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/*******************************************************************************
* *
* (C) 1997-2014 by Ernst W. Mayer. *
* *
* This program is free software; you can redistribute it and/or modify it *
* under the terms of the GNU General Public License as published by the *
* Free Software Foundation; either version 2 of the License, or (at your *
* option) any later version. *
* *
* This program 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 General Public License for *
* more details. *
* *
* You should have received a copy of the GNU General Public License along *
* with this program; see the file GPL.txt. If not, you may view one at *
* http://www.fsf.org/licenses/licenses.html, or obtain one by writing to the *
* Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA *
* 02111-1307, USA. *
* *
*******************************************************************************/
/****************************************************************************
* We now include this header file if it was not included before.
****************************************************************************/
#ifndef fac_test_dat128_included
#define fac_test_dat128_included
#include "types.h"
struct testFac128{
uint32 p;
uint64 d1;
uint64 d0;
};
struct testFac128x2{
uint64 phi;
uint64 plo;
uint64 d1;
uint64 d0;
};
/*******************************************/
/* Fermat-number test factors: */
/*******************************************/
// Here interpret the above testFac128 struct as a minimalist [n,k1,k0]-trio format,
// where k = k1*2^64 + k0, Fn = 2^2^n+1 is the Fermat number and q = k.2^(n+2)+1 the factor.
// To check any particular (alleged) factor q of Fn using Pari, use Mod(2,q)^(2^n)+1.
// Testcases with factors < 2^128:
static const struct testFac128 ffac128[] =
{
{ 7, 0ull,11141971095088142685ull}, // 1970 Morrison/Brillhart
{11,0ull, 20506415569062558ull},{11,0ull,434673084282938711ull}, // 1988 Brent
{13, 528ull,11889784005418124336ull}, // 1995 Brent
{15, 69801146ull,13376893484985149619ull}, // 1997 Crandall/van Halewyn
{16, 39ull, 1485176525646847404ull}, // 1996 Crandall/Dilcher
{18, 0ull, 77509585098133576ull}, // 1999 Crandall/McIntosh/Tardif
{19,971680160ull,15036099344401914846ull}, // 2009 Bessell/Woltman
{22,208923546ull,18410182759848881875ull}, // 2010 Bessell/Woltman
{31, 0ull, 5463561471303ull}, // 2001 Kruppa/Forbes
{37, 0ull, 1275438465ull}, // 1991 Gostin
{39, 0ull, 2864929972774011ull}, // 2012 Rajala/Woltman
{42, 0ull, 222636358286122ull}, // 2011 Maznichenko/Rodenkirch
{43, 0ull, 212675402445ull}, // 2000 Samidoost/Durman
{48, 0ull, 2139543641769ull}, // 2001 Bodschwinna/Durman
{52,0ull, 4119ull},{52,0ull, 21626655ull},{52,0ull,81909357657279ull}, // 1963 Wrathall, 1982 Keller, 2010 Vonck/Durman
{58, 0ull, 190ull}, // 1957 Robinson
{61, 0ull, 439880504ull}, // 1986 Gostin
{62, 0ull, 697ull}, // 1977 Shippee
{63, 0ull, 36ull}, // 1956 Robinson
{64, 0ull, 35707278ull}, // 1986 Gostin
{65, 0ull, 2421791520862166ull}, // 2011 Maznichenko/Woltman
{66, 0ull, 15102ull}, // 1977 Shippee
{71, 0ull, 683ull}, // 1977 Shippee
{72, 0ull, 76432329ull}, // 1986 Gostin
{73, 0ull, 5ull}, // 1906 Morehead
{75, 0ull, 3447431ull}, // 1982 Gostin
{77,0ull, 425ull},{77,0ull,5940341195ull}, // 1957 Robinson/Selfridge, 1999 Taura
{81, 0ull, 542ull}, // 1957 Robinson/Selfridge
{83, 0ull, 6383454640628ull}, // 2005 Danilov/Durman
{88, 0ull, 119942751127ull}, // 2001 Nohara/Durman
{99, 0ull, 129864ull}, // 1979 Gostin/McLaughlin/Suyama
{117, 0ull, 14ull}, // 1956 Robinson
{0,0ull,0ull}
};
// Testcases with factors > 256 bits (i.e. larger than our current largest fixed-length
// modpow support, hence necessitating the use of the arbitrary-length mi64-code modpow).
// Here interpret the above testFac128 struct as a [n,pow2,k] trio, Fn = 2^2^n+1 is the
// Fermat number and q = k.2^pow2 + 1 the factor. Limit ourselves to n < 10000 in order
// to keep the resulting self-test timings reasonable.
// To check any particular (alleged) factor q of Fn using Pari, use Mod(2,q)^(2^n)+1.
static const struct testFac128 ffacBig[] =
{
{ 230, 232ull,372236097ull},
{ 232, 236ull,70899775ull},
{ 250, 252ull,403ull},
{ 251, 254ull,85801657ull},
{ 255, 257ull,629ull},
{ 256, 258ull,36986355ull},
{ 259, 262ull,36654265ull},
{ 267, 271ull,177ull},
{ 268, 276ull,21ull},
{ 275, 279ull,22347ull},
{ 284, 286ull,1061341513ull},
{ 286, 288ull,78472588395ull},
{ 287, 289ull,5915ull},
{ 297, 301ull,72677552745ull},
{ 298, 302ull,247ull},
{ 299, 304ull,272392805475ull},
{ 301, 304ull,7183437ull},
{ 316, 320ull,7ull},
{ 329, 333ull,1211ull},
{ 334, 341ull,27609ull},
{ 338, 342ull,27654487ull},
{ 343, 345ull,4844391185ull},
{ 353, 355ull,18908555ull},
{ 370, 373ull,573230511ull},
{ 375, 377ull,733251ull},
{ 376, 378ull,810373ull},
{ 380, 385ull,321116871ull},
{ 398, 401ull,120845ull},
{ 416, 419ull,38039ull},
{ 417, 420ull,303472680883ull},
{ 431, 434ull,5769285ull},
{ 452, 455ull,27ull},
{ 459, 465ull,5449229488169ull},
{ 468, 471ull,27114089ull},
{ 480, 484ull,5673968845ull},
{ 517, 520ull,84977118993ull},
{ 544, 547ull,225ull},
{ 547, 550ull,77377ull},
{ 556, 558ull,127ull},
{ 569, 575ull,6616590375ull},
{ 579, 581ull,63856313ull},
{ 600, 605ull,6213186413ull},
{ 620, 624ull,10084141ull},
{ 635, 645ull,4258979ull},
{ 637, 643ull,11969ull},
{ 642, 644ull,52943971ull},
{ 666, 668ull,217924552867ull},
{ 667, 669ull,491628159ull},
{ 692, 695ull,717ull},
{ 723, 730ull,554815ull},
{ 744, 747ull,17ull},
{ 851, 859ull,497531ull},
{ 885, 887ull,16578999ull},
{ 906, 908ull,57063ull},
{ 931, 933ull,1985ull},
{ 943, 954ull,4785972759ull},
{ 971, 976ull,541664191ull},
{1069,1073ull,137883ull},
{1082,1084ull,82165ull},
{1114,1116ull,11618577ull},
{1123,1125ull,25835ull},
{1132,1136ull,10111717305ull},
{1160,1162ull,2018719057ull},
{1201,1203ull,837747239ull},
{1225,1231ull,79707ull},
{1229,1233ull,29139ull},
{1394,1396ull,62705223ull},
{1451,1454ull,13143ull},
{1551,1553ull,291ull},
{1598,1600ull,10923781ull},
{1710,1719ull,351276975ull},
{1722,1724ull,364182745ull},
{1849,1851ull,98855ull},
{1945,1947ull,5ull},
{1990,1993ull,150863ull},
{2023,2027ull,29ull},
{2059,2063ull,591909ull},
{2089,2099ull,431ull},
{2420,2422ull,103257279ull},
{2456,2458ull,85ull},
{2606,2608ull,238451805ull},
{3310,3313ull,5ull},
{3314,3322ull,406860969ull},
{3335,3337ull,43714055ull},
{3506,3508ull,501ull},
{3703,3706ull,262254673ull},
{3723,3725ull,13308899ull},
{4184,4189ull,465917283ull},
{4250,4252ull,173373ull},
{4258,4262ull,1435ull},
{4260,4262ull,209161375ull},
{4265,4269ull,72179955ull},
{4332,4334ull,2466157ull},
{4652,4654ull,143918649ull},
{4724,4727ull,29ull},
{5320,5323ull,21341ull},
{5531,5533ull,1503975ull},
{5792,5794ull,8872947ull},
{5957,5960ull,421435ull},
{6208,6210ull,763ull},
{6355,6358ull,115185ull},
{6390,6393ull,303ull},
{6537,6539ull,17ull},
{6835,6838ull,19ull},
{6909,6912ull,6021ull},
{7181,7187ull,168329ull},
{7309,7312ull,145ull},
{8239,8242ull,7473ull},
{8269,8271ull,592131ull},
{8298,8300ull,1054057ull},
{8555,8557ull,645ull},
{9322,9324ull,8247ull},
{9428,9431ull,9ull},
{9447,9449ull,5505161ull},
{9448,9450ull,19ull},
{9549,9551ull,1211ull},
{9691,9693ull,260435ull},
{9747,9749ull,44670651ull},
{ 0, 0ull,0ull}
};
/*******************************************/
/* Mersenne-number test factors: */
/*******************************************/
/* Factors > 96 but <= 128 bits. If desired, we can construct more test factors
by multiplying together a 63/64-bit factor q1 of M(p1) and a 65/64-bit factor q2 of M(p2)
and checking whether q1*q2 divides M(p1*p2).*/
static const struct testFac128 fac128[] =
{
{ 695, 12240518780192025ull, 1654746039858251761ull},
{ 845, 2923447923687422893ull, 353773459776294223ull},
{ 1113, 128099917305337ull, 7733695761441692271ull},
{ 1145, 10811609908058563ull, 5349936413307099433ull},
{ 1149, 700245770430ull, 701890237964104231ull},
{ 733, 756146046438660814ull, 7804835620876695225ull},
{ 737, 106450884062962221ull,17050154159176967743ull},
{ 871, 7448657723978021346ull,15223106393317212577ull},
{ 947, 644719741813452ull,16055621295463638505ull},
{ 953, 44696312570505ull, 4961431981940124743ull},
{ 989, 99970972632587991ull, 1738540175825943815ull},
{ 1081, 67677680549ull,13887741953162944095ull},
{ 1091, 5287390011750720ull, 2894679571106043497ull},
{ 1097, 11129117045170ull,10375766809019373543ull},
{ 1099, 1551337752834ull, 8321741389535251703ull},
{ 1133, 133834206206032981ull, 6586095673132787791ull},
{ 1141, 5747037125100ull, 2460710484528304153ull},
{ 1181, 10824073357153ull, 7361144750966677159ull},
{ 1189, 32559650929209964ull, 8212830436061989903ull},
{ 27691, 94004235929829273ull, 4235226679561594903ull},
{ 319057, 103337218078ull, 8676403300852410079ull},
{17363977, 62897895526806ull,14211535226588354713ull},
{10624093, 5492917609ull,14854696485656401105ull},
{10698673, 5799457823ull,10285356664749312993ull},
{20799431, 4303087381ull,16578386512849109713ull},
{33652757, 5202063708ull,18263664019678288919ull},
{21823211, 7785579841ull, 7607475409566672241ull},
{22330859, 7593776864ull, 5630449305759171207ull},
{11808917, 20308449831ull, 9058738039473012457ull},
{20090969, 15531431134ull, 5034609389988515233ull},
{20313967, 18216394609ull, 8291172543411688687ull},
{20544481, 16259503442ull,15859685870849762975ull},
{22217387, 20551559047ull,11995354231649723881ull},
{10207999, 28364424832ull,15122069645900159367ull},
{19964723, 34441477586ull, 9636073161914837921ull},
{21145199, 30977655046ull, 1304857345634219175ull},
{22030163, 43144178324ull, 4788416424359163737ull},
{33562153, 45963786472ull, 2258783450670948535ull},
{33693587, 66325700032ull,15262466751214122975ull},
{11865241, 57210216387ull, 3082735332820781609ull},
{21801929, 80355238912ull,15689518004012743009ull},
{19951201, 109346652057ull,10819675441336938065ull},
{20616781, 17534809723250ull,10329047311584913071ull},
{20648443, 1221873279710ull, 2595613477835803991ull},
{21250771, 12549422209078ull, 8612165677489771129ull},
{21547787, 112416184026ull, 9015544550402598895ull},
{21675733, 142220976614ull,11385509628023387489ull},
{15714269, 14320762091913ull, 2773697912020767049ull},
{19687561, 1996508583829ull, 7515490546312285159ull},
{20152333, 365842230851ull, 2388855518206098663ull},
{20510053, 261078947686ull, 465403687781705377ull},
{20759821, 199835753775288ull,17079803649869853575ull},
{20989043, 202355339943ull,15105677628487752455ull},
{33713123, 18738454648009ull,16692905930976531153ull},
{20542751, 412571049040ull,18170931828058363183ull},
{20812849, 534505286298455ull, 2216600112648316881ull},
{0,0,0ull}
};
/* Factors > 96 but <= 128 bits, with p > 64 bits - most of these are from my Jan 2003 runs of primes near 2^89: */
static const struct testFac128x2 fac128x2[] =
{
{33554431ull,18446744073709551175ull, 30899672449023ull,18446744073303442655ull},
{33554431ull,18446744073709551295ull, 85098334519295ull,18446744072895454529ull},
{33554431ull,18446744073709551513ull, 430360347665235967ull,18446742752658555745ull},
{33554431ull,18446744073709551513ull, 259661119604391935ull,18446743276643598623ull},
{33554431ull,18446744073709551513ull, 293843670505881599ull,18446743171715500217ull},
{33554431ull,18446744073709551567ull, 12593691025735679ull,18446744055318810857ull},
{33554431ull,18446744073709551595ull, 67108863ull,18446744073709551575ull},
{33554431ull,18446744073709551595ull, 631158865919ull,18446744073709156607ull},
{33554432ull, 89ull, 16384159383552ull, 43457455ull},
{33554432ull, 705ull, 7006880245689090048ull, 147219019329871ull},
{33554432ull, 741ull, 882615779328ull, 19491265ull},
{33554432ull, 741ull, 220386851553280ull, 4866917641ull},
{33554432ull, 767ull, 460834488713216ull, 10533930447ull},
{33554432ull, 837ull, 3613005073874944ull, 90124763455ull},
{33554432ull, 837ull, 1504315717976064ull, 37524469375ull},
{33554432ull, 1059ull, 67108864ull, 2119ull},
{33554432ull, 1275ull, 4898947072ull, 186151ull},
/*{33554432ull, 1275ull, 1096248325046272ull, 41655201151ull},*/
{33554432ull, 1337ull, 16333760626688ull, 650830209ull},
{33554432ull, 1337ull, 1481763717120ull, 59041921ull},
{33554432ull, 1521ull, 19343955296518144ull, 876848578633ull},
{33554432ull, 1547ull, 2147483648ull, 99009ull},
{33554432ull, 1917ull, 1124806032359424ull, 64261351945ull},
/*{33554432ull, 1917ull, 2192593957945344ull, 125265199465ull},*/
{33554432ull, 1917ull, 22749904896ull, 1299727ull},
{33554432ull, 2097ull, 34829164871680ull, 2176665031ull},
{33554432ull, 2585ull, 37028188127232ull, 2852614711ull},
/*{33554432ull, 2585ull, 1096267786616832ull, 84455377711ull},*/
{33554432ull, 2661ull, 2080374784ull, 164983ull},
{33554432ull, 2675ull, 805306368ull, 64201ull},
{33554432ull, 2729ull, 42057326395392ull, 3420544975ull},
{33554432ull, 2729ull, 4876868255744ull, 396638319ull},
{33554432ull, 2907ull, 22615687168ull, 1959319ull},
{33554432ull, 3045ull, 1301649700159488ull, 118122200281ull},
{33554432ull, 3045ull, 99321118720ull, 9013201ull},
{33554432ull, 3155ull, 26011932557312ull, 2445806481ull},
{33554432ull, 3159ull, 413994582016ull, 38975743ull},
{33554432ull, 3507ull, 250450280448ull, 26176249ull},
{33554432ull, 4155ull, 62084915730055168ull, 7687891270471ull},
{33554432ull, 4451ull, 7851737088ull, 1041535ull},
{33554432ull, 4485ull, 434328567808ull, 58053841ull},
{33554432ull, 4745ull, 82678120448ull, 11691681ull},
{33554432ull, 4745ull, 71672266752ull, 10135321ull},
{33554432ull, 5121ull, 143814295552ull, 21948607ull},
{33554432ull, 5247ull, 67108864ull, 10495ull},
{33554432ull, 5411ull, 544322411823104ull, 87777631593ull},
{33554432ull, 5499ull, 1739631741632512ull, 285096017935ull},
{33554432ull, 5735ull, 10563740499968ull, 1805515641ull},
{33554432ull, 5837ull, 7317214986240ull, 1272874591ull},
{0ull,0ull,0ull,0ull}
};
#endif /* #ifndef fac_test_dat128_included */
|
