000000, 0x4e000000000, 0x138000000000, 0x4e0000000000, 0x1380000000000, 0x4e00000000000, 0x13800000000000, 0x4e000000000000, 0x138000000000000, 0x4e0000000000000, 0x1380000000000000, 0xe0000000000004e, 0x180000000000011f});
constexpr StatTable61 SQR2_TABLE_61({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x1000000000000000, 0x138, 0x1380, 0x13800, 0x138000, 0x1380000, 0x13800000, 0x138000000, 0x1380000000, 0x13800000000, 0x138000000000, 0x1380000000000, 0x13800000000000, 0x138000000000000, 0x1380000000000000, 0x180000000000011f, 0x1054, 0x10540, 0x105400, 0x1054000, 0x10540000, 0x105400000, 0x1054000000, 0x10540000000, 0x105400000000, 0x1054000000000, 0x10540000000000, 0x105400000000000, 0x1054000000000000, 0x540000000000138, 0x14000000000013ce, 0x13d96, 0x13d960, 0x13d9600, 0x13d96000, 0x13d960000, 0x13d9600000, 0x13d96000000, 0x13d960000000, 0x13d9600000000, 0x13d96000000000, 0x13d960000000000, 0x13d9600000000000, 0x1d9600000000011f, 0x196000000000101a, 0x1600000000010004});
constexpr StatTable61 SQR4_TABLE_61({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x138, 0x1380000, 0x13800000000, 0x138000000000000, 0x10540, 0x105400000, 0x1054000000000, 0x540000000000138, 0x13d9600, 0x13d96000000, 0x13d960000000000, 0x1600000000010004, 0x100111000, 0x1001110000000, 0x11100000000138, 0x10000000013812b8, 0x13812ab8000, 0x13812ab80000000, 0x12ab800000010540, 0x105514114, 0x1055141140000, 0x551411400000138, 0x1140000013d84f6, 0x13d84f72f60, 0x13d84f72f600000, 0x4f72f6000010004, 0xf6000010000010f, 0x1000001010100, 0x10101000138, 0x101010001380000, 0x100013800013938, 0x138000139393800, 0x1393938010540, 0x193938010540011f, 0x180105400104445f, 0x540010444454138, 0x1044445413d9600, 0x445413d96013cae, 0x13d96013caaab96, 0x16013caaab970004, 0x1caaab970011111f, 0xb9700111101100b, 0x11110110010028, 0x11011001002812b8, 0x1001002812aab938, 0x2812aab92b8138, 0x12aab92b81382ec0, 0x192b81382ed1400b, 0x1382ed140105514, 0xed1401055150567, 0x105515056890f6, 0x1515056890f613ce, 0x56890f613d84e58, 0x10f613d84e5db85c, 0x13d84e5db84f6010, 0xe5db84f6000000e, 0x184f600000010123});
constexpr StatTable61 SQR8_TABLE_61({0x1, 0x100111000, 0x10101000138, 0x1001002812aab938, 0x1000001390478, 0x113916c2d28792b8, 0x1904457c4545aa5f, 0x13aa7f0f280c5e20, 0x1047900101540, 0x13be84504128808e, 0x839d72c6e39c0f1, 0x16a18bbeafc6bac6, 0x7290382d6ea1584, 0x1d7d80a66b181691, 0x19d2aaa6110c5d47, 0x1b613d85f602c96f, 0x3812870738, 0x113dbce704cbbd40, 0xd92856e5392f94b, 0x84f76c3d7c304a3, 0x1a519225fe5ce8cf, 0x1704aca0c7190b8e, 0xb7fb1620ed7d025, 0x12831368539314f6, 0x748fb7c048744be, 0x78cc8029440fcba, 0x10eb05b6015eb730, 0xfd3c38351ebc6bd, 0x1665bcfabbfbe624, 0x136549cb4738e1ec, 0x6db6139d4b707f2, 0x1000057853aeac78, 0x104401500109340, 0x554c25992c8f3d8, 0x192dd4b6c0886747, 0x219c35ac73165fc, 0xdf27daa47ee296b, 0x73ab415a10863d2, 0x1f06884b4f2dc1dd, 0xb56c8c3efd7847f, 0x7a6a82768a4a3f2, 0x8773791c3b9f69f, 0x1e4d128bbd8fa105, 0x16977fb4d8984d86, 0xb9a5106882f60bf, 0xc5102ee91822469, 0xdab44dc3cdf7a0b, 0x18d48e2841f63e4, 0x165b8e4d03de40d4, 0x11a7aec6ef42385a, 0x17064ddd9b5041ea, 0xf89b61f74d1f401, 0x18583a8c57e6cb7f, 0x607279105fda3be, 0x905e9c0d58240c7, 0x1ed3c0319519fa7d, 0xa3227b6d1cc17a1, 0xf6cb7bb2aa84563, 0xdda77eb9b649e97, 0x15480a00ec829caf, 0x62cb6da6128c272});
constexpr StatTable61 SQR16_TABLE_61({0x1, 0x1c7cd18a3a216933, 0xd201ddad374eb4, 0xee4694049c47289, 0x40db9f51130a1e6, 0x134cab3c67ec43f4, 0x97823873a2fc00f, 0xc08b772e8161a43, 0x128159f3d3611eac, 0x1f002f36181d6c4, 0x9de899abbd8d18f, 0x1a6ecb093fbb558b, 0xa6a1251b5961643, 0x1b285c169fb6616d, 0x9c04f5fcf0a4ce5, 0xd050c0ab89025ad, 0xdab152bf63418d9, 0xad3e33af7686059, 0x1561180155ac0dc8, 0x1d9e862521ab7d29, 0xa21b06e1e7632b5, 0x29b84e35cfc95ac, 0x17a27c78dac90e2c, 0x1312fa5f7b1e4ea2, 0xfe66bf53de6a93d, 0x182041e17dde85e9, 0x1289eb06f1803a2e, 0x129449a509af818c, 0x1f308057c81ab449, 0x419981420870054, 0x19f853b859910eb1, 0x9b422c0e9d60871, 0x9e6aec92bfcfa99, 0x15a788f1748b8f44, 0x1fa9a9c171dd83a1, 0x14096af6c0840cc6, 0x1bbe256976515067, 0x14f853fd9e5c0002, 0xf6256b0235f7a8, 0x37e727448043cf6, 0xbb0f467dd137c3f, 0x2538d574ceec19e, 0x15ff26c652c82188, 0x1c22b1e2a9ed31f3, 0x1f56b4b705c21301, 0x1502df3e9aa51832, 0x89c3dec02a6a543, 0x15eac5a464a4f736, 0x1d5023636fc14fa7, 0x499c5d458f9699e, 0x355b147c1703428, 0x1864a11df3efee51, 0x9af0f612e9c1265, 0x9c613962a1c08d9, 0x1cee6fc68f73b3f7, 0x185720007e663719, 0x101dd90a4502bf06, 0x1569af254da87eb0, 0x1781376276013a90, 0x10d2bf3d5e191483, 0x6215713bdc7d250});
constexpr StatTable61 QRT_TABLE_61({0x171d34fcdac955d0, 0x12cfc8c049e1c96, 0x12cfc8c049e1c94, 0x71d34fcdac955c2, 0x12cfc8c049e1c90, 0x631c871de564852, 0x71d34fcdac955ca, 0x129fa6407f27300, 0x12cfc8c049e1c80, 0x7094f6fdd0a3b12, 0x631c871de564872, 0xdb28cee59c8256a, 0x71d34fcdac9558a, 0xc8a0be15a915472, 0x129fa6407f27380, 0x12dfcb4058e0b80, 0x12cfc8c049e1d80, 0x117d7f04ad0118, 0x7094f6fdd0a3912, 0x621b576dbe35b6a, 0x631c871de564c72, 0x13c808a013a1ee0, 0xdb28cee59c82d6a, 0x113d79842a0272, 0x71d34fcdac9458a, 0x719776b580b6a98, 0xc8a0be15a917472, 0x6633498d6db760a, 0x129fa6407f23380, 0xbd4ae9e8c3e7560, 0x12dfcb4058e8b80, 0x8000000a, 0x12cfc8c049f1d80, 0x634ce9add3b26ea, 0x117d7f04af0118, 0xda3f19c5d66258a, 0x7094f6fdd0e3912, 0xb87427e85e71560, 0x621b576dbeb5b6a, 0xc8b0b085b8c4e0a, 0x631c871de464c72, 0x1538fc8649458a, 0x13c808a011a1ee0, 0xcddbca6d1cfe360, 0xdb28cee59882d6a, 0xae80f550d1ffff2, 0x113d7984aa0272, 0xda7770f5f195912, 0x71d34fcdbc9458a, 0x137c8a049a1ee0, 0x719776b5a0b6a98, 0xded39a9d236ba78, 0xc8a0be15e917472, 0x6732488ca7ce0a, 0x6633498dedb760a, 0xc0406d0527cb80a, 0x129fa6417f23380, 0x3d4ae9eac3e756a, 0xbd4ae9eac3e7560, 0, 0x12dfcb4458e8b80});
typedef Field<uint64_t, 61, 39, StatTable61, &SQR_TABLE_61, &SQR2_TABLE_61, &SQR4_TABLE_61, &SQR8_TABLE_61, &SQR16_TABLE_61, &QRT_TABLE_61, IdTrans, &ID_TRANS, &ID_TRANS> Field61;
#endif
 
#ifdef ENABLE_FIELD_INT_62
// 62 bit field
typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5> StatTable62;
constexpr StatTable62 SQR_TABLE_62({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x20000001, 0x80000004, 0x200000010, 0x800000040, 0x2000000100, 0x8000000400, 0x20000001000, 0x80000004000, 0x200000010000, 0x800000040000, 0x2000000100000, 0x8000000400000, 0x20000001000000, 0x80000004000000, 0x200000010000000, 0x800000040000000, 0x2000000100000000, 0x440000002, 0x1100000008, 0x4400000020, 0x11000000080, 0x44000000200, 0x110000000800, 0x440000002000, 0x1100000008000, 0x4400000020000, 0x11000000080000, 0x44000000200000, 0x110000000800000, 0x440000002000000, 0x1100000008000000});
constexpr StatTable62 SQR2_TABLE_62({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x1000000000000000, 0x80000004, 0x800000040, 0x8000000400, 0x80000004000, 0x800000040000, 0x8000000400000, 0x80000004000000, 0x800000040000000, 0x440000002, 0x4400000020, 0x44000000200, 0x440000002000, 0x4400000020000, 0x44000000200000, 0x440000002000000, 0x400000000000001, 0x20000011, 0x200000110, 0x2000001100, 0x20000011000, 0x200000110000, 0x2000001100000, 0x20000011000000, 0x200000110000000, 0x2000001100000000, 0x11100000008, 0x111000000080, 0x1110000000800, 0x11100000008000, 0x111000000080000, 0x1110000000800000, 0x1100000088000004, 0x1000000800000044, 0x8080000444, 0x80800004440, 0x808000044400, 0x8080000444000, 0x80800004440000, 0x808000044400000, 0x80000404000002, 0x800004040000020, 0x40440000202, 0x404400002020, 0x4044000020200, 0x40440000202000, 0x404400002020000});
constexpr StatTable62 SQR4_TABLE_62({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x80000004, 0x800000040000, 0x440000002, 0x4400000020000, 0x20000011, 0x200000110000, 0x2000001100000000, 0x11100000008000, 0x1000000800000044, 0x8080000444000, 0x800004040000020, 0x40440000202000, 0x400000000000101, 0x20001011000, 0x200010110000000, 0x101110000000800, 0x1100008088000404, 0x80808004044400, 0x80044404000202, 0x444044002020200, 0x440002002001110, 0x20002011101100, 0x20110011000080, 0x1100111000800080, 0x1110080000804400, 0x800080844004440, 0x808400044402000, 0x404400002021, 0x44000000210001, 0x300010110, 0x3000101100000, 0x101118000000c, 0x1118000800c0004, 0x8084c0040446, 0x84c00444460002, 0x4440460020213, 0x404600022130011, 0x2000201120111011, 0x2011301110118000, 0x3011001900008044, 0x1918080044c044, 0x1808004840440064, 0x484c4000646020, 0xc40004040200121, 0x40460001213100, 0x600010111000101, 0x101120001011800, 0x1200018198000404, 0x181910004044800, 0x110004c488000606, 0x4c4808006064400, 0x80046404001312, 0x464044013120200, 0x440112002001190, 0x1120002011901100, 0x20190011004480, 0x1900111044800080, 0x1110480000806400});
constexpr StatTable62 SQR8_TABLE_62({0x1, 0x400000000000101, 0x44000000210001, 0x40460001213100, 0x404500002021, 0xe40014150200121, 0x80b400145512000, 0x1495c4000646820, 0x8000808c4004445, 0xd0800c8c8440561, 0x1045c80080ad6405, 0x1988b0805419944, 0x190110048480008e, 0x2891049dcc008662, 0x8ac190411026482, 0x241574511233a020, 0x1120002031901110, 0x3040203922110044, 0x1110792020b25580, 0x282a4830647355, 0x2c60001037102032, 0x26e4507065221080, 0x2036c57040579390, 0x3450409552c0cc02, 0x5c4000c66824017, 0x5508ce8e2845301, 0x4934eca8d59343, 0x1c28a918f7c9c0d1, 0xb080581194c8e4, 0x1018495dc440e46a, 0x1ac80985d8604226, 0xc7044545722023, 0x145120003031900, 0x4440003a0200005, 0x134447a19a002514, 0x510e645a31f1135, 0xae4834446175200, 0x264f451435730311, 0x7220c2004155891, 0x2153045891358c65, 0x154154800ca02904, 0x54dc0c88ce92565, 0xdc54bc04d28bc20, 0x8c54b0401283d8b, 0x29088e8109411f28, 0x12d0dc41982620a, 0xc0030c89a712640, 0x1dc8192422907592, 0x145554681022a075, 0x470792013225580, 0x346c6a7130667300, 0x39147d7004b077b2, 0x6c83e2d354461c6, 0xcf6d0046247a030, 0x3221c0f063a45c80, 0x303645fc20539787, 0x21004cf150409b10, 0x1dd380444d78042, 0x1c709df8b7145381, 0x185834a4e8d51327, 0x1420e118b389a4d1, 0xf0c41811b4e8c4});
constexpr StatTable62 SQR16_TABLE_62({0x1, 0x147095f0731417c5, 0x3189fad107702e11, 0x3d3937fd86a460ab, 0x3ff26c959b47c587, 0x1e2ecbec4bf22bd6, 0x168ebaeceaf71b82, 0x216d6c4471f75c10, 0x1f6d31ccabfaee58, 0x1652ef2066ec0c61, 0x3d62ef6847f808fc, 0x26a33c99ec1b43d4, 0x32f26e79367c91ed, 0x361dcdd0d1e73240, 0xe2d494d081269e2, 0x33d231b9098b6045, 0x3c4e93c22fb78a3, 0x2f655fa56e578df3, 0x3a2b9600532c2609, 0x864e125951bbdb7, 0x2e2fca705bb62c58, 0x28e0629106401eaa, 0x7ac20f0ed6cdc1f, 0x3bd50add28a35850, 0x1a6e5ea19a59ab5d, 0x2add6d1d8c0aaefb, 0x2c3cf9842e6956a3, 0x1906944685f2c7c, 0x925997c95ed1de2, 0xcb9eb5d43c6f2e9, 0x1795f2b48a0fa71d, 0x19de5de41acc2100, 0x2e30c3a8444ef165, 0x29433812a3c4b1cd, 0xcbfa65dcdae6d63, 0x2580f2100e56c068, 0x25ce14544acc08cb, 0x24fa7059a7c87e18, 0x2a01d608b5d57d70, 0x3cefa2f54bdabc51, 0x29225fd40de84dea, 0x2d2276d8df087f20, 0x1a077580d9c5e840, 0x33b71879319b7de1, 0x16017e84617bddf4, 0x2596d6b0bd1a954c, 0x10267caddadbf666, 0x22c43bd90eaa3e05, 0xcaf6704a39c29fc, 0x25a0b38132106551, 0x1a78d1fcfd98f2a2, 0x1924d0b08fe1cc34, 0x3ea0a05c4cb14ee5, 0xa9b505540022072, 0x1e65cd1d5556d710, 0x3682cccd684103f1, 0x20a58fb864d70967, 0x35bfeeacb88f9b9b, 0x3b72dce9c4b09b87, 0x839908c285aaa64, 0x2ed676dc722e9732, 0x3dd67b08dc071450});
constexpr StatTable62 QRT_TABLE_62({0x30268b6fba455d2c, 0x200000006, 0x200000004, 0x3d67cb6c1fe66c76, 0x200000000, 0x3fc4f1901abfa400, 0x3d67cb6c1fe66c7e, 0x35e79b6c0a66bcbe, 0x200000010, 0x1e9372bc57a9941e, 0x3fc4f1901abfa420, 0x21ec9d424957a5b0, 0x3d67cb6c1fe66c3e, 0x1cb35a6e52f5fb0e, 0x35e79b6c0a66bc3e, 0x215481024c13a730, 0x200000110, 0x1c324a6c52f75b08, 0x1e9372bc57a9961e, 0x3764a9d00f676820, 0x3fc4f1901abfa020, 0x355481020e132730, 0x21ec9d424957adb0, 0x3c43c32c0f34301e, 0x3d67cb6c1fe67c3e, 0x1496122c45259728, 0x1cb35a6e52f5db0e, 0x15e418405b72ec20, 0x35e79b6c0a66fc3e, 0x30268b6e3a445c38, 0x215481024c132730, 0x100010114, 0x200010110, 0, 0x1c324a6c52f55b08, 0x215581044d133776, 0x1e9372bc57ad961e, 0x2155810e4d133766, 0x3764a9d00f6f6820, 0x2157833c4d12323e, 0x3fc4f1901aafa020, 0x1c324a4252f55b58, 0x355481020e332730, 0x28332fc0509d41e, 0x21ec9d424917adb0, 0x215783be4d12332e, 0x3c43c32c0fb4301e, 0x2157822c4d06363e, 0x3d67cb6c1ee67c3e, 0x23f6b9d2484afb78, 0x1496122c47259728, 0x14b8184047648a80, 0x1cb35a6e56f5db0e, 0x3fe4f1901aefa820, 0x15e418405372ec20, 0x3d5fd72c1be276be, 0x35e79b6c1a66fc3e, 0x14b038d24774cf10, 0x30268b6e1a445c38, 0x1d17022e43a7172e, 0x215481020c132730, 0x2157022e4d07372e});
typedef Field<uint64_t, 62, 536870913, StatTable62, &SQR_TABLE_62, &SQR2_TABLE_62, &SQR4_TABLE_62, &SQR8_TABLE_62, &SQR16_TABLE_62, &QRT_TABLE_62, IdTrans, &ID_TRANS, &ID_TRANS> Field62;
typedef FieldTri<uint64_t, 62, 29, RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5, 5>, &SQR_TABLE_62, &SQR2_TABLE_62, &SQR4_TABLE_62, &SQR8_TABLE_62, &SQR16_TABLE_62, &QRT_TABLE_62, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri62;
#endif
 
#ifdef ENABLE_FIELD_INT_63
// 63 bit field
typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5, 5> StatTableTRI63;
constexpr StatTableTRI63 SQR_TABLE_TRI63({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x4000000000000000, 0x6, 0x18, 0x60, 0x180, 0x600, 0x1800, 0x6000, 0x18000, 0x60000, 0x180000, 0x600000, 0x1800000, 0x6000000, 0x18000000, 0x60000000, 0x180000000, 0x600000000, 0x1800000000, 0x6000000000, 0x18000000000, 0x60000000000, 0x180000000000, 0x600000000000, 0x1800000000000, 0x6000000000000, 0x18000000000000, 0x60000000000000, 0x180000000000000, 0x600000000000000, 0x1800000000000000, 0x6000000000000000});
constexpr StatTableTRI63 SQR2_TABLE_TRI63({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x1000000000000000, 0x6, 0x60, 0x600, 0x6000, 0x60000, 0x600000, 0x6000000, 0x60000000, 0x600000000, 0x6000000000, 0x60000000000, 0x600000000000, 0x6000000000000, 0x60000000000000, 0x600000000000000, 0x6000000000000000, 0x14, 0x140, 0x1400, 0x14000, 0x140000, 0x1400000, 0x14000000, 0x140000000, 0x1400000000, 0x14000000000, 0x140000000000, 0x1400000000000, 0x14000000000000, 0x140000000000000, 0x1400000000000000, 0x4000000000000006, 0x78, 0x780, 0x7800, 0x78000, 0x780000, 0x7800000, 0x78000000, 0x780000000, 0x7800000000, 0x78000000000, 0x780000000000, 0x7800000000000, 0x78000000000000, 0x780000000000000, 0x7800000000000000});
constexpr StatTableTRI63 SQR4_TABLE_TRI63({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x6, 0x60000, 0x600000000, 0x6000000000000, 0x14, 0x140000, 0x1400000000, 0x14000000000000, 0x78, 0x780000, 0x7800000000, 0x78000000000000, 0x110, 0x1100000, 0x11000000000, 0x110000000000000, 0x660, 0x6600000, 0x66000000000, 0x660000000000000, 0x1540, 0x15400000, 0x154000000000, 0x1540000000000000, 0x7f80, 0x7f800000, 0x7f8000000000, 0x7f80000000000000, 0x10100, 0x101000000, 0x1010000000000, 0x100000000000006, 0x60600, 0x606000000, 0x6060000000000, 0x600000000000014, 0x141400, 0x1414000000, 0x14140000000000, 0x1400000000000078, 0x787800, 0x7878000000, 0x78780000000000, 0x7800000000000110, 0x1111000, 0x11110000000, 0x111100000000000, 0x1000000000000666, 0x6666000, 0x66660000000, 0x666600000000000, 0x6000000000001554, 0x15554000, 0x155540000000, 0x1555400000000000, 0x4000000000007ffe, 0x7fff8000, 0x7fff80000000, 0x7fff800000000000});
constexpr StatTableTRI63 SQR8_TABLE_TRI63({0x1, 0x110, 0x10100, 0x1111000, 0x100010000, 0x11001100000, 0x1010101000000, 0x111111110000000, 0x100000006, 0x11000000660, 0x1010000060600, 0x111100006666000, 0x1000600060006, 0x110066006600660, 0x106060606060606, 0x1666666666666666, 0x12, 0x1320, 0x121200, 0x13332000, 0x1200120000, 0x132013200000, 0x12121212000000, 0x1333333320000000, 0x120000006c, 0x132000006ac0, 0x121200006c6c00, 0x133320006aaac000, 0x12006c006c006c, 0x13206ac06ac06ac0, 0x126c6c6c6c6c6c6c, 0x4aaaaaaaaaaaaaaa, 0x104, 0x11440, 0x1050400, 0x115544000, 0x10401040000, 0x1144114400000, 0x105050504000000, 0x1555555440000006, 0x10400000618, 0x1144000067980, 0x1050400061e1800, 0x155440067ff98006, 0x104061806180618, 0x1446798679867986, 0x21e1e1e1e1e1e1e, 0x3fffffffffffffec, 0x1248, 0x136c80, 0x125a4800, 0x137fec8000, 0x124812480000, 0x136c936c800000, 0x125a5a5a48000000, 0x7fffffec8000006a, 0x124800006db0, 0x136c80006b6b00, 0x125a48006dddb000, 0x7fec806b006b006a, 0x12486db06db06db0, 0x6ceb6b6b6b6b6b6a, 0x25dddddddddddddc});
constexpr StatTableTRI63 SQR16_TABLE_TRI63({0x1, 0x10006, 0x100000014, 0x1000600140078, 0x116, 0x1160674, 0x11600001538, 0x116067415387e90, 0x10114, 0x101120678, 0x1011400141510, 0x112066c15687e66, 0x1170338, 0x117054a0a90, 0x1170338152c3f60, 0x54a1fbc41888532, 0x100010110, 0x1000701160660, 0x1010400141546, 0x102060c153e7f92, 0x11601170760, 0x116076301121340, 0x1171258152c6df4, 0x142a78fc131d6a4a, 0x1011500050540, 0x113067b055e1f86, 0x1110440042477e, 0x102261da46f39362, 0x117022e054b0b80, 0x45c09af143a3f72, 0x106721d847ee9ae4, 0x408a833f0a833f0a, 0x100010106, 0x1000701000614, 0x101120014147e, 0x114067814067902, 0x11601171074, 0x116076316066138, 0x117054c152d40e4, 0x33e0a853e0b842a, 0x1011500131278, 0x113066d12126d16, 0x7077c017b681e, 0x76e12736f057056, 0x117022e12493290, 0x45c1ead5f26a912, 0x76518c96bc5efa4, 0xb97397297387286, 0x1700171666, 0x17006516147554, 0x17174a012d3f8a, 0x173872913964814e, 0x160216157534, 0x16026219014b3eb8, 0x16144d1d3902f39c, 0x3964974c65925d30, 0x17163b005d59f8, 0x164974c75837d462, 0x17062a404d28cfa, 0x65854b0a96152d3c, 0x16152c2a5943b390, 0x5854b1be6419dd1e, 0x6045c19c854b1fba});
constexpr StatTableTRI63 QRT_TABLE_TRI63({0, 0x100010114, 0x100010116, 0x1001701051372, 0x100010112, 0x1000040220, 0x100170105137a, 0x5107703453bba, 0x100010102, 0x101130117155a, 0x1000040200, 0x40000200800, 0x100170105133a, 0x103151a137276d8, 0x5107703453b3a, 0x134e65fc7c222be0, 0x100010002, 0x100030103115a, 0x101130117175a, 0x106052d103f4de2, 0x1000040600, 0x15122707691d3a, 0x40000200000, 0x4530770bc57b3a, 0x100170105033a, 0x103011a131256d8, 0x103151a137256d8, 0x176f29eb55c7a8da, 0x5107703457b3a, 0x130b158b7767d0da, 0x134e65fc7c22abe0, 0x7bcaf59d2f62d3e2, 0x100000002, 0x1001401041260, 0x100030101115a, 0x5107e03443ab8, 0x101130113175a, 0x1043701251b3a, 0x106052d10374de2, 0x134e657d7c232be2, 0x1000140600, 0x106073d103b4be2, 0x15122707491d3a, 0x4438600ac07800, 0x40000600000, 0x176a199c5682d3e0, 0x4530770b457b3a, 0x7bca759c2f62d3e0, 0x100170005033a, 0x6116d02572de2, 0x103011a111256d8, 0x1346656d7c372de2, 0x103151a177256d8, 0x643c600aa07800, 0x176f29eb5dc7a8da, 0x7b4b758b2f67d0da, 0x5107713457b3a, 0x104570776b457b3a, 0x130b158b5767d0da, 0x734e65fc3c22abe0, 0x134e65fc3c22abe0, 0x4000000000000000, 0x7bcaf59daf62d3e2});
typedef FieldTri<uint64_t, 63, 1, StatTableTRI63, &SQR_TABLE_TRI63, &SQR2_TABLE_TRI63, &SQR4_TABLE_TRI63, &SQR8_TABLE_TRI63, &SQR16_TABLE_TRI63, &QRT_TABLE_TRI63, IdTrans, &ID_TRANS, &ID_TRANS> FieldTri63;
#endif
 
#ifdef ENABLE_FIELD_INT_64
// 64 bit field
typedef RecLinTrans<uint64_t, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 5> StatTable64;
constexpr StatTable64 SQR_TABLE_64({0x1, 0x4, 0x10, 0x40, 0x100, 0x400, 0x1000, 0x4000, 0x10000, 0x40000, 0x100000, 0x400000, 0x1000000, 0x4000000, 0x10000000, 0x40000000, 0x100000000, 0x400000000, 0x1000000000, 0x4000000000, 0x10000000000, 0x40000000000, 0x100000000000, 0x400000000000, 0x1000000000000, 0x4000000000000, 0x10000000000000, 0x40000000000000, 0x100000000000000, 0x400000000000000, 0x1000000000000000, 0x4000000000000000, 0x1b, 0x6c, 0x1b0, 0x6c0, 0x1b00, 0x6c00, 0x1b000, 0x6c000, 0x1b0000, 0x6c0000, 0x1b00000, 0x6c00000, 0x1b000000, 0x6c000000, 0x1b0000000, 0x6c0000000, 0x1b00000000, 0x6c00000000, 0x1b000000000, 0x6c000000000, 0x1b0000000000, 0x6c0000000000, 0x1b00000000000, 0x6c00000000000, 0x1b000000000000, 0x6c000000000000, 0x1b0000000000000, 0x6c0000000000000, 0x1b00000000000000, 0x6c00000000000000, 0xb00000000000001b, 0xc00000000000005a});
constexpr StatTable64 SQR2_TABLE_64({0x1, 0x10, 0x100, 0x1000, 0x10000, 0x100000, 0x1000000, 0x10000000, 0x100000000, 0x1000000000, 0x10000000000, 0x100000000000, 0x1000000000000, 0x10000000000000, 0x100000000000000, 0x1000000000000000, 0x1b, 0x1b0, 0x1b00, 0x1b000, 0x1b0000, 0x1b00000, 0x1b000000, 0x1b0000000, 0x1b00000000, 0x1b000000000, 0x1b0000000000, 0x1b00000000000, 0x1b000000000000, 0x1b0000000000000, 0x1b00000000000000, 0xb00000000000001b, 0x145, 0x1450, 0x14500, 0x145000, 0x1450000, 0x14500000, 0x145000000, 0x1450000000, 0x14500000000, 0x145000000000, 0x1450000000000, 0x14500000000000, 0x145000000000000, 0x1450000000000000, 0x450000000000001b, 0x50000000000001dc, 0x1db7, 0x1db70, 0x1db700, 0x1db7000, 0x1db70000, 0x1db700000, 0x1db7000000, 0x1db70000000, 0x1db700000000, 0x1db7000000000, 0x1db70000000000, 0x1db700000000000, 0x1db7000000000000, 0xdb7000000000001b, 0xb70000000000011f, 0x7000000000001105});
constexpr StatTable64 SQR4_TABLE_64({0x1, 0x10000, 0x100000000, 0x1000000000000, 0x1b, 0x1b0000, 0x1b00000000, 0x1b000000000000, 0x145, 0x1450000, 0x14500000000, 0x145000000000000, 0x1db7, 0x1db70000, 0x1db700000000, 0x1db7000000000000, 0x11011, 0x110110000, 0x1101100000000, 0x101100000000001b, 0x1ab1ab, 0x1ab1ab0000, 0x1ab1ab00000000, 0xb1ab00000000015e, 0x1514515, 0x15145150000, 0x151451500000000, 0x4515000000001c6b, 0x1c6db6c7, 0x1c6db6c70000, 0x1c6db6c700000000, 0xb6c700000001010f, 0x101000101, 0x1010001010000, 0x10001010000001b, 0x1010000001b1b00, 0x1b1b001b1b, 0x1b1b001b1b0000, 0x1b001b1b00000145, 0x1b1b000001444500, 0x14445014445, 0x144450144450000, 0x4501444500001dac, 0x444500001daab71b, 0x1daab71daab7, 0x1daab71daab70000, 0xb71daab70001110e, 0xaab700011101101f, 0x1110110110111, 0x110110110111001b, 0x10110111001aab1b, 0x111001aab1ab1ab, 0x1aab1ab1ab1aab, 0xab1ab1ab1aab015e, 0xb1ab1aab0150145e, 0x1aab015014514515, 0x150145145145015, 0x1451451450151c70, 0x451450151c71db6b, 0x50151c71db6db6dc, 0x1c71db6db6db71c7, 0xdb6db6db71c6000b, 0xb6db71c60001000f, 0x71c6000100000005});
constexpr StatTable64 SQR8_TABLE_64({0x1, 0x11011, 0x101000101, 0x1110110110111, 0x100000001001a, 0x10110001100aa1a1, 0x100011a1b1a011a, 0x100baa100bb1aa0a, 0x1a00000144, 0x1ba1ba01505504, 0x1a001b5f4401441a, 0xa0eb1eea544fee41, 0x15e0144001a1ce8, 0xf5ee551fbc9d4f5d, 0x1b4543b0eee81b44, 0xb89a98b89a98b894, 0x10dbc, 0x11d76167c, 0x10cb1bd0cb1bc, 0x1c6b617617606a67, 0xdbc00010da6ad43, 0x167d1d6d105be392, 0xbd170ae2484f0af7, 0x162bc80d36e8d468, 0x1aad58014ae5f0, 0x63df9865e4bbbb5, 0x43fc5a4cbafe0d17, 0xe3d18fd6f8de2666, 0x49e2e5eab134a710, 0x1c78a1664f19bdd8, 0xf0829cea9886f08a, 0x4d8f634d8f625cdd, 0x100514550, 0x1104554401050, 0x15115140114154b, 0x10050551444aec57, 0x4551004b4277f24b, 0xef2afe861bdfb, 0x1d64ceb6c85ed2c9, 0x4975810172576524, 0x73cf4644451101e, 0x4fd1b234005fb6a7, 0x1bddd12e486f9a6f, 0xaa3c6f23ad5e9724, 0xa02b0a9206ef4923, 0x18a08533d5a4e65e, 0x1fc83ef027d0132b, 0x5e54f45f48c9a13c, 0x10deeff7bf8c0, 0x1d21c38d4f8874db, 0x10886029449884cd, 0xfe25b26c0190be86, 0xf5345525adfcb67e, 0xb606f05c0f274ae6, 0x49303a49c3147e89, 0xe3dec1f0cb3467b8, 0xf3dd197b59b91bb7, 0x6e062ec482dfc7e, 0xc24c087e94b8c9c, 0x42e75f2649a63926, 0x4646807e89775aa9, 0xca57e67631079503, 0xf738d302cd26e621, 0xda8702da9702da9d});
constexpr StatTable64 SQR16_TABLE_64({0x1, 0x15f0144001a114f, 0x1aad43011ba1e5, 0xe34916e80106e21d, 0x11cefef6be466, 0xab943b855d3d776b, 0x1c77b6cf4edf1bd0, 0x46923ddea5ce4e34, 0x5455145e48670f13, 0xfb7d34d8e2b804bb, 0xbbe0dfe164a4d5b4, 0x431d528b1f73a8a2, 0xc259794b79e2607, 0x5945c54c76a8d132, 0xf5cb8b3860386917, 0xb345180ffd7a5551, 0xbaf1bebe1ae4ad02, 0x45562dad588c6260, 0x55b2852b76a728c4, 0xb5908b73d457d739, 0xa5a058173d115951, 0x11e605f10dd49e16, 0xb122096fef2a82a8, 0xfb95933559736ac7, 0x42652cf9ded5daa5, 0xe9a56590d5ab5301, 0xb8cef5ec20abb26f, 0xb50edcd1421d92e0, 0x12ac73f1d2f67094, 0x1c5815d4c184bd2, 0xe227a4ef0cd1165c, 0xe8d4a3a319b07491, 0xb0ef530df44bb042, 0xfbcbf52ff08d7ea3, 0xa0eaea8c7f69bf70, 0xedc22185164a14b1, 0xbfb9f37fc5eb3abc, 0x3712083e323193a, 0xe7bdca1397a3c26c, 0xf2d44dcbd1d02306, 0xa8fcad00bc810b9c, 0x4f7014f9d2186ea, 0x1b4d4ccc40f8060f, 0xe9ecf1e0105dab78, 0xe34e682846de9f1d, 0xace6cd21bf5ef658, 0x10f0cfa8cf3326ff, 0x71a97b1c73b8a63, 0xe1398cba3a3345d1, 0xa439e4c62ecb0615, 0x4bcce9efcca8db40, 0x176e95394759914e, 0xb5c7335e43a80f7f, 0xeb5439d8e177d64d, 0xa6af064a2d733f41, 0x5efc52c7e2f99007, 0x4a6efe65d270460b, 0xfe0ff44f5baa9a6a, 0x104c70edd05ffd6f, 0xf07d029f554aa763, 0x1c3c3cc0aca30a16, 0x7a0a5f6c85237d50, 0x1b862fb6b961ed37, 0xdcd1bd32f8a7d3ba});
constexpr StatTable64 QRT_TABLE_64({0x19c9369f278adc02, 0x84b2b22ab2383ee4, 0x84b2b22ab2383ee6, 0x9d7b84b495b3e3f6, 0x84b2b22ab2383ee2, 0x37c470b49213f790, 0x9d7b84b495b3e3fe, 0x1000a0105137c, 0x84b2b22ab2383ef2, 0x368e964a8edce1fc, 0x37c470b49213f7b0, 0x19c9368e278fdf4c, 0x9d7b84b495b3e3be, 0x2e4da23cbc7d4570, 0x1000a010513fc, 0x84f35772bac24232, 0x84b2b22ab2383ff2, 0x37c570ba9314e4fc, 0x368e964a8edce3fc, 0xb377c390213cdb0e, 0x37c470b49213f3b0, 0x85ed5a3aa99c24f2, 0x19c9368e278fd74c, 0xaabff0000780000e, 0x9d7b84b495b3f3be, 0x84b6b3dab03038f2, 0x2e4da23cbc7d6570, 0x511ea03494ffc, 0x1000a010553fc, 0xae0c0220343c6c0e, 0x84f35772bac2c232, 0x800000008000000e, 0x84b2b22ab2393ff2, 0xb376c29c202bc97e, 0x37c570ba9316e4fc, 0x9c3062488879e6ce, 0x368e964a8ed8e3fc, 0x41e42c08e47e70, 0xb377c3902134db0e, 0x85b9b108a60f56ce, 0x37c470b49203f3b0, 0x19dd3b6e21f3cb4c, 0x85ed5a3aa9bc24f2, 0x198ddf682c428ac0, 0x19c9368e27cfd74c, 0x4b7c68431ca84b0, 0xaabff0000700000e, 0x8040655489ffefbe, 0x9d7b84b494b3f3be, 0x18c1354e32bfa74c, 0x84b6b3dab23038f2, 0xaaf613cc0f74627e, 0x2e4da23cb87d6570, 0x3248b3d6b3342a8c, 0x511ea0b494ffc, 0xb60813c00e70700e, 0x1000a110553fc, 0x1e0d022a05393ffc, 0xae0c0220143c6c0e, 0xe0c0220143c6c00, 0x84f35772fac2c232, 0xc041e55948fbfdce, 0x800000000000000e, 0});
typedef Field<uint64_t, 64, 27, StatTable64, &SQR_TABLE_64, &SQR2_TABLE_64, &SQR4_TABLE_64, &SQR8_TABLE_64, &SQR16_TABLE_64, &QRT_TABLE_64, IdTrans, &ID_TRANS, &ID_TRANS> Field64;
#endif
}
 
Sketch* ConstructClMul8Bytes(int bits, int implementation) {
    switch (bits) {
#ifdef ENABLE_FIELD_INT_57
    case 57: return new SketchImpl<Field57>(implementation, 57);
#endif
#ifdef ENABLE_FIELD_INT_58
    case 58: return new SketchImpl<Field58>(implementation, 58);
#endif
#ifdef ENABLE_FIELD_INT_59
    case 59: return new SketchImpl<Field59>(implementation, 59);
#endif
#ifdef ENABLE_FIELD_INT_61
    case 61: return new SketchImpl<Field61>(implementation, 61);
#endif
#ifdef ENABLE_FIELD_INT_62
    case 62: return new SketchImpl<Field62>(implementation, 62);
#endif
#ifdef ENABLE_FIELD_INT_64
    case 64: return new SketchImpl<Field64>(implementation, 64);
#endif
    }
    return nullptr;
}
 
Sketch* ConstructClMulTri8Bytes(int bits, int implementation) {
    switch (bits) {
#ifdef ENABLE_FIELD_INT_57
    case 57: return new SketchImpl<FieldTri57>(implementation, 57);
#endif
#ifdef ENABLE_FIELD_INT_58
    case 58: return new SketchImpl<FieldTri58>(implementation, 58);
#endif
#ifdef ENABLE_FIELD_INT_60
    case 60: return new SketchImpl<FieldTri60>(implementation, 60);
#endif
#ifdef ENABLE_FIELD_INT_62
    case 62: return new SketchImpl<FieldTri62>(implementation, 62);
#endif
#ifdef ENABLE_FIELD_INT_63
    case 63: return new SketchImpl<FieldTri63>(implementation, 63);
#endif
    }
    return nullptr;
}