diff options
Diffstat (limited to 'Build/source/libs/mpfr/mpfr-src/src/invsqrt_limb.h')
-rw-r--r-- | Build/source/libs/mpfr/mpfr-src/src/invsqrt_limb.h | 365 |
1 files changed, 365 insertions, 0 deletions
diff --git a/Build/source/libs/mpfr/mpfr-src/src/invsqrt_limb.h b/Build/source/libs/mpfr/mpfr-src/src/invsqrt_limb.h new file mode 100644 index 00000000000..54af7b76c9b --- /dev/null +++ b/Build/source/libs/mpfr/mpfr-src/src/invsqrt_limb.h @@ -0,0 +1,365 @@ +/* __gmpfr_invsqrt_limb_approx -- reciprocal approximate square root of a limb + +Copyright 2017 Free Software Foundation, Inc. +Contributed by the AriC and Caramba projects, INRIA. + +This file is part of the GNU MPFR Library. + +The GNU MPFR 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 3 of the License, or (at your +option) any later version. + +The GNU MPFR 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 the GNU MPFR Library; see the file COPYING.LESSER. If not, see +http://www.gnu.org/licenses/ or write to the Free Software Foundation, Inc., +51 Franklin St, Fifth Floor, Boston, MA 02110-1301, USA. */ + +#define MPFR_NEED_LONGLONG_H +#include "mpfr-impl.h" + +/* for now, we only provide __gmpfr_invert_limb for 64-bit limb */ +#if GMP_NUMB_BITS == 64 + +/* For 257 <= d10 <= 1024, T[d10-257] = floor(sqrt(2^30/d10)). + Sage code: + T = [floor(sqrt(2^30/d10)) for d10 in [257..1024]] */ +static const mp_limb_t T[768] = + { 2044, 2040, 2036, 2032, 2028, 2024, 2020, 2016, 2012, 2009, 2005, + 2001, 1997, 1994, 1990, 1986, 1983, 1979, 1975, 1972, 1968, 1965, 1961, + 1958, 1954, 1951, 1947, 1944, 1941, 1937, 1934, 1930, 1927, 1924, 1920, + 1917, 1914, 1911, 1907, 1904, 1901, 1898, 1895, 1891, 1888, 1885, 1882, + 1879, 1876, 1873, 1870, 1867, 1864, 1861, 1858, 1855, 1852, 1849, 1846, + 1843, 1840, 1837, 1834, 1831, 1828, 1826, 1823, 1820, 1817, 1814, 1812, + 1809, 1806, 1803, 1801, 1798, 1795, 1792, 1790, 1787, 1784, 1782, 1779, + 1777, 1774, 1771, 1769, 1766, 1764, 1761, 1759, 1756, 1754, 1751, 1749, + 1746, 1744, 1741, 1739, 1736, 1734, 1731, 1729, 1727, 1724, 1722, 1719, + 1717, 1715, 1712, 1710, 1708, 1705, 1703, 1701, 1698, 1696, 1694, 1692, + 1689, 1687, 1685, 1683, 1680, 1678, 1676, 1674, 1672, 1670, 1667, 1665, + 1663, 1661, 1659, 1657, 1655, 1652, 1650, 1648, 1646, 1644, 1642, 1640, + 1638, 1636, 1634, 1632, 1630, 1628, 1626, 1624, 1622, 1620, 1618, 1616, + 1614, 1612, 1610, 1608, 1606, 1604, 1602, 1600, 1598, 1597, 1595, 1593, + 1591, 1589, 1587, 1585, 1583, 1582, 1580, 1578, 1576, 1574, 1572, 1571, + 1569, 1567, 1565, 1563, 1562, 1560, 1558, 1556, 1555, 1553, 1551, 1549, + 1548, 1546, 1544, 1542, 1541, 1539, 1537, 1536, 1534, 1532, 1531, 1529, + 1527, 1526, 1524, 1522, 1521, 1519, 1517, 1516, 1514, 1513, 1511, 1509, + 1508, 1506, 1505, 1503, 1501, 1500, 1498, 1497, 1495, 1494, 1492, 1490, + 1489, 1487, 1486, 1484, 1483, 1481, 1480, 1478, 1477, 1475, 1474, 1472, + 1471, 1469, 1468, 1466, 1465, 1463, 1462, 1461, 1459, 1458, 1456, 1455, + 1453, 1452, 1450, 1449, 1448, 1446, 1445, 1443, 1442, 1441, 1439, 1438, + 1436, 1435, 1434, 1432, 1431, 1430, 1428, 1427, 1426, 1424, 1423, 1422, + 1420, 1419, 1418, 1416, 1415, 1414, 1412, 1411, 1410, 1408, 1407, 1406, + 1404, 1403, 1402, 1401, 1399, 1398, 1397, 1395, 1394, 1393, 1392, 1390, + 1389, 1388, 1387, 1385, 1384, 1383, 1382, 1381, 1379, 1378, 1377, 1376, + 1374, 1373, 1372, 1371, 1370, 1368, 1367, 1366, 1365, 1364, 1362, 1361, + 1360, 1359, 1358, 1357, 1355, 1354, 1353, 1352, 1351, 1350, 1349, 1347, + 1346, 1345, 1344, 1343, 1342, 1341, 1339, 1338, 1337, 1336, 1335, 1334, + 1333, 1332, 1331, 1330, 1328, 1327, 1326, 1325, 1324, 1323, 1322, 1321, + 1320, 1319, 1318, 1317, 1315, 1314, 1313, 1312, 1311, 1310, 1309, 1308, + 1307, 1306, 1305, 1304, 1303, 1302, 1301, 1300, 1299, 1298, 1297, 1296, + 1295, 1294, 1293, 1292, 1291, 1290, 1289, 1288, 1287, 1286, 1285, 1284, + 1283, 1282, 1281, 1280, 1279, 1278, 1277, 1276, 1275, 1274, 1273, 1272, + 1271, 1270, 1269, 1268, 1267, 1266, 1265, 1264, 1264, 1263, 1262, 1261, + 1260, 1259, 1258, 1257, 1256, 1255, 1254, 1253, 1252, 1252, 1251, 1250, + 1249, 1248, 1247, 1246, 1245, 1244, 1243, 1242, 1242, 1241, 1240, 1239, + 1238, 1237, 1236, 1235, 1234, 1234, 1233, 1232, 1231, 1230, 1229, 1228, + 1228, 1227, 1226, 1225, 1224, 1223, 1222, 1222, 1221, 1220, 1219, 1218, + 1217, 1216, 1216, 1215, 1214, 1213, 1212, 1211, 1211, 1210, 1209, 1208, + 1207, 1207, 1206, 1205, 1204, 1203, 1202, 1202, 1201, 1200, 1199, 1198, + 1198, 1197, 1196, 1195, 1194, 1194, 1193, 1192, 1191, 1190, 1190, 1189, + 1188, 1187, 1187, 1186, 1185, 1184, 1183, 1183, 1182, 1181, 1180, 1180, + 1179, 1178, 1177, 1177, 1176, 1175, 1174, 1174, 1173, 1172, 1171, 1171, + 1170, 1169, 1168, 1168, 1167, 1166, 1165, 1165, 1164, 1163, 1162, 1162, + 1161, 1160, 1159, 1159, 1158, 1157, 1157, 1156, 1155, 1154, 1154, 1153, + 1152, 1152, 1151, 1150, 1149, 1149, 1148, 1147, 1147, 1146, 1145, 1145, + 1144, 1143, 1142, 1142, 1141, 1140, 1140, 1139, 1138, 1138, 1137, 1136, + 1136, 1135, 1134, 1133, 1133, 1132, 1131, 1131, 1130, 1129, 1129, 1128, + 1127, 1127, 1126, 1125, 1125, 1124, 1123, 1123, 1122, 1121, 1121, 1120, + 1119, 1119, 1118, 1118, 1117, 1116, 1116, 1115, 1114, 1114, 1113, 1112, + 1112, 1111, 1110, 1110, 1109, 1109, 1108, 1107, 1107, 1106, 1105, 1105, + 1104, 1103, 1103, 1102, 1102, 1101, 1100, 1100, 1099, 1099, 1098, 1097, + 1097, 1096, 1095, 1095, 1094, 1094, 1093, 1092, 1092, 1091, 1091, 1090, + 1089, 1089, 1088, 1088, 1087, 1086, 1086, 1085, 1085, 1084, 1083, 1083, + 1082, 1082, 1081, 1080, 1080, 1079, 1079, 1078, 1077, 1077, 1076, 1076, + 1075, 1075, 1074, 1073, 1073, 1072, 1072, 1071, 1071, 1070, 1069, 1069, + 1068, 1068, 1067, 1067, 1066, 1065, 1065, 1064, 1064, 1063, 1063, 1062, + 1062, 1061, 1060, 1060, 1059, 1059, 1058, 1058, 1057, 1057, 1056, 1055, + 1055, 1054, 1054, 1053, 1053, 1052, 1052, 1051, 1051, 1050, 1049, 1049, + 1048, 1048, 1047, 1047, 1046, 1046, 1045, 1045, 1044, 1044, 1043, 1043, + 1042, 1041, 1041, 1040, 1040, 1039, 1039, 1038, 1038, 1037, 1037, 1036, + 1036, 1035, 1035, 1034, 1034, 1033, 1033, 1032, 1032, 1031, 1031, 1030, + 1030, 1029, 1029, 1028, 1028, 1027, 1027, 1026, 1026, 1025, 1025, 1024, + 1024 }; + +/* table of v0^3 */ +static const mp_limb_t T3[768] = + { 8539701184, 8489664000, 8439822656, 8390176768, 8340725952, + 8291469824, 8242408000, 8193540096, 8144865728, 8108486729, 8060150125, + 8012006001, 7964053973, 7928215784, 7880599000, 7833173256, 7797729087, + 7750636739, 7703734375, 7668682048, 7622111232, 7587307125, 7541066681, + 7506509912, 7460598664, 7426288351, 7380705123, 7346640384, 7312680621, + 7267563953, 7233848504, 7189057000, 7155584983, 7122217024, 7077888000, + 7044762213, 7011739944, 6978821031, 6935089643, 6902411264, 6869835701, + 6837362792, 6804992375, 6761990971, 6729859072, 6697829125, 6665900968, + 6634074439, 6602349376, 6570725617, 6539203000, 6507781363, 6476460544, + 6445240381, 6414120712, 6383101375, 6352182208, 6321363049, 6290643736, + 6260024107, 6229504000, 6199083253, 6168761704, 6138539191, 6108415552, + 6088387976, 6058428767, 6028568000, 5998805513, 5969141144, 5949419328, + 5919918129, 5890514616, 5861208627, 5841725401, 5812581592, 5783534875, + 5754585088, 5735339000, 5706550403, 5677858304, 5658783768, 5630252139, + 5611284433, 5582912824, 5554637011, 5535839609, 5507723096, 5489031744, + 5461074081, 5442488479, 5414689216, 5396209064, 5368567751, 5350192749, + 5322708936, 5304438784, 5277112021, 5258946419, 5231776256, 5213714904, + 5186700891, 5168743489, 5150827583, 5124031424, 5106219048, 5079577959, + 5061868813, 5044200875, 5017776128, 5000211000, 4982686912, 4956477625, + 4939055927, 4921675101, 4895680392, 4878401536, 4861163384, 4843965888, + 4818245769, 4801149703, 4784094125, 4767078987, 4741632000, 4724717752, + 4707843776, 4691010024, 4674216448, 4657463000, 4632407963, 4615754625, + 4599141247, 4582567781, 4566034179, 4549540393, 4533086375, 4508479808, + 4492125000, 4475809792, 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1174241375, + 1174241375, 1170905464, 1170905464, 1167575877, 1167575877, 1164252608, + 1164252608, 1160935651, 1160935651, 1157625000, 1154320649, 1154320649, + 1151022592, 1151022592, 1147730823, 1147730823, 1144445336, 1144445336, + 1141166125, 1141166125, 1137893184, 1137893184, 1134626507, 1134626507, + 1131366088, 1128111921, 1128111921, 1124864000, 1124864000, 1121622319, + 1121622319, 1118386872, 1118386872, 1115157653, 1115157653, 1111934656, + 1111934656, 1108717875, 1108717875, 1105507304, 1105507304, 1102302937, + 1102302937, 1099104768, 1099104768, 1095912791, 1095912791, 1092727000, + 1092727000, 1089547389, 1089547389, 1086373952, 1086373952, 1083206683, + 1083206683, 1080045576, 1080045576, 1076890625, 1076890625, 1073741824, + 1073741824 }; + +/* umul_hi(h, x, y) puts in h the high part of x*y */ +#ifdef HAVE_MULX_U64 +#include <immintrin.h> +#define umul_hi(h, x, y) _mulx_u64 (x, y, (unsigned long long *) &h) +#else +#define umul_hi(h, x, y) \ + do { \ + mp_limb_t _l; \ + umul_ppmm (h, _l, x, y); \ + } while (0) +#endif + +/* given 2^62 <= d < 2^64, put in r an approximation of + s = floor(2^96/sqrt(r)) - 2^64, with r <= s <= r + 15 */ +#define __gmpfr_invsqrt_limb_approx(r, d) \ + do { \ + mp_limb_t _d, _i, _v0, _e0, _d37, _v1, _e1, _h, _v2, _e2; \ + _d = (d); \ + _i = (_d >> 54) - 256; \ + /* i = d10 - 256 */ \ + _v0 = T[_i]; \ + _d37 = 1 + (_d >> 27); \ + _e0 = T3[_i] * _d37; \ + /* the value (_v0 << 57) - _e0 is less than 2^61 */ \ + _v1 = (_v0 << 11) + (((_v0 << 57) - _e0) >> 47); \ + _e1 = - _v1 * _v1 * _d37; \ + umul_hi (_h, _v1, _e1); \ + /* _h = floor(e_1*v_1/2^64) */ \ + _v2 = (_v1 << 10) + (_h >> 6); \ + umul_hi (_h, _v2 * _v2, _d); \ + /* in _h + 2, one +1 accounts for the lower neglected part of */ \ + /* v2^2*d. the other +1 is to compute ceil((h+1)/2) */ \ + _e2 = (MPFR_LIMB_ONE << 61) - ((_h + 2) >> 1); \ + _h = _v2 * _e2; \ + (r) = (_v2 << 33) + (_h >> 29); \ + } while (0) + +/* given 2^62 <= d < 2^64, return a 32-bit approximation r of + sqrt(2^126/d) */ +#define __gmpfr_invsqrt_halflimb_approx(r, d) \ + do { \ + mp_limb_t _d, _i, _v0, _e0, _d37, _v1, _e1, _h; \ + _d = (d); \ + _i = (_d >> 54) - 256; \ + /* i = d10 - 256 */ \ + _v0 = T[_i]; \ + _d37 = 1 + (_d >> 27); \ + _e0 = T3[_i] * _d37; \ + /* the value (_v0 << 57) - _e0 is less than 2^61 */ \ + _v1 = (_v0 << 11) + (((_v0 << 57) - _e0) >> 47); \ + _e1 = - _v1 * _v1 * _d37; \ + umul_hi (_h, _v1, _e1); \ + /* _h = floor(e_1*v_1/2^64) */ \ + (r) = (_v1 << 10) + (_h >> 6); \ + } while (0) + +/* given 2^62 <= n < 2^64, put in s an approximation of sqrt(2^64*n), + with: s <= floor(sqrt(2^64*u)) <= s + 7 */ +#define __gmpfr_sqrt_limb_approx(s, n) \ + do { \ + mp_limb_t _n, _x, _y, _z, _t; \ + _n = (n); \ + __gmpfr_invsqrt_halflimb_approx (_x, _n); \ + MPFR_ASSERTD(_x < MPFR_LIMB_ONE << 32); \ + /* x has 32 bits, and is near (by below) sqrt(2^126/n) */ \ + _y = (_x * (_n >> 31)) >> 32; \ + MPFR_ASSERTD(_y < MPFR_LIMB_ONE << 32); \ + /* y is near (by below) sqrt(n) */ \ + _z = _n - _y * _y; \ + /* reduce _z so that _z <= 2*_y */ \ + /* the maximal value of _z is 2*(2^32-1) */ \ + while (_z > 2 * ((MPFR_LIMB_ONE << 32) - 1)) \ + { \ + _z -= (_y + _y) + 1; \ + _y ++; \ + } \ + /* now z <= 2*(2^32-1): one reduction is enough */ \ + if (_z > _y + _y) \ + { \ + _z -= (_y + _y) + 1; \ + _y ++; \ + } \ + /* _x * _z should be < 2^64 */ \ + _t = (_x * _z) >> 32; \ + (s) = (_y << 32) + _t; \ + } while (0) + +/* given 2^62 <= u < 2^64, put in s the value floor(sqrt(2^64*u)), + and in rh in rl the remainder: 2^64*u - s^2 = 2^64*rh + rl, with + 2^64*rh + rl <= 2*s, and in invs the approximation of 2^96/sqrt(u) */ +#define __gmpfr_sqrt_limb(s, rh, rl, invs, u) \ + do { \ + mp_limb_t _u, _invs, _r, _h, _l; \ + _u = (u); \ + __gmpfr_invsqrt_limb_approx (_invs, _u); \ + umul_hi (_h, _invs, _u); \ + _r = _h + _u; \ + /* make sure _r has its most significant bit set */ \ + if (MPFR_UNLIKELY(_r < MPFR_LIMB_HIGHBIT)) \ + _r = MPFR_LIMB_HIGHBIT; \ + /* we know _r <= sqrt(2^64*u) <= _r + 16 */ \ + umul_ppmm (_h, _l, _r, _r); \ + sub_ddmmss (_h, _l, _u, 0, _h, _l); \ + /* now h:l <= 30*_r */ \ + MPFR_ASSERTD(_h < 30); \ + if (_h >= 16) \ + { /* subtract 16r+64 to h:l, add 8 to _r */ \ + sub_ddmmss (_h, _l, _h, _l, _r >> 60, _r << 4); \ + sub_ddmmss (_h, _l, _h, _l, 0, 64); \ + _r += 8; \ + } \ + if (_h >= 8) \ + { /* subtract 8r+16 to h:l, add 4 to _r */ \ + sub_ddmmss (_h, _l, _h, _l, _r >> 61, _r << 3); \ + sub_ddmmss (_h, _l, _h, _l, 0, 16); \ + _r += 4; \ + } \ + if (_h >= 4) \ + { /* subtract 4r+4 to h:l, add 2 to _r */ \ + sub_ddmmss (_h, _l, _h, _l, _r >> 62, _r << 2); \ + sub_ddmmss (_h, _l, _h, _l, 0, 4); \ + _r += 2; \ + } \ + while (_h > 1 || ((_h == 1) && (_l > 2 * _r))) \ + { /* subtract 2r+1 to h:l, add 1 to _r */ \ + sub_ddmmss (_h, _l, _h, _l, _r >> 63, (_r << 1) + 1); \ + _r ++; \ + } \ + (s) = _r; \ + (rh) = _h; \ + (rl) = _l; \ + (invs) = _invs; \ + } while (0) + +#endif /* GMP_NUMB_BITS == 64 */ |