atof_eisel_lemire.c

/*
 * Copyright 2021 ByteDance Inc.
 *
 * Licensed under the Apache License, Version 2.0 (the "License");
 * you may not use this file except in compliance with the License.
 * You may obtain a copy of the License at
 *
 *     http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS,
 * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 * See the License for the specific language governing permissions and
 * limitations under the License.
 * 
 * Copyright (c) Daniel Lemire
 * 
 * Boost Software License - Version 1.0 - August 17th, 2003
 * 
 * Permission is hereby granted, free of charge, to any person or organization
 * obtaining a copy of the software and accompanying documentation covered by
 * this license (the "Software") to use, reproduce, display, distribute,
 * execute, and transmit the Software, and to prepare derivative works of the
 * Software, and to permit third-parties to whom the Software is furnished to
 * do so, all subject to the following:
 * 
 * The copyright notices in the Software and this entire statement, including
 * the above license grant, this restriction and the following disclaimer,
 * must be included in all copies of the Software, in whole or in part, and
 * all derivative works of the Software, unless such copies or derivative
 * works are solely in the form of machine-executable object code generated by
 * a source language processor.
 * 
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE, TITLE AND NON-INFRINGEMENT. IN NO EVENT
 * SHALL THE COPYRIGHT HOLDERS OR ANYONE DISTRIBUTING THE SOFTWARE BE LIABLE
 * FOR ANY DAMAGES OR OTHER LIABILITY, WHETHER IN CONTRACT, TORT OR OTHERWISE,
 * ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
 * DEALINGS IN THE SOFTWARE.
 * 
 * This file may have been modified by ByteDance authors. All ByteDance
 * Modifications are Copyright 2022 ByteDance Authors.
 */

#include "native.h"

/* two uint64_t represent a 128-bit unsigned integer */
typedef struct u128_output {
    uint64_t hi;
    uint64_t lo;
} u128_output;

static const uint64_t POW10_M128_TAB[697][2];

static inline int count_leading_zeroes_u64(uint64_t u) {
    return u ? __builtin_clzl(u) : 64;
}

static inline u128_output mul_u64(uint64_t x, uint64_t y) {
    u128_output ret;
    __uint128_t z = ((__uint128_t)x) * ((__uint128_t)y);
    ret.hi = (uint64_t)(z >> 64);
    ret.lo = (uint64_t)z;
    return ret;
}

/* This is Eisel Lemire ParseFloat algorithm implemented in C.
 * reference: https://nigeltao.github.io/blog/2020/eisel-lemire.html 
 */
bool atof_eisel_lemire64(uint64_t mant, int exp10, int sgn, double *val) {
    if (exp10 < -348 || exp10 > 347) {
        return false;
    }

    /* Calculate the 2-base exponent of float */
    int clz = count_leading_zeroes_u64(mant);
    mant <<= clz;
    /* lg10/lg2 ≈ 217706>>16 */
    uint64_t ret_exp2 = ((uint64_t)((217706 * exp10) >> 16) + 64 + 1023) - ((uint64_t)clz);

    /* Calculate the mantissa of float */
    u128_output x = mul_u64(mant, POW10_M128_TAB[exp10 + 348][1]); // higher 64 bits of POW10 mantissa
    uint64_t x_hi = x.hi;
    uint64_t x_lo = x.lo;

    /* Wider approximation for the float.
     * mant * PWO10_M * exp2 <= ret float < mant * (PWO10_M + 1) * exp2.
     * mant * PWO10_M <= ret_man < mant * (PWO10_M + 1)
     * If the lower 9 bits of x_hi is 0x1FF and the mant + x_lo is overflow，
     * x_hi needs to add 1 for the upper bound, and it is ambiguous for higher 54 bits of ret_man.
     */
    if ((x_hi & 0x1FF) == 0x1FF && (x_lo + mant) < mant) {
        /* lower 64 bits of POW10 mantissa */
        u128_output y = mul_u64(mant, POW10_M128_TAB[exp10 + 348][0]);
        uint64_t merged_hi = x_hi;
        uint64_t merged_lo = x_lo + y.hi; 

        /* lower 64 bits of multiply output overflow */
        if (merged_lo < x_lo) {
            merged_hi ++;
        }

        /* Still ambigunous */
        if ((merged_hi & 0x1FF) == 0x1FF && (merged_lo + 1) == 0 && (y.lo + mant) < mant) {
            return false;
        }

        x_hi = merged_hi;
        x_lo = merged_lo;
    }

    /* Remain 54 bits */
    int msb = x_hi >> 63;
    uint64_t ret_man = x_hi >> (msb + 9);
    ret_exp2 -= 1 ^ msb;

    /* Half-way Ambiguity */
    if ((x_lo == 0) && ((x_hi & 0x1FF) == 0) && ((ret_man & 3) == 1)) {
        return false;
    }

    /* If not half-way, then it's rounding to-nearest 
     * Remain 53 bits.
     */
    ret_man += ret_man & 1;
    ret_man >>= 1;
    /* If rounding overflowed, shift again */
    if ((ret_man >> 53) > 0) {
        ret_man >>= 1;
        ret_exp2 += 1;
    }

    /* ret_exp2 < 0 means subnormal double.
     * ret_exp2 >= 0x7FF means INF/inf.
     */
    if ((ret_exp2 - 1) >= (0x7FF - 1)) {
        return false;
    }

    /* Get the lower 52 bits as finnal mantissa */
    uint64_t bits = (ret_exp2 << 52) | (ret_man & 0x000FFFFFFFFFFFFF);
    if (sgn == -1) {
        bits |= 1ull << 63;
    }
    *(int64_t*)val = bits;

    return true;
}

/* Including 128-bit mantissa approximations (rounded down) of the powers of 10.
 * For example: 
 * 1e-348 ≈ 0xFA8FD5A0081C0288_1732C869CD60E453 * (2 ** (-348 * lg10 / lg2 - 127)).
 * 1e-348 ≈ 0xFA8FD5A0081C0288 * (2 ** (-348 * lg10 / lg2 - 63)).
 * lg10/lg2 ≈ 217706.0/65536.0.
 */
static const uint64_t POW10_M128_TAB[697][2] = {
    {0x1732C869CD60E453, 0xFA8FD5A0081C0288}, // 1e-348
    {0x0E7FBD42205C8EB4, 0x9C99E58405118195}, // 1e-347
    {0x521FAC92A873B261, 0xC3C05EE50655E1FA}, // 1e-346
    {0xE6A797B752909EF9, 0xF4B0769E47EB5A78}, // 1e-345
    {0x9028BED2939A635C, 0x98EE4A22ECF3188B}, // 1e-344
    {0x7432EE873880FC33, 0xBF29DCABA82FDEAE}, // 1e-343
    {0x113FAA2906A13B3F, 0xEEF453D6923BD65A}, // 1e-342
    {0x4AC7CA59A424C507, 0x9558B4661B6565F8}, // 1e-341
    {0x5D79BCF00D2DF649, 0xBAAEE17FA23EBF76}, // 1e-340
    {0xF4D82C2C107973DC, 0xE95A99DF8ACE6F53}, // 1e-339
    {0x79071B9B8A4BE869, 0x91D8A02BB6C10594}, // 1e-338
    {0x9748E2826CDEE284, 0xB64EC836A47146F9}, // 1e-337
    {0xFD1B1B2308169B25, 0xE3E27A444D8D98B7}, // 1e-336
    {0xFE30F0F5E50E20F7, 0x8E6D8C6AB0787F72}, // 1e-335
    {0xBDBD2D335E51A935, 0xB208EF855C969F4F}, // 1e-334
    {0xAD2C788035E61382, 0xDE8B2B66B3BC4723}, // 1e-333
    {0x4C3BCB5021AFCC31, 0x8B16FB203055AC76}, // 1e-332
    {0xDF4ABE242A1BBF3D, 0xADDCB9E83C6B1793}, // 1e-331
    {0xD71D6DAD34A2AF0D, 0xD953E8624B85DD78}, // 1e-330
    {0x8672648C40E5AD68, 0x87D4713D6F33AA6B}, // 1e-329
    {0x680EFDAF511F18C2, 0xA9C98D8CCB009506}, // 1e-328
    {0x0212BD1B2566DEF2, 0xD43BF0EFFDC0BA48}, // 1e-327
    {0x014BB630F7604B57, 0x84A57695FE98746D}, // 1e-326
    {0x419EA3BD35385E2D, 0xA5CED43B7E3E9188}, // 1e-325
    {0x52064CAC828675B9, 0xCF42894A5DCE35EA}, // 1e-324
    {0x7343EFEBD1940993, 0x818995CE7AA0E1B2}, // 1e-323
    {0x1014EBE6C5F90BF8, 0xA1EBFB4219491A1F}, // 1e-322
    {0xD41A26E077774EF6, 0xCA66FA129F9B60A6}, // 1e-321
    {0x8920B098955522B4, 0xFD00B897478238D0}, // 1e-320
    {0x55B46E5F5D5535B0, 0x9E20735E8CB16382}, // 1e-319
    {0xEB2189F734AA831D, 0xC5A890362FDDBC62}, // 1e-318
    {0xA5E9EC7501D523E4, 0xF712B443BBD52B7B}, // 1e-317
    {0x47B233C92125366E, 0x9A6BB0AA55653B2D}, // 1e-316
    {0x999EC0BB696E840A, 0xC1069CD4EABE89F8}, // 1e-315
    {0xC00670EA43CA250D, 0xF148440A256E2C76}, // 1e-314
    {0x380406926A5E5728, 0x96CD2A865764DBCA}, // 1e-313
    {0xC605083704F5ECF2, 0xBC807527ED3E12BC}, // 1e-312
    {0xF7864A44C633682E, 0xEBA09271E88D976B}, // 1e-311
    {0x7AB3EE6AFBE0211D, 0x93445B8731587EA3}, // 1e-310
    {0x5960EA05BAD82964, 0xB8157268FDAE9E4C}, // 1e-309
    {0x6FB92487298E33BD, 0xE61ACF033D1A45DF}, // 1e-308
    {0xA5D3B6D479F8E056, 0x8FD0C16206306BAB}, // 1e-307
    {0x8F48A4899877186C, 0xB3C4F1BA87BC8696}, // 1e-306
    {0x331ACDABFE94DE87, 0xE0B62E2929ABA83C}, // 1e-305
    {0x9FF0C08B7F1D0B14, 0x8C71DCD9BA0B4925}, // 1e-304
    {0x07ECF0AE5EE44DD9, 0xAF8E5410288E1B6F}, // 1e-303
    {0xC9E82CD9F69D6150, 0xDB71E91432B1A24A}, // 1e-302
    {0xBE311C083A225CD2, 0x892731AC9FAF056E}, // 1e-301
    {0x6DBD630A48AAF406, 0xAB70FE17C79AC6CA}, // 1e-300
    {0x092CBBCCDAD5B108, 0xD64D3D9DB981787D}, // 1e-299
    {0x25BBF56008C58EA5, 0x85F0468293F0EB4E}, // 1e-298
    {0xAF2AF2B80AF6F24E, 0xA76C582338ED2621}, // 1e-297
    {0x1AF5AF660DB4AEE1, 0xD1476E2C07286FAA}, // 1e-296
    {0x50D98D9FC890ED4D, 0x82CCA4DB847945CA}, // 1e-295
    {0xE50FF107BAB528A0, 0xA37FCE126597973C}, // 1e-294
    {0x1E53ED49A96272C8, 0xCC5FC196FEFD7D0C}, // 1e-293
    {0x25E8E89C13BB0F7A, 0xFF77B1FCBEBCDC4F}, // 1e-292
    {0x77B191618C54E9AC, 0x9FAACF3DF73609B1}, // 1e-291
    {0xD59DF5B9EF6A2417, 0xC795830D75038C1D}, // 1e-290
    {0x4B0573286B44AD1D, 0xF97AE3D0D2446F25}, // 1e-289
    {0x4EE367F9430AEC32, 0x9BECCE62836AC577}, // 1e-288
    {0x229C41F793CDA73F, 0xC2E801FB244576D5}, // 1e-287
    {0x6B43527578C1110F, 0xF3A20279ED56D48A}, // 1e-286
    {0x830A13896B78AAA9, 0x9845418C345644D6}, // 1e-285
    {0x23CC986BC656D553, 0xBE5691EF416BD60C}, // 1e-284
    {0x2CBFBE86B7EC8AA8, 0xEDEC366B11C6CB8F}, // 1e-283
    {0x7BF7D71432F3D6A9, 0x94B3A202EB1C3F39}, // 1e-282
    {0xDAF5CCD93FB0CC53, 0xB9E08A83A5E34F07}, // 1e-281
    {0xD1B3400F8F9CFF68, 0xE858AD248F5C22C9}, // 1e-280
    {0x23100809B9C21FA1, 0x91376C36D99995BE}, // 1e-279
    {0xABD40A0C2832A78A, 0xB58547448FFFFB2D}, // 1e-278
    {0x16C90C8F323F516C, 0xE2E69915B3FFF9F9}, // 1e-277
    {0xAE3DA7D97F6792E3, 0x8DD01FAD907FFC3B}, // 1e-276
    {0x99CD11CFDF41779C, 0xB1442798F49FFB4A}, // 1e-275
    {0x40405643D711D583, 0xDD95317F31C7FA1D}, // 1e-274
    {0x482835EA666B2572, 0x8A7D3EEF7F1CFC52}, // 1e-273
    {0xDA3243650005EECF, 0xAD1C8EAB5EE43B66}, // 1e-272
    {0x90BED43E40076A82, 0xD863B256369D4A40}, // 1e-271
    {0x5A7744A6E804A291, 0x873E4F75E2224E68}, // 1e-270
    {0x711515D0A205CB36, 0xA90DE3535AAAE202}, // 1e-269
    {0x0D5A5B44CA873E03, 0xD3515C2831559A83}, // 1e-268
    {0xE858790AFE9486C2, 0x8412D9991ED58091}, // 1e-267
    {0x626E974DBE39A872, 0xA5178FFF668AE0B6}, // 1e-266
    {0xFB0A3D212DC8128F, 0xCE5D73FF402D98E3}, // 1e-265
    {0x7CE66634BC9D0B99, 0x80FA687F881C7F8E}, // 1e-264
    {0x1C1FFFC1EBC44E80, 0xA139029F6A239F72}, // 1e-263
    {0xA327FFB266B56220, 0xC987434744AC874E}, // 1e-262
    {0x4BF1FF9F0062BAA8, 0xFBE9141915D7A922}, // 1e-261
    {0x6F773FC3603DB4A9, 0x9D71AC8FADA6C9B5}, // 1e-260
    {0xCB550FB4384D21D3, 0xC4CE17B399107C22}, // 1e-259
    {0x7E2A53A146606A48, 0xF6019DA07F549B2B}, // 1e-258
    {0x2EDA7444CBFC426D, 0x99C102844F94E0FB}, // 1e-257
    {0xFA911155FEFB5308, 0xC0314325637A1939}, // 1e-256
    {0x793555AB7EBA27CA, 0xF03D93EEBC589F88}, // 1e-255
    {0x4BC1558B2F3458DE, 0x96267C7535B763B5}, // 1e-254
    {0x9EB1AAEDFB016F16, 0xBBB01B9283253CA2}, // 1e-253
    {0x465E15A979C1CADC, 0xEA9C227723EE8BCB}, // 1e-252
    {0x0BFACD89EC191EC9, 0x92A1958A7675175F}, // 1e-251
    {0xCEF980EC671F667B, 0xB749FAED14125D36}, // 1e-250
    {0x82B7E12780E7401A, 0xE51C79A85916F484}, // 1e-249
    {0xD1B2ECB8B0908810, 0x8F31CC0937AE58D2}, // 1e-248
    {0x861FA7E6DCB4AA15, 0xB2FE3F0B8599EF07}, // 1e-247
    {0x67A791E093E1D49A, 0xDFBDCECE67006AC9}, // 1e-246
    {0xE0C8BB2C5C6D24E0, 0x8BD6A141006042BD}, // 1e-245
    {0x58FAE9F773886E18, 0xAECC49914078536D}, // 1e-244
    {0xAF39A475506A899E, 0xDA7F5BF590966848}, // 1e-243
    {0x6D8406C952429603, 0x888F99797A5E012D}, // 1e-242
    {0xC8E5087BA6D33B83, 0xAAB37FD7D8F58178}, // 1e-241
    {0xFB1E4A9A90880A64, 0xD5605FCDCF32E1D6}, // 1e-240
    {0x5CF2EEA09A55067F, 0x855C3BE0A17FCD26}, // 1e-239
    {0xF42FAA48C0EA481E, 0xA6B34AD8C9DFC06F}, // 1e-238
    {0xF13B94DAF124DA26, 0xD0601D8EFC57B08B}, // 1e-237
    {0x76C53D08D6B70858, 0x823C12795DB6CE57}, // 1e-236
    {0x54768C4B0C64CA6E, 0xA2CB1717B52481ED}, // 1e-235
    {0xA9942F5DCF7DFD09, 0xCB7DDCDDA26DA268}, // 1e-234
    {0xD3F93B35435D7C4C, 0xFE5D54150B090B02}, // 1e-233
    {0xC47BC5014A1A6DAF, 0x9EFA548D26E5A6E1}, // 1e-232
    {0x359AB6419CA1091B, 0xC6B8E9B0709F109A}, // 1e-231
    {0xC30163D203C94B62, 0xF867241C8CC6D4C0}, // 1e-230
    {0x79E0DE63425DCF1D, 0x9B407691D7FC44F8}, // 1e-229
    {0x985915FC12F542E4, 0xC21094364DFB5636}, // 1e-228
    {0x3E6F5B7B17B2939D, 0xF294B943E17A2BC4}, // 1e-227
    {0xA705992CEECF9C42, 0x979CF3CA6CEC5B5A}, // 1e-226
    {0x50C6FF782A838353, 0xBD8430BD08277231}, // 1e-225
    {0xA4F8BF5635246428, 0xECE53CEC4A314EBD}, // 1e-224
    {0x871B7795E136BE99, 0x940F4613AE5ED136}, // 1e-223
    {0x28E2557B59846E3F, 0xB913179899F68584}, // 1e-222
    {0x331AEADA2FE589CF, 0xE757DD7EC07426E5}, // 1e-221
    {0x3FF0D2C85DEF7621, 0x9096EA6F3848984F}, // 1e-220
    {0x0FED077A756B53A9, 0xB4BCA50B065ABE63}, // 1e-219
    {0xD3E8495912C62894, 0xE1EBCE4DC7F16DFB}, // 1e-218
    {0x64712DD7ABBBD95C, 0x8D3360F09CF6E4BD}, // 1e-217
    {0xBD8D794D96AACFB3, 0xB080392CC4349DEC}, // 1e-216
    {0xECF0D7A0FC5583A0, 0xDCA04777F541C567}, // 1e-215
    {0xF41686C49DB57244, 0x89E42CAAF9491B60}, // 1e-214
    {0x311C2875C522CED5, 0xAC5D37D5B79B6239}, // 1e-213
    {0x7D633293366B828B, 0xD77485CB25823AC7}, // 1e-212
    {0xAE5DFF9C02033197, 0x86A8D39EF77164BC}, // 1e-211
    {0xD9F57F830283FDFC, 0xA8530886B54DBDEB}, // 1e-210
    {0xD072DF63C324FD7B, 0xD267CAA862A12D66}, // 1e-209
    {0x4247CB9E59F71E6D, 0x8380DEA93DA4BC60}, // 1e-208
    {0x52D9BE85F074E608, 0xA46116538D0DEB78}, // 1e-207
    {0x67902E276C921F8B, 0xCD795BE870516656}, // 1e-206
    {0x00BA1CD8A3DB53B6, 0x806BD9714632DFF6}, // 1e-205
    {0x80E8A40ECCD228A4, 0xA086CFCD97BF97F3}, // 1e-204
    {0x6122CD128006B2CD, 0xC8A883C0FDAF7DF0}, // 1e-203
    {0x796B805720085F81, 0xFAD2A4B13D1B5D6C}, // 1e-202
    {0xCBE3303674053BB0, 0x9CC3A6EEC6311A63}, // 1e-201
    {0xBEDBFC4411068A9C, 0xC3F490AA77BD60FC}, // 1e-200
    {0xEE92FB5515482D44, 0xF4F1B4D515ACB93B}, // 1e-199
    {0x751BDD152D4D1C4A, 0x991711052D8BF3C5}, // 1e-198
    {0xD262D45A78A0635D, 0xBF5CD54678EEF0B6}, // 1e-197
    {0x86FB897116C87C34, 0xEF340A98172AACE4}, // 1e-196
    {0xD45D35E6AE3D4DA0, 0x9580869F0E7AAC0E}, // 1e-195
    {0x8974836059CCA109, 0xBAE0A846D2195712}, // 1e-194
    {0x2BD1A438703FC94B, 0xE998D258869FACD7}, // 1e-193
    {0x7B6306A34627DDCF, 0x91FF83775423CC06}, // 1e-192
    {0x1A3BC84C17B1D542, 0xB67F6455292CBF08}, // 1e-191
    {0x20CABA5F1D9E4A93, 0xE41F3D6A7377EECA}, // 1e-190
    {0x547EB47B7282EE9C, 0x8E938662882AF53E}, // 1e-189
    {0xE99E619A4F23AA43, 0xB23867FB2A35B28D}, // 1e-188
    {0x6405FA00E2EC94D4, 0xDEC681F9F4C31F31}, // 1e-187
    {0xDE83BC408DD3DD04, 0x8B3C113C38F9F37E}, // 1e-186
    {0x9624AB50B148D445, 0xAE0B158B4738705E}, // 1e-185
    {0x3BADD624DD9B0957, 0xD98DDAEE19068C76}, // 1e-184
    {0xE54CA5D70A80E5D6, 0x87F8A8D4CFA417C9}, // 1e-183
    {0x5E9FCF4CCD211F4C, 0xA9F6D30A038D1DBC}, // 1e-182
    {0x7647C3200069671F, 0xD47487CC8470652B}, // 1e-181
    {0x29ECD9F40041E073, 0x84C8D4DFD2C63F3B}, // 1e-180
    {0xF468107100525890, 0xA5FB0A17C777CF09}, // 1e-179
    {0x7182148D4066EEB4, 0xCF79CC9DB955C2CC}, // 1e-178
    {0xC6F14CD848405530, 0x81AC1FE293D599BF}, // 1e-177
    {0xB8ADA00E5A506A7C, 0xA21727DB38CB002F}, // 1e-176
    {0xA6D90811F0E4851C, 0xCA9CF1D206FDC03B}, // 1e-175
    {0x908F4A166D1DA663, 0xFD442E4688BD304A}, // 1e-174
    {0x9A598E4E043287FE, 0x9E4A9CEC15763E2E}, // 1e-173
    {0x40EFF1E1853F29FD, 0xC5DD44271AD3CDBA}, // 1e-172
    {0xD12BEE59E68EF47C, 0xF7549530E188C128}, // 1e-171
    {0x82BB74F8301958CE, 0x9A94DD3E8CF578B9}, // 1e-170
    {0xE36A52363C1FAF01, 0xC13A148E3032D6E7}, // 1e-169
    {0xDC44E6C3CB279AC1, 0xF18899B1BC3F8CA1}, // 1e-168
    {0x29AB103A5EF8C0B9, 0x96F5600F15A7B7E5}, // 1e-167
    {0x7415D448F6B6F0E7, 0xBCB2B812DB11A5DE}, // 1e-166
    {0x111B495B3464AD21, 0xEBDF661791D60F56}, // 1e-165
    {0xCAB10DD900BEEC34, 0x936B9FCEBB25C995}, // 1e-164
    {0x3D5D514F40EEA742, 0xB84687C269EF3BFB}, // 1e-163
    {0x0CB4A5A3112A5112, 0xE65829B3046B0AFA}, // 1e-162
    {0x47F0E785EABA72AB, 0x8FF71A0FE2C2E6DC}, // 1e-161
    {0x59ED216765690F56, 0xB3F4E093DB73A093}, // 1e-160
    {0x306869C13EC3532C, 0xE0F218B8D25088B8}, // 1e-159
    {0x1E414218C73A13FB, 0x8C974F7383725573}, // 1e-158
    {0xE5D1929EF90898FA, 0xAFBD2350644EEACF}, // 1e-157
    {0xDF45F746B74ABF39, 0xDBAC6C247D62A583}, // 1e-156
    {0x6B8BBA8C328EB783, 0x894BC396CE5DA772}, // 1e-155
    {0x066EA92F3F326564, 0xAB9EB47C81F5114F}, // 1e-154
    {0xC80A537B0EFEFEBD, 0xD686619BA27255A2}, // 1e-153
    {0xBD06742CE95F5F36, 0x8613FD0145877585}, // 1e-152
    {0x2C48113823B73704, 0xA798FC4196E952E7}, // 1e-151
    {0xF75A15862CA504C5, 0xD17F3B51FCA3A7A0}, // 1e-150
    {0x9A984D73DBE722FB, 0x82EF85133DE648C4}, // 1e-149
    {0xC13E60D0D2E0EBBA, 0xA3AB66580D5FDAF5}, // 1e-148
    {0x318DF905079926A8, 0xCC963FEE10B7D1B3}, // 1e-147
    {0xFDF17746497F7052, 0xFFBBCFE994E5C61F}, // 1e-146
    {0xFEB6EA8BEDEFA633, 0x9FD561F1FD0F9BD3}, // 1e-145
    {0xFE64A52EE96B8FC0, 0xC7CABA6E7C5382C8}, // 1e-144
    {0x3DFDCE7AA3C673B0, 0xF9BD690A1B68637B}, // 1e-143
    {0x06BEA10CA65C084E, 0x9C1661A651213E2D}, // 1e-142
    {0x486E494FCFF30A62, 0xC31BFA0FE5698DB8}, // 1e-141
    {0x5A89DBA3C3EFCCFA, 0xF3E2F893DEC3F126}, // 1e-140
    {0xF89629465A75E01C, 0x986DDB5C6B3A76B7}, // 1e-139
    {0xF6BBB397F1135823, 0xBE89523386091465}, // 1e-138
    {0x746AA07DED582E2C, 0xEE2BA6C0678B597F}, // 1e-137
    {0xA8C2A44EB4571CDC, 0x94DB483840B717EF}, // 1e-136
    {0x92F34D62616CE413, 0xBA121A4650E4DDEB}, // 1e-135
    {0x77B020BAF9C81D17, 0xE896A0D7E51E1566}, // 1e-134
    {0x0ACE1474DC1D122E, 0x915E2486EF32CD60}, // 1e-133
    {0x0D819992132456BA, 0xB5B5ADA8AAFF80B8}, // 1e-132
    {0x10E1FFF697ED6C69, 0xE3231912D5BF60E6}, // 1e-131
    {0xCA8D3FFA1EF463C1, 0x8DF5EFABC5979C8F}, // 1e-130
    {0xBD308FF8A6B17CB2, 0xB1736B96B6FD83B3}, // 1e-129
    {0xAC7CB3F6D05DDBDE, 0xDDD0467C64BCE4A0}, // 1e-128
    {0x6BCDF07A423AA96B, 0x8AA22C0DBEF60EE4}, // 1e-127
    {0x86C16C98D2C953C6, 0xAD4AB7112EB3929D}, // 1e-126
    {0xE871C7BF077BA8B7, 0xD89D64D57A607744}, // 1e-125
    {0x11471CD764AD4972, 0x87625F056C7C4A8B}, // 1e-124
    {0xD598E40D3DD89BCF, 0xA93AF6C6C79B5D2D}, // 1e-123
    {0x4AFF1D108D4EC2C3, 0xD389B47879823479}, // 1e-122
    {0xCEDF722A585139BA, 0x843610CB4BF160CB}, // 1e-121
    {0xC2974EB4EE658828, 0xA54394FE1EEDB8FE}, // 1e-120
    {0x733D226229FEEA32, 0xCE947A3DA6A9273E}, // 1e-119
    {0x0806357D5A3F525F, 0x811CCC668829B887}, // 1e-118
    {0xCA07C2DCB0CF26F7, 0xA163FF802A3426A8}, // 1e-117
    {0xFC89B393DD02F0B5, 0xC9BCFF6034C13052}, // 1e-116
    {0xBBAC2078D443ACE2, 0xFC2C3F3841F17C67}, // 1e-115
    {0xD54B944B84AA4C0D, 0x9D9BA7832936EDC0}, // 1e-114
    {0x0A9E795E65D4DF11, 0xC5029163F384A931}, // 1e-113
    {0x4D4617B5FF4A16D5, 0xF64335BCF065D37D}, // 1e-112
    {0x504BCED1BF8E4E45, 0x99EA0196163FA42E}, // 1e-111
    {0xE45EC2862F71E1D6, 0xC06481FB9BCF8D39}, // 1e-110
    {0x5D767327BB4E5A4C, 0xF07DA27A82C37088}, // 1e-109
    {0x3A6A07F8D510F86F, 0x964E858C91BA2655}, // 1e-108
    {0x890489F70A55368B, 0xBBE226EFB628AFEA}, // 1e-107
    {0x2B45AC74CCEA842E, 0xEADAB0ABA3B2DBE5}, // 1e-106
    {0x3B0B8BC90012929D, 0x92C8AE6B464FC96F}, // 1e-105
    {0x09CE6EBB40173744, 0xB77ADA0617E3BBCB}, // 1e-104
    {0xCC420A6A101D0515, 0xE55990879DDCAABD}, // 1e-103
    {0x9FA946824A12232D, 0x8F57FA54C2A9EAB6}, // 1e-102
    {0x47939822DC96ABF9, 0xB32DF8E9F3546564}, // 1e-101
    {0x59787E2B93BC56F7, 0xDFF9772470297EBD}, // 1e-100
    {0x57EB4EDB3C55B65A, 0x8BFBEA76C619EF36}, // 1e-99
    {0xEDE622920B6B23F1, 0xAEFAE51477A06B03}, // 1e-98
    {0xE95FAB368E45ECED, 0xDAB99E59958885C4}, // 1e-97
    {0x11DBCB0218EBB414, 0x88B402F7FD75539B}, // 1e-96
    {0xD652BDC29F26A119, 0xAAE103B5FCD2A881}, // 1e-95
    {0x4BE76D3346F0495F, 0xD59944A37C0752A2}, // 1e-94
    {0x6F70A4400C562DDB, 0x857FCAE62D8493A5}, // 1e-93
    {0xCB4CCD500F6BB952, 0xA6DFBD9FB8E5B88E}, // 1e-92
    {0x7E2000A41346A7A7, 0xD097AD07A71F26B2}, // 1e-91
    {0x8ED400668C0C28C8, 0x825ECC24C873782F}, // 1e-90
    {0x728900802F0F32FA, 0xA2F67F2DFA90563B}, // 1e-89
    {0x4F2B40A03AD2FFB9, 0xCBB41EF979346BCA}, // 1e-88
    {0xE2F610C84987BFA8, 0xFEA126B7D78186BC}, // 1e-87
    {0x0DD9CA7D2DF4D7C9, 0x9F24B832E6B0F436}, // 1e-86
    {0x91503D1C79720DBB, 0xC6EDE63FA05D3143}, // 1e-85
    {0x75A44C6397CE912A, 0xF8A95FCF88747D94}, // 1e-84
    {0xC986AFBE3EE11ABA, 0x9B69DBE1B548CE7C}, // 1e-83
    {0xFBE85BADCE996168, 0xC24452DA229B021B}, // 1e-82
    {0xFAE27299423FB9C3, 0xF2D56790AB41C2A2}, // 1e-81
    {0xDCCD879FC967D41A, 0x97C560BA6B0919A5}, // 1e-80
    {0x5400E987BBC1C920, 0xBDB6B8E905CB600F}, // 1e-79
    {0x290123E9AAB23B68, 0xED246723473E3813}, // 1e-78
    {0xF9A0B6720AAF6521, 0x9436C0760C86E30B}, // 1e-77
    {0xF808E40E8D5B3E69, 0xB94470938FA89BCE}, // 1e-76
    {0xB60B1D1230B20E04, 0xE7958CB87392C2C2}, // 1e-75
    {0xB1C6F22B5E6F48C2, 0x90BD77F3483BB9B9}, // 1e-74
    {0x1E38AEB6360B1AF3, 0xB4ECD5F01A4AA828}, // 1e-73
    {0x25C6DA63C38DE1B0, 0xE2280B6C20DD5232}, // 1e-72
    {0x579C487E5A38AD0E, 0x8D590723948A535F}, // 1e-71
    {0x2D835A9DF0C6D851, 0xB0AF48EC79ACE837}, // 1e-70
    {0xF8E431456CF88E65, 0xDCDB1B2798182244}, // 1e-69
    {0x1B8E9ECB641B58FF, 0x8A08F0F8BF0F156B}, // 1e-68
    {0xE272467E3D222F3F, 0xAC8B2D36EED2DAC5}, // 1e-67
    {0x5B0ED81DCC6ABB0F, 0xD7ADF884AA879177}, // 1e-66
    {0x98E947129FC2B4E9, 0x86CCBB52EA94BAEA}, // 1e-65
    {0x3F2398D747B36224, 0xA87FEA27A539E9A5}, // 1e-64
    {0x8EEC7F0D19A03AAD, 0xD29FE4B18E88640E}, // 1e-63
    {0x1953CF68300424AC, 0x83A3EEEEF9153E89}, // 1e-62
    {0x5FA8C3423C052DD7, 0xA48CEAAAB75A8E2B}, // 1e-61
    {0x3792F412CB06794D, 0xCDB02555653131B6}, // 1e-60
    {0xE2BBD88BBEE40BD0, 0x808E17555F3EBF11}, // 1e-59
    {0x5B6ACEAEAE9D0EC4, 0xA0B19D2AB70E6ED6}, // 1e-58
    {0xF245825A5A445275, 0xC8DE047564D20A8B}, // 1e-57
    {0xEED6E2F0F0D56712, 0xFB158592BE068D2E}, // 1e-56
    {0x55464DD69685606B, 0x9CED737BB6C4183D}, // 1e-55
    {0xAA97E14C3C26B886, 0xC428D05AA4751E4C}, // 1e-54
    {0xD53DD99F4B3066A8, 0xF53304714D9265DF}, // 1e-53
    {0xE546A8038EFE4029, 0x993FE2C6D07B7FAB}, // 1e-52
    {0xDE98520472BDD033, 0xBF8FDB78849A5F96}, // 1e-51
    {0x963E66858F6D4440, 0xEF73D256A5C0F77C}, // 1e-50
    {0xDDE7001379A44AA8, 0x95A8637627989AAD}, // 1e-49
    {0x5560C018580D5D52, 0xBB127C53B17EC159}, // 1e-48
    {0xAAB8F01E6E10B4A6, 0xE9D71B689DDE71AF}, // 1e-47
    {0xCAB3961304CA70E8, 0x9226712162AB070D}, // 1e-46
    {0x3D607B97C5FD0D22, 0xB6B00D69BB55C8D1}, // 1e-45
    {0x8CB89A7DB77C506A, 0xE45C10C42A2B3B05}, // 1e-44
    {0x77F3608E92ADB242, 0x8EB98A7A9A5B04E3}, // 1e-43
    {0x55F038B237591ED3, 0xB267ED1940F1C61C}, // 1e-42
    {0x6B6C46DEC52F6688, 0xDF01E85F912E37A3}, // 1e-41
    {0x2323AC4B3B3DA015, 0x8B61313BBABCE2C6}, // 1e-40
    {0xABEC975E0A0D081A, 0xAE397D8AA96C1B77}, // 1e-39
    {0x96E7BD358C904A21, 0xD9C7DCED53C72255}, // 1e-38
    {0x7E50D64177DA2E54, 0x881CEA14545C7575}, // 1e-37
    {0xDDE50BD1D5D0B9E9, 0xAA242499697392D2}, // 1e-36
    {0x955E4EC64B44E864, 0xD4AD2DBFC3D07787}, // 1e-35
    {0xBD5AF13BEF0B113E, 0x84EC3C97DA624AB4}, // 1e-34
    {0xECB1AD8AEACDD58E, 0xA6274BBDD0FADD61}, // 1e-33
    {0x67DE18EDA5814AF2, 0xCFB11EAD453994BA}, // 1e-32
    {0x80EACF948770CED7, 0x81CEB32C4B43FCF4}, // 1e-31
    {0xA1258379A94D028D, 0xA2425FF75E14FC31}, // 1e-30
    {0x096EE45813A04330, 0xCAD2F7F5359A3B3E}, // 1e-29
    {0x8BCA9D6E188853FC, 0xFD87B5F28300CA0D}, // 1e-28
    {0x775EA264CF55347D, 0x9E74D1B791E07E48}, // 1e-27
    {0x95364AFE032A819D, 0xC612062576589DDA}, // 1e-26
    {0x3A83DDBD83F52204, 0xF79687AED3EEC551}, // 1e-25
    {0xC4926A9672793542, 0x9ABE14CD44753B52}, // 1e-24
    {0x75B7053C0F178293, 0xC16D9A0095928A27}, // 1e-23
    {0x5324C68B12DD6338, 0xF1C90080BAF72CB1}, // 1e-22
    {0xD3F6FC16EBCA5E03, 0x971DA05074DA7BEE}, // 1e-21
    {0x88F4BB1CA6BCF584, 0xBCE5086492111AEA}, // 1e-20
    {0x2B31E9E3D06C32E5, 0xEC1E4A7DB69561A5}, // 1e-19
    {0x3AFF322E62439FCF, 0x9392EE8E921D5D07}, // 1e-18
    {0x09BEFEB9FAD487C2, 0xB877AA3236A4B449}, // 1e-17
    {0x4C2EBE687989A9B3, 0xE69594BEC44DE15B}, // 1e-16
    {0x0F9D37014BF60A10, 0x901D7CF73AB0ACD9}, // 1e-15
    {0x538484C19EF38C94, 0xB424DC35095CD80F}, // 1e-14
    {0x2865A5F206B06FB9, 0xE12E13424BB40E13}, // 1e-13
    {0xF93F87B7442E45D3, 0x8CBCCC096F5088CB}, // 1e-12
    {0xF78F69A51539D748, 0xAFEBFF0BCB24AAFE}, // 1e-11
    {0xB573440E5A884D1B, 0xDBE6FECEBDEDD5BE}, // 1e-10
    {0x31680A88F8953030, 0x89705F4136B4A597}, // 1e-9
    {0xFDC20D2B36BA7C3D, 0xABCC77118461CEFC}, // 1e-8
    {0x3D32907604691B4C, 0xD6BF94D5E57A42BC}, // 1e-7
    {0xA63F9A49C2C1B10F, 0x8637BD05AF6C69B5}, // 1e-6
    {0x0FCF80DC33721D53, 0xA7C5AC471B478423}, // 1e-5
    {0xD3C36113404EA4A8, 0xD1B71758E219652B}, // 1e-4
    {0x645A1CAC083126E9, 0x83126E978D4FDF3B}, // 1e-3
    {0x3D70A3D70A3D70A3, 0xA3D70A3D70A3D70A}, // 1e-2
    {0xCCCCCCCCCCCCCCCC, 0xCCCCCCCCCCCCCCCC}, // 1e-1
    {0x0000000000000000, 0x8000000000000000}, // 1e0
    {0x0000000000000000, 0xA000000000000000}, // 1e1
    {0x0000000000000000, 0xC800000000000000}, // 1e2
    {0x0000000000000000, 0xFA00000000000000}, // 1e3
    {0x0000000000000000, 0x9C40000000000000}, // 1e4
    {0x0000000000000000, 0xC350000000000000}, // 1e5
    {0x0000000000000000, 0xF424000000000000}, // 1e6
    {0x0000000000000000, 0x9896800000000000}, // 1e7
    {0x0000000000000000, 0xBEBC200000000000}, // 1e8
    {0x0000000000000000, 0xEE6B280000000000}, // 1e9
    {0x0000000000000000, 0x9502F90000000000}, // 1e10
    {0x0000000000000000, 0xBA43B74000000000}, // 1e11
    {0x0000000000000000, 0xE8D4A51000000000}, // 1e12
    {0x0000000000000000, 0x9184E72A00000000}, // 1e13
    {0x0000000000000000, 0xB5E620F480000000}, // 1e14
    {0x0000000000000000, 0xE35FA931A0000000}, // 1e15
    {0x0000000000000000, 0x8E1BC9BF04000000}, // 1e16
    {0x0000000000000000, 0xB1A2BC2EC5000000}, // 1e17
    {0x0000000000000000, 0xDE0B6B3A76400000}, // 1e18
    {0x0000000000000000, 0x8AC7230489E80000}, // 1e19
    {0x0000000000000000, 0xAD78EBC5AC620000}, // 1e20
    {0x0000000000000000, 0xD8D726B7177A8000}, // 1e21
    {0x0000000000000000, 0x878678326EAC9000}, // 1e22
    {0x0000000000000000, 0xA968163F0A57B400}, // 1e23
    {0x0000000000000000, 0xD3C21BCECCEDA100}, // 1e24
    {0x0000000000000000, 0x84595161401484A0}, // 1e25
    {0x0000000000000000, 0xA56FA5B99019A5C8}, // 1e26
    {0x0000000000000000, 0xCECB8F27F4200F3A}, // 1e27
    {0x4000000000000000, 0x813F3978F8940984}, // 1e28
    {0x5000000000000000, 0xA18F07D736B90BE5}, // 1e29
    {0xA400000000000000, 0xC9F2C9CD04674EDE}, // 1e30
    {0x4D00000000000000, 0xFC6F7C4045812296}, // 1e31
    {0xF020000000000000, 0x9DC5ADA82B70B59D}, // 1e32
    {0x6C28000000000000, 0xC5371912364CE305}, // 1e33
    {0xC732000000000000, 0xF684DF56C3E01BC6}, // 1e34
    {0x3C7F400000000000, 0x9A130B963A6C115C}, // 1e35
    {0x4B9F100000000000, 0xC097CE7BC90715B3}, // 1e36
    {0x1E86D40000000000, 0xF0BDC21ABB48DB20}, // 1e37
    {0x1314448000000000, 0x96769950B50D88F4}, // 1e38
    {0x17D955A000000000, 0xBC143FA4E250EB31}, // 1e39
    {0x5DCFAB0800000000, 0xEB194F8E1AE525FD}, // 1e40
    {0x5AA1CAE500000000, 0x92EFD1B8D0CF37BE}, // 1e41
    {0xF14A3D9E40000000, 0xB7ABC627050305AD}, // 1e42
    {0x6D9CCD05D0000000, 0xE596B7B0C643C719}, // 1e43
    {0xE4820023A2000000, 0x8F7E32CE7BEA5C6F}, // 1e44
    {0xDDA2802C8A800000, 0xB35DBF821AE4F38B}, // 1e45
    {0xD50B2037AD200000, 0xE0352F62A19E306E}, // 1e46
    {0x4526F422CC340000, 0x8C213D9DA502DE45}, // 1e47
    {0x9670B12B7F410000, 0xAF298D050E4395D6}, // 1e48
    {0x3C0CDD765F114000, 0xDAF3F04651D47B4C}, // 1e49
    {0xA5880A69FB6AC800, 0x88D8762BF324CD0F}, // 1e50
    {0x8EEA0D047A457A00, 0xAB0E93B6EFEE0053}, // 1e51
    {0x72A4904598D6D880, 0xD5D238A4ABE98068}, // 1e52
    {0x47A6DA2B7F864750, 0x85A36366EB71F041}, // 1e53
    {0x999090B65F67D924, 0xA70C3C40A64E6C51}, // 1e54
    {0xFFF4B4E3F741CF6D, 0xD0CF4B50CFE20765}, // 1e55
    {0xBFF8F10E7A8921A4, 0x82818F1281ED449F}, // 1e56
    {0xAFF72D52192B6A0D, 0xA321F2D7226895C7}, // 1e57
    {0x9BF4F8A69F764490, 0xCBEA6F8CEB02BB39}, // 1e58
    {0x02F236D04753D5B4, 0xFEE50B7025C36A08}, // 1e59
    {0x01D762422C946590, 0x9F4F2726179A2245}, // 1e60
    {0x424D3AD2B7B97EF5, 0xC722F0EF9D80AAD6}, // 1e61
    {0xD2E0898765A7DEB2, 0xF8EBAD2B84E0D58B}, // 1e62
    {0x63CC55F49F88EB2F, 0x9B934C3B330C8577}, // 1e63
    {0x3CBF6B71C76B25FB, 0xC2781F49FFCFA6D5}, // 1e64
    {0x8BEF464E3945EF7A, 0xF316271C7FC3908A}, // 1e65
    {0x97758BF0E3CBB5AC, 0x97EDD871CFDA3A56}, // 1e66
    {0x3D52EEED1CBEA317, 0xBDE94E8E43D0C8EC}, // 1e67
    {0x4CA7AAA863EE4BDD, 0xED63A231D4C4FB27}, // 1e68
    {0x8FE8CAA93E74EF6A, 0x945E455F24FB1CF8}, // 1e69
    {0xB3E2FD538E122B44, 0xB975D6B6EE39E436}, // 1e70
    {0x60DBBCA87196B616, 0xE7D34C64A9C85D44}, // 1e71
    {0xBC8955E946FE31CD, 0x90E40FBEEA1D3A4A}, // 1e72
    {0x6BABAB6398BDBE41, 0xB51D13AEA4A488DD}, // 1e73
    {0xC696963C7EED2DD1, 0xE264589A4DCDAB14}, // 1e74
    {0xFC1E1DE5CF543CA2, 0x8D7EB76070A08AEC}, // 1e75
    {0x3B25A55F43294BCB, 0xB0DE65388CC8ADA8}, // 1e76
    {0x49EF0EB713F39EBE, 0xDD15FE86AFFAD912}, // 1e77
    {0x6E3569326C784337, 0x8A2DBF142DFCC7AB}, // 1e78
    {0x49C2C37F07965404, 0xACB92ED9397BF996}, // 1e79
    {0xDC33745EC97BE906, 0xD7E77A8F87DAF7FB}, // 1e80
    {0x69A028BB3DED71A3, 0x86F0AC99B4E8DAFD}, // 1e81
    {0xC40832EA0D68CE0C, 0xA8ACD7C0222311BC}, // 1e82
    {0xF50A3FA490C30190, 0xD2D80DB02AABD62B}, // 1e83
    {0x792667C6DA79E0FA, 0x83C7088E1AAB65DB}, // 1e84
    {0x577001B891185938, 0xA4B8CAB1A1563F52}, // 1e85
    {0xED4C0226B55E6F86, 0xCDE6FD5E09ABCF26}, // 1e86
    {0x544F8158315B05B4, 0x80B05E5AC60B6178}, // 1e87
    {0x696361AE3DB1C721, 0xA0DC75F1778E39D6}, // 1e88
    {0x03BC3A19CD1E38E9, 0xC913936DD571C84C}, // 1e89
    {0x04AB48A04065C723, 0xFB5878494ACE3A5F}, // 1e90
    {0x62EB0D64283F9C76, 0x9D174B2DCEC0E47B}, // 1e91
    {0x3BA5D0BD324F8394, 0xC45D1DF942711D9A}, // 1e92
    {0xCA8F44EC7EE36479, 0xF5746577930D6500}, // 1e93
    {0x7E998B13CF4E1ECB, 0x9968BF6ABBE85F20}, // 1e94
    {0x9E3FEDD8C321A67E, 0xBFC2EF456AE276E8}, // 1e95
    {0xC5CFE94EF3EA101E, 0xEFB3AB16C59B14A2}, // 1e96
    {0xBBA1F1D158724A12, 0x95D04AEE3B80ECE5}, // 1e97
    {0x2A8A6E45AE8EDC97, 0xBB445DA9CA61281F}, // 1e98
    {0xF52D09D71A3293BD, 0xEA1575143CF97226}, // 1e99
    {0x593C2626705F9C56, 0x924D692CA61BE758}, // 1e100
    {0x6F8B2FB00C77836C, 0xB6E0C377CFA2E12E}, // 1e101
    {0x0B6DFB9C0F956447, 0xE498F455C38B997A}, // 1e102
    {0x4724BD4189BD5EAC, 0x8EDF98B59A373FEC}, // 1e103
    {0x58EDEC91EC2CB657, 0xB2977EE300C50FE7}, // 1e104
    {0x2F2967B66737E3ED, 0xDF3D5E9BC0F653E1}, // 1e105
    {0xBD79E0D20082EE74, 0x8B865B215899F46C}, // 1e106
    {0xECD8590680A3AA11, 0xAE67F1E9AEC07187}, // 1e107
    {0xE80E6F4820CC9495, 0xDA01EE641A708DE9}, // 1e108
    {0x3109058D147FDCDD, 0x884134FE908658B2}, // 1e109
    {0xBD4B46F0599FD415, 0xAA51823E34A7EEDE}, // 1e110
    {0x6C9E18AC7007C91A, 0xD4E5E2CDC1D1EA96}, // 1e111
    {0x03E2CF6BC604DDB0, 0x850FADC09923329E}, // 1e112
    {0x84DB8346B786151C, 0xA6539930BF6BFF45}, // 1e113
    {0xE612641865679A63, 0xCFE87F7CEF46FF16}, // 1e114
    {0x4FCB7E8F3F60C07E, 0x81F14FAE158C5F6E}, // 1e115
    {0xE3BE5E330F38F09D, 0xA26DA3999AEF7749}, // 1e116
    {0x5CADF5BFD3072CC5, 0xCB090C8001AB551C}, // 1e117
    {0x73D9732FC7C8F7F6, 0xFDCB4FA002162A63}, // 1e118
    {0x2867E7FDDCDD9AFA, 0x9E9F11C4014DDA7E}, // 1e119
    {0xB281E1FD541501B8, 0xC646D63501A1511D}, // 1e120
    {0x1F225A7CA91A4226, 0xF7D88BC24209A565}, // 1e121
    {0x3375788DE9B06958, 0x9AE757596946075F}, // 1e122
    {0x0052D6B1641C83AE, 0xC1A12D2FC3978937}, // 1e123
    {0xC0678C5DBD23A49A, 0xF209787BB47D6B84}, // 1e124
    {0xF840B7BA963646E0, 0x9745EB4D50CE6332}, // 1e125
    {0xB650E5A93BC3D898, 0xBD176620A501FBFF}, // 1e126
    {0xA3E51F138AB4CEBE, 0xEC5D3FA8CE427AFF}, // 1e127
    {0xC66F336C36B10137, 0x93BA47C980E98CDF}, // 1e128
    {0xB80B0047445D4184, 0xB8A8D9BBE123F017}, // 1e129
    {0xA60DC059157491E5, 0xE6D3102AD96CEC1D}, // 1e130
    {0x87C89837AD68DB2F, 0x9043EA1AC7E41392}, // 1e131
    {0x29BABE4598C311FB, 0xB454E4A179DD1877}, // 1e132
    {0xF4296DD6FEF3D67A, 0xE16A1DC9D8545E94}, // 1e133
    {0x1899E4A65F58660C, 0x8CE2529E2734BB1D}, // 1e134
    {0x5EC05DCFF72E7F8F, 0xB01AE745B101E9E4}, // 1e135
    {0x76707543F4FA1F73, 0xDC21A1171D42645D}, // 1e136
    {0x6A06494A791C53A8, 0x899504AE72497EBA}, // 1e137
    {0x0487DB9D17636892, 0xABFA45DA0EDBDE69}, // 1e138
    {0x45A9D2845D3C42B6, 0xD6F8D7509292D603}, // 1e139
    {0x0B8A2392BA45A9B2, 0x865B86925B9BC5C2}, // 1e140
    {0x8E6CAC7768D7141E, 0xA7F26836F282B732}, // 1e141
    {0x3207D795430CD926, 0xD1EF0244AF2364FF}, // 1e142
    {0x7F44E6BD49E807B8, 0x8335616AED761F1F}, // 1e143
    {0x5F16206C9C6209A6, 0xA402B9C5A8D3A6E7}, // 1e144
    {0x36DBA887C37A8C0F, 0xCD036837130890A1}, // 1e145
    {0xC2494954DA2C9789, 0x802221226BE55A64}, // 1e146
    {0xF2DB9BAA10B7BD6C, 0xA02AA96B06DEB0FD}, // 1e147
    {0x6F92829494E5ACC7, 0xC83553C5C8965D3D}, // 1e148
    {0xCB772339BA1F17F9, 0xFA42A8B73ABBF48C}, // 1e149
    {0xFF2A760414536EFB, 0x9C69A97284B578D7}, // 1e150
    {0xFEF5138519684ABA, 0xC38413CF25E2D70D}, // 1e151
    {0x7EB258665FC25D69, 0xF46518C2EF5B8CD1}, // 1e152
    {0xEF2F773FFBD97A61, 0x98BF2F79D5993802}, // 1e153
    {0xAAFB550FFACFD8FA, 0xBEEEFB584AFF8603}, // 1e154
    {0x95BA2A53F983CF38, 0xEEAABA2E5DBF6784}, // 1e155
    {0xDD945A747BF26183, 0x952AB45CFA97A0B2}, // 1e156
    {0x94F971119AEEF9E4, 0xBA756174393D88DF}, // 1e157
    {0x7A37CD5601AAB85D, 0xE912B9D1478CEB17}, // 1e158
    {0xAC62E055C10AB33A, 0x91ABB422CCB812EE}, // 1e159
    {0x577B986B314D6009, 0xB616A12B7FE617AA}, // 1e160
    {0xED5A7E85FDA0B80B, 0xE39C49765FDF9D94}, // 1e161
    {0x14588F13BE847307, 0x8E41ADE9FBEBC27D}, // 1e162
    {0x596EB2D8AE258FC8, 0xB1D219647AE6B31C}, // 1e163
    {0x6FCA5F8ED9AEF3BB, 0xDE469FBD99A05FE3}, // 1e164
    {0x25DE7BB9480D5854, 0x8AEC23D680043BEE}, // 1e165
    {0xAF561AA79A10AE6A, 0xADA72CCC20054AE9}, // 1e166
    {0x1B2BA1518094DA04, 0xD910F7FF28069DA4}, // 1e167
    {0x90FB44D2F05D0842, 0x87AA9AFF79042286}, // 1e168
    {0x353A1607AC744A53, 0xA99541BF57452B28}, // 1e169
    {0x42889B8997915CE8, 0xD3FA922F2D1675F2}, // 1e170
    {0x69956135FEBADA11, 0x847C9B5D7C2E09B7}, // 1e171
    {0x43FAB9837E699095, 0xA59BC234DB398C25}, // 1e172
    {0x94F967E45E03F4BB, 0xCF02B2C21207EF2E}, // 1e173
    {0x1D1BE0EEBAC278F5, 0x8161AFB94B44F57D}, // 1e174
    {0x6462D92A69731732, 0xA1BA1BA79E1632DC}, // 1e175
    {0x7D7B8F7503CFDCFE, 0xCA28A291859BBF93}, // 1e176
    {0x5CDA735244C3D43E, 0xFCB2CB35E702AF78}, // 1e177
    {0x3A0888136AFA64A7, 0x9DEFBF01B061ADAB}, // 1e178
    {0x088AAA1845B8FDD0, 0xC56BAEC21C7A1916}, // 1e179
    {0x8AAD549E57273D45, 0xF6C69A72A3989F5B}, // 1e180
    {0x36AC54E2F678864B, 0x9A3C2087A63F6399}, // 1e181
    {0x84576A1BB416A7DD, 0xC0CB28A98FCF3C7F}, // 1e182
    {0x656D44A2A11C51D5, 0xF0FDF2D3F3C30B9F}, // 1e183
    {0x9F644AE5A4B1B325, 0x969EB7C47859E743}, // 1e184
    {0x873D5D9F0DDE1FEE, 0xBC4665B596706114}, // 1e185
    {0xA90CB506D155A7EA, 0xEB57FF22FC0C7959}, // 1e186
    {0x09A7F12442D588F2, 0x9316FF75DD87CBD8}, // 1e187
    {0x0C11ED6D538AEB2F, 0xB7DCBF5354E9BECE}, // 1e188
    {0x8F1668C8A86DA5FA, 0xE5D3EF282A242E81}, // 1e189
    {0xF96E017D694487BC, 0x8FA475791A569D10}, // 1e190
    {0x37C981DCC395A9AC, 0xB38D92D760EC4455}, // 1e191
    {0x85BBE253F47B1417, 0xE070F78D3927556A}, // 1e192
    {0x93956D7478CCEC8E, 0x8C469AB843B89562}, // 1e193
    {0x387AC8D1970027B2, 0xAF58416654A6BABB}, // 1e194
    {0x06997B05FCC0319E, 0xDB2E51BFE9D0696A}, // 1e195
    {0x441FECE3BDF81F03, 0x88FCF317F22241E2}, // 1e196
    {0xD527E81CAD7626C3, 0xAB3C2FDDEEAAD25A}, // 1e197
    {0x8A71E223D8D3B074, 0xD60B3BD56A5586F1}, // 1e198
    {0xF6872D5667844E49, 0x85C7056562757456}, // 1e199
    {0xB428F8AC016561DB, 0xA738C6BEBB12D16C}, // 1e200
    {0xE13336D701BEBA52, 0xD106F86E69D785C7}, // 1e201
    {0xECC0024661173473, 0x82A45B450226B39C}, // 1e202
    {0x27F002D7F95D0190, 0xA34D721642B06084}, // 1e203
    {0x31EC038DF7B441F4, 0xCC20CE9BD35C78A5}, // 1e204
    {0x7E67047175A15271, 0xFF290242C83396CE}, // 1e205
    {0x0F0062C6E984D386, 0x9F79A169BD203E41}, // 1e206
    {0x52C07B78A3E60868, 0xC75809C42C684DD1}, // 1e207
    {0xA7709A56CCDF8A82, 0xF92E0C3537826145}, // 1e208
    {0x88A66076400BB691, 0x9BBCC7A142B17CCB}, // 1e209
    {0x6ACFF893D00EA435, 0xC2ABF989935DDBFE}, // 1e210
    {0x0583F6B8C4124D43, 0xF356F7EBF83552FE}, // 1e211
    {0xC3727A337A8B704A, 0x98165AF37B2153DE}, // 1e212
    {0x744F18C0592E4C5C, 0xBE1BF1B059E9A8D6}, // 1e213
    {0x1162DEF06F79DF73, 0xEDA2EE1C7064130C}, // 1e214
    {0x8ADDCB5645AC2BA8, 0x9485D4D1C63E8BE7}, // 1e215
    {0x6D953E2BD7173692, 0xB9A74A0637CE2EE1}, // 1e216
    {0xC8FA8DB6CCDD0437, 0xE8111C87C5C1BA99}, // 1e217
    {0x1D9C9892400A22A2, 0x910AB1D4DB9914A0}, // 1e218
    {0x2503BEB6D00CAB4B, 0xB54D5E4A127F59C8}, // 1e219
    {0x2E44AE64840FD61D, 0xE2A0B5DC971F303A}, // 1e220
    {0x5CEAECFED289E5D2, 0x8DA471A9DE737E24}, // 1e221
    {0x7425A83E872C5F47, 0xB10D8E1456105DAD}, // 1e222
    {0xD12F124E28F77719, 0xDD50F1996B947518}, // 1e223
    {0x82BD6B70D99AAA6F, 0x8A5296FFE33CC92F}, // 1e224
    {0x636CC64D1001550B, 0xACE73CBFDC0BFB7B}, // 1e225
    {0x3C47F7E05401AA4E, 0xD8210BEFD30EFA5A}, // 1e226
    {0x65ACFAEC34810A71, 0x8714A775E3E95C78}, // 1e227
    {0x7F1839A741A14D0D, 0xA8D9D1535CE3B396}, // 1e228
    {0x1EDE48111209A050, 0xD31045A8341CA07C}, // 1e229
    {0x934AED0AAB460432, 0x83EA2B892091E44D}, // 1e230
    {0xF81DA84D5617853F, 0xA4E4B66B68B65D60}, // 1e231
    {0x36251260AB9D668E, 0xCE1DE40642E3F4B9}, // 1e232
    {0xC1D72B7C6B426019, 0x80D2AE83E9CE78F3}, // 1e233
    {0xB24CF65B8612F81F, 0xA1075A24E4421730}, // 1e234
    {0xDEE033F26797B627, 0xC94930AE1D529CFC}, // 1e235
    {0x169840EF017DA3B1, 0xFB9B7CD9A4A7443C}, // 1e236
    {0x8E1F289560EE864E, 0x9D412E0806E88AA5}, // 1e237
    {0xF1A6F2BAB92A27E2, 0xC491798A08A2AD4E}, // 1e238
    {0xAE10AF696774B1DB, 0xF5B5D7EC8ACB58A2}, // 1e239
    {0xACCA6DA1E0A8EF29, 0x9991A6F3D6BF1765}, // 1e240
    {0x17FD090A58D32AF3, 0xBFF610B0CC6EDD3F}, // 1e241
    {0xDDFC4B4CEF07F5B0, 0xEFF394DCFF8A948E}, // 1e242
    {0x4ABDAF101564F98E, 0x95F83D0A1FB69CD9}, // 1e243
    {0x9D6D1AD41ABE37F1, 0xBB764C4CA7A4440F}, // 1e244
    {0x84C86189216DC5ED, 0xEA53DF5FD18D5513}, // 1e245
    {0x32FD3CF5B4E49BB4, 0x92746B9BE2F8552C}, // 1e246
    {0x3FBC8C33221DC2A1, 0xB7118682DBB66A77}, // 1e247
    {0x0FABAF3FEAA5334A, 0xE4D5E82392A40515}, // 1e248
    {0x29CB4D87F2A7400E, 0x8F05B1163BA6832D}, // 1e249
    {0x743E20E9EF511012, 0xB2C71D5BCA9023F8}, // 1e250
    {0x914DA9246B255416, 0xDF78E4B2BD342CF6}, // 1e251
    {0x1AD089B6C2F7548E, 0x8BAB8EEFB6409C1A}, // 1e252
    {0xA184AC2473B529B1, 0xAE9672ABA3D0C320}, // 1e253
    {0xC9E5D72D90A2741E, 0xDA3C0F568CC4F3E8}, // 1e254
    {0x7E2FA67C7A658892, 0x8865899617FB1871}, // 1e255
    {0xDDBB901B98FEEAB7, 0xAA7EEBFB9DF9DE8D}, // 1e256
    {0x552A74227F3EA565, 0xD51EA6FA85785631}, // 1e257
    {0xD53A88958F87275F, 0x8533285C936B35DE}, // 1e258
    {0x8A892ABAF368F137, 0xA67FF273B8460356}, // 1e259
    {0x2D2B7569B0432D85, 0xD01FEF10A657842C}, // 1e260
    {0x9C3B29620E29FC73, 0x8213F56A67F6B29B}, // 1e261
    {0x8349F3BA91B47B8F, 0xA298F2C501F45F42}, // 1e262
    {0x241C70A936219A73, 0xCB3F2F7642717713}, // 1e263
    {0xED238CD383AA0110, 0xFE0EFB53D30DD4D7}, // 1e264
    {0xF4363804324A40AA, 0x9EC95D1463E8A506}, // 1e265
    {0xB143C6053EDCD0D5, 0xC67BB4597CE2CE48}, // 1e266
    {0xDD94B7868E94050A, 0xF81AA16FDC1B81DA}, // 1e267
    {0xCA7CF2B4191C8326, 0x9B10A4E5E9913128}, // 1e268
    {0xFD1C2F611F63A3F0, 0xC1D4CE1F63F57D72}, // 1e269
    {0xBC633B39673C8CEC, 0xF24A01A73CF2DCCF}, // 1e270
    {0xD5BE0503E085D813, 0x976E41088617CA01}, // 1e271
    {0x4B2D8644D8A74E18, 0xBD49D14AA79DBC82}, // 1e272
    {0xDDF8E7D60ED1219E, 0xEC9C459D51852BA2}, // 1e273
    {0xCABB90E5C942B503, 0x93E1AB8252F33B45}, // 1e274
    {0x3D6A751F3B936243, 0xB8DA1662E7B00A17}, // 1e275
    {0x0CC512670A783AD4, 0xE7109BFBA19C0C9D}, // 1e276
    {0x27FB2B80668B24C5, 0x906A617D450187E2}, // 1e277
    {0xB1F9F660802DEDF6, 0xB484F9DC9641E9DA}, // 1e278
    {0x5E7873F8A0396973, 0xE1A63853BBD26451}, // 1e279
    {0xDB0B487B6423E1E8, 0x8D07E33455637EB2}, // 1e280
    {0x91CE1A9A3D2CDA62, 0xB049DC016ABC5E5F}, // 1e281
    {0x7641A140CC7810FB, 0xDC5C5301C56B75F7}, // 1e282
    {0xA9E904C87FCB0A9D, 0x89B9B3E11B6329BA}, // 1e283
    {0x546345FA9FBDCD44, 0xAC2820D9623BF429}, // 1e284
    {0xA97C177947AD4095, 0xD732290FBACAF133}, // 1e285
    {0x49ED8EABCCCC485D, 0x867F59A9D4BED6C0}, // 1e286
    {0x5C68F256BFFF5A74, 0xA81F301449EE8C70}, // 1e287
    {0x73832EEC6FFF3111, 0xD226FC195C6A2F8C}, // 1e288
    {0xC831FD53C5FF7EAB, 0x83585D8FD9C25DB7}, // 1e289
    {0xBA3E7CA8B77F5E55, 0xA42E74F3D032F525}, // 1e290
    {0x28CE1BD2E55F35EB, 0xCD3A1230C43FB26F}, // 1e291
    {0x7980D163CF5B81B3, 0x80444B5E7AA7CF85}, // 1e292
    {0xD7E105BCC332621F, 0xA0555E361951C366}, // 1e293
    {0x8DD9472BF3FEFAA7, 0xC86AB5C39FA63440}, // 1e294
    {0xB14F98F6F0FEB951, 0xFA856334878FC150}, // 1e295
    {0x6ED1BF9A569F33D3, 0x9C935E00D4B9D8D2}, // 1e296
    {0x0A862F80EC4700C8, 0xC3B8358109E84F07}, // 1e297
    {0xCD27BB612758C0FA, 0xF4A642E14C6262C8}, // 1e298
    {0x8038D51CB897789C, 0x98E7E9CCCFBD7DBD}, // 1e299
    {0xE0470A63E6BD56C3, 0xBF21E44003ACDD2C}, // 1e300
    {0x1858CCFCE06CAC74, 0xEEEA5D5004981478}, // 1e301
    {0x0F37801E0C43EBC8, 0x95527A5202DF0CCB}, // 1e302
    {0xD30560258F54E6BA, 0xBAA718E68396CFFD}, // 1e303
    {0x47C6B82EF32A2069, 0xE950DF20247C83FD}, // 1e304
    {0x4CDC331D57FA5441, 0x91D28B7416CDD27E}, // 1e305
    {0xE0133FE4ADF8E952, 0xB6472E511C81471D}, // 1e306
    {0x58180FDDD97723A6, 0xE3D8F9E563A198E5}, // 1e307
    {0x570F09EAA7EA7648, 0x8E679C2F5E44FF8F}, // 1e308
    {0x2CD2CC6551E513DA, 0xB201833B35D63F73}, // 1e309
    {0xF8077F7EA65E58D1, 0xDE81E40A034BCF4F}, // 1e310
    {0xFB04AFAF27FAF782, 0x8B112E86420F6191}, // 1e311
    {0x79C5DB9AF1F9B563, 0xADD57A27D29339F6}, // 1e312
    {0x18375281AE7822BC, 0xD94AD8B1C7380874}, // 1e313
    {0x8F2293910D0B15B5, 0x87CEC76F1C830548}, // 1e314
    {0xB2EB3875504DDB22, 0xA9C2794AE3A3C69A}, // 1e315
    {0x5FA60692A46151EB, 0xD433179D9C8CB841}, // 1e316
    {0xDBC7C41BA6BCD333, 0x849FEEC281D7F328}, // 1e317
    {0x12B9B522906C0800, 0xA5C7EA73224DEFF3}, // 1e318
    {0xD768226B34870A00, 0xCF39E50FEAE16BEF}, // 1e319
    {0xE6A1158300D46640, 0x81842F29F2CCE375}, // 1e320
    {0x60495AE3C1097FD0, 0xA1E53AF46F801C53}, // 1e321
    {0x385BB19CB14BDFC4, 0xCA5E89B18B602368}, // 1e322
    {0x46729E03DD9ED7B5, 0xFCF62C1DEE382C42}, // 1e323
    {0x6C07A2C26A8346D1, 0x9E19DB92B4E31BA9}, // 1e324
    {0xC7098B7305241885, 0xC5A05277621BE293}, // 1e325
    {0xB8CBEE4FC66D1EA7, 0xF70867153AA2DB38}, // 1e326
    {0x737F74F1DC043328, 0x9A65406D44A5C903}, // 1e327
    {0x505F522E53053FF2, 0xC0FE908895CF3B44}, // 1e328
    {0x647726B9E7C68FEF, 0xF13E34AABB430A15}, // 1e329
    {0x5ECA783430DC19F5, 0x96C6E0EAB509E64D}, // 1e330
    {0xB67D16413D132072, 0xBC789925624C5FE0}, // 1e331
    {0xE41C5BD18C57E88F, 0xEB96BF6EBADF77D8}, // 1e332
    {0x8E91B962F7B6F159, 0x933E37A534CBAAE7}, // 1e333
    {0x723627BBB5A4ADB0, 0xB80DC58E81FE95A1}, // 1e334
    {0xCEC3B1AAA30DD91C, 0xE61136F2227E3B09}, // 1e335
    {0x213A4F0AA5E8A7B1, 0x8FCAC257558EE4E6}, // 1e336
    {0xA988E2CD4F62D19D, 0xB3BD72ED2AF29E1F}, // 1e337
    {0x93EB1B80A33B8605, 0xE0ACCFA875AF45A7}, // 1e338
    {0xBC72F130660533C3, 0x8C6C01C9498D8B88}, // 1e339
    {0xEB8FAD7C7F8680B4, 0xAF87023B9BF0EE6A}, // 1e340
    {0xA67398DB9F6820E1, 0xDB68C2CA82ED2A05}, // 1e341
    {0x88083F8943A1148C, 0x892179BE91D43A43}, // 1e342
    {0x6A0A4F6B948959B0, 0xAB69D82E364948D4}, // 1e343
    {0x848CE34679ABB01C, 0xD6444E39C3DB9B09}, // 1e344
    {0xF2D80E0C0C0B4E11, 0x85EAB0E41A6940E5}, // 1e345
    {0x6F8E118F0F0E2195, 0xA7655D1D2103911F}, // 1e346
    {0x4B7195F2D2D1A9FB, 0xD13EB46469447567}, // 1e347
};