flint-sys 0.9.0

Bindings to the FLINT C library
Documentation 
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/*
    Copyright 1991, 1992, 1993, 1994, 1996, 1997, 1999, 2000, 2001, 2002, 2003,
    2004, 2005 Free Software Foundation, Inc.

    Copyright 2009, 2015 William Hart
    Copyright 2025 Fredrik Johansson

    This file is part of FLINT.

    FLINT 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 3 of the License, or
    (at your option) any later version.  See <https://www.gnu.org/licenses/>.
*/

#include "flint-mparam.h"
#include "ulong_extras.h"

#if FLINT_PREINVERT_LIMB_USE_NATIVE

ulong n_preinvert_limb(ulong n)
{
    ulong ninv, r;
    unsigned int norm;

    norm = flint_clz(n);
    n <<= norm;

    udiv_qrnnd(ninv, r, ~n, ~UWORD(0), n);
    return ninv;
}

ulong n_preinvert_limb_prenorm(ulong n)
{
    ulong ninv, r;

    udiv_qrnnd(ninv, r, ~n, ~UWORD(0), n);
    return ninv;
}

#else


#if FLINT_BITS == 32

/* rec_word_tab[i] = div(2^24 - 2^14 + 2^9, 2^9 + i) */
static const unsigned short rec_word_tab[512] = {
   32737, 32673, 32609, 32546, 32483, 32420, 32357, 32295, 32233, 32171, 32109, 32048, 31987, 31926, 31865, 31805,
   31744, 31684, 31625, 31565, 31506, 31447, 31388, 31329, 31271, 31212, 31154, 31097, 31039, 30982, 30924, 30868,
   30811, 30754, 30698, 30642, 30586, 30530, 30475, 30419, 30364, 30309, 30255, 30200, 30146, 30092, 30038, 29984,
   29930, 29877, 29824, 29771, 29718, 29666, 29613, 29561, 29509, 29457, 29405, 29354, 29303, 29251, 29200, 29150,
   29099, 29049, 28998, 28948, 28898, 28849, 28799, 28750, 28700, 28651, 28602, 28554, 28505, 28457, 28409, 28360,
   28313, 28265, 28217, 28170, 28123, 28075, 28029, 27982, 27935, 27889, 27842, 27796, 27750, 27704, 27658, 27613,
   27568, 27522, 27477, 27432, 27387, 27343, 27298, 27254, 27209, 27165, 27121, 27078, 27034, 26990, 26947, 26904,
   26861, 26818, 26775, 26732, 26690, 26647, 26605, 26563, 26521, 26479, 26437, 26395, 26354, 26312, 26271, 26230,
   26189, 26148, 26108, 26067, 26026, 25986, 25946, 25906, 25866, 25826, 25786, 25747, 25707, 25668, 25628, 25589,
   25550, 25511, 25473, 25434, 25395, 25357, 25319, 25281, 25242, 25205, 25167, 25129, 25091, 25054, 25016, 24979,
   24942, 24905, 24868, 24831, 24794, 24758, 24721, 24685, 24649, 24612, 24576, 24540, 24504, 24469, 24433, 24397,
   24362, 24327, 24291, 24256, 24221, 24186, 24151, 24117, 24082, 24047, 24013, 23979, 23944, 23910, 23876, 23842,
   23808, 23774, 23741, 23707, 23674, 23640, 23607, 23574, 23541, 23508, 23475, 23442, 23409, 23377, 23344, 23312,
   23279, 23247, 23215, 23183, 23151, 23119, 23087, 23055, 23023, 22992, 22960, 22929, 22898, 22866, 22835, 22804,
   22773, 22742, 22711, 22681, 22650, 22619, 22589, 22559, 22528, 22498, 22468, 22438, 22408, 22378, 22348, 22318,
   22289, 22259, 22229, 22200, 22171, 22141, 22112, 22083, 22054, 22025, 21996, 21967, 21938, 21910, 21881, 21853,
   21824, 21796, 21767, 21739, 21711, 21683, 21655, 21627, 21599, 21571, 21544, 21516, 21488, 21461, 21433, 21406,
   21379, 21352, 21324, 21297, 21270, 21243, 21216, 21190, 21163, 21136, 21110, 21083, 21056, 21030, 21004, 20977,
   20951, 20925, 20899, 20873, 20847, 20821, 20795, 20769, 20744, 20718, 20693, 20667, 20642, 20616, 20591, 20566,
   20540, 20515, 20490, 20465, 20440, 20415, 20390, 20366, 20341, 20316, 20292, 20267, 20243, 20218, 20194, 20170,
   20145, 20121, 20097, 20073, 20049, 20025, 20001, 19977, 19953, 19930, 19906, 19882, 19859, 19835, 19812, 19789,
   19765, 19742, 19719, 19696, 19672, 19649, 19626, 19603, 19581, 19558, 19535, 19512, 19489, 19467, 19444, 19422,
   19399, 19377, 19354, 19332, 19310, 19288, 19265, 19243, 19221, 19199, 19177, 19155, 19133, 19112, 19090, 19068,
   19046, 19025, 19003, 18982, 18960, 18939, 18917, 18896, 18875, 18854, 18832, 18811, 18790, 18769, 18748, 18727,
   18706, 18686, 18665, 18644, 18623, 18603, 18582, 18561, 18541, 18520, 18500, 18479, 18459, 18439, 18419, 18398,
   18378, 18358, 18338, 18318, 18298, 18278, 18258, 18238, 18218, 18199, 18179, 18159, 18139, 18120, 18100, 18081,
   18061, 18042, 18022, 18003, 17984, 17964, 17945, 17926, 17907, 17888, 17869, 17850, 17831, 17812, 17793, 17774,
   17755, 17736, 17718, 17699, 17680, 17662, 17643, 17624, 17606, 17587, 17569, 17551, 17532, 17514, 17496, 17477,
   17459, 17441, 17423, 17405, 17387, 17369, 17351, 17333, 17315, 17297, 17279, 17261, 17244, 17226, 17208, 17191,
   17173, 17155, 17138, 17120, 17103, 17085, 17068, 17051, 17033, 17016, 16999, 16982, 16964, 16947, 16930, 16913,
   16896, 16879, 16862, 16845, 16828, 16811, 16794, 16778, 16761, 16744, 16727, 16711, 16694, 16677, 16661, 16644,
   16628, 16611, 16595, 16578, 16562, 16546, 16529, 16513, 16497, 16481, 16464, 16448, 16432, 16416, 16400, 16384
};

#define _invert_limb(dinv, d)                                      \
   do {                                                           \
      ulong _v0, _v1, _v2, _d21, _e, _m0;                     \
      FLINT_ASSERT(((d) & (UWORD(1)<<(FLINT_BITS - 1))) != 0); \
      _v0 = rec_word_tab[((d) >> 22) & 0x1FF];                    \
      _d21 = ((d) >> 11) + 1;                                     \
      _m0 = _v0*_v0;                                              \
      umul_ppmm(_v1, _e, _m0, _d21);                              \
      _v1 = (_v0 << 4) - _v1 - 1;                                 \
      _e = -_v1*((d) >> 1);                                       \
      _m0 = -((d) & (ulong) 1);                               \
      _e -= ((_v1 - (_v1 >> 1)) & _m0);                           \
      umul_ppmm(_v2, _m0, _v1, _e);                               \
      _v2 = (_v1 << 15) + (_v2 >> 1);                             \
      umul_ppmm(_v0, _d21, _v2, (d));                             \
      add_ssaaaa(_v0, _d21, _v0, _d21, (ulong) 0, (d));       \
      (dinv) = _v2 - (_v0 + (d));                                 \
   } while(0)

#else

/* rec_word_tab[i] = div(2^19 - 3*2^8, 2^8 + i) */
static const unsigned short rec_word_tab[256] = {
   2045, 2037, 2029, 2021, 2013, 2005, 1998, 1990, 1983, 1975, 1968, 1960, 1953, 1946, 1938, 1931,
   1924, 1917, 1910, 1903, 1896, 1889, 1883, 1876, 1869, 1863, 1856, 1849, 1843, 1836, 1830, 1824,
   1817, 1811, 1805, 1799, 1792, 1786, 1780, 1774, 1768, 1762, 1756, 1750, 1745, 1739, 1733, 1727,
   1722, 1716, 1710, 1705, 1699, 1694, 1688, 1683, 1677, 1672, 1667, 1661, 1656, 1651, 1646, 1641,
   1636, 1630, 1625, 1620, 1615, 1610, 1605, 1600, 1596, 1591, 1586, 1581, 1576, 1572, 1567, 1562,
   1558, 1553, 1548, 1544, 1539, 1535, 1530, 1526, 1521, 1517, 1513, 1508, 1504, 1500, 1495, 1491,
   1487, 1483, 1478, 1474, 1470, 1466, 1462, 1458, 1454, 1450, 1446, 1442, 1438, 1434, 1430, 1426,
   1422, 1418, 1414, 1411, 1407, 1403, 1399, 1396, 1392, 1388, 1384, 1381, 1377, 1374, 1370, 1366,
   1363, 1359, 1356, 1352, 1349, 1345, 1342, 1338, 1335, 1332, 1328, 1325, 1322, 1318, 1315, 1312,
   1308, 1305, 1302, 1299, 1295, 1292, 1289, 1286, 1283, 1280, 1276, 1273, 1270, 1267, 1264, 1261,
   1258, 1255, 1252, 1249, 1246, 1243, 1240, 1237, 1234, 1231, 1228, 1226, 1223, 1220, 1217, 1214,
   1211, 1209, 1206, 1203, 1200, 1197, 1195, 1192, 1189, 1187, 1184, 1181, 1179, 1176, 1173, 1171,
   1168, 1165, 1163, 1160, 1158, 1155, 1153, 1150, 1148, 1145, 1143, 1140, 1138, 1135, 1133, 1130,
   1128, 1125, 1123, 1121, 1118, 1116, 1113, 1111, 1109, 1106, 1104, 1102, 1099, 1097, 1095, 1092,
   1090, 1088, 1086, 1083, 1081, 1079, 1077, 1074, 1072, 1070, 1068, 1066, 1064, 1061, 1059, 1057,
   1055, 1053, 1051, 1049, 1047, 1044, 1042, 1040, 1038, 1036, 1034, 1032, 1030, 1028, 1026, 1024
};

#define _invert_limb(dinv, d)                                      \
   do {                                                           \
      ulong _v0, _v2, _d40, _e, _m0;                          \
      FLINT_ASSERT(((d) & (UWORD(1)<<(FLINT_BITS - 1))) != 0); \
      _d40 = ((d) >> 24) + 1;                                     \
      _v0 = rec_word_tab[((d) >> 55) & 0xFF];                     \
      _v0 = (_v0 << 11) - ((_v0*_v0*_d40) >> 40) - 1;             \
      _v2 = ((_v0*((((ulong) 1) << 60) - _v0*_d40)) >> 47);   \
      _v2 += (_v0 << 13);                                         \
      _e = -_v2*((d) >> 1);                                       \
      _m0 = -((d) & (ulong) 1);                               \
      _e -= ((_v2 - (_v2 >> 1)) & _m0);                           \
      umul_ppmm(_v0, _d40, _v2, _e);                              \
      _v2 = (_v2 << 31) + (_v0 >> 1);                             \
      umul_ppmm(_v0, _d40, _v2, (d));                             \
      add_ssaaaa(_v0, _d40, _v0, _d40, (ulong) 0, (d));       \
      (dinv) = _v2 - (_v0 + (d));                                 \
   } while (0)

#endif /* 64 bits */

ulong n_preinvert_limb(ulong n)
{
    ulong norm, ninv;

    norm = flint_clz(n);
    _invert_limb(ninv, n << norm);
    return ninv;
}

ulong n_preinvert_limb_prenorm(ulong n)
{
    ulong ninv;
    _invert_limb(ninv, n);
    return ninv;
}

#endif