bn256math.c

/* -----------------------------------------------------------------------------
 *
 * Copyright (c) 2014-2019 Alexis Naveros.
 *
 * This software is provided 'as-is', without any express or implied
 * warranty. In no event will the authors be held liable for any damages
 * arising from the use of this software.
 *
 * Permission is granted to anyone to use this software for any purpose,
 * including commercial applications, and to alter it and redistribute it
 * freely, subject to the following restrictions:
 *
 * 1. The origin of this software must not be misrepresented; you must not
 * claim that you wrote the original software. If you use this software
 * in a product, an acknowledgment in the product documentation would be
 * appreciated but is not required.
 * 2. Altered source versions must be plainly marked as such, and must not be
 * misrepresented as being the original software.
 * 3. This notice may not be removed or altered from any source distribution.
 *
 * -----------------------------------------------------------------------------
 */

#include <stdio.h>
#include <stdlib.h>
#include <stddef.h>
#include <stdint.h>
#include <string.h>
#include <math.h>
#include <limits.h>
#include <float.h>
#include <time.h>
#include <stdarg.h>
#include <errno.h>
#include <assert.h>

#include <sys/types.h>
#include <sys/stat.h>
#include <unistd.h>

#include "cpuconfig.h"
#include "cc.h"
#include "ccstr.h"
#include "mm.h"

#define BN_XP_SUPPORT_128 0
#define BN_XP_SUPPORT_192 0
#define BN_XP_SUPPORT_256 1
#define BN_XP_SUPPORT_512 0
#define BN_XP_SUPPORT_1024 0
#include "bn.h"



////



#define BN256_LOG2_SHIFT (256)
#define BN256_LOG1P0625_SHIFT (256)
#define BN256_MUL1P0625_SHIFT (256-1)
#define BN256_DIV1P0625_SHIFT (256)
#define BN256_EXP1_SHIFT (256-2)
#define BN256_EXP1INV_SHIFT (256)
#define BN256_EXP0P125_SHIFT (256-1)
#define BN256_DIV_SHIFT (256-1)
#define BN256_PI_SHIFT (256-2)

#define BN256_DIV_TABLE_SIZE (256)

#define BN256_USE_INVERSE_DIVISION


#if BN_UNIT_BITS == 64

const bn256 bn256InfPos = 
{
 .unit = { 0xffffffffffffffff, 0xffffffffffffffff, 0xffffffffffffffff, 0x7fffffffffffffff }
};

const bn256 bn256InfNeg = 
{
 .unit = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x8000000000000000 }
};

const bn256 bn256Log2 = 
{
 .unit = { 0x8a0d175b8baaf85b, 0x40f343267298b62d, 0xc9e3b39803f2f6af, 0xb17217f7d1cf79ab }
};

const bn256 bn256Log1p0625 = 
{
 .unit = { 0x71851f0a96f69849, 0xd3474d3375b52596, 0xbe64b8b775997898, 0x0f85186008b15330 }
};

const bn256 bn256Mul1p0625 = 
{
 .unit = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x8800000000000000 }
};

const bn256 bn256Div1p0625 = 
{
 .unit = { 0xf0f0f0f0f0f0f0f0, 0xf0f0f0f0f0f0f0f0, 0xf0f0f0f0f0f0f0f0, 0xf0f0f0f0f0f0f0f0 }
};

const bn256 bn256Exp1 = 
{
 .unit = { 0xa9e1364114643388, 0xd8b9c583ce2d3695, 0xafdc5620273d3cf1, 0xadf85458a2bb4a9a }
};

const bn256 bn256Exp1Inv = 
{
 .unit = { 0x3024b9d0a507d8d1, 0xda9805aab56c7733, 0xbadec7829054f90d, 0x5e2d58d8b3bcdf1a }
};

const bn256 bn256Exp0p125 = 
{
 .unit = { 0xbbb5b0f28118966c, 0x3c5f864254ab82be, 0x76b441c27035c6a1, 0x910b022db7ae67ce }
};

const bn256 bn256Pi = 
{
 .unit = { 0x020bbea63b139ab3, 0x29024e088a67cc74, 0xc4c6628b80dc1cd1, 0xc90fdaa22168c234 }
};

const bn256 bn256DivFactor[BN256_DIV_TABLE_SIZE] = 
{
  [0] = { .unit = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000 } },
  [1] = { .unit = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0000000000000000 } },
  [2] = { .unit = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x4000000000000000 } },
  [3] = { .unit = { 0xaaaaaaaaaaaaaaab, 0xaaaaaaaaaaaaaaaa, 0xaaaaaaaaaaaaaaaa, 0x2aaaaaaaaaaaaaaa } },
  [4] = { .unit = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x2000000000000000 } },
  [5] = { .unit = { 0x999999999999999a, 0x9999999999999999, 0x9999999999999999, 0x1999999999999999 } },
  [6] = { .unit = { 0x5555555555555555, 0x5555555555555555, 0x5555555555555555, 0x1555555555555555 } },
  [7] = { .unit = { 0x9249249249249249, 0x4924924924924924, 0x2492492492492492, 0x1249249249249249 } },
  [8] = { .unit = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x1000000000000000 } },
  [9] = { .unit = { 0x8e38e38e38e38e39, 0x38e38e38e38e38e3, 0xe38e38e38e38e38e, 0x0e38e38e38e38e38 } },
  [10] = { .unit = { 0xcccccccccccccccd, 0xcccccccccccccccc, 0xcccccccccccccccc, 0x0ccccccccccccccc } },
  [11] = { .unit = { 0x2e8ba2e8ba2e8ba3, 0xa2e8ba2e8ba2e8ba, 0xba2e8ba2e8ba2e8b, 0x0ba2e8ba2e8ba2e8 } },
  [12] = { .unit = { 0xaaaaaaaaaaaaaaab, 0xaaaaaaaaaaaaaaaa, 0xaaaaaaaaaaaaaaaa, 0x0aaaaaaaaaaaaaaa } },
  [13] = { .unit = { 0x89d89d89d89d89d9, 0xd89d89d89d89d89d, 0x9d89d89d89d89d89, 0x09d89d89d89d89d8 } },
  [14] = { .unit = { 0x4924924924924925, 0x2492492492492492, 0x9249249249249249, 0x0924924924924924 } },
  [15] = { .unit = { 0x8888888888888889, 0x8888888888888888, 0x8888888888888888, 0x0888888888888888 } },
  [16] = { .unit = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0800000000000000 } },
  [17] = { .unit = { 0x8787878787878788, 0x8787878787878787, 0x8787878787878787, 0x0787878787878787 } },
  [18] = { .unit = { 0xc71c71c71c71c71c, 0x1c71c71c71c71c71, 0x71c71c71c71c71c7, 0x071c71c71c71c71c } },
  [19] = { .unit = { 0xca1af286bca1af28, 0x1af286bca1af286b, 0xf286bca1af286bca, 0x06bca1af286bca1a } },
  [20] = { .unit = { 0x6666666666666666, 0x6666666666666666, 0x6666666666666666, 0x0666666666666666 } },
  [21] = { .unit = { 0x8618618618618618, 0x1861861861861861, 0x6186186186186186, 0x0618618618618618 } },
  [22] = { .unit = { 0x1745d1745d1745d1, 0xd1745d1745d1745d, 0x5d1745d1745d1745, 0x05d1745d1745d174 } },
  [23] = { .unit = { 0xb21642c8590b2164, 0xc8590b21642c8590, 0x21642c8590b21642, 0x0590b21642c8590b } },
  [24] = { .unit = { 0x5555555555555555, 0x5555555555555555, 0x5555555555555555, 0x0555555555555555 } },
  [25] = { .unit = { 0xeb851eb851eb851f, 0x1eb851eb851eb851, 0x51eb851eb851eb85, 0x051eb851eb851eb8 } },
  [26] = { .unit = { 0xc4ec4ec4ec4ec4ec, 0xec4ec4ec4ec4ec4e, 0x4ec4ec4ec4ec4ec4, 0x04ec4ec4ec4ec4ec } },
  [27] = { .unit = { 0xda12f684bda12f68, 0x12f684bda12f684b, 0xf684bda12f684bda, 0x04bda12f684bda12 } },
  [28] = { .unit = { 0x2492492492492492, 0x9249249249249249, 0x4924924924924924, 0x0492492492492492 } },
  [29] = { .unit = { 0x58469ee58469ee58, 0xee58469ee58469ee, 0x69ee58469ee58469, 0x0469ee58469ee584 } },
  [30] = { .unit = { 0x4444444444444444, 0x4444444444444444, 0x4444444444444444, 0x0444444444444444 } },
  [31] = { .unit = { 0x1084210842108421, 0x2108421084210842, 0x4210842108421084, 0x0421084210842108 } },
  [32] = { .unit = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0400000000000000 } },
  [33] = { .unit = { 0x0f83e0f83e0f83e1, 0xe0f83e0f83e0f83e, 0x3e0f83e0f83e0f83, 0x03e0f83e0f83e0f8 } },
  [34] = { .unit = { 0xc3c3c3c3c3c3c3c4, 0xc3c3c3c3c3c3c3c3, 0xc3c3c3c3c3c3c3c3, 0x03c3c3c3c3c3c3c3 } },
  [35] = { .unit = { 0x83a83a83a83a83a8, 0xa83a83a83a83a83a, 0x3a83a83a83a83a83, 0x03a83a83a83a83a8 } },
  [36] = { .unit = { 0xe38e38e38e38e38e, 0x8e38e38e38e38e38, 0x38e38e38e38e38e3, 0x038e38e38e38e38e } },
  [37] = { .unit = { 0x59f22983759f2298, 0xf22983759f229837, 0x2983759f22983759, 0x03759f22983759f2 } },
  [38] = { .unit = { 0xe50d79435e50d794, 0x0d79435e50d79435, 0x79435e50d79435e5, 0x035e50d79435e50d } },
  [39] = { .unit = { 0x8348348348348348, 0x4834834834834834, 0x3483483483483483, 0x0348348348348348 } },
  [40] = { .unit = { 0x3333333333333333, 0x3333333333333333, 0x3333333333333333, 0x0333333333333333 } },
  [41] = { .unit = { 0xf3831f3831f3831f, 0x1f3831f3831f3831, 0x31f3831f3831f383, 0x031f3831f3831f38 } },
  [42] = { .unit = { 0xc30c30c30c30c30c, 0x0c30c30c30c30c30, 0x30c30c30c30c30c3, 0x030c30c30c30c30c } },
  [43] = { .unit = { 0xe82fa0be82fa0be8, 0x0be82fa0be82fa0b, 0xfa0be82fa0be82fa, 0x02fa0be82fa0be82 } },
  [44] = { .unit = { 0x8ba2e8ba2e8ba2e9, 0xe8ba2e8ba2e8ba2e, 0x2e8ba2e8ba2e8ba2, 0x02e8ba2e8ba2e8ba } },
  [45] = { .unit = { 0x82d82d82d82d82d8, 0xd82d82d82d82d82d, 0x2d82d82d82d82d82, 0x02d82d82d82d82d8 } },
  [46] = { .unit = { 0x590b21642c8590b2, 0x642c8590b21642c8, 0x90b21642c8590b21, 0x02c8590b21642c85 } },
  [47] = { .unit = { 0xb9310572620ae4c4, 0x2620ae4c415c9882, 0xc415c9882b931057, 0x02b9310572620ae4 } },
  [48] = { .unit = { 0xaaaaaaaaaaaaaaab, 0xaaaaaaaaaaaaaaaa, 0xaaaaaaaaaaaaaaaa, 0x02aaaaaaaaaaaaaa } },
  [49] = { .unit = { 0x14e5e0a72f053978, 0x0a72f05397829cbc, 0x05397829cbc14e5e, 0x029cbc14e5e0a72f } },
  [50] = { .unit = { 0xf5c28f5c28f5c28f, 0x8f5c28f5c28f5c28, 0x28f5c28f5c28f5c2, 0x028f5c28f5c28f5c } },
  [51] = { .unit = { 0x8282828282828283, 0x8282828282828282, 0x8282828282828282, 0x0282828282828282 } },
  [52] = { .unit = { 0x6276276276276276, 0x7627627627627627, 0x2762762762762762, 0x0276276276276276 } },
  [53] = { .unit = { 0x56f1826a439f656f, 0x9f656f1826a439f6, 0xa439f656f1826a43, 0x026a439f656f1826 } },
  [54] = { .unit = { 0xed097b425ed097b4, 0x097b425ed097b425, 0x7b425ed097b425ed, 0x025ed097b425ed09 } },
  [55] = { .unit = { 0x3c8253c8253c8254, 0x53c8253c8253c825, 0x253c8253c8253c82, 0x0253c8253c8253c8 } },
  [56] = { .unit = { 0x9249249249249249, 0x4924924924924924, 0x2492492492492492, 0x0249249249249249 } },
  [57] = { .unit = { 0xee08fb823ee08fb8, 0x08fb823ee08fb823, 0xfb823ee08fb823ee, 0x023ee08fb823ee08 } },
  [58] = { .unit = { 0x2c234f72c234f72c, 0xf72c234f72c234f7, 0x34f72c234f72c234, 0x0234f72c234f72c2 } },
  [59] = { .unit = { 0x8f2fba9386822b64, 0xb63cbeea4e1a08ad, 0x8ad8f2fba9386822, 0x022b63cbeea4e1a0 } },
  [60] = { .unit = { 0x2222222222222222, 0x2222222222222222, 0x2222222222222222, 0x0222222222222222 } },
  [61] = { .unit = { 0x92e29f79b4758219, 0x192e29f79b475821, 0x2192e29f79b47582, 0x02192e29f79b4758 } },
  [62] = { .unit = { 0x0842108421084211, 0x1084210842108421, 0x2108421084210842, 0x0210842108421084 } },
  [63] = { .unit = { 0x8208208208208208, 0x0820820820820820, 0x2082082082082082, 0x0208208208208208 } },
  [64] = { .unit = { 0x0000000000000000, 0x0000000000000000, 0x0000000000000000, 0x0200000000000000 } },
  [65] = { .unit = { 0x81f81f81f81f81f8, 0xf81f81f81f81f81f, 0x1f81f81f81f81f81, 0x01f81f81f81f81f8 } },
  [66] = { .unit = { 0x07c1f07c1f07c1f0, 0xf07c1f07c1f07c1f, 0x1f07c1f07c1f07c1, 0x01f07c1f07c1f07c } },
  [67] = { .unit = { 0x2a07a44c6afc2dda, 0xa81e9131abf0b767, 0xa07a44c6afc2dd9c, 0x01e9131abf0b7672 } },
  [68] = { .unit = { 0xe1e1e1e1e1e1e1e2, 0xe1e1e1e1e1e1e1e1, 0xe1e1e1e1e1e1e1e1, 0x01e1e1e1e1e1e1e1 } },
  [69] = { .unit = { 0xe6076b981dae6077, 0x981dae6076b981da, 0x6076b981dae6076b, 0x01dae6076b981dae } },
  [70] = { .unit = { 0x41d41d41d41d41d4, 0xd41d41d41d41d41d, 0x1d41d41d41d41d41, 0x01d41d41d41d41d4 } },
  [71] = { .unit = { 0x0ad12073615a240e, 0xb4481cd85689039b, 0x12073615a240e6c2, 0x01cd85689039b0ad } },
  [72] = { .unit = { 0x71c71c71c71c71c7, 0xc71c71c71c71c71c, 0x1c71c71c71c71c71, 0x01c71c71c71c71c7 } },
  [73] = { .unit = { 0x0e070381c0e07038, 0x070381c0e070381c, 0x0381c0e070381c0e, 0x01c0e070381c0e07 } },
  [74] = { .unit = { 0xacf914c1bacf914c, 0xf914c1bacf914c1b, 0x14c1bacf914c1bac, 0x01bacf914c1bacf9 } },
  [75] = { .unit = { 0x4e81b4e81b4e81b5, 0xb4e81b4e81b4e81b, 0x1b4e81b4e81b4e81, 0x01b4e81b4e81b4e8 } },
  [76] = { .unit = { 0xf286bca1af286bca, 0x86bca1af286bca1a, 0xbca1af286bca1af2, 0x01af286bca1af286 } },
  [77] = { .unit = { 0x98ef606a63bd81aa, 0xa98ef606a63bd81a, 0x1a98ef606a63bd81, 0x01a98ef606a63bd8 } },
  [78] = { .unit = { 0x41a41a41a41a41a4, 0xa41a41a41a41a41a, 0x1a41a41a41a41a41, 0x01a41a41a41a41a4 } },
  [79] = { .unit = { 0x1033d91d2a2067b2, 0xf6474a8819ec8e95, 0xd2a2067b23a5440c, 0x019ec8e951033d91 } },
  [80] = { .unit = { 0x999999999999999a, 0x9999999999999999, 0x9999999999999999, 0x0199999999999999 } },
  [81] = { .unit = { 0xf35ba781948b0fcd, 0xb0fcd6e9e06522c3, 0x522c3f35ba781948, 0x01948b0fcd6e9e06 } },
  [82] = { .unit = { 0xf9c18f9c18f9c190, 0x8f9c18f9c18f9c18, 0x18f9c18f9c18f9c1, 0x018f9c18f9c18f9c } },
  [83] = { .unit = { 0x0f6bf3a9a3784a06, 0xcea68de12818acb9, 0x3784a062b2e43daf, 0x018acb90f6bf3a9a } },
  [84] = { .unit = { 0x6186186186186186, 0x8618618618618618, 0x1861861861861861, 0x0186186186186186 } },
  [85] = { .unit = { 0x8181818181818182, 0x8181818181818181, 0x8181818181818181, 0x0181818181818181 } },
  [86] = { .unit = { 0xf417d05f417d05f4, 0x05f417d05f417d05, 0x7d05f417d05f417d, 0x017d05f417d05f41 } },
  [87] = { .unit = { 0xc8178a4c8178a4c8, 0xa4c8178a4c8178a4, 0x78a4c8178a4c8178, 0x0178a4c8178a4c81 } },
  [88] = { .unit = { 0x45d1745d1745d174, 0x745d1745d1745d17, 0x1745d1745d1745d1, 0x01745d1745d1745d } },
  [89] = { .unit = { 0x2e05c0b81702e05c, 0xb81702e05c0b8170, 0xe05c0b81702e05c0, 0x01702e05c0b81702 } },
  [90] = { .unit = { 0xc16c16c16c16c16c, 0x6c16c16c16c16c16, 0x16c16c16c16c16c1, 0x016c16c16c16c16c } },
  [91] = { .unit = { 0x8168168168168168, 0x6816816816816816, 0x1681681681681681, 0x0168168168168168 } },
  [92] = { .unit = { 0x2c8590b21642c859, 0xb21642c8590b2164, 0xc8590b21642c8590, 0x01642c8590b21642 } },
  [93] = { .unit = { 0x0581605816058160, 0x6058160581605816, 0x1605816058160581, 0x0160581605816058 } },
  [94] = { .unit = { 0x5c9882b931057262, 0x9310572620ae4c41, 0x620ae4c415c9882b, 0x015c9882b9310572 } },
  [95] = { .unit = { 0x8ed2308158ed2308, 0xd2308158ed230815, 0x308158ed2308158e, 0x0158ed2308158ed2 } },
  [96] = { .unit = { 0x5555555555555555, 0x5555555555555555, 0x5555555555555555, 0x0155555555555555 } },
  [97] = { .unit = { 0x8151d07eae2f8152, 0xae2f8151d07eae2f, 0xd07eae2f8151d07e, 0x0151d07eae2f8151 } },
  [98] = { .unit = { 0x0a72f05397829cbc, 0x05397829cbc14e5e, 0x829cbc14e5e0a72f, 0x014e5e0a72f05397 } },
  [99] = { .unit = { 0xafd6a052bf5a814b, 0x4afd6a052bf5a814, 0x14afd6a052bf5a81, 0x014afd6a052bf5a8 } },
  [100] = { .unit = { 0x7ae147ae147ae148, 0x47ae147ae147ae14, 0x147ae147ae147ae1, 0x0147ae147ae147ae } },
  [101] = { .unit = { 0x4981446f86562da0, 0x6562d9faee41e6a7, 0xe41e6a74981446f8, 0x01446f86562d9fae } },
  [102] = { .unit = { 0x4141414141414141, 0x4141414141414141, 0x4141414141414141, 0x0141414141414141 } },
  [103] = { .unit = { 0x254813e22cbce4a9, 0x2f392a409f1165e7, 0xc45979c95204f88b, 0x013e22cbce4a9027 } },
  [104] = { .unit = { 0xb13b13b13b13b13b, 0x3b13b13b13b13b13, 0x13b13b13b13b13b1, 0x013b13b13b13b13b } },
  [105] = { .unit = { 0x8138138138138138, 0x3813813813813813, 0x1381381381381381, 0x0138138138138138 } },
  [106] = { .unit = { 0x2b78c13521cfb2b8, 0xcfb2b78c13521cfb, 0x521cfb2b78c13521, 0x013521cfb2b78c13 } },
  [107] = { .unit = { 0xba9de81323e34a2b, 0x8d28ac42fd9b8396, 0x6e0e5aea77a04c8f, 0x01323e34a2b10bf6 } },
  [108] = { .unit = { 0xf684bda12f684bda, 0x84bda12f684bda12, 0xbda12f684bda12f6, 0x012f684bda12f684 } },
  [109] = { .unit = { 0xc9fb4d812c9fb4d8, 0xfb4d812c9fb4d812, 0x4d812c9fb4d812c9, 0x012c9fb4d812c9fb } },
  [110] = { .unit = { 0x9e4129e4129e412a, 0x29e4129e4129e412, 0x129e4129e4129e41, 0x0129e4129e4129e4 } },
  [111] = { .unit = { 0x7350b88127350b88, 0x50b88127350b8812, 0xb88127350b881273, 0x0127350b88127350 } },
  [112] = { .unit = { 0x4924924924924925, 0x2492492492492492, 0x9249249249249249, 0x0124924924924924 } },
  [113] = { .unit = { 0x78121fb78121fb78, 0xfb78121fb78121fb, 0x21fb78121fb78121, 0x0121fb78121fb781 } },
  [114] = { .unit = { 0xf7047dc11f7047dc, 0x047dc11f7047dc11, 0x7dc11f7047dc11f7, 0x011f7047dc11f704 } },
  [115] = { .unit = { 0xf06ada2811cf06ae, 0x2811cf06ada2811c, 0x06ada2811cf06ada, 0x011cf06ada2811cf } },
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  [246] = { .unit = { 0x5340853408534085, 0x8534085340853408, 0x0853408534085340, 0x0085340853408534 } },
  [247] = { .unit = { 0x4a9f9c8084a9f9c8, 0x9f9c8084a9f9c808, 0x9c8084a9f9c8084a, 0x0084a9f9c8084a9f } },
  [248] = { .unit = { 0x4210842108421084, 0x8421084210842108, 0x0842108421084210, 0x0084210842108421 } },
  [249] = { .unit = { 0x0523fbe3367d6e02, 0xef8cd9f5b8083993, 0x67d6e020e64c148f, 0x00839930523fbe33 } },
  [250] = { .unit = { 0xcac083126e978d50, 0xe978d4fdf3b645a1, 0x3b645a1cac083126, 0x0083126e978d4fdf } },
  [251] = { .unit = { 0xe680828cbfbeb9a0, 0xfbeb9a020a32fefa, 0xa32fefae680828cb, 0x00828cbfbeb9a020 } },
  [252] = { .unit = { 0x2082082082082082, 0x8208208208208208, 0x0820820820820820, 0x0082082082082082 } },
  [253] = { .unit = { 0xca5f1d58081848db, 0x1236a3ebc349dd98, 0x77663297c7560206, 0x0081848da8faf0d2 } },
  [254] = { .unit = { 0x0408102040810204, 0x0204081020408102, 0x8102040810204081, 0x0081020408102040 } },
  [255] = { .unit = { 0x8080808080808081, 0x8080808080808080, 0x8080808080808080, 0x0080808080808080 } },
};

#elif BN_UNIT_BITS == 32

const bn256 bn256InfPos = 
{
 .unit = { 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0xffffffff, 0x7fffffff }
};

const bn256 bn256InfNeg = 
{
 .unit = { 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x80000000 }
};

const bn256 bn256Log2 = 
{
 .unit = { 0x8baaf85b, 0x8a0d175b, 0x7298b62d, 0x40f34326, 0x03f2f6af, 0xc9e3b398, 0xd1cf79ab, 0xb17217f7 }
};

const bn256 bn256Log1p0625 = 
{
 .unit = { 0x96f69849, 0x71851f0a, 0x75b52596, 0xd3474d33, 0x75997898, 0xbe64b8b7, 0x08b15330, 0x0f851860 }
};

const bn256 bn256Mul1p0625 = 
{
 .unit = { 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x88000000 }
};

const bn256 bn256Div1p0625 = 
{
 .unit = { 0xf0f0f0f0, 0xf0f0f0f0, 0xf0f0f0f0, 0xf0f0f0f0, 0xf0f0f0f0, 0xf0f0f0f0, 0xf0f0f0f0, 0xf0f0f0f0 }
};

const bn256 bn256Exp1 = 
{
 .unit = { 0x14643388, 0xa9e13641, 0xce2d3695, 0xd8b9c583, 0x273d3cf1, 0xafdc5620, 0xa2bb4a9a, 0xadf85458 }
};

const bn256 bn256Exp1Inv = 
{
 .unit = { 0xa507d8d1, 0x3024b9d0, 0xb56c7733, 0xda9805aa, 0x9054f90d, 0xbadec782, 0xb3bcdf1a, 0x5e2d58d8 }
};

const bn256 bn256Exp0p125 = 
{
 .unit = { 0x8118966c, 0xbbb5b0f2, 0x54ab82be, 0x3c5f8642, 0x7035c6a1, 0x76b441c2, 0xb7ae67ce, 0x910b022d }
};

const bn256 bn256Pi = 
{
 .unit = { 0x3b139ab3, 0x020bbea6, 0x8a67cc74, 0x29024e08, 0x80dc1cd1, 0xc4c6628b, 0x2168c234, 0xc90fdaa2 }
};

const bn256 bn256DivFactor[BN256_DIV_TABLE_SIZE] = 
{
  [0] = { .unit = { 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000 } },
  [1] = { .unit = { 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000 } },
  [2] = { .unit = { 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x40000000 } },
  [3] = { .unit = { 0xaaaaaaab, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0x2aaaaaaa } },
  [4] = { .unit = { 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x20000000 } },
  [5] = { .unit = { 0x9999999a, 0x99999999, 0x99999999, 0x99999999, 0x99999999, 0x99999999, 0x99999999, 0x19999999 } },
  [6] = { .unit = { 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x15555555 } },
  [7] = { .unit = { 0x49249249, 0x92492492, 0x24924924, 0x49249249, 0x92492492, 0x24924924, 0x49249249, 0x12492492 } },
  [8] = { .unit = { 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x10000000 } },
  [9] = { .unit = { 0x38e38e39, 0x8e38e38e, 0xe38e38e3, 0x38e38e38, 0x8e38e38e, 0xe38e38e3, 0x38e38e38, 0x0e38e38e } },
  [10] = { .unit = { 0xcccccccd, 0xcccccccc, 0xcccccccc, 0xcccccccc, 0xcccccccc, 0xcccccccc, 0xcccccccc, 0x0ccccccc } },
  [11] = { .unit = { 0xba2e8ba3, 0x2e8ba2e8, 0x8ba2e8ba, 0xa2e8ba2e, 0xe8ba2e8b, 0xba2e8ba2, 0x2e8ba2e8, 0x0ba2e8ba } },
  [12] = { .unit = { 0xaaaaaaab, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0x0aaaaaaa } },
  [13] = { .unit = { 0xd89d89d9, 0x89d89d89, 0x9d89d89d, 0xd89d89d8, 0x89d89d89, 0x9d89d89d, 0xd89d89d8, 0x09d89d89 } },
  [14] = { .unit = { 0x24924925, 0x49249249, 0x92492492, 0x24924924, 0x49249249, 0x92492492, 0x24924924, 0x09249249 } },
  [15] = { .unit = { 0x88888889, 0x88888888, 0x88888888, 0x88888888, 0x88888888, 0x88888888, 0x88888888, 0x08888888 } },
  [16] = { .unit = { 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x08000000 } },
  [17] = { .unit = { 0x87878788, 0x87878787, 0x87878787, 0x87878787, 0x87878787, 0x87878787, 0x87878787, 0x07878787 } },
  [18] = { .unit = { 0x1c71c71c, 0xc71c71c7, 0x71c71c71, 0x1c71c71c, 0xc71c71c7, 0x71c71c71, 0x1c71c71c, 0x071c71c7 } },
  [19] = { .unit = { 0xbca1af28, 0xca1af286, 0xa1af286b, 0x1af286bc, 0xaf286bca, 0xf286bca1, 0x286bca1a, 0x06bca1af } },
  [20] = { .unit = { 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x66666666, 0x06666666 } },
  [21] = { .unit = { 0x18618618, 0x86186186, 0x61861861, 0x18618618, 0x86186186, 0x61861861, 0x18618618, 0x06186186 } },
  [22] = { .unit = { 0x5d1745d1, 0x1745d174, 0x45d1745d, 0xd1745d17, 0x745d1745, 0x5d1745d1, 0x1745d174, 0x05d1745d } },
  [23] = { .unit = { 0x590b2164, 0xb21642c8, 0x642c8590, 0xc8590b21, 0x90b21642, 0x21642c85, 0x42c8590b, 0x0590b216 } },
  [24] = { .unit = { 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x05555555 } },
  [25] = { .unit = { 0x51eb851f, 0xeb851eb8, 0x851eb851, 0x1eb851eb, 0xb851eb85, 0x51eb851e, 0xeb851eb8, 0x051eb851 } },
  [26] = { .unit = { 0xec4ec4ec, 0xc4ec4ec4, 0x4ec4ec4e, 0xec4ec4ec, 0xc4ec4ec4, 0x4ec4ec4e, 0xec4ec4ec, 0x04ec4ec4 } },
  [27] = { .unit = { 0xbda12f68, 0xda12f684, 0xa12f684b, 0x12f684bd, 0x2f684bda, 0xf684bda1, 0x684bda12, 0x04bda12f } },
  [28] = { .unit = { 0x92492492, 0x24924924, 0x49249249, 0x92492492, 0x24924924, 0x49249249, 0x92492492, 0x04924924 } },
  [29] = { .unit = { 0x8469ee58, 0x58469ee5, 0xe58469ee, 0xee58469e, 0x9ee58469, 0x69ee5846, 0x469ee584, 0x0469ee58 } },
  [30] = { .unit = { 0x44444444, 0x44444444, 0x44444444, 0x44444444, 0x44444444, 0x44444444, 0x44444444, 0x04444444 } },
  [31] = { .unit = { 0x42108421, 0x10842108, 0x84210842, 0x21084210, 0x08421084, 0x42108421, 0x10842108, 0x04210842 } },
  [32] = { .unit = { 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x04000000 } },
  [33] = { .unit = { 0x3e0f83e1, 0x0f83e0f8, 0x83e0f83e, 0xe0f83e0f, 0xf83e0f83, 0x3e0f83e0, 0x0f83e0f8, 0x03e0f83e } },
  [34] = { .unit = { 0xc3c3c3c4, 0xc3c3c3c3, 0xc3c3c3c3, 0xc3c3c3c3, 0xc3c3c3c3, 0xc3c3c3c3, 0xc3c3c3c3, 0x03c3c3c3 } },
  [35] = { .unit = { 0xa83a83a8, 0x83a83a83, 0x3a83a83a, 0xa83a83a8, 0x83a83a83, 0x3a83a83a, 0xa83a83a8, 0x03a83a83 } },
  [36] = { .unit = { 0x8e38e38e, 0xe38e38e3, 0x38e38e38, 0x8e38e38e, 0xe38e38e3, 0x38e38e38, 0x8e38e38e, 0x038e38e3 } },
  [37] = { .unit = { 0x759f2298, 0x59f22983, 0x9f229837, 0xf2298375, 0x22983759, 0x2983759f, 0x983759f2, 0x03759f22 } },
  [38] = { .unit = { 0x5e50d794, 0xe50d7943, 0x50d79435, 0x0d79435e, 0xd79435e5, 0x79435e50, 0x9435e50d, 0x035e50d7 } },
  [39] = { .unit = { 0x48348348, 0x83483483, 0x34834834, 0x48348348, 0x83483483, 0x34834834, 0x48348348, 0x03483483 } },
  [40] = { .unit = { 0x33333333, 0x33333333, 0x33333333, 0x33333333, 0x33333333, 0x33333333, 0x33333333, 0x03333333 } },
  [41] = { .unit = { 0x31f3831f, 0xf3831f38, 0x831f3831, 0x1f3831f3, 0x3831f383, 0x31f3831f, 0xf3831f38, 0x031f3831 } },
  [42] = { .unit = { 0x0c30c30c, 0xc30c30c3, 0x30c30c30, 0x0c30c30c, 0xc30c30c3, 0x30c30c30, 0x0c30c30c, 0x030c30c3 } },
  [43] = { .unit = { 0x82fa0be8, 0xe82fa0be, 0xbe82fa0b, 0x0be82fa0, 0xa0be82fa, 0xfa0be82f, 0x2fa0be82, 0x02fa0be8 } },
  [44] = { .unit = { 0x2e8ba2e9, 0x8ba2e8ba, 0xa2e8ba2e, 0xe8ba2e8b, 0xba2e8ba2, 0x2e8ba2e8, 0x8ba2e8ba, 0x02e8ba2e } },
  [45] = { .unit = { 0xd82d82d8, 0x82d82d82, 0x2d82d82d, 0xd82d82d8, 0x82d82d82, 0x2d82d82d, 0xd82d82d8, 0x02d82d82 } },
  [46] = { .unit = { 0x2c8590b2, 0x590b2164, 0xb21642c8, 0x642c8590, 0xc8590b21, 0x90b21642, 0x21642c85, 0x02c8590b } },
  [47] = { .unit = { 0x620ae4c4, 0xb9310572, 0x415c9882, 0x2620ae4c, 0x2b931057, 0xc415c988, 0x72620ae4, 0x02b93105 } },
  [48] = { .unit = { 0xaaaaaaab, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0xaaaaaaaa, 0x02aaaaaa } },
  [49] = { .unit = { 0x2f053978, 0x14e5e0a7, 0x97829cbc, 0x0a72f053, 0xcbc14e5e, 0x05397829, 0xe5e0a72f, 0x029cbc14 } },
  [50] = { .unit = { 0x28f5c28f, 0xf5c28f5c, 0xc28f5c28, 0x8f5c28f5, 0x5c28f5c2, 0x28f5c28f, 0xf5c28f5c, 0x028f5c28 } },
  [51] = { .unit = { 0x82828283, 0x82828282, 0x82828282, 0x82828282, 0x82828282, 0x82828282, 0x82828282, 0x02828282 } },
  [52] = { .unit = { 0x76276276, 0x62762762, 0x27627627, 0x76276276, 0x62762762, 0x27627627, 0x76276276, 0x02762762 } },
  [53] = { .unit = { 0x439f656f, 0x56f1826a, 0x26a439f6, 0x9f656f18, 0xf1826a43, 0xa439f656, 0x656f1826, 0x026a439f } },
  [54] = { .unit = { 0x5ed097b4, 0xed097b42, 0xd097b425, 0x097b425e, 0x97b425ed, 0x7b425ed0, 0xb425ed09, 0x025ed097 } },
  [55] = { .unit = { 0x253c8254, 0x3c8253c8, 0x8253c825, 0x53c8253c, 0xc8253c82, 0x253c8253, 0x3c8253c8, 0x0253c825 } },
  [56] = { .unit = { 0x49249249, 0x92492492, 0x24924924, 0x49249249, 0x92492492, 0x24924924, 0x49249249, 0x02492492 } },
  [57] = { .unit = { 0x3ee08fb8, 0xee08fb82, 0xe08fb823, 0x08fb823e, 0x8fb823ee, 0xfb823ee0, 0xb823ee08, 0x023ee08f } },
  [58] = { .unit = { 0xc234f72c, 0x2c234f72, 0x72c234f7, 0xf72c234f, 0x4f72c234, 0x34f72c23, 0x234f72c2, 0x0234f72c } },
  [59] = { .unit = { 0x86822b64, 0x8f2fba93, 0x4e1a08ad, 0xb63cbeea, 0xa9386822, 0x8ad8f2fb, 0xeea4e1a0, 0x022b63cb } },
  [60] = { .unit = { 0x22222222, 0x22222222, 0x22222222, 0x22222222, 0x22222222, 0x22222222, 0x22222222, 0x02222222 } },
  [61] = { .unit = { 0xb4758219, 0x92e29f79, 0x9b475821, 0x192e29f7, 0x79b47582, 0x2192e29f, 0xf79b4758, 0x02192e29 } },
  [62] = { .unit = { 0x21084211, 0x08421084, 0x42108421, 0x10842108, 0x84210842, 0x21084210, 0x08421084, 0x02108421 } },
  [63] = { .unit = { 0x08208208, 0x82082082, 0x20820820, 0x08208208, 0x82082082, 0x20820820, 0x08208208, 0x02082082 } },
  [64] = { .unit = { 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x00000000, 0x02000000 } },
  [65] = { .unit = { 0xf81f81f8, 0x81f81f81, 0x1f81f81f, 0xf81f81f8, 0x81f81f81, 0x1f81f81f, 0xf81f81f8, 0x01f81f81 } },
  [66] = { .unit = { 0x1f07c1f0, 0x07c1f07c, 0xc1f07c1f, 0xf07c1f07, 0x7c1f07c1, 0x1f07c1f0, 0x07c1f07c, 0x01f07c1f } },
  [67] = { .unit = { 0x6afc2dda, 0x2a07a44c, 0xabf0b767, 0xa81e9131, 0xafc2dd9c, 0xa07a44c6, 0xbf0b7672, 0x01e9131a } },
  [68] = { .unit = { 0xe1e1e1e2, 0xe1e1e1e1, 0xe1e1e1e1, 0xe1e1e1e1, 0xe1e1e1e1, 0xe1e1e1e1, 0xe1e1e1e1, 0x01e1e1e1 } },
  [69] = { .unit = { 0x1dae6077, 0xe6076b98, 0x76b981da, 0x981dae60, 0xdae6076b, 0x6076b981, 0x6b981dae, 0x01dae607 } },
  [70] = { .unit = { 0xd41d41d4, 0x41d41d41, 0x1d41d41d, 0xd41d41d4, 0x41d41d41, 0x1d41d41d, 0xd41d41d4, 0x01d41d41 } },
  [71] = { .unit = { 0x615a240e, 0x0ad12073, 0x5689039b, 0xb4481cd8, 0xa240e6c2, 0x12073615, 0x9039b0ad, 0x01cd8568 } },
  [72] = { .unit = { 0xc71c71c7, 0x71c71c71, 0x1c71c71c, 0xc71c71c7, 0x71c71c71, 0x1c71c71c, 0xc71c71c7, 0x01c71c71 } },
  [73] = { .unit = { 0xc0e07038, 0x0e070381, 0xe070381c, 0x070381c0, 0x70381c0e, 0x0381c0e0, 0x381c0e07, 0x01c0e070 } },
  [74] = { .unit = { 0xbacf914c, 0xacf914c1, 0xcf914c1b, 0xf914c1ba, 0x914c1bac, 0x14c1bacf, 0x4c1bacf9, 0x01bacf91 } },
  [75] = { .unit = { 0x1b4e81b5, 0x4e81b4e8, 0x81b4e81b, 0xb4e81b4e, 0xe81b4e81, 0x1b4e81b4, 0x4e81b4e8, 0x01b4e81b } },
  [76] = { .unit = { 0xaf286bca, 0xf286bca1, 0x286bca1a, 0x86bca1af, 0x6bca1af2, 0xbca1af28, 0xca1af286, 0x01af286b } },
  [77] = { .unit = { 0x63bd81aa, 0x98ef606a, 0xa63bd81a, 0xa98ef606, 0x6a63bd81, 0x1a98ef60, 0x06a63bd8, 0x01a98ef6 } },
  [78] = { .unit = { 0xa41a41a4, 0x41a41a41, 0x1a41a41a, 0xa41a41a4, 0x41a41a41, 0x1a41a41a, 0xa41a41a4, 0x01a41a41 } },
  [79] = { .unit = { 0x2a2067b2, 0x1033d91d, 0x19ec8e95, 0xf6474a88, 0x23a5440c, 0xd2a2067b, 0x51033d91, 0x019ec8e9 } },
  [80] = { .unit = { 0x9999999a, 0x99999999, 0x99999999, 0x99999999, 0x99999999, 0x99999999, 0x99999999, 0x01999999 } },
  [81] = { .unit = { 0x948b0fcd, 0xf35ba781, 0xe06522c3, 0xb0fcd6e9, 0xba781948, 0x522c3f35, 0xcd6e9e06, 0x01948b0f } },
  [82] = { .unit = { 0x18f9c190, 0xf9c18f9c, 0xc18f9c18, 0x8f9c18f9, 0x9c18f9c1, 0x18f9c18f, 0xf9c18f9c, 0x018f9c18 } },
  [83] = { .unit = { 0xa3784a06, 0x0f6bf3a9, 0x2818acb9, 0xcea68de1, 0xb2e43daf, 0x3784a062, 0xf6bf3a9a, 0x018acb90 } },
  [84] = { .unit = { 0x86186186, 0x61861861, 0x18618618, 0x86186186, 0x61861861, 0x18618618, 0x86186186, 0x01861861 } },
  [85] = { .unit = { 0x81818182, 0x81818181, 0x81818181, 0x81818181, 0x81818181, 0x81818181, 0x81818181, 0x01818181 } },
  [86] = { .unit = { 0x417d05f4, 0xf417d05f, 0x5f417d05, 0x05f417d0, 0xd05f417d, 0x7d05f417, 0x17d05f41, 0x017d05f4 } },
  [87] = { .unit = { 0x8178a4c8, 0xc8178a4c, 0x4c8178a4, 0xa4c8178a, 0x8a4c8178, 0x78a4c817, 0x178a4c81, 0x0178a4c8 } },
  [88] = { .unit = { 0x1745d174, 0x45d1745d, 0xd1745d17, 0x745d1745, 0x5d1745d1, 0x1745d174, 0x45d1745d, 0x01745d17 } },
  [89] = { .unit = { 0x1702e05c, 0x2e05c0b8, 0x5c0b8170, 0xb81702e0, 0x702e05c0, 0xe05c0b81, 0xc0b81702, 0x01702e05 } },
  [90] = { .unit = { 0x6c16c16c, 0xc16c16c1, 0x16c16c16, 0x6c16c16c, 0xc16c16c1, 0x16c16c16, 0x6c16c16c, 0x016c16c1 } },
  [91] = { .unit = { 0x68168168, 0x81681681, 0x16816816, 0x68168168, 0x81681681, 0x16816816, 0x68168168, 0x01681681 } },
  [92] = { .unit = { 0x1642c859, 0x2c8590b2, 0x590b2164, 0xb21642c8, 0x642c8590, 0xc8590b21, 0x90b21642, 0x01642c85 } },
  [93] = { .unit = { 0x16058160, 0x05816058, 0x81605816, 0x60581605, 0x58160581, 0x16058160, 0x05816058, 0x01605816 } },
  [94] = { .unit = { 0x31057262, 0x5c9882b9, 0x20ae4c41, 0x93105726, 0x15c9882b, 0x620ae4c4, 0xb9310572, 0x015c9882 } },
  [95] = { .unit = { 0x58ed2308, 0x8ed23081, 0xed230815, 0xd2308158, 0x2308158e, 0x308158ed, 0x08158ed2, 0x0158ed23 } },
  [96] = { .unit = { 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x55555555, 0x01555555 } },
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  [203] = { .unit = { 0x377cd8e8, 0x312ea8fc, 0x8e80a16b, 0x8fc377cd, 0x16b312ea, 0x7cd8e80a, 0x2ea8fc37, 0x00a16b31 } },
  [204] = { .unit = { 0xa0a0a0a1, 0xa0a0a0a0, 0xa0a0a0a0, 0xa0a0a0a0, 0xa0a0a0a0, 0xa0a0a0a0, 0xa0a0a0a0, 0x00a0a0a0 } },
  [205] = { .unit = { 0x09fd80a0, 0xfd809fd8, 0x809fd809, 0x9fd809fd, 0xd809fd80, 0x09fd809f, 0xfd809fd8, 0x009fd809 } },
  [206] = { .unit = { 0x165e7255, 0x92a409f1, 0x4f88b2f3, 0x979c9520, 0xa9027c45, 0xe22cbce4, 0xe7254813, 0x009f1165 } },
  [207] = { .unit = { 0xb48f757d, 0xa2027932, 0xd23dd5f3, 0x8809e4ca, 0x48f757ce, 0x2027932b, 0x23dd5f3a, 0x009e4cad } },
  [208] = { .unit = { 0x9d89d89e, 0xd89d89d8, 0x89d89d89, 0x9d89d89d, 0xd89d89d8, 0x89d89d89, 0x9d89d89d, 0x009d89d8 } },
  [209] = { .unit = { 0x3fb19b8f, 0xcc8e160c, 0x3d3e7809, 0x30fec66e, 0x27323858, 0xb8f4f9e0, 0x60c3fb19, 0x009cc8e1 } },
  [210] = { .unit = { 0x9c09c09c, 0xc09c09c0, 0x09c09c09, 0x9c09c09c, 0xc09c09c0, 0x09c09c09, 0x9c09c09c, 0x009c09c0 } },
  [211] = { .unit = { 0xd31be7bc, 0xf514a026, 0xe1ab1232, 0xc83087e2, 0xd6bfb259, 0xa9db9a15, 0x9ef03a3c, 0x009b4c6f } },
  [212] = { .unit = { 0x90e7d95c, 0x95bc609a, 0x09a90e7d, 0xe7d95bc6, 0xbc609a90, 0xa90e7d95, 0xd95bc609, 0x009a90e7 } },
  [213] = { .unit = { 0x75c8b6af, 0x58f06026, 0x722dabde, 0x3c18099d, 0x8b6af796, 0x0602675c, 0xdabde58f, 0x0099d722 } },
  [214] = { .unit = { 0x91f1a516, 0x5d4ef409, 0x7ecdc1cb, 0xc6945621, 0x3bd02647, 0x37072d75, 0x515885fb, 0x00991f1a } },
  [215] = { .unit = { 0x809868c8, 0xc809868c, 0x8c809868, 0x68c80986, 0x868c8098, 0x9868c809, 0x09868c80, 0x009868c8 } },
  [216] = { .unit = { 0x97b425ed, 0x7b425ed0, 0xb425ed09, 0x425ed097, 0x25ed097b, 0x5ed097b4, 0xed097b42, 0x0097b425 } },
  [217] = { .unit = { 0xc04b8097, 0x7012e025, 0x5c04b809, 0x97012e02, 0x25c04b80, 0x097012e0, 0x025c04b8, 0x0097012e } },
  [218] = { .unit = { 0x964fda6c, 0x64fda6c0, 0x4fda6c09, 0xfda6c096, 0xda6c0964, 0xa6c0964f, 0x6c0964fd, 0x00964fda } },
  [219] = { .unit = { 0x95a02568, 0x5a025680, 0xa0256809, 0x02568095, 0x2568095a, 0x568095a0, 0x68095a02, 0x0095a025 } },
  [220] = { .unit = { 0x094f2095, 0x4f2094f2, 0x2094f209, 0x94f2094f, 0xf2094f20, 0x094f2094, 0x4f2094f2, 0x0094f209 } },
  [221] = { .unit = { 0x94458094, 0x80944580, 0x45809445, 0x94458094, 0x80944580, 0x45809445, 0x94458094, 0x00944580 } },
  [222] = { .unit = { 0x939a85c4, 0x39a85c40, 0x9a85c409, 0xa85c4093, 0x85c40939, 0x5c40939a, 0xc40939a8, 0x00939a85 } },
  [223] = { .unit = { 0x024bc44e, 0x497889c2, 0x2f113840, 0xe2270809, 0x44e10125, 0x9c2024bc, 0x84049788, 0x0092f113 } },
  [224] = { .unit = { 0x92492492, 0x24924924, 0x49249249, 0x92492492, 0x24924924, 0x49249249, 0x92492492, 0x00924924 } },
  [225] = { .unit = { 0x5e6f8092, 0x1a2b3c4d, 0xd5e6f809, 0x91a2b3c4, 0x4d5e6f80, 0x091a2b3c, 0xc4d5e6f8, 0x0091a2b3 } },
  [226] = { .unit = { 0xc090fdbc, 0xbc090fdb, 0xdbc090fd, 0xfdbc090f, 0x0fdbc090, 0x90fdbc09, 0x090fdbc0, 0x0090fdbc } },
  [227] = { .unit = { 0xa024168e, 0xac8bd766, 0xfc9de2ad, 0xd2e3ce60, 0x5132bfb7, 0x3aa4a6e8, 0x633e06c4, 0x00905a38 } },
  [228] = { .unit = { 0x8fb823ee, 0xfb823ee0, 0xb823ee08, 0x823ee08f, 0x23ee08fb, 0x3ee08fb8, 0xee08fb82, 0x008fb823 } },
  [229] = { .unit = { 0x9808f178, 0xfdc3a218, 0x8f1779d9, 0x3a218980, 0x779d9fdc, 0x189808f1, 0xd9fdc3a2, 0x008f1779 } },
  [230] = { .unit = { 0x08e78357, 0x78356d14, 0x56d1408e, 0x1408e783, 0x8e78356d, 0x8356d140, 0x6d1408e7, 0x008e7835 } },
  [231] = { .unit = { 0x7694808e, 0xdda52023, 0x37694808, 0x8dda5202, 0x23769480, 0x08dda520, 0x02376948, 0x008dda52 } },
  [232] = { .unit = { 0xb08d3dcb, 0xcb08d3dc, 0xdcb08d3d, 0x3dcb08d3, 0xd3dcb08d, 0x8d3dcb08, 0x08d3dcb0, 0x008d3dcb } },
  [233] = { .unit = { 0x53808ca3, 0x8a701194, 0x514e0232, 0xca29c046, 0x19453808, 0x2328a701, 0x046514e0, 0x008ca29c } },
  [234] = { .unit = { 0x8c08c08c, 0xc08c08c0, 0x08c08c08, 0x8c08c08c, 0xc08c08c0, 0x08c08c08, 0x8c08c08c, 0x008c08c0 } },
  [235] = { .unit = { 0x139bc75a, 0x8b70344a, 0xa6ac1e80, 0xa139bc75, 0x08b70344, 0x5a6ac1e8, 0x4a139bc7, 0x008b7034 } },
  [236] = { .unit = { 0xe1a08ad9, 0x63cbeea4, 0x9386822b, 0xad8f2fba, 0xea4e1a08, 0x22b63cbe, 0xfba93868, 0x008ad8f2 } },
  [237] = { .unit = { 0x63602291, 0x05669db4, 0x08a42f87, 0xa76d18d8, 0x0be1c159, 0x46360229, 0x705669db, 0x008a42f8 } },
  [238] = { .unit = { 0x89ae408a, 0x4089ae40, 0xae4089ae, 0x89ae4089, 0x4089ae40, 0xae4089ae, 0x89ae4089, 0x0089ae40 } },
  [239] = { .unit = { 0xa3e20224, 0xab617909, 0xd30336a0, 0x12358e75, 0x84d1f101, 0x5055b0bc, 0x3ae9819b, 0x00891ac7 } },
  [240] = { .unit = { 0x88888889, 0x88888888, 0x88888888, 0x88888888, 0x88888888, 0x88888888, 0x88888888, 0x00888888 } },
  [241] = { .unit = { 0x87f78088, 0x8087f780, 0xf78087f7, 0x87f78087, 0x8087f780, 0xf78087f7, 0x87f78087, 0x0087f780 } },
  [242] = { .unit = { 0x08767ab6, 0xa50658dc, 0x91fbc4c2, 0x9ead7cd3, 0x9637021d, 0xf130a941, 0x5f34e47e, 0x008767ab } },
  [243] = { .unit = { 0x3183afef, 0x511e8d2b, 0xa021b641, 0xe5a99cf8, 0x937d5dc2, 0xc60ebfbc, 0x447a34ac, 0x0086d905 } },
  [244] = { .unit = { 0x6d1d6086, 0x64b8a7de, 0xe6d1d608, 0x864b8a7d, 0xde6d1d60, 0x0864b8a7, 0x7de6d1d6, 0x00864b8a } },
  [245] = { .unit = { 0x3c9aa518, 0x37612cee, 0x518085bf, 0xcee3c9aa, 0x5bf37612, 0x9aa51808, 0x612cee3c, 0x0085bf37 } },
  [246] = { .unit = { 0x08534085, 0x53408534, 0x40853408, 0x85340853, 0x34085340, 0x08534085, 0x53408534, 0x00853408 } },
  [247] = { .unit = { 0x84a9f9c8, 0x4a9f9c80, 0xa9f9c808, 0x9f9c8084, 0xf9c8084a, 0x9c8084a9, 0xc8084a9f, 0x0084a9f9 } },
  [248] = { .unit = { 0x08421084, 0x42108421, 0x10842108, 0x84210842, 0x21084210, 0x08421084, 0x42108421, 0x00842108 } },
  [249] = { .unit = { 0x367d6e02, 0x0523fbe3, 0xb8083993, 0xef8cd9f5, 0xe64c148f, 0x67d6e020, 0x523fbe33, 0x00839930 } },
  [250] = { .unit = { 0x6e978d50, 0xcac08312, 0xf3b645a1, 0xe978d4fd, 0xac083126, 0x3b645a1c, 0x978d4fdf, 0x0083126e } },
  [251] = { .unit = { 0xbfbeb9a0, 0xe680828c, 0x0a32fefa, 0xfbeb9a02, 0x680828cb, 0xa32fefae, 0xbeb9a020, 0x00828cbf } },
  [252] = { .unit = { 0x82082082, 0x20820820, 0x08208208, 0x82082082, 0x20820820, 0x08208208, 0x82082082, 0x00820820 } },
  [253] = { .unit = { 0x081848db, 0xca5f1d58, 0xc349dd98, 0x1236a3eb, 0xc7560206, 0x77663297, 0xa8faf0d2, 0x0081848d } },
  [254] = { .unit = { 0x40810204, 0x04081020, 0x20408102, 0x02040810, 0x10204081, 0x81020408, 0x08102040, 0x00810204 } },
  [255] = { .unit = { 0x80808081, 0x80808080, 0x80808080, 0x80808080, 0x80808080, 0x80808080, 0x80808080, 0x00808080 } },
};

#endif



////



static inline void bn256Shr2( bn256 *dst )
{
#if BN_UNIT_BITS == 64
  dst->unit[0] = ( dst->unit[0] >> 2 ) | ( dst->unit[1] << (BN_UNIT_BITS-2) );
  dst->unit[1] = ( dst->unit[1] >> 2 ) | ( dst->unit[2] << (BN_UNIT_BITS-2) );
  dst->unit[2] = ( dst->unit[2] >> 2 ) | ( dst->unit[3] << (BN_UNIT_BITS-2) );
  dst->unit[3] = ( dst->unit[3] >> 2 );
#else
  dst->unit[0] = ( dst->unit[0] >> 2 ) | ( dst->unit[1] << (BN_UNIT_BITS-2) );
  dst->unit[1] = ( dst->unit[1] >> 2 ) | ( dst->unit[2] << (BN_UNIT_BITS-2) );
  dst->unit[2] = ( dst->unit[2] >> 2 ) | ( dst->unit[3] << (BN_UNIT_BITS-2) );
  dst->unit[3] = ( dst->unit[3] >> 2 ) | ( dst->unit[4] << (BN_UNIT_BITS-2) );
  dst->unit[4] = ( dst->unit[4] >> 2 ) | ( dst->unit[5] << (BN_UNIT_BITS-2) );
  dst->unit[5] = ( dst->unit[5] >> 2 ) | ( dst->unit[6] << (BN_UNIT_BITS-2) );
  dst->unit[6] = ( dst->unit[6] >> 2 ) | ( dst->unit[7] << (BN_UNIT_BITS-2) );
  dst->unit[7] = ( dst->unit[7] >> 2 );
#endif
  return;
}


void bn256Sqrt( bn256 *dst, const bn256 * const src, bnShift shift )
{
  int msb, oneshift;
  bn256 base, one, tmp;

  bn256Set( &base, src );
  bn256Zero( dst );
  msb = bn256GetIndexMSB( &base );
  oneshift = ( msb & ~0x1 ) | ( shift & 0x1 );
  bn256Zero( &one );
  bn256SetBit( &one, oneshift );
  for( ; bn256CmpGt( &one, &base ) ; )
  {
    oneshift -= 2;
    bn256Shr2( &one );
  }
  for( ; ; )
  {
    bn256SetOr( &tmp, dst, &one );
    bn256Shr1( dst );
    if( bn256CmpGe( &base, &tmp ) )
    {
      bn256Sub( &base, &tmp );
      bn256Or( dst, &one );
    }
    if( oneshift < 2 )
    {
      if( shift < 2 )
        break;
      shift -= 2;
      bn256Shl( dst, dst, 2 );
      bn256Shl( &base, &base, 2 );
    }
    else
    {
      oneshift -= 2;
      bn256Zero( &one );
      bn256SetBit( &one, oneshift );
    }
  }
  if( bn256CmpGt( &base, dst ) )
    bn256Add32( dst, 1 );

  return;
}


void bn256Log( bn256 *dst, const bn256 * const src, bnShift shift )
{
  int divisor;
  bn256 one, limit, base, fsub, fadd, part, bnlog, tmp;
#ifndef BN256_USE_INVERSE_DIVISION
  bn256 factor;
#endif

  bn256Zero( dst );
  if( bn256CmpNegative( src ) )
    return;
  bn256Set( &base, src );
  bn256Set32Shl( &one, 1, shift );
  if( bn256CmpGt( &base, &one ) )
  {
    bn256Set32Shl( &limit, 2, shift-0 );
    if( bn256CmpGt( &base, &limit ) )
    {
      bn256ShrRound( &bnlog, &bn256Log2, BN256_LOG2_SHIFT - shift );
      do
      {
        bn256Add( dst, &bnlog );
        bn256Shr1( &base );
      } while( bn256CmpGt( &base, &limit ) );
    }
    bn256Set32Shl( &limit, 33, shift-5 );
    if( bn256CmpGt( &base, &limit ) )
    {
      bn256ShrRound( &bnlog, &bn256Log1p0625, BN256_LOG1P0625_SHIFT - shift );
      do
      {
        bn256Add( dst, &bnlog );
        bn256MulShr( &tmp, &bn256Div1p0625, &base, BN256_DIV1P0625_SHIFT );
        if( bn256CmpEq( &base, &tmp ) )
          break;
        bn256Set( &base, &tmp );
      } while( bn256CmpGt( &base, &limit ) );
    }
  }
  else
  {
    bn256Set32Shl( &limit, 1, shift-1 );
    if( bn256CmpLt( &base, &limit ) )
    {
      bn256ShrRound( &bnlog, &bn256Log2, BN256_LOG2_SHIFT - shift );
      do
      {
        bn256Sub( dst, &bnlog );
        bn256Shl1( &base );
      } while( bn256CmpLt( &base, &limit ) );
    }
    bn256Set32Shl( &limit, 31, shift-5 );
    if( bn256CmpLt( &base, &limit ) )
    {
      bn256ShrRound( &bnlog, &bn256Log1p0625, BN256_LOG1P0625_SHIFT - shift );
      do
      {
        bn256Sub( dst, &bnlog );
        bn256MulShr( &tmp, &bn256Mul1p0625, &base, BN256_MUL1P0625_SHIFT );
        if( bn256CmpEq( &base, &tmp ) )
          break;
        bn256Set( &base, &tmp );
      } while( bn256CmpLt( &base, &limit ) );
    }
  }

  bn256Sub( &base, &one );
  bn256SquareShr( &fsub, &base, shift );
  bn256Add( dst, &base );
  for( divisor = 2 ; divisor < BN256_DIV_TABLE_SIZE ; divisor += 2 )
  {
#ifdef BN256_USE_INVERSE_DIVISION
    bn256MulSignedShr( &part, &bn256DivFactor[divisor+0], &fsub, BN256_DIV_SHIFT );
#else
    bn256Set( &factor, &one );
    bn256Div32Round( &factor, divisor+0 );
    bn256MulSignedShr( &part, &factor, &fsub, shift );
#endif
    bn256Sub( dst, &part );
    bn256MulSignedShr( &fadd, &fsub, &base, shift );
    if( bn256CmpEqOrZero( &fadd, &fsub ) )
      break;
#ifdef BN256_USE_INVERSE_DIVISION
    bn256MulSignedShr( &part, &bn256DivFactor[divisor+1], &fadd, BN256_DIV_SHIFT );
#else
    bn256Set( &factor, &one );
    bn256Div32Round( &factor, divisor+1 );
    bn256MulSignedShr( &part, &factor, &fadd, shift );
#endif
    bn256Add( dst, &part );
    bn256MulSignedShr( &fsub, &fadd, &base, shift );
    if( bn256CmpEqOrZero( &fsub, &fadd ) )
      break;
  }
#ifdef BN256_PRINT_REPORT
  printf( "Log Iteration Count : %d\n", (divisor-2)/2 );
#endif

  return;
}


void bn256Exp( bn256 *dst, const bn256 * const src, bnShift shift )
{
  int divisor, factorflag;
  bn256 term0, term1, one, factor, tmp, base, limit, bnexp, div8;

  bn256Set32Shl( &one, 1, shift );
  bn256Set( &base, src );

  factorflag = 0;
  bn256Set( &factor, &one );
  if( bn256CmpPositive( &base ) )
  {
    bn256Set( &limit, &one );
    if( bn256CmpGt( &base, &limit ) )
    {
      bn256ShrRound( &bnexp, &bn256Exp1, BN256_EXP1_SHIFT - shift );
      factorflag = 1;
      do
      {
        if( bn256MulCheckShr( &tmp, &factor, &bnexp, shift ) )
        {
          bn256Set( dst, &bn256InfPos );
          return;
        }
        bn256Set( &factor, &tmp );
        bn256Sub( &base, &one );
      } while( bn256CmpGt( &base, &limit ) );
    }
  }
  else
  {
    bn256Zero( &limit );
    if( bn256CmpSignedLt( &base, &limit ) )
    {
      bn256ShrRound( &bnexp, &bn256Exp1Inv, BN256_EXP1INV_SHIFT - shift );
      factorflag = 1;
      do
      {
        bn256MulShr( &tmp, &factor, &bnexp, shift );
        if( bn256CmpZero( &tmp ) )
        {
          bn256CmpZero( dst );
          return;
        }
        bn256Set( &factor, &tmp );
        bn256Add( &base, &one );
      } while( bn256CmpSignedLt( &base, &limit ) );
    }
  }

  bn256Set32Shl( &limit, 1, shift-4 );
  if( bn256CmpSignedGt( &base, &limit ) )
  {
    bn256Set32Shl( &div8, 1, shift-3 );
    if( bn256CmpNotZero( &div8 ) )
    {
      bn256ShrRound( &bnexp, &bn256Exp0p125, BN256_EXP0P125_SHIFT - shift );
      factorflag = 1;
      do
      {
        if( bn256MulCheckShr( &tmp, &factor, &bnexp, shift ) )
        {
          bn256Set( dst, &bn256InfPos );
          return;
        }
        bn256Set( &factor, &tmp );
        bn256Sub( &base, &div8 );
      } while( bn256CmpSignedGt( &base, &limit ) );
    }
  }

  bn256SetAdd( dst, &one, &base );
  bn256Set( &term0, &base );
  for( divisor = 2 ; divisor < BN256_DIV_TABLE_SIZE ; divisor += 2 )
  {
#ifdef BN256_USE_INVERSE_DIVISION
    bn256MulSignedShr( &tmp, &bn256DivFactor[divisor+0], &base, BN256_DIV_SHIFT );
#else
    bn256Set( &tmp, &base );
    bn256Div32RoundSigned( &tmp, divisor+0 );
#endif
    bn256MulSignedShr( &term1, &tmp, &term0, shift );
    if( bn256CmpEqOrZero( &term1, &term0 ) )
      break;
    bn256Add( dst, &term1 );
#ifdef BN256_USE_INVERSE_DIVISION
    bn256MulSignedShr( &tmp, &bn256DivFactor[divisor+1], &base, BN256_DIV_SHIFT );
#else
    bn256Set( &tmp, &base );
    bn256Div32RoundSigned( &tmp, divisor+1 );
#endif
    bn256MulSignedShr( &term0, &tmp, &term1, shift );
    if( bn256CmpEqOrZero( &term0, &term1 ) )
      break;
    bn256Add( dst, &term0 );
  }
  if( factorflag )
  {
    bn256MulSignedShr( &tmp, &factor, dst, shift );
    bn256Set( dst, &tmp );
  }
#ifdef BN256_PRINT_REPORT
  printf( "Exp Iteration Count : %d\n", (divisor-2)/2 );
#endif

  return;
}


void bn256Pow( bn256 *dst, const bn256 * const src, const bn256 * const exponent, bnShift shift )
{
  bn256 tmp, expf;
  bn256Log( &tmp, src, shift );
  bn256MulSignedShr( &expf, &tmp, exponent, shift );
  bn256Exp( dst, &expf, shift );
  return;
}


void bn256PowInt( bn256 *dst, const bn256 * const src, uint32_t exponent, bnShift shift )
{
  uint32_t exlevel, mulflag;
  bn256 tmp, mul;
  if( exponent == 0 )
  {
    bn256Set32Shl( dst, 1, shift );
    return;
  }
  mulflag = 0;
  bn256Set( &mul, src );
  exlevel = 1;
  for( ; ; )
  {
    if( exponent & exlevel )
    {
      if( !( mulflag ) )
      {
        bn256Set( dst, &mul );
        mulflag = 1;
      }
      else
      {
        bn256MulSignedShr( &tmp, dst, &mul, shift );
        bn256Set( dst, &tmp );
      }
      exponent -= exlevel;
      if( !( exponent ) )
        break;
    }
    exlevel <<= 1;
    bn256SquareShr( &tmp, &mul, shift );
    bn256Set( &mul, &tmp );
  }
  return;
}


void bn256Cos( bn256 *dst, const bn256 * const src, bnShift shift )
{
  int divisor, negflag, divproduct, msbdiff;
  bn256 term0, term1, one, tmp, tmp2, base, bn2pi, bnpi, bnhpi, basesq, rem;

  if( bn256CmpPositive( src ) )
    bn256Set( &base, src );
  else
    bn256SetNeg( &base, src );
  bn256ShrRound( &bn2pi, &bn256Pi, BN256_PI_SHIFT-1 - shift );
  if( bn256CmpGt( &base, &bn2pi ) )
  {
    msbdiff = bn256GetIndexMSB( &base ) - bn256GetIndexMSB( &bn2pi );
    if( msbdiff >= 3 )
    {
      bn256Div( &base, &bn2pi, &rem );
      bn256Set( &base, &rem );
    }
    else
    {
      for( ; bn256CmpGt( &base, &bn2pi ) ; )
        bn256Sub( &base, &bn2pi );
    }
  }
  bn256ShrRound( &bnpi, &bn256Pi, BN256_PI_SHIFT+0 - shift );
  if( bn256CmpGt( &base, &bnpi ) )
  {
    bn256SetSub( &tmp, &bn2pi, &base );
    bn256Set( &base, &tmp );
  }
  negflag = 0;
  bn256ShrRound( &bnhpi, &bn256Pi, BN256_PI_SHIFT+1 - shift );
  if( bn256CmpGt( &base, &bnhpi ) )
  {
    bn256SetSub( &tmp, &bnpi, &base );
    bn256Set( &base, &tmp );
    negflag = 1;
  }

  bn256Set32Shl( &one, 1, shift );
  bn256SquareShr( &basesq, &base, shift );
  bn256Set( dst, &one );
  bn256SetShr1( &term0, &basesq );
  bn256Sub( dst, &term0 );
  for( divisor = 4 ; divisor < BN256_DIV_TABLE_SIZE ; divisor += 4 )
  {
#ifdef BN256_USE_INVERSE_DIVISION
    divproduct = (divisor-1) * (divisor+0);
    if( divproduct < BN256_DIV_TABLE_SIZE )
      bn256MulShr( &tmp, &basesq, &bn256DivFactor[divproduct], BN256_DIV_SHIFT );
    else
    {
      bn256MulShr( &tmp2, &bn256DivFactor[divisor-1], &bn256DivFactor[divisor+0], BN256_DIV_SHIFT );
      bn256MulShr( &tmp, &basesq, &tmp2, BN256_DIV_SHIFT );
    }
#else
    bn256Set( &tmp, &basesq );
    bn256Div32Round( &tmp, (divisor-1)*(divisor+0) );
#endif
    bn256MulShr( &term1, &tmp, &term0, shift );
    if( bn256CmpEqOrZero( &term1, &term0 ) )
      break;
    if( bn256CmpZero( &term1 ) )
      break;
    bn256Add( dst, &term1 );
#ifdef BN256_USE_INVERSE_DIVISION
    divproduct = (divisor+1) * (divisor+2);
    if( divproduct < BN256_DIV_TABLE_SIZE )
      bn256MulShr( &tmp, &basesq, &bn256DivFactor[divproduct], BN256_DIV_SHIFT );
    else
    {
      bn256MulShr( &tmp2, &bn256DivFactor[divisor+1], &bn256DivFactor[divisor+2], BN256_DIV_SHIFT );
      bn256MulShr( &tmp, &basesq, &tmp2, BN256_DIV_SHIFT );
    }
#else
    bn256Set( &tmp, &basesq );
    bn256Div32Round( &tmp, (divisor+1)*(divisor+2) );
#endif
    bn256MulShr( &term0, &tmp, &term1, shift );
    if( bn256CmpEqOrZero( &term0, &term1 ) )
      break;
    bn256Sub( dst, &term0 );
  }
  if( negflag )
    bn256Neg( dst );
#ifdef BN256_PRINT_REPORT
  printf( "Cos Iteration Count : %d\n", (divisor-4)/4 );
#endif

  return;
}


void bn256Sin( bn256 *dst, const bn256 * const src, bnShift shift )
{
  bn256 bncos, bnhpi;
  bn256ShrRound( &bnhpi, &bn256Pi, BN256_PI_SHIFT+1 - shift );
  bn256SetSub( &bncos, src, &bnhpi );
  bn256Cos( dst, &bncos, shift );
  return;
}


void bn256Tan( bn256 *dst, const bn256 * const src, bnShift shift )
{
  bn256 bncos;
  bn256Cos( &bncos, src, shift );
  if( bn256CmpNotZero( &bncos ) )
  {
    bn256Sin( dst, src, shift );
    bn256DivRoundSignedShl( dst, &bncos, shift );
  }
  else
    bn256Set( dst, bn256CmpPositive( src ) ? &bn256InfPos : &bn256InfNeg );
  return;
}