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ton/tdfec/td/fec/raptorq/Rfc.cpp
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/*
This file is part of TON Blockchain Library.
TON Blockchain Library is free software: you can redistribute it and/or modify
it under the terms of the GNU Lesser General Public License as published by
the Free Software Foundation, either version 2 of the License, or
(at your option) any later version.
TON Blockchain Library is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License
along with TON Blockchain Library. If not, see <http://www.gnu.org/licenses/>.
Copyright 2017-2019 Telegram Systems LLP
*/
#include "td/fec/raptorq/Rfc.h"
#include <array>
namespace td {
namespace raptorq {
// 5.5. Random Numbers
//
// The four arrays V0, V1, V2, and V3 used in Section 5.3.5.1 are
// provided below. There are 256 entries in each of the four arrays.
// The indexing into each array starts at 0, and the entries are 32-bit
// unsigned integers.
namespace {
constexpr size_t V_size{256};
constexpr std::array<uint32, V_size> V0 = {
{251291136, 3952231631, 3370958628, 4070167936, 123631495, 3351110283, 3218676425, 2011642291, 774603218,
2402805061, 1004366930, 1843948209, 428891132, 3746331984, 1591258008, 3067016507, 1433388735, 504005498,
2032657933, 3419319784, 2805686246, 3102436986, 3808671154, 2501582075, 3978944421, 246043949, 4016898363,
649743608, 1974987508, 2651273766, 2357956801, 689605112, 715807172, 2722736134, 191939188, 3535520147,
3277019569, 1470435941, 3763101702, 3232409631, 122701163, 3920852693, 782246947, 372121310, 2995604341,
2045698575, 2332962102, 4005368743, 218596347, 3415381967, 4207612806, 861117671, 3676575285, 2581671944,
3312220480, 681232419, 307306866, 4112503940, 1158111502, 709227802, 2724140433, 4201101115, 4215970289,
4048876515, 3031661061, 1909085522, 510985033, 1361682810, 129243379, 3142379587, 2569842483, 3033268270,
1658118006, 932109358, 1982290045, 2983082771, 3007670818, 3448104768, 683749698, 778296777, 1399125101,
1939403708, 1692176003, 3868299200, 1422476658, 593093658, 1878973865, 2526292949, 1591602827, 3986158854,
3964389521, 2695031039, 1942050155, 424618399, 1347204291, 2669179716, 2434425874, 2540801947, 1384069776,
4123580443, 1523670218, 2708475297, 1046771089, 2229796016, 1255426612, 4213663089, 1521339547, 3041843489,
420130494, 10677091, 515623176, 3457502702, 2115821274, 2720124766, 3242576090, 854310108, 425973987,
325832382, 1796851292, 2462744411, 1976681690, 1408671665, 1228817808, 3917210003, 263976645, 2593736473,
2471651269, 4291353919, 650792940, 1191583883, 3046561335, 2466530435, 2545983082, 969168436, 2019348792,
2268075521, 1169345068, 3250240009, 3963499681, 2560755113, 911182396, 760842409, 3569308693, 2687243553,
381854665, 2613828404, 2761078866, 1456668111, 883760091, 3294951678, 1604598575, 1985308198, 1014570543,
2724959607, 3062518035, 3115293053, 138853680, 4160398285, 3322241130, 2068983570, 2247491078, 3669524410,
1575146607, 828029864, 3732001371, 3422026452, 3370954177, 4006626915, 543812220, 1243116171, 3928372514,
2791443445, 4081325272, 2280435605, 885616073, 616452097, 3188863436, 2780382310, 2340014831, 1208439576,
258356309, 3837963200, 2075009450, 3214181212, 3303882142, 880813252, 1355575717, 207231484, 2420803184,
358923368, 1617557768, 3272161958, 1771154147, 2842106362, 1751209208, 1421030790, 658316681, 194065839,
3241510581, 38625260, 301875395, 4176141739, 297312930, 2137802113, 1502984205, 3669376622, 3728477036,
234652930, 2213589897, 2734638932, 1129721478, 3187422815, 2859178611, 3284308411, 3819792700, 3557526733,
451874476, 1740576081, 3592838701, 1709429513, 3702918379, 3533351328, 1641660745, 179350258, 2380520112,
3936163904, 3685256204, 3156252216, 1854258901, 2861641019, 3176611298, 834787554, 331353807, 517858103,
3010168884, 4012642001, 2217188075, 3756943137, 3077882590, 2054995199, 3081443129, 3895398812, 1141097543,
2376261053, 2626898255, 2554703076, 401233789, 1460049922, 678083952, 1064990737, 940909784, 1673396780,
528881783, 1712547446, 3629685652, 1358307511}};
constexpr std::array<uint32, V_size> V1 = {
{807385413, 2043073223, 3336749796, 1302105833, 2278607931, 541015020, 1684564270, 372709334, 3508252125,
1768346005, 1270451292, 2603029534, 2049387273, 3891424859, 2152948345, 4114760273, 915180310, 3754787998,
700503826, 2131559305, 1308908630, 224437350, 4065424007, 3638665944, 1679385496, 3431345226, 1779595665,
3068494238, 1424062773, 1033448464, 4050396853, 3302235057, 420600373, 2868446243, 311689386, 259047959,
4057180909, 1575367248, 4151214153, 110249784, 3006865921, 4293710613, 3501256572, 998007483, 499288295,
1205710710, 2997199489, 640417429, 3044194711, 486690751, 2686640734, 2394526209, 2521660077, 49993987,
3843885867, 4201106668, 415906198, 19296841, 2402488407, 2137119134, 1744097284, 579965637, 2037662632,
852173610, 2681403713, 1047144830, 2982173936, 910285038, 4187576520, 2589870048, 989448887, 3292758024,
506322719, 176010738, 1865471968, 2619324712, 564829442, 1996870325, 339697593, 4071072948, 3618966336,
2111320126, 1093955153, 957978696, 892010560, 1854601078, 1873407527, 2498544695, 2694156259, 1927339682,
1650555729, 183933047, 3061444337, 2067387204, 228962564, 3904109414, 1595995433, 1780701372, 2463145963,
307281463, 3237929991, 3852995239, 2398693510, 3754138664, 522074127, 146352474, 4104915256, 3029415884,
3545667983, 332038910, 976628269, 3123492423, 3041418372, 2258059298, 2139377204, 3243642973, 3226247917,
3674004636, 2698992189, 3453843574, 1963216666, 3509855005, 2358481858, 747331248, 1957348676, 1097574450,
2435697214, 3870972145, 1888833893, 2914085525, 4161315584, 1273113343, 3269644828, 3681293816, 412536684,
1156034077, 3823026442, 1066971017, 3598330293, 1979273937, 2079029895, 1195045909, 1071986421, 2712821515,
3377754595, 2184151095, 750918864, 2585729879, 4249895712, 1832579367, 1192240192, 946734366, 31230688,
3174399083, 3549375728, 1642430184, 1904857554, 861877404, 3277825584, 4267074718, 3122860549, 666423581,
644189126, 226475395, 307789415, 1196105631, 3191691839, 782852669, 1608507813, 1847685900, 4069766876,
3931548641, 2526471011, 766865139, 2115084288, 4259411376, 3323683436, 568512177, 3736601419, 1800276898,
4012458395, 1823982, 27980198, 2023839966, 869505096, 431161506, 1024804023, 1853869307, 3393537983,
1500703614, 3019471560, 1351086955, 3096933631, 3034634988, 2544598006, 1230942551, 3362230798, 159984793,
491590373, 3993872886, 3681855622, 903593547, 3535062472, 1799803217, 772984149, 895863112, 1899036275,
4187322100, 101856048, 234650315, 3183125617, 3190039692, 525584357, 1286834489, 455810374, 1869181575,
922673938, 3877430102, 3422391938, 1414347295, 1971054608, 3061798054, 830555096, 2822905141, 167033190,
1079139428, 4210126723, 3593797804, 429192890, 372093950, 1779187770, 3312189287, 204349348, 452421568,
2800540462, 3733109044, 1235082423, 1765319556, 3174729780, 3762994475, 3171962488, 442160826, 198349622,
45942637, 1324086311, 2901868599, 678860040, 3812229107, 19936821, 1119590141, 3640121682, 3545931032,
2102949142, 2828208598, 3603378023, 4135048896}};
constexpr std::array<uint32, V_size> V2 = {
{1629829892, 282540176, 2794583710, 496504798, 2990494426, 3070701851, 2575963183, 4094823972, 2775723650,
4079480416, 176028725, 2246241423, 3732217647, 2196843075, 1306949278, 4170992780, 4039345809, 3209664269,
3387499533, 293063229, 3660290503, 2648440860, 2531406539, 3537879412, 773374739, 4184691853, 1804207821,
3347126643, 3479377103, 3970515774,
1891731298, 2368003842, 3537588307, 2969158410, 4230745262, 831906319, 2935838131, 264029468, 120852739,
3200326460, 355445271, 2296305141, 1566296040, 1760127056, 20073893, 3427103620, 2866979760, 2359075957,
2025314291, 1725696734, 3346087406, 2690756527, 99815156, 4248519977, 2253762642, 3274144518, 598024568,
3299672435, 556579346, 4121041856, 2896948975, 3620123492, 918453629, 3249461198, 2231414958, 3803272287,
3657597946, 2588911389, 242262274, 1725007475, 2026427718, 46776484, 2873281403, 2919275846, 3177933051,
1918859160, 2517854537, 1857818511, 3234262050, 479353687, 200201308, 2801945841, 1621715769, 483977159,
423502325, 3689396064, 1850168397, 3359959416, 3459831930, 841488699, 3570506095, 930267420, 1564520841,
2505122797, 593824107, 1116572080, 819179184, 3139123629, 1414339336, 1076360795, 512403845, 177759256,
1701060666, 2239736419, 515179302, 2935012727, 3821357612, 1376520851, 2700745271, 966853647, 1041862223,
715860553, 171592961, 1607044257, 1227236688, 3647136358, 1417559141, 4087067551, 2241705880, 4194136288,
1439041934, 20464430, 119668151, 2021257232, 2551262694, 1381539058, 4082839035, 498179069, 311508499,
3580908637, 2889149671, 142719814, 1232184754, 3356662582, 2973775623, 1469897084, 1728205304, 1415793613,
50111003, 3133413359, 4074115275, 2710540611, 2700083070, 2457757663, 2612845330, 3775943755, 2469309260,
2560142753, 3020996369, 1691667711, 4219602776, 1687672168, 1017921622, 2307642321, 368711460, 3282925988,
213208029, 4150757489, 3443211944, 2846101972, 4106826684, 4272438675, 2199416468, 3710621281, 497564971,
285138276, 765042313, 916220877, 3402623607, 2768784621, 1722849097, 3386397442, 487920061, 3569027007,
3424544196, 217781973, 2356938519, 3252429414, 145109750, 2692588106, 2454747135, 1299493354, 4120241887,
2088917094, 932304329, 1442609203, 952586974, 3509186750, 753369054, 854421006, 1954046388, 2708927882,
4047539230, 3048925996, 1667505809, 805166441, 1182069088, 4265546268, 4215029527, 3374748959, 373532666,
2454243090, 2371530493, 3651087521, 2619878153, 1651809518, 1553646893, 1227452842, 703887512, 3696674163,
2552507603, 2635912901, 895130484, 3287782244, 3098973502, 990078774, 3780326506, 2290845203, 41729428,
1949580860, 2283959805, 1036946170, 1694887523, 4880696, 466000198, 2765355283, 3318686998, 1266458025,
3919578154, 3545413527, 2627009988, 3744680394, 1696890173, 3250684705, 4142417708, 915739411, 3308488877,
1289361460, 2942552331, 1169105979, 3342228712, 698560958, 1356041230, 2401944293, 107705232, 3701895363,
903928723, 3646581385, 844950914, 1944371367, 3863894844, 2946773319, 1972431613, 1706989237, 29917467,
3497665928}};
constexpr std::array<uint32, V_size> V3 = {
{1191369816, 744902811, 2539772235, 3213192037, 3286061266, 1200571165, 2463281260, 754888894, 714651270,
1968220972, 3628497775, 1277626456, 1493398934, 364289757, 2055487592, 3913468088, 2930259465, 902504567,
3967050355, 2056499403, 692132390, 186386657, 832834706, 859795816, 1283120926, 2253183716, 3003475205,
1755803552, 2239315142, 4271056352, 2184848469, 769228092, 1249230754, 1193269205, 2660094102, 642979613,
1687087994, 2726106182, 446402913, 4122186606, 3771347282, 37667136, 192775425, 3578702187, 1952659096,
3989584400, 3069013882, 2900516158, 4045316336, 3057163251, 1702104819, 4116613420, 3575472384, 2674023117,
1409126723, 3215095429, 1430726429, 2544497368, 1029565676, 1855801827, 4262184627, 1854326881, 2906728593,
3277836557, 2787697002, 2787333385, 3105430738, 2477073192, 748038573, 1088396515, 1611204853, 201964005,
3745818380, 3654683549, 3816120877, 3915783622, 2563198722, 1181149055, 33158084, 3723047845, 3790270906,
3832415204, 2959617497, 372900708, 1286738499, 1932439099, 3677748309, 2454711182, 2757856469, 2134027055,
2780052465, 3190347618, 3758510138, 3626329451, 1120743107, 1623585693, 1389834102, 2719230375, 3038609003,
462617590, 260254189, 3706349764, 2556762744, 2874272296, 2502399286, 4216263978, 2683431180, 2168560535,
3561507175, 668095726, 680412330, 3726693946, 4180630637, 3335170953, 942140968, 2711851085, 2059233412,
4265696278, 3204373534, 232855056, 881788313, 2258252172, 2043595984, 3758795150, 3615341325, 2138837681,
1351208537, 2923692473, 3402482785, 2105383425, 2346772751, 499245323, 3417846006, 2366116814, 2543090583,
1828551634, 3148696244, 3853884867, 1364737681, 2200687771, 2689775688, 232720625, 4071657318, 2671968983,
3531415031, 1212852141, 867923311, 3740109711, 1923146533, 3237071777, 3100729255, 3247856816, 906742566,
4047640575, 4007211572, 3495700105, 1171285262, 2835682655, 1634301229, 3115169925, 2289874706, 2252450179,
944880097, 371933491, 1649074501, 2208617414, 2524305981, 2496569844, 2667037160, 1257550794, 3399219045,
3194894295, 1643249887, 342911473, 891025733, 3146861835, 3789181526, 938847812, 1854580183, 2112653794,
2960702988, 1238603378, 2205280635, 1666784014, 2520274614, 3355493726, 2310872278, 3153920489, 2745882591,
1200203158, 3033612415, 2311650167, 1048129133, 4206710184, 4209176741, 2640950279, 2096382177, 4116899089,
3631017851, 4104488173, 1857650503, 3801102932, 445806934, 3055654640, 897898279, 3234007399, 1325494930,
2982247189, 1619020475, 2720040856, 885096170, 3485255499, 2983202469, 3891011124, 546522756, 1524439205,
2644317889, 2170076800, 2969618716, 961183518, 1081831074, 1037015347, 3289016286, 2331748669, 620887395,
303042654, 3990027945, 1562756376, 3413341792, 2059647769, 2823844432, 674595301, 2457639984, 4076754716,
2447737904, 1583323324, 625627134, 3076006391, 345777990, 1684954145, 879227329, 3436182180, 1522273219,
3802543817, 1456017040, 1897819847, 2970081129, 1382576028, 3820044861, 1044428167, 612252599, 3340478395,
2150613904, 3397625662, 3573635640, 3432275192}};
} // namespace
// 5.3.5.1. Random Number Generator
// The random number generator Rand[y, i, m] is defined as follows,
// where y is a non-negative integer, i is a non-negative integer less
// than 256, and m is a positive integer, and the value produced is an
// integer between 0 and m-1. Let V0, V1, V2, and V3 be the arrays
// provided in Section 5.5.
//
// Let
//
// o x0 = (y + i) mod 2^^8
//
// o x1 = (floor(y / 2^^8) + i) mod 2^^8
//
// o x2 = (floor(y / 2^^16) + i) mod 2^^8
//
// o x3 = (floor(y / 2^^24) + i) mod 2^^8
//
// Then
//
// Rand[y, i, m] = (V0[x0] ^ V1[x1] ^ V2[x2] ^ V3[x3]) % m
uint32 Rfc::random(uint32 y, uint32 i, uint32 m) {
auto x0 = (y + i) % 256;
auto x1 = (y / 256 + i) % 256;
auto x2 = (y / 256 / 256 + i) % 256;
auto x3 = (y / 256 / 256 / 256 + i) % 256;
auto res = V0[x0] ^ V1[x1] ^ V2[x2] ^ V3[x3];
if (m != 0) {
res %= m;
}
return res;
}
namespace {
constexpr std::array<Rfc::RawParameters, 1232> rfc_parameters = {
{{10, 254, 7, 10, 17}, {12, 630, 7, 10, 19}, {18, 682, 11, 10, 29},
{20, 293, 11, 10, 31}, {26, 80, 11, 10, 37}, {30, 566, 11, 10, 41},
{32, 860, 11, 10, 43}, {36, 267, 11, 10, 47}, {42, 822, 11, 10, 53},
{46, 506, 13, 10, 59}, {48, 589, 13, 10, 61}, {49, 87, 13, 10, 61},
{55, 520, 13, 10, 67}, {60, 159, 13, 10, 71}, {62, 235, 13, 10, 73},
{69, 157, 13, 10, 79}, {75, 502, 17, 10, 89}, {84, 334, 17, 10, 97},
{88, 583, 17, 10, 101}, {91, 66, 17, 10, 103}, {95, 352, 17, 10, 107},
{97, 365, 17, 10, 109}, {101, 562, 17, 10, 113}, {114, 5, 19, 10, 127},
{119, 603, 19, 10, 131}, {125, 721, 19, 10, 137}, {127, 28, 19, 10, 139},
{138, 660, 19, 10, 149}, {140, 829, 19, 10, 151}, {149, 900, 23, 10, 163},
{153, 930, 23, 10, 167}, {160, 814, 23, 10, 173}, {166, 661, 23, 10, 179},
{168, 693, 23, 10, 181}, {179, 780, 23, 10, 191}, {181, 605, 23, 10, 193},
{185, 551, 23, 10, 197}, {187, 777, 23, 10, 199}, {200, 491, 23, 10, 211},
{213, 396, 23, 10, 223}, {217, 764, 29, 10, 233}, {225, 843, 29, 10, 241},
{236, 646, 29, 10, 251}, {242, 557, 29, 10, 257}, {248, 608, 29, 10, 263},
{257, 265, 29, 10, 271}, {263, 505, 29, 10, 277}, {269, 722, 29, 10, 283},
{280, 263, 29, 10, 293}, {295, 999, 29, 10, 307}, {301, 874, 29, 10, 313},
{305, 160, 29, 10, 317}, {324, 575, 31, 10, 337}, {337, 210, 31, 10, 349},
{341, 513, 31, 10, 353}, {347, 503, 31, 10, 359}, {355, 558, 31, 10, 367},
{362, 932, 31, 10, 373}, {368, 404, 31, 10, 379}, {372, 520, 37, 10, 389},
{380, 846, 37, 10, 397}, {385, 485, 37, 10, 401}, {393, 728, 37, 10, 409},
{405, 554, 37, 10, 421}, {418, 471, 37, 10, 433}, {428, 641, 37, 10, 443},
{434, 732, 37, 10, 449}, {447, 193, 37, 10, 461}, {453, 934, 37, 10, 467},
{466, 864, 37, 10, 479}, {478, 790, 37, 10, 491}, {486, 912, 37, 10, 499},
{491, 617, 37, 10, 503}, {497, 587, 37, 10, 509}, {511, 800, 37, 10, 523},
{526, 923, 41, 10, 541}, {532, 998, 41, 10, 547}, {542, 92, 41, 10, 557},
{549, 497, 41, 10, 563}, {557, 559, 41, 10, 571}, {563, 667, 41, 10, 577},
{573, 912, 41, 10, 587}, {580, 262, 41, 10, 593}, {588, 152, 41, 10, 601},
{594, 526, 41, 10, 607}, {600, 268, 41, 10, 613}, {606, 212, 41, 10, 619},
{619, 45, 41, 10, 631}, {633, 898, 43, 10, 647}, {640, 527, 43, 10, 653},
{648, 558, 43, 10, 661}, {666, 460, 47, 10, 683}, {675, 5, 47, 10, 691},
{685, 895, 47, 10, 701}, {693, 996, 47, 10, 709}, {703, 282, 47, 10, 719},
{718, 513, 47, 10, 733}, {728, 865, 47, 10, 743}, {736, 870, 47, 10, 751},
{747, 239, 47, 10, 761}, {759, 452, 47, 10, 773}, {778, 862, 53, 10, 797},
{792, 852, 53, 10, 811}, {802, 643, 53, 10, 821}, {811, 543, 53, 10, 829},
{821, 447, 53, 10, 839}, {835, 321, 53, 10, 853}, {845, 287, 53, 10, 863},
{860, 12, 53, 10, 877}, {870, 251, 53, 10, 887}, {891, 30, 53, 10, 907},
{903, 621, 53, 10, 919}, {913, 555, 53, 10, 929}, {926, 127, 53, 10, 941},
{938, 400, 53, 10, 953}, {950, 91, 59, 10, 971}, {963, 916, 59, 10, 983},
{977, 935, 59, 10, 997}, {989, 691, 59, 10, 1009}, {1002, 299, 59, 10, 1021},
{1020, 282, 59, 10, 1039}, {1032, 824, 59, 10, 1051}, {1050, 536, 59, 11, 1069},
{1074, 596, 59, 11, 1093}, {1085, 28, 59, 11, 1103}, {1099, 947, 59, 11, 1117},
{1111, 162, 59, 11, 1129}, {1136, 536, 59, 11, 1153}, {1152, 1000, 61, 11, 1171},
{1169, 251, 61, 11, 1187}, {1183, 673, 61, 11, 1201}, {1205, 559, 61, 11, 1223},
{1220, 923, 61, 11, 1237}, {1236, 81, 67, 11, 1259}, {1255, 478, 67, 11, 1277},
{1269, 198, 67, 11, 1291}, {1285, 137, 67, 11, 1307}, {1306, 75, 67, 11, 1327},
{1347, 29, 67, 11, 1367}, {1361, 231, 67, 11, 1381}, {1389, 532, 67, 11, 1409},
{1404, 58, 67, 11, 1423}, {1420, 60, 67, 11, 1439}, {1436, 964, 71, 11, 1459},
{1461, 624, 71, 11, 1483}, {1477, 502, 71, 11, 1499}, {1502, 636, 71, 11, 1523},
{1522, 986, 71, 11, 1543}, {1539, 950, 71, 11, 1559}, {1561, 735, 73, 11, 1583},
{1579, 866, 73, 11, 1601}, {1600, 203, 73, 11, 1621}, {1616, 83, 73, 11, 1637},
{1649, 14, 73, 11, 1669}, {1673, 522, 79, 11, 1699}, {1698, 226, 79, 11, 1723},
{1716, 282, 79, 11, 1741}, {1734, 88, 79, 11, 1759}, {1759, 636, 79, 11, 1783},
{1777, 860, 79, 11, 1801}, {1800, 324, 79, 11, 1823}, {1824, 424, 79, 11, 1847},
{1844, 999, 79, 11, 1867}, {1863, 682, 83, 11, 1889}, {1887, 814, 83, 11, 1913},
{1906, 979, 83, 11, 1931}, {1926, 538, 83, 11, 1951}, {1954, 278, 83, 11, 1979},
{1979, 580, 83, 11, 2003}, {2005, 773, 83, 11, 2029}, {2040, 911, 89, 11, 2069},
{2070, 506, 89, 11, 2099}, {2103, 628, 89, 11, 2131}, {2125, 282, 89, 11, 2153},
{2152, 309, 89, 11, 2179}, {2195, 858, 89, 11, 2221}, {2217, 442, 89, 11, 2243},
{2247, 654, 89, 11, 2273}, {2278, 82, 97, 11, 2311}, {2315, 428, 97, 11, 2347},
{2339, 442, 97, 11, 2371}, {2367, 283, 97, 11, 2399}, {2392, 538, 97, 11, 2423},
{2416, 189, 97, 11, 2447}, {2447, 438, 97, 11, 2477}, {2473, 912, 97, 11, 2503},
{2502, 1, 97, 11, 2531}, {2528, 167, 97, 11, 2557}, {2565, 272, 97, 11, 2593},
{2601, 209, 101, 11, 2633}, {2640, 927, 101, 11, 2671}, {2668, 386, 101, 11, 2699},
{2701, 653, 101, 11, 2731}, {2737, 669, 101, 11, 2767}, {2772, 431, 101, 11, 2801},
{2802, 793, 103, 11, 2833}, {2831, 588, 103, 11, 2861}, {2875, 777, 107, 11, 2909},
{2906, 939, 107, 11, 2939}, {2938, 864, 107, 11, 2971}, {2979, 627, 107, 11, 3011},
{3015, 265, 109, 11, 3049}, {3056, 976, 109, 11, 3089}, {3101, 988, 113, 11, 3137},
{3151, 507, 113, 11, 3187}, {3186, 640, 113, 11, 3221}, {3224, 15, 113, 11, 3259},
{3265, 667, 113, 11, 3299}, {3299, 24, 127, 11, 3347}, {3344, 877, 127, 11, 3391},
{3387, 240, 127, 11, 3433}, {3423, 720, 127, 11, 3469}, {3466, 93, 127, 11, 3511},
{3502, 919, 127, 11, 3547}, {3539, 635, 127, 11, 3583}, {3579, 174, 127, 11, 3623},
{3616, 647, 127, 11, 3659}, {3658, 820, 127, 11, 3701}, {3697, 56, 127, 11, 3739},
{3751, 485, 127, 11, 3793}, {3792, 210, 127, 11, 3833}, {3840, 124, 127, 11, 3881},
{3883, 546, 127, 11, 3923}, {3924, 954, 131, 11, 3967}, {3970, 262, 131, 11, 4013},
{4015, 927, 131, 11, 4057}, {4069, 957, 131, 11, 4111}, {4112, 726, 137, 11, 4159},
{4165, 583, 137, 11, 4211}, {4207, 782, 137, 11, 4253}, {4252, 37, 137, 11, 4297},
{4318, 758, 137, 11, 4363}, {4365, 777, 137, 11, 4409}, {4418, 104, 139, 11, 4463},
{4468, 476, 139, 11, 4513}, {4513, 113, 149, 11, 4567}, {4567, 313, 149, 11, 4621},
{4626, 102, 149, 11, 4679}, {4681, 501, 149, 11, 4733}, {4731, 332, 149, 11, 4783},
{4780, 786, 149, 11, 4831}, {4838, 99, 149, 11, 4889}, {4901, 658, 149, 11, 4951},
{4954, 794, 149, 11, 5003}, {5008, 37, 151, 11, 5059}, {5063, 471, 151, 11, 5113},
{5116, 94, 157, 11, 5171}, {5172, 873, 157, 11, 5227}, {5225, 918, 157, 11, 5279},
{5279, 945, 157, 11, 5333}, {5334, 211, 157, 11, 5387}, {5391, 341, 157, 11, 5443},
{5449, 11, 163, 11, 5507}, {5506, 578, 163, 11, 5563}, {5566, 494, 163, 11, 5623},
{5637, 694, 163, 11, 5693}, {5694, 252, 163, 11, 5749}, {5763, 451, 167, 11, 5821},
{5823, 83, 167, 11, 5881}, {5896, 689, 167, 11, 5953}, {5975, 488, 173, 11, 6037},
{6039, 214, 173, 11, 6101}, {6102, 17, 173, 11, 6163}, {6169, 469, 173, 11, 6229},
{6233, 263, 179, 11, 6299}, {6296, 309, 179, 11, 6361}, {6363, 984, 179, 11, 6427},
{6427, 123, 179, 11, 6491}, {6518, 360, 179, 11, 6581}, {6589, 863, 181, 11, 6653},
{6655, 122, 181, 11, 6719}, {6730, 522, 191, 11, 6803}, {6799, 539, 191, 11, 6871},
{6878, 181, 191, 11, 6949}, {6956, 64, 191, 11, 7027}, {7033, 387, 191, 11, 7103},
{7108, 967, 191, 11, 7177}, {7185, 843, 191, 11, 7253}, {7281, 999, 193, 11, 7351},
{7360, 76, 197, 11, 7433}, {7445, 142, 197, 11, 7517}, {7520, 599, 197, 11, 7591},
{7596, 576, 199, 11, 7669}, {7675, 176, 211, 11, 7759}, {7770, 392, 211, 11, 7853},
{7855, 332, 211, 11, 7937}, {7935, 291, 211, 11, 8017}, {8030, 913, 211, 11, 8111},
{8111, 608, 211, 11, 8191}, {8194, 212, 211, 11, 8273}, {8290, 696, 211, 11, 8369},
{8377, 931, 223, 11, 8467}, {8474, 326, 223, 11, 8563}, {8559, 228, 223, 11, 8647},
{8654, 706, 223, 11, 8741}, {8744, 144, 223, 11, 8831}, {8837, 83, 223, 11, 8923},
{8928, 743, 223, 11, 9013}, {9019, 187, 223, 11, 9103}, {9111, 654, 227, 11, 9199},
{9206, 359, 227, 11, 9293}, {9303, 493, 229, 11, 9391}, {9400, 369, 233, 11, 9491},
{9497, 981, 233, 11, 9587}, {9601, 276, 239, 11, 9697}, {9708, 647, 239, 11, 9803},
{9813, 389, 239, 11, 9907}, {9916, 80, 239, 11, 10009}, {10017, 396, 241, 11, 10111},
{10120, 580, 251, 11, 10223}, {10241, 873, 251, 11, 10343}, {10351, 15, 251, 11, 10453},
{10458, 976, 251, 11, 10559}, {10567, 584, 251, 11, 10667}, {10676, 267, 257, 11, 10781},
{10787, 876, 257, 11, 10891}, {10899, 642, 257, 12, 11003}, {11015, 794, 257, 12, 11119},
{11130, 78, 263, 12, 11239}, {11245, 736, 263, 12, 11353}, {11358, 882, 269, 12, 11471},
{11475, 251, 269, 12, 11587}, {11590, 434, 269, 12, 11701}, {11711, 204, 269, 12, 11821},
{11829, 256, 271, 12, 11941}, {11956, 106, 277, 12, 12073}, {12087, 375, 277, 12, 12203},
{12208, 148, 277, 12, 12323}, {12333, 496, 281, 12, 12451}, {12460, 88, 281, 12, 12577},
{12593, 826, 293, 12, 12721}, {12726, 71, 293, 12, 12853}, {12857, 925, 293, 12, 12983},
{13002, 760, 293, 12, 13127}, {13143, 130, 293, 12, 13267}, {13284, 641, 307, 12, 13421},
{13417, 400, 307, 12, 13553}, {13558, 480, 307, 12, 13693}, {13695, 76, 307, 12, 13829},
{13833, 665, 307, 12, 13967}, {13974, 910, 307, 12, 14107}, {14115, 467, 311, 12, 14251},
{14272, 964, 311, 12, 14407}, {14415, 625, 313, 12, 14551}, {14560, 362, 317, 12, 14699},
{14713, 759, 317, 12, 14851}, {14862, 728, 331, 12, 15013}, {15011, 343, 331, 12, 15161},
{15170, 113, 331, 12, 15319}, {15325, 137, 331, 12, 15473}, {15496, 308, 331, 12, 15643},
{15651, 800, 337, 12, 15803}, {15808, 177, 337, 12, 15959}, {15977, 961, 337, 12, 16127},
{16161, 958, 347, 12, 16319}, {16336, 72, 347, 12, 16493}, {16505, 732, 347, 12, 16661},
{16674, 145, 349, 12, 16831}, {16851, 577, 353, 12, 17011}, {17024, 305, 353, 12, 17183},
{17195, 50, 359, 12, 17359}, {17376, 351, 359, 12, 17539}, {17559, 175, 367, 12, 17729},
{17742, 727, 367, 12, 17911}, {17929, 902, 367, 12, 18097}, {18116, 409, 373, 12, 18289},
{18309, 776, 373, 12, 18481}, {18503, 586, 379, 12, 18679}, {18694, 451, 379, 12, 18869},
{18909, 287, 383, 12, 19087}, {19126, 246, 389, 12, 19309}, {19325, 222, 389, 12, 19507},
{19539, 563, 397, 12, 19727}, {19740, 839, 397, 12, 19927}, {19939, 897, 401, 12, 20129},
{20152, 409, 401, 12, 20341}, {20355, 618, 409, 12, 20551}, {20564, 439, 409, 12, 20759},
{20778, 95, 419, 13, 20983}, {20988, 448, 419, 13, 21191}, {21199, 133, 419, 13, 21401},
{21412, 938, 419, 13, 21613}, {21629, 423, 431, 13, 21841}, {21852, 90, 431, 13, 22063},
{22073, 640, 431, 13, 22283}, {22301, 922, 433, 13, 22511}, {22536, 250, 439, 13, 22751},
{22779, 367, 439, 13, 22993}, {23010, 447, 443, 13, 23227}, {23252, 559, 449, 13, 23473},
{23491, 121, 457, 13, 23719}, {23730, 623, 457, 13, 23957}, {23971, 450, 457, 13, 24197},
{24215, 253, 461, 13, 24443}, {24476, 106, 467, 13, 24709}, {24721, 863, 467, 13, 24953},
{24976, 148, 479, 13, 25219}, {25230, 427, 479, 13, 25471}, {25493, 138, 479, 13, 25733},
{25756, 794, 487, 13, 26003}, {26022, 247, 487, 13, 26267}, {26291, 562, 491, 13, 26539},
{26566, 53, 499, 13, 26821}, {26838, 135, 499, 13, 27091}, {27111, 21, 503, 13, 27367},
{27392, 201, 509, 13, 27653}, {27682, 169, 521, 13, 27953}, {27959, 70, 521, 13, 28229},
{28248, 386, 521, 13, 28517}, {28548, 226, 523, 13, 28817}, {28845, 3, 541, 13, 29131},
{29138, 769, 541, 13, 29423}, {29434, 590, 541, 13, 29717}, {29731, 672, 541, 13, 30013},
{30037, 713, 547, 13, 30323}, {30346, 967, 547, 13, 30631}, {30654, 368, 557, 14, 30949},
{30974, 348, 557, 14, 31267}, {31285, 119, 563, 14, 31583}, {31605, 503, 569, 14, 31907},
{31948, 181, 571, 14, 32251}, {32272, 394, 577, 14, 32579}, {32601, 189, 587, 14, 32917},
{32932, 210, 587, 14, 33247}, {33282, 62, 593, 14, 33601}, {33623, 273, 593, 14, 33941},
{33961, 554, 599, 14, 34283}, {34302, 936, 607, 14, 34631}, {34654, 483, 607, 14, 34981},
{35031, 397, 613, 14, 35363}, {35395, 241, 619, 14, 35731}, {35750, 500, 631, 14, 36097},
{36112, 12, 631, 14, 36457}, {36479, 958, 641, 14, 36833}, {36849, 524, 641, 14, 37201},
{37227, 8, 643, 14, 37579}, {37606, 100, 653, 14, 37967}, {37992, 339, 653, 14, 38351},
{38385, 804, 659, 14, 38749}, {38787, 510, 673, 14, 39163}, {39176, 18, 673, 14, 39551},
{39576, 412, 677, 14, 39953}, {39980, 394, 683, 14, 40361}, {40398, 830, 691, 15, 40787},
{40816, 535, 701, 15, 41213}, {41226, 199, 701, 15, 41621}, {41641, 27, 709, 15, 42043},
{42067, 298, 709, 15, 42467}, {42490, 368, 719, 15, 42899}, {42916, 755, 727, 15, 43331},
{43388, 379, 727, 15, 43801}, {43840, 73, 733, 15, 44257}, {44279, 387, 739, 15, 44701},
{44729, 457, 751, 15, 45161}, {45183, 761, 751, 15, 45613}, {45638, 855, 757, 15, 46073},
{46104, 370, 769, 15, 46549}, {46574, 261, 769, 15, 47017}, {47047, 299, 787, 15, 47507},
{47523, 920, 787, 15, 47981}, {48007, 269, 787, 15, 48463}, {48489, 862, 797, 15, 48953},
{48976, 349, 809, 15, 49451}, {49470, 103, 809, 15, 49943}, {49978, 115, 821, 15, 50461},
{50511, 93, 821, 16, 50993}, {51017, 982, 827, 16, 51503}, {51530, 432, 839, 16, 52027},
{52062, 340, 853, 16, 52571}, {52586, 173, 853, 16, 53093}, {53114, 421, 857, 16, 53623},
{53650, 330, 863, 16, 54163}, {54188, 624, 877, 16, 54713}, {54735, 233, 877, 16, 55259},
{55289, 362, 883, 16, 55817}, {55843, 963, 907, 16, 56393}, {56403, 471, 907, 16, 56951}}};
} // namespace
Result<Rfc::Parameters> Rfc::get_parameters(size_t K) {
for (auto &p : rfc_parameters) {
if (p.K_padded >= K) {
return Rfc::Parameters(narrow_cast<uint32>(K), p);
}
}
return Status::Error("K is too big");
}
Rfc::Parameters::Parameters(uint32 K, RawParameters raw_parameters) {
this->K = K;
K_padded = raw_parameters.K_padded;
J = raw_parameters.J;
S = raw_parameters.S;
H = raw_parameters.H;
W = raw_parameters.W;
L = K_padded + S + H;
P = L - W;
U = P - H;
B = W - S;
P1 = P + 1;
auto is_prime = [](uint32 n) {
if (n <= 3)
return true;
if (n % 2 == 0 || n % 3 == 0)
return false;
uint32 i = 5;
uint32 w = 2;
while (i * i <= n) {
if (n % i == 0)
return false;
i += w;
w = 6 - w;
}
return true;
};
while (!is_prime(P1)) {
P1++;
}
}
uint32 Rfc::Parameters::get_degree(uint32 v) const {
static const std::array<uint32, 31> degree_distribution = {
{0, 5243, 529531, 704294, 791675, 844104, 879057, 904023, 922747, 937311, 948962,
958494, 966438, 973160, 978921, 983914, 988283, 992138, 995565, 998631, 1001391, 1003887,
1006157, 1008229, 1010129, 1011876, 1013490, 1014983, 1016370, 1017662, 1048576}};
for (uint32 i = 0; i < degree_distribution.size(); i++) {
if (v < degree_distribution[i]) {
return std::min(W - 2, i);
}
}
UNREACHABLE();
return 0;
}
Rfc::EncodingRow Rfc::Parameters::get_encoding_row(uint32 X /*ISI*/) const {
uint32 A = 53591 + J * 997;
if (A % 2 == 0) {
A++;
}
uint32 B_local = 10267 * (J + 1);
uint32 y = B_local + X * A;
uint32 v = random(y, 0, 1 << 20);
uint32 d = get_degree(v);
uint32 a = 1 + random(y, 1, W - 1);
uint32 b = random(y, 2, W);
uint32 d1;
if (d < 4) {
d1 = 2 + random(X, 3, 2);
} else {
d1 = 2;
}
uint32 a1 = 1 + random(X, 4, P1 - 1);
uint32 b1 = random(X, 5, P1);
EncodingRow r;
std::tie(r.d, r.a, r.b, r.d1, r.a1, r.b1) = std::tie(d, a, b, d1, a1, b1);
return r;
}
uint32 Rfc::Parameters::encoding_row_size(const EncodingRow &t) const {
return t.d + t.d1;
}
} // namespace raptorq
} // namespace td
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