arb/mag/fac_ui.c

/*
    Copyright (C) 2014 Fredrik Johansson

    This file is part of Arb.

    Arb is free software: you can redistribute it and/or modify it under
    the terms of the GNU Lesser General Public License (LGPL) as published
    by the Free Software Foundation; either version 2.1 of the License, or
    (at your option) any later version.  See <http://www.gnu.org/licenses/>.
*/

#include "mag.h"

#define MAG_FAC_TABLE_NUM 256

const int mag_fac_tab[MAG_FAC_TABLE_NUM * 2] =
{
    1, 536870912,
    1, 536870912,
    2, 536870912,
    3, 805306368,
    5, 805306368,
    7, 1006632960,
    10, 754974720,
    13, 660602880,
    16, 660602880,
    19, 743178240,
    22, 928972800,
    26, 638668800,
    29, 958003200,
    33, 778377600,
    37, 681080400,
    41, 638512875,
    45, 638512875,
    49, 678419930,
    53, 763222421,
    57, 906326625,
    62, 566454141,
    66, 743471060,
    70, 1022272707,
    75, 734758508,
    80, 551068881,
    84, 861045127,
    89, 699599166,
    94, 590286796,
    98, 1033001893,
    103, 936157966,
    108, 877648093,
    113, 850221590,
    118, 850221590,
    123, 876791015,
    128, 931590453,
    133, 1018927058,
    139, 573146470,
    144, 662700606,
    149, 786956970,
    154, 959103807,
    160, 599439879,
    165, 768032345,
    170, 1008042453,
    176, 677278523,
    181, 931257969,
    187, 654790760,
    192, 941261717,
    198, 691239074,
    203, 1036858610,
    209, 793844874,
    215, 620191308,
    220, 988429896,
    226, 803099291,
    232, 665066600,
    238, 561149944,
    243, 964476466,
    249, 843916908,
    255, 751613496,
    261, 681149731,
    267, 627934908,
    273, 588688976,
    279, 561094181,
    285, 543559988,
    290, 1070133725,
    296, 1070133725,
    303, 543427282,
    309, 560409385,
    315, 586678575,
    321, 623345986,
    327, 672044891,
    333, 735049099,
    339, 815445095,
    345, 917375731,
    351, 1046381693,
    358, 604939417,
    364, 708913379,
    370, 841834637,
    376, 1012832298,
    383, 617194682,
    389, 761849685,
    395, 952312106,
    402, 602635005,
    408, 772126100,
    414, 1001351036,
    421, 657136617,
    427, 872759570,
    434, 586385336,
    440, 797117566,
    447, 548018327,
    453, 762087986,
    459, 1071686230,
    466, 761901929,
    473, 547617012,
    479, 795755970,
    486, 584383290,
    492, 867443946,
    499, 650582960,
    505, 986039798,
    512, 754936721,
    519, 583896370,
    525, 912338078,
    532, 719891765,
    539, 573663750,
    545, 923240098,
    552, 750132579,
    559, 615343132,
    565, 1019162061,
    572, 851955786,
    579, 718837694,
    586, 612135224,
    592, 1052107416,
    599, 912374400,
    606, 798327600,
    613, 704773585,
    620, 627688974,
    627, 563939312,
    633, 1022140003,
    640, 934299847,
    647, 861307671,
    654, 800746976,
    661, 750700290,
    668, 709646368,
    675, 676381694,
    682, 649960534,
    689, 629649268,
    696, 614891863,
    703, 605284178,
    710, 600555395,
    717, 600555395,
    724, 605247234,
    731, 614704222,
    738, 629111352,
    745, 648771082,
    752, 674113702,
    759, 705712782,
    766, 744306450,
    773, 790825603,
    780, 846430528,
    787, 912557913,
    794, 990980859,
    802, 541942657,
    809, 596983708,
    816, 662278801,
    823, 739889598,
    830, 832375798,
    837, 942925709,
    845, 537762319,
    852, 617586413,
    859, 714084290,
    866, 831238743,
    873, 974107902,
    881, 574571458,
    888, 682303606,
    895, 815566029,
    902, 981227879,
    910, 594102818,
    917, 724062809,
    924, 888108289,
    932, 548129335,
    939, 680879408,
    946, 851099260,
    953, 1070523287,
    961, 677440518,
    968, 862678159,
    976, 552653196,
    983, 712404510,
    990, 923899599,
    998, 602700129,
    1005, 791043920,
    1012, 1044425175,
    1020, 693563593,
    1027, 926557612,
    1035, 622530896,
    1042, 841389414,
    1050, 571881867,
    1057, 781869740,
    1065, 537535447,
    1072, 743310735,
    1079, 1033666490,
    1087, 722758991,
    1094, 1016379831,
    1102, 718612303,
    1109, 1021776868,
    1117, 730410808,
    1124, 1049965536,
    1132, 758764157,
    1140, 551289583,
    1147, 805399625,
    1155, 591465350,
    1162, 873335555,
    1170, 648178733,
    1177, 967204202,
    1185, 725403152,
    1193, 546885970,
    1200, 828874048,
    1208, 631368904,
    1215, 966783634,
    1223, 743970218,
    1231, 575414466,
    1238, 894589677,
    1246, 698898186,
    1254, 548744279,
    1261, 865987064,
    1269, 686700680,
    1277, 547214604,
    1284, 876398390,
    1292, 705226829,
    1300, 570242007,
    1307, 926643260,
    1315, 756517349,
    1323, 620580638,
    1330, 1022988396,
    1338, 847162265,
    1346, 704865479,
    1354, 589223486,
    1361, 989711324,
    1369, 835068930,
    1377, 707851397,
    1385, 602779706,
    1392, 1031318402,
    1400, 886289252,
    1408, 765116894,
    1416, 663499806,
    1424, 577970534,
    1431, 1011448435,
    1439, 888968351,
    1447, 784792372,
    1455, 695890111,
    1463, 619777131,
    1471, 554410011,
    1478, 996205489,
    1486, 898919797,
    1494, 814646066,
    1502, 741455208,
    1510, 677736401,
    1518, 622140837,
    1526, 573536084,
    1533, 1061937906,
    1541, 987270397,
    1549, 921709472,
    1557, 864102630,
    1565, 813471617,
    1573, 768984888,
    1581, 729934874,
    1589, 695719177,
    1597, 665824993,
    1605, 639816204,
    1613, 617322666,
    1621, 598031333,
    1629, 581678914,
    1637, 568045814,
    1645, 556951169,
    1653, 548248807,
    1661, 541824017,
    1669, 537591016,
    1676, 1070982102,
};

const int mag_rfac_tab[MAG_FAC_TABLE_NUM * 2] =
{
    1, 536870912,
    1, 536870912,
    0, 536870912,
    -2, 715827883,
    -4, 715827883,
    -6, 572662307,
    -9, 763549742,
    -12, 872628277,
    -15, 872628277,
    -18, 775669579,
    -21, 620535663,
    -25, 902597328,
    -28, 601731552,
    -32, 740592680,
    -36, 846391634,
    -40, 902817743,
    -44, 902817743,
    -48, 849710817,
    -52, 755298504,
    -56, 636040846,
    -61, 1017665353,
    -65, 775364078,
    -69, 563901148,
    -74, 784558119,
    -79, 1046077491,
    -83, 669489595,
    -88, 823987193,
    -93, 976577414,
    -97, 558044237,
    -102, 615772951,
    -107, 656824481,
    -112, 678012368,
    -117, 678012368,
    -122, 657466538,
    -127, 618792036,
    -132, 565752719,
    -138, 1005782611,
    -143, 869866042,
    -148, 732518772,
    -153, 601041044,
    -159, 961665670,
    -164, 750568328,
    -169, 571861583,
    -175, 851142821,
    -180, 619012961,
    -186, 880373989,
    -191, 612434079,
    -197, 833952789,
    -202, 555968526,
    -208, 726162972,
    -214, 929488605,
    -219, 583208536,
    -225, 717795122,
    -231, 866771468,
    -237, 1027284702,
    -242, 597692918,
    -248, 683077620,
    -254, 766964346,
    -260, 846305485,
    -266, 918026288,
    -272, 979228041,
    -278, 1027386797,
    -284, 1060528307,
    -289, 538681045,
    -295, 538681045,
    -302, 1060787288,
    -308, 1028642219,
    -314, 982583612,
    -320, 924784576,
    -326, 857771201,
    -332, 784247955,
    -338, 706927734,
    -344, 628380208,
    -350, 550908676,
    -357, 952923115,
    -363, 813161058,
    -369, 684767207,
    -375, 569157159,
    -382, 934001491,
    -388, 756659436,
    -394, 605327549,
    -401, 956566990,
    -407, 746588871,
    -413, 575682985,
    -420, 877231215,
    -426, 660503503,
    -433, 983074981,
    -439, 723181595,
    -446, 1051900502,
    -452, 756422833,
    -458, 537900681,
    -465, 756607552,
    -472, 1052671376,
    -478, 724419012,
    -485, 986442909,
    -491, 664551013,
    -498, 886068017,
    -504, 584622197,
    -511, 763588175,
    -518, 987265519,
    -524, 631849933,
    -531, 800760310,
    -538, 1004875684,
    -544, 624388774,
    -551, 768478492,
    -558, 936811875,
    -564, 565622264,
    -571, 676632242,
    -578, 801934508,
    -585, 941721257,
    -591, 547910550,
    -598, 631824778,
    -605, 722085461,
    -612, 817937513,
    -619, 918385980,
    -626, 1022203525,
    -632, 563974359,
    -639, 616997589,
    -646, 669285520,
    -653, 719903753,
    -660, 767897336,
    -667, 812321149,
    -674, 852271370,
    -681, 886916547,
    -688, 915526759,
    -695, 937499401,
    -702, 952380344,
    -709, 959879401,
    -716, 959879401,
    -723, 952438476,
    -730, 937785576,
    -737, 916309571,
    -744, 888542614,
    -751, 855138756,
    -758, 816848961,
    -765, 774493830,
    -772, 728935369,
    -779, 681049104,
    -786, 631697720,
    -793, 581707253,
    -801, 1063693262,
    -808, 965622252,
    -815, 870420058,
    -822, 779117255,
    -829, 692548671,
    -836, 611353310,
    -844, 1071961968,
    -851, 933409060,
    -858, 807272701,
    -865, 693496012,
    -872, 591783263,
    -880, 1003288181,
    -887, 844874258,
    -894, 706822909,
    -901, 587489171,
    -909, 970304695,
    -916, 796147442,
    -923, 649088360,
    -931, 1051687470,
    -938, 846641485,
    -945, 677313188,
    -952, 538485019,
    -960, 850939290,
    -967, 668222264,
    -975, 1043078656,
    -982, 809176170,
    -989, 623943071,
    -997, 956463629,
    -1004, 728734194,
    -1011, 551940691,
    -1019, 831157747,
    -1026, 622153167,
    -1034, 925995411,
    -1041, 685129553,
    -1049, 1008006698,
    -1056, 737284900,
    -1064, 1072414399,
    -1071, 775531317,
    -1078, 557685442,
    -1086, 797583648,
    -1093, 567170594,
    -1101, 802186034,
    -1108, 564174793,
    -1116, 789228126,
    -1123, 549028262,
    -1131, 759736405,
    -1139, 1045658708,
    -1146, 715744998,
    -1154, 974631486,
    -1161, 660067885,
    -1169, 889354624,
    -1176, 596007287,
    -1184, 794676383,
    -1192, 1054078518,
    -1199, 695474487,
    -1207, 913033172,
    -1214, 596266561,
    -1222, 774843856,
    -1230, 1001818319,
    -1237, 644385653,
    -1245, 824813635,
    -1253, 1050508908,
    -1260, 665669011,
    -1268, 839464369,
    -1276, 1053445483,
    -1283, 657761082,
    -1291, 817411830,
    -1299, 1010905451,
    -1306, 622095663,
    -1314, 761992773,
    -1322, 928905476,
    -1329, 563506640,
    -1337, 680460848,
    -1345, 817830878,
    -1353, 978339742,
    -1360, 582453428,
    -1368, 690315174,
    -1376, 814381034,
    -1384, 956337361,
    -1391, 558955170,
    -1399, 650420562,
    -1407, 753428343,
    -1415, 868818269,
    -1423, 997387789,
    -1430, 569935879,
    -1438, 648460378,
    -1446, 734539189,
    -1454, 828378998,
    -1462, 930109752,
    -1470, 1039773347,
    -1477, 578656472,
    -1485, 641281631,
    -1493, 707621110,
    -1501, 777472121,
    -1509, 850567790,
    -1517, 926575975,
    -1525, 1005099363,
    -1532, 542838475,
    -1540, 583893485,
    -1548, 625425658,
    -1556, 667120702,
    -1564, 708642737,
    -1572, 749638598,
    -1580, 789742721,
    -1588, 828582526,
    -1596, 865784191,
    -1604, 900978670,
    -1612, 933807852,
    -1620, 963930686,
    -1628, 991029139,
    -1636, 1014813839,
    -1644, 1035029254,
    -1652, 1051458290,
    -1660, 1063926174,
    -1668, 1072303546,
    -1675, 538254329,
};

void
mag_fac_ui(mag_t z, ulong n)
{
    if (n < MAG_FAC_TABLE_NUM)
    {
        _fmpz_demote(MAG_EXPREF(z));
        MAG_EXP(z) = mag_fac_tab[n * 2];
        MAG_MAN(z) = mag_fac_tab[n * 2 + 1];
    }
    else
    {
        double x = n;

        x = ceil((((x+0.5)*mag_d_log_upper_bound(x) - x) * 1.4426950408889634074 + 2) * 1.0000001);

        /* x + 1 could round down for huge x, but this doesn't matter
           as long as the result was perturbed up above */
        fmpz_set_d(MAG_EXPREF(z), x + 1);
        MAG_MAN(z) = MAG_ONE_HALF;
    }
}

void
mag_rfac_ui(mag_t z, ulong n)
{
    if (n < MAG_FAC_TABLE_NUM)
    {
        _fmpz_demote(MAG_EXPREF(z));
        MAG_EXP(z) = mag_rfac_tab[n * 2];
        MAG_MAN(z) = mag_rfac_tab[n * 2 + 1];
    }
    else
    {
        double x = n;

        x = ceil((((x+0.5)*mag_d_log_lower_bound(x) - x) * 1.4426950408889634074) * -0.9999999);

        /* x + 1 could round down for huge x, but this doesn't matter
           as long as the value was perturbed up above */
        fmpz_set_d(MAG_EXPREF(z), x + 1);
        MAG_MAN(z) = MAG_ONE_HALF;
    }
}