Check if a number is perfect square

http://stackoverflow.com/questions/295579/fastest-way-to-determine-if-an-integers-square-root-is-an-integer
detel · Oct 2, 2015 · 541027c · 541027c
1 parent 369e9e4
commit 541027c
Showing 1 changed file with 125 additions and 0 deletions.
diff --git a/Perfect Square.py b/Perfect Square.py
@@ -0,0 +1,125 @@
+start = [1,3,1769,5,1937,1741,7,1451,479,157,9,91,945,659,1817,11,
+1983,707,1321,1211,1071,13,1479,405,415,1501,1609,741,15,339,1703,203,
+129,1411,873,1669,17,1715,1145,1835,351,1251,887,1573,975,19,1127,395,
+1855,1981,425,453,1105,653,327,21,287,93,713,1691,1935,301,551,587,
+257,1277,23,763,1903,1075,1799,1877,223,1437,1783,859,1201,621,25,779,
+1727,573,471,1979,815,1293,825,363,159,1315,183,27,241,941,601,971,
+385,131,919,901,273,435,647,1493,95,29,1417,805,719,1261,1177,1163,
+1599,835,1367,315,1361,1933,1977,747,31,1373,1079,1637,1679,1581,1753,1355,
+513,1539,1815,1531,1647,205,505,1109,33,1379,521,1627,1457,1901,1767,1547,
+1471,1853,1833,1349,559,1523,967,1131,97,35,1975,795,497,1875,1191,1739,
+641,1149,1385,133,529,845,1657,725,161,1309,375,37,463,1555,615,1931,
+1343,445,937,1083,1617,883,185,1515,225,1443,1225,869,1423,1235,39,1973,
+769,259,489,1797,1391,1485,1287,341,289,99,1271,1701,1713,915,537,1781,
+1215,963,41,581,303,243,1337,1899,353,1245,329,1563,753,595,1113,1589,
+897,1667,407,635,785,1971,135,43,417,1507,1929,731,207,275,1689,1397,
+1087,1725,855,1851,1873,397,1607,1813,481,163,567,101,1167,45,1831,1205,
+1025,1021,1303,1029,1135,1331,1017,427,545,1181,1033,933,1969,365,1255,1013,
+959,317,1751,187,47,1037,455,1429,609,1571,1463,1765,1009,685,679,821,
+1153,387,1897,1403,1041,691,1927,811,673,227,137,1499,49,1005,103,629,
+831,1091,1449,1477,1967,1677,697,1045,737,1117,1737,667,911,1325,473,437,
+1281,1795,1001,261,879,51,775,1195,801,1635,759,165,1871,1645,1049,245,
+703,1597,553,955,209,1779,1849,661,865,291,841,997,1265,1965,1625,53,
+1409,893,105,1925,1297,589,377,1579,929,1053,1655,1829,305,1811,1895,139,
+575,189,343,709,1711,1139,1095,277,993,1699,55,1435,655,1491,1319,331,
+1537,515,791,507,623,1229,1529,1963,1057,355,1545,603,1615,1171,743,523,
+447,1219,1239,1723,465,499,57,107,1121,989,951,229,1521,851,167,715,
+1665,1923,1687,1157,1553,1869,1415,1749,1185,1763,649,1061,561,531,409,907,
+319,1469,1961,59,1455,141,1209,491,1249,419,1847,1893,399,211,985,1099,
+1793,765,1513,1275,367,1587,263,1365,1313,925,247,1371,1359,109,1561,1291,
+191,61,1065,1605,721,781,1735,875,1377,1827,1353,539,1777,429,1959,1483,
+1921,643,617,389,1809,947,889,981,1441,483,1143,293,817,749,1383,1675,
+63,1347,169,827,1199,1421,583,1259,1505,861,457,1125,143,1069,807,1867,
+2047,2045,279,2043,111,307,2041,597,1569,1891,2039,1957,1103,1389,231,2037,
+65,1341,727,837,977,2035,569,1643,1633,547,439,1307,2033,1709,345,1845,
+1919,637,1175,379,2031,333,903,213,1697,797,1161,475,1073,2029,921,1653,
+193,67,1623,1595,943,1395,1721,2027,1761,1955,1335,357,113,1747,1497,1461,
+1791,771,2025,1285,145,973,249,171,1825,611,265,1189,847,1427,2023,1269,
+321,1475,1577,69,1233,755,1223,1685,1889,733,1865,2021,1807,1107,1447,1077,
+1663,1917,1129,1147,1775,1613,1401,555,1953,2019,631,1243,1329,787,871,885,
+449,1213,681,1733,687,115,71,1301,2017,675,969,411,369,467,295,693,
+1535,509,233,517,401,1843,1543,939,2015,669,1527,421,591,147,281,501,
+577,195,215,699,1489,525,1081,917,1951,2013,73,1253,1551,173,857,309,
+1407,899,663,1915,1519,1203,391,1323,1887,739,1673,2011,1585,493,1433,117,
+705,1603,1111,965,431,1165,1863,533,1823,605,823,1179,625,813,2009,75,
+1279,1789,1559,251,657,563,761,1707,1759,1949,777,347,335,1133,1511,267,
+833,1085,2007,1467,1745,1805,711,149,1695,803,1719,485,1295,1453,935,459,
+1151,381,1641,1413,1263,77,1913,2005,1631,541,119,1317,1841,1773,359,651,
+961,323,1193,197,175,1651,441,235,1567,1885,1481,1947,881,2003,217,843,
+1023,1027,745,1019,913,717,1031,1621,1503,867,1015,1115,79,1683,793,1035,
+1089,1731,297,1861,2001,1011,1593,619,1439,477,585,283,1039,1363,1369,1227,
+895,1661,151,645,1007,1357,121,1237,1375,1821,1911,549,1999,1043,1945,1419,
+1217,957,599,571,81,371,1351,1003,1311,931,311,1381,1137,723,1575,1611,
+767,253,1047,1787,1169,1997,1273,853,1247,413,1289,1883,177,403,999,1803,
+1345,451,1495,1093,1839,269,199,1387,1183,1757,1207,1051,783,83,423,1995,
+639,1155,1943,123,751,1459,1671,469,1119,995,393,219,1743,237,153,1909,
+1473,1859,1705,1339,337,909,953,1771,1055,349,1993,613,1393,557,729,1717,
+511,1533,1257,1541,1425,819,519,85,991,1693,503,1445,433,877,1305,1525,
+1601,829,809,325,1583,1549,1991,1941,927,1059,1097,1819,527,1197,1881,1333,
+383,125,361,891,495,179,633,299,863,285,1399,987,1487,1517,1639,1141,
+1729,579,87,1989,593,1907,839,1557,799,1629,201,155,1649,1837,1063,949,
+255,1283,535,773,1681,461,1785,683,735,1123,1801,677,689,1939,487,757,
+1857,1987,983,443,1327,1267,313,1173,671,221,695,1509,271,1619,89,565,
+127,1405,1431,1659,239,1101,1159,1067,607,1565,905,1755,1231,1299,665,373,
+1985,701,1879,1221,849,627,1465,789,543,1187,1591,923,1905,979,1241,181]
+
+bad = [0,0,1,1,0,1,1,1,1,0,1,1,1,1,1,0,0,1,1,0,1,0,1,1,1,0,1,1,1,1,0,1,
+ 1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,1,1,0,1,1,1,1,0,1,1,1,
+ 0,1,0,1,1,0,0,1,1,1,1,1,0,1,1,1,1,0,1,1,0,0,1,1,1,1,1,1,1,1,0,1,
+ 1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,1,0,0,1,1,1,1,1,1,
+ 1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,1,1,1,1,1,0,1,1,0,1,1,1,1,1,
+ 1,1,1,1,1,1,0,1,1,0,1,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,
+ 1,1,1,0,0,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,
+ 1,0,1,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,
+ 0,0,1,1,0,1,1,1,1,0,1,1,1,1,1,0,0,1,1,0,1,0,1,1,1,0,1,1,1,1,0,1,
+ 1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1,1,0,1,0,1,1,1,0,1,1,1,1,0,1,1,1,
+ 0,1,0,1,1,0,0,1,1,1,1,1,0,1,1,1,1,0,1,1,0,0,1,1,1,1,1,1,1,1,0,1,
+ 1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1,1,0,1,1,1,1,0,0,1,1,1,1,1,1,
+ 1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,0,0,1,1,1,1,1,0,1,1,0,1,1,1,1,1,
+ 1,1,1,1,1,1,0,1,1,0,1,0,1,1,0,1,1,1,1,1,1,1,1,1,1,1,0,1,1,0,1,1,
+ 1,1,1,0,0,1,1,1,1,1,1,1,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,0,0,1,1,1,
+ 1,0,1,1,1,0,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,1,1,
+ 0,0]
+
+def check(x):
+	if x < 0 or x&2 or ((x & 7) == 5) or ((x & 11) == 8):
+		return False
+	if x == 0:
+		return True
+
+	y = x
+	y = (y & 4294967295) + (y >> 32)
+	y = (y & 65535) + (y >> 16)
+	y = (y & 255) + ((y >> 8) & 255) + (y >> 16)
+	if bad[y]:
+		return False
+
+	if x & 4294967295 == 0:
+		x >>= 32
+	if x & 65535 == 0:
+		x >>= 16
+	if x & 255 == 0:
+		x >>= 8
+	if x & 15 == 0:
+		x >>= 4
+	if x & 3 == 0:
+		x >>= 2
+
+	if x & 7 != 1:
+		return False
+
+	r = start[(x >> 3) & 1023]
+	while True:
+		z = x - r * r
+		if z == 0:
+			return True
+		if z < 0:
+			return False
+		t = z & (-z)
+		r += (z & t) >> 1
+		if r > (t  >> 1):
+			r = t - r
+		if ( t > (1L << 33)):
+			break
+
+	return False