init.luau

--!optimize 2
--!native
--!strict

-- HyperLogLog++ class for cardinality estimation
-- Documentation: https://github.com/kohltastrophe/HyperLogLog
-- Reference: https://research.google.com/pubs/archive/40671.pdf

local EncodingService = game:GetService("EncodingService")

-- Pre-computed lookup table for the estimate loop
local POW_2_NEG = table.create(256)
for i = 0, 255 do
	POW_2_NEG[i + 1] = 2 ^ -i
end

--stylua: ignore
-- Means of the empirically determined bias corrections. These values have been determined in a
-- simulation of HLL++ on random input data and are used to correct the bias of the raw estimate.
local MEAN_DATA = table.freeze({
	-- precision 4
	{
		11, 11.717, 12.207, 12.7896, 13.2882, 13.8204, 14.3772, 14.9342, 15.5202, 16.161, 16.7722,
		17.4636, 18.0396, 18.6766, 19.3566, 20.0454, 20.7936, 21.4856, 22.2666, 22.9946, 23.766,
		24.4692, 25.3638, 26.0764, 26.7864, 27.7602, 28.4814, 29.433, 30.2926, 31.0664, 31.9996,
		32.7956, 33.5366, 34.5894, 35.5738, 36.2698, 37.3682, 38.0544, 39.2342, 40.0108, 40.7966,
		41.9298, 42.8704, 43.6358, 44.5194, 45.773, 46.6772, 47.6174, 48.4888, 49.3304, 50.2506,
		51.4996, 52.3824, 53.3078, 54.3984, 55.5838, 56.6618, 57.2174, 58.3514, 59.0802, 60.1482,
		61.0376, 62.3598, 62.8078, 63.9744, 64.914, 65.781, 67.1806, 68.0594, 68.8446, 69.7928,
		70.8248, 71.8324, 72.8598, 73.6246, 74.7014, 75.393, 76.6708, 77.2394,
	},
	-- precision 5
	{
		23, 23.1194, 23.8208, 24.2318, 24.77, 25.2436, 25.7774, 26.2848, 26.8224, 27.3742, 27.9336,
		28.503, 29.0494, 29.6292, 30.2124, 30.798, 31.367, 31.9728, 32.5944, 33.217, 33.8438, 34.3696,
		35.0956, 35.7044, 36.324, 37.0668, 37.6698, 38.3644, 39.049, 39.6918, 40.4146, 41.082, 41.687,
		42.5398, 43.2462, 43.857, 44.6606, 45.4168, 46.1248, 46.9222, 47.6804, 48.447, 49.3454,
		49.9594, 50.7636, 51.5776, 52.331, 53.19, 53.9676, 54.7564, 55.5314, 56.4442, 57.3708,
		57.9774, 58.9624, 59.8796, 60.755, 61.472, 62.2076, 63.1024, 63.8908, 64.7338, 65.7728,
		66.629, 67.413, 68.3266, 69.1524, 70.2642, 71.1806, 72.0566, 72.9192, 73.7598, 74.3516,
		75.5802, 76.4386, 77.4916, 78.1524, 79.1892, 79.8414, 80.8798, 81.8376, 82.4698, 83.7656,
		84.331, 85.5914, 86.6012, 87.7016, 88.5582, 89.3394, 90.3544, 91.4912, 92.308, 93.3552,
		93.9746, 95.2052, 95.727, 97.1322, 98.3944, 98.7588, 100.242, 101.1914, 102.2538, 102.8776,
		103.6292, 105.1932, 105.9152, 107.0868, 107.6728, 108.7144, 110.3114, 110.8716, 111.245,
		112.7908, 113.7064, 114.636, 115.7464, 116.1788, 117.7464, 118.4896, 119.6166, 120.5082,
		121.7798, 122.9028, 123.4426, 124.8854, 125.705, 126.4652, 128.3464, 128.3462, 130.0398,
		131.0342, 131.0042, 132.4766, 133.511, 134.7252, 135.425, 136.5172, 138.0572, 138.6694,
		139.3712, 140.8598, 141.4594, 142.554, 143.4006, 144.7374, 146.1634, 146.8994, 147.605,
		147.9304, 149.1636, 150.2468, 151.5876, 152.2096, 153.7032, 154.7146, 155.807, 156.9228,
		157.0372, 158.5852,
	},
	-- precision 6
	{
		46, 46.1902, 47.271, 47.8358, 48.8142, 49.2854, 50.317, 51.354, 51.8924, 52.9436, 53.4596,
		54.5262, 55.6248, 56.1574, 57.2822, 57.837, 58.9636, 60.074, 60.7042, 61.7976, 62.4772,
		63.6564, 64.7942, 65.5004, 66.686, 67.291, 68.5672, 69.8556, 70.4982, 71.8204, 72.4252,
		73.7744, 75.0786, 75.8344, 77.0294, 77.8098, 79.0794, 80.5732, 81.1878, 82.5648, 83.2902,
		84.6784, 85.3352, 86.8946, 88.3712, 89.0852, 90.499, 91.2686, 92.6844, 94.2234, 94.9732,
		96.3356, 97.2286, 98.7262, 100.3284, 101.1048, 102.5962, 103.3562, 105.1272, 106.4184,
		107.4974, 109.0822, 109.856, 111.48, 113.2834, 114.0208, 115.637, 116.5174, 118.0576,
		119.7476, 120.427, 122.1326, 123.2372, 125.2788, 126.6776, 127.7926, 129.1952, 129.9564,
		131.6454, 133.87, 134.5428, 136.2, 137.0294, 138.6278, 139.6782, 141.792, 143.3516, 144.2832,
		146.0394, 147.0748, 148.4912, 150.849, 151.696, 153.5404, 154.073, 156.3714, 157.7216,
		158.7328, 160.4208, 161.4184, 163.9424, 165.2772, 166.411, 168.1308, 168.769, 170.9258,
		172.6828, 173.7502, 175.706, 176.3886, 179.0186, 180.4518, 181.927, 183.4172, 184.4114,
		186.033, 188.5124, 189.5564, 191.6008, 192.4172, 193.8044, 194.997, 197.4548, 198.8948,
		200.2346, 202.3086, 203.1548, 204.8842, 206.6508, 206.6772, 209.7254, 210.4752, 212.7228,
		214.6614, 215.1676, 217.793, 218.0006, 219.9052, 221.66, 223.5588, 225.1636, 225.6882,
		227.7126, 229.4502, 231.1978, 232.9756, 233.1654, 236.727, 238.1974, 237.7474, 241.1346,
		242.3048, 244.1948, 245.3134, 246.879, 249.1204, 249.853, 252.6792, 253.857, 254.4486,
		257.2362, 257.9534, 260.0286, 260.5632, 262.663, 264.723, 265.7566, 267.2566, 267.1624,
		270.62, 272.8216, 273.2166, 275.2056, 276.2202, 278.3726, 280.3344, 281.9284, 283.9728,
		284.1924, 286.4872, 287.587, 289.807, 291.1206, 292.769, 294.8708, 296.665, 297.1182,
		299.4012, 300.6352, 302.1354, 304.1756, 306.1606, 307.3462, 308.5214, 309.4134, 310.8352,
		313.9684, 315.837, 316.7796, 318.9858,
	},
	-- precision 7
	{
		92, 93.4934, 94.9758, 96.4574, 97.9718, 99.4954, 101.5302, 103.0756, 104.6374, 106.1782,
		107.7888, 109.9522, 111.592, 113.2532, 114.9086, 116.5938, 118.9474, 120.6796, 122.4394,
		124.2176, 125.9768, 128.4214, 130.2528, 132.0102, 133.8658, 135.7278, 138.3044, 140.1316,
		142.093, 144.0032, 145.9092, 148.6306, 150.5294, 152.5756, 154.6508, 156.662, 159.552,
		161.3724, 163.617, 165.5754, 167.7872, 169.8444, 172.7988, 174.8606, 177.2118, 179.3566,
		181.4476, 184.5882, 186.6816, 189.0824, 191.0258, 193.6048, 196.4436, 198.7274, 200.957,
		203.147, 205.4364, 208.7592, 211.3386, 213.781, 215.8028, 218.656, 221.6544, 223.996,
		226.4718, 229.1544, 231.6098, 234.5956, 237.0616, 239.5758, 242.4878, 244.5244, 248.2146,
		250.724, 252.8722, 255.5198, 258.0414, 261.941, 264.9048, 266.87, 269.4304, 272.028, 274.4708,
		278.37, 281.0624, 283.4668, 286.5532, 289.4352, 293.2564, 295.2744, 298.2118, 300.7472,
		304.1456, 307.2928, 309.7504, 312.5528, 315.979, 318.2102, 322.1834, 324.3494, 327.325,
		330.6614, 332.903, 337.2544, 339.9042, 343.215, 345.2864, 348.0814, 352.6764, 355.301,
		357.139, 360.658, 363.1732, 366.5902, 369.9538, 373.0828, 375.922, 378.9902, 382.7328,
		386.4538, 388.1136, 391.2234, 394.0878, 396.708, 401.1556, 404.1852, 406.6372, 409.6822,
		412.7796, 416.6078, 418.4916, 422.131, 424.5376, 428.1988, 432.211, 434.4502, 438.5282,
		440.912, 444.0448, 447.7432, 450.8524, 453.7988, 456.7858, 458.8868, 463.9886, 466.5064,
		468.9124, 472.6616, 475.4682, 478.582, 481.304, 485.2738, 488.6894, 490.329, 496.106,
		497.6908, 501.1374, 504.5322, 506.8848, 510.3324, 513.4512, 516.179, 520.4412, 522.6066,
		526.167, 528.7794, 533.379, 536.067, 538.46, 542.9116, 545.692, 547.9546, 552.493, 555.2722,
		557.335, 562.449, 564.2014, 569.0738, 571.0974, 574.8564, 578.2996, 581.409, 583.9704,
		585.8098, 589.6528, 594.5998, 595.958, 600.068, 603.3278, 608.2016, 609.9632, 612.864, 615.43,
		620.7794, 621.272, 625.8644, 629.206, 633.219, 634.5154, 638.6102,
	},
	-- precision 8
	{
		184.2152, 187.2454, 190.2096, 193.6652, 196.6312, 199.6822, 203.249, 206.3296, 210.0038,
		213.2074, 216.4612, 220.27, 223.5178, 227.4412, 230.8032, 234.1634, 238.1688, 241.6074,
		245.6946, 249.2664, 252.8228, 257.0432, 260.6824, 264.9464, 268.6268, 272.2626, 276.8376,
		280.4034, 284.8956, 288.8522, 292.7638, 297.3552, 301.3556, 305.7526, 309.9292, 313.8954,
		318.8198, 322.7668, 327.298, 331.6688, 335.9466, 340.9746, 345.1672, 349.3474, 354.3028,
		358.8912, 364.114, 368.4646, 372.9744, 378.4092, 382.6022, 387.843, 392.5684, 397.1652,
		402.5426, 407.4152, 412.5388, 417.3592, 422.1366, 427.486, 432.3918, 437.5076, 442.509,
		447.3834, 453.3498, 458.0668, 463.7346, 469.1228, 473.4528, 479.7, 484.644, 491.0518,
		495.5774, 500.9068, 506.432, 512.1666, 517.434, 522.6644, 527.4894, 533.6312, 538.3804,
		544.292, 550.5496, 556.0234, 562.8206, 566.6146, 572.4188, 579.117, 583.6762, 590.6576,
		595.7864, 601.509, 607.5334, 612.9204, 619.772, 624.2924, 630.8654, 636.1836, 642.745,
		649.1316, 655.0386, 660.0136, 666.6342, 671.6196, 678.1866, 684.4282, 689.3324, 695.4794,
		702.5038, 708.129, 713.528, 720.3204, 726.463, 732.7928, 739.123, 744.7418, 751.2192,
		756.5102, 762.6066, 769.0184, 775.2224, 781.4014, 787.7618, 794.1436, 798.6506, 805.6378,
		811.766, 819.7514, 824.5776, 828.7322, 837.8048, 843.6302, 849.9336, 854.4798, 861.3388,
		867.9894, 873.8196, 880.3136, 886.2308, 892.4588, 899.0816, 905.4076, 912.0064, 917.3878,
		923.619, 929.998, 937.3482, 943.9506, 947.991, 955.1144, 962.203, 968.8222, 975.7324,
		981.7826, 988.7666, 994.2648, 1000.3128, 1007.4082, 1013.7536, 1020.3376, 1026.7156,
		1031.7478, 1037.4292, 1045.393, 1051.2278, 1058.3434, 1062.8726, 1071.884, 1076.806,
		1082.9176, 1089.1678, 1095.5032, 1102.525, 1107.2264, 1115.315, 1120.93, 1127.252, 1134.1496,
		1139.0408, 1147.5448, 1153.3296, 1158.1974, 1166.5262, 1174.3328, 1175.657, 1184.4222,
		1190.9172, 1197.1292, 1204.4606, 1210.4578, 1218.8728, 1225.3336, 1226.6592, 1236.5768,
		1241.363, 1249.4074, 1254.6566, 1260.8014, 1266.5454, 1274.5192,
	},
	-- precision 9
	{
		369, 374.8294, 381.2452, 387.6698, 394.1464, 400.2024, 406.8782, 413.6598, 420.462, 427.2826,
		433.7102, 440.7416, 447.9366, 455.1046, 462.285, 469.0668, 476.306, 483.8448, 491.301,
		498.9886, 506.2422, 513.8138, 521.7074, 529.7428, 537.8402, 545.1664, 553.3534, 561.594,
		569.6886, 577.7876, 585.65, 594.228, 602.8036, 611.1666, 620.0818, 628.0824, 637.2574,
		646.302, 655.1644, 664.0056, 672.3802, 681.7192, 690.5234, 700.2084, 708.831, 718.485,
		728.1112, 737.4764, 746.76, 756.3368, 766.5538, 775.5058, 785.2646, 795.5902, 804.3818,
		814.8998, 824.9532, 835.2062, 845.2798, 854.4728, 864.9582, 875.3292, 886.171, 896.781,
		906.5716, 916.7048, 927.5322, 937.875, 949.3972, 958.3464, 969.7274, 980.2834, 992.1444,
		1003.4264, 1013.0166, 1024.018, 1035.0438, 1046.34, 1057.6856, 1068.9836, 1079.0312, 1091.677,
		1102.3188, 1113.4846, 1124.4424, 1135.739, 1147.1488, 1158.9202, 1169.406, 1181.5342,
		1193.2834, 1203.8954, 1216.3286, 1226.2146, 1239.6684, 1251.9946, 1262.123, 1275.4338,
		1285.7378, 1296.076, 1308.9692, 1320.4964, 1333.0998, 1343.9864, 1357.7754, 1368.3208,
		1380.4838, 1392.7388, 1406.0758, 1416.9098, 1428.9728, 1440.9228, 1453.9292, 1462.617,
		1476.05, 1490.2996, 1500.6128, 1513.7392, 1524.5174, 1536.6322, 1548.2584, 1562.3766,
		1572.423, 1587.1232, 1596.5164, 1610.5938, 1622.5972, 1633.1222, 1647.7674, 1658.5044,
		1671.57, 1683.7044, 1695.4142, 1708.7102, 1720.6094, 1732.6522, 1747.841, 1756.4072,
		1769.9786, 1782.3276, 1797.5216, 1808.3186, 1819.0694, 1834.354, 1844.575, 1856.2808,
		1871.1288, 1880.7852, 1893.9622, 1906.3418, 1920.6548, 1932.9302, 1945.8584, 1955.473,
		1968.8248, 1980.6446, 1995.9598, 2008.349, 2019.8556, 2033.0334, 2044.0206, 2059.3956,
		2069.9174, 2082.6084, 2093.7036, 2106.6108, 2118.9124, 2132.301, 2144.7628, 2159.8422,
		2171.0212, 2183.101, 2193.5112, 2208.052, 2221.3194, 2233.3282, 2247.295, 2257.7222, 2273.342,
		2286.5638, 2299.6786, 2310.8114, 2322.3312, 2335.516, 2349.874, 2363.5968, 2373.865,
		2387.1918, 2401.8328, 2414.8496, 2424.544, 2436.7592, 2447.1682, 2464.1958, 2474.3438,
		2489.0006, 2497.4526, 2513.6586, 2527.19, 2540.7028, 2553.768,
	},
	-- prec 10
	{
		738.1256, 750.4234, 763.1064, 775.4732, 788.4636, 801.0644, 814.488, 827.9654, 841.0832,
		854.7864, 868.1992, 882.2176, 896.5228, 910.1716, 924.7752, 938.899, 953.6126, 968.6492,
		982.9474, 998.5214, 1013.1064, 1028.6364, 1044.2468, 1059.4588, 1075.3832, 1091.0584,
		1106.8606, 1123.3868, 1139.5062, 1156.1862, 1172.463, 1189.339, 1206.1936, 1223.1292,
		1240.1854, 1257.2908, 1275.3324, 1292.8518, 1310.5204, 1328.4854, 1345.9318, 1364.552,
		1381.4658, 1400.4256, 1419.849, 1438.152, 1456.8956, 1474.8792, 1494.118, 1513.62, 1532.5132,
		1551.9322, 1570.7726, 1590.6086, 1610.5332, 1630.5918, 1650.4294, 1669.7662, 1690.4106,
		1710.7338, 1730.9012, 1750.4486, 1770.1556, 1791.6338, 1812.7312, 1833.6264, 1853.9526,
		1874.8742, 1896.8326, 1918.1966, 1939.5594, 1961.07, 1983.037, 2003.1804, 2026.071, 2047.4884,
		2070.0848, 2091.2944, 2114.333, 2135.9626, 2158.2902, 2181.0814, 2202.0334, 2224.4832,
		2246.39, 2269.7202, 2292.1714, 2314.2358, 2338.9346, 2360.891, 2384.0264, 2408.3834,
		2430.1544, 2454.8684, 2476.9896, 2501.4368, 2522.8702, 2548.0408, 2570.6738, 2593.5208,
		2617.0158, 2640.2302, 2664.0962, 2687.4986, 2714.2588, 2735.3914, 2759.6244, 2781.8378,
		2808.0072, 2830.6516, 2856.2454, 2877.2136, 2903.4546, 2926.785, 2951.2294, 2976.468,
		3000.867, 3023.6508, 3049.91, 3073.5984, 3098.162, 3121.5564, 3146.2328, 3170.9484, 3195.5902,
		3221.3346, 3242.7032, 3271.6112, 3296.5546, 3317.7376, 3345.072, 3369.9518, 3394.326,
		3418.1818, 3444.6926, 3469.086, 3494.2754, 3517.8698, 3544.248, 3565.3768, 3588.7234,
		3616.979, 3643.7504, 3668.6812, 3695.72, 3719.7392, 3742.6224, 3770.4456, 3795.6602,
		3819.9058, 3844.002, 3869.517, 3895.6824, 3920.8622, 3947.1364, 3973.985, 3995.4772, 4021.62,
		4046.628, 4074.65, 4096.2256, 4121.831, 4146.6406, 4173.276, 4195.0744, 4223.9696, 4251.3708,
		4272.9966, 4300.8046, 4326.302, 4353.1248, 4374.312, 4403.0322, 4426.819, 4450.0598,
		4478.5206, 4504.8116, 4528.8928, 4553.9584, 4578.8712, 4603.8384, 4632.3872, 4655.5128,
		4675.821, 4704.6222, 4731.9862, 4755.4174, 4781.2628, 4804.332, 4832.3048, 4862.8752,
		4883.4148, 4906.9544, 4935.3516, 4954.3532, 4984.0248, 5011.217, 5035.3258, 5057.3672,
		5084.1828,
	},
	-- prec 11
	{
		1477, 1501.6014, 1526.5802, 1551.7942, 1577.3042, 1603.2062, 1629.8402, 1656.2292,
		1682.9462, 1709.9926, 1737.3026, 1765.4252, 1793.0578, 1821.6092, 1849.626, 1878.5568,
		1908.527, 1937.5154, 1967.1874, 1997.3878, 2027.37, 2058.1972, 2089.5728, 2120.1012,
		2151.9668, 2183.292, 2216.0772, 2247.8578, 2280.6562, 2313.041, 2345.714, 2380.3112,
		2414.1806, 2447.9854, 2481.656, 2516.346, 2551.5154, 2586.8378, 2621.7448, 2656.6722,
		2693.5722, 2729.1462, 2765.4124, 2802.8728, 2838.898, 2876.408, 2913.4926, 2951.4938,
		2989.6776, 3026.282, 3065.7704, 3104.1012, 3143.7388, 3181.6876, 3221.1872, 3261.5048,
		3300.0214, 3339.806, 3381.409, 3421.4144, 3461.4294, 3502.2286, 3544.651, 3586.6156,
		3627.337, 3670.083, 3711.1538, 3753.5094, 3797.01, 3838.6686, 3882.1678, 3922.8116,
		3967.9978, 4009.9204, 4054.3286, 4097.5706, 4140.6014, 4185.544, 4229.5976, 4274.583,
		4316.9438, 4361.672, 4406.2786, 4451.8628, 4496.1834, 4543.505, 4589.1816, 4632.5188,
		4678.2294, 4724.8908, 4769.0194, 4817.052, 4861.4588, 4910.1596, 4956.4344, 5002.5238,
		5048.13, 5093.6374, 5142.8162, 5187.7894, 5237.3984, 5285.6078, 5331.0858, 5379.1036,
		5428.6258, 5474.6018, 5522.7618, 5571.5822, 5618.59, 5667.9992, 5714.88, 5763.454,
		5808.6982, 5860.3644, 5910.2914, 5953.571, 6005.9232, 6055.1914, 6104.5882, 6154.5702,
		6199.7036, 6251.1764, 6298.7596, 6350.0302, 6398.061, 6448.4694, 6495.933, 6548.0474,
		6597.7166, 6646.9416, 6695.9208, 6742.6328, 6793.5276, 6842.1934, 6894.2372, 6945.3864,
		6996.9228, 7044.2372, 7094.1374, 7142.2272, 7192.2942, 7238.8338, 7288.9006, 7344.0908,
		7394.8544, 7443.5176, 7490.4148, 7542.9314, 7595.6738, 7641.9878, 7694.3688, 7743.0448,
		7797.522, 7845.53, 7899.594, 7950.3132, 7996.455, 8050.9442, 8092.9114, 8153.1374,
		8197.4472, 8252.8278, 8301.8728, 8348.6776, 8401.4698, 8453.551, 8504.6598, 8553.8944,
		8604.1276, 8657.6514, 8710.3062, 8758.908, 8807.8706, 8862.1702, 8910.4668, 8960.77,
		9007.2766, 9063.164, 9121.0534, 9164.1354, 9218.1594, 9267.767, 9319.0594, 9372.155,
		9419.7126, 9474.3722, 9520.1338, 9572.368, 9622.7702, 9675.8448, 9726.5396, 9778.7378,
		9827.6554, 9878.1922, 9928.7782, 9978.3984, 10026.578, 10076.5626, 10137.1618, 10177.5244,
		10229.9176,
	},
	-- prec 12
	{
		2954, 3003.4782, 3053.3568, 3104.3666, 3155.324, 3206.9598, 3259.648, 3312.539, 3366.1474,
		3420.2576, 3474.8376, 3530.6076, 3586.451, 3643.38, 3700.4104, 3757.5638, 3815.9676, 3875.193,
		3934.838, 3994.8548, 4055.018, 4117.1742, 4178.4482, 4241.1294, 4304.4776, 4367.4044,
		4431.8724, 4496.3732, 4561.4304, 4627.5326, 4693.949, 4761.5532, 4828.7256, 4897.6182,
		4965.5186, 5034.4528, 5104.865, 5174.7164, 5244.6828, 5316.6708, 5387.8312, 5459.9036,
		5532.476, 5604.8652, 5679.6718, 5753.757, 5830.2072, 5905.2828, 5980.0434, 6056.6264,
		6134.3192, 6211.5746, 6290.0816, 6367.1176, 6447.9796, 6526.5576, 6606.1858, 6686.9144,
		6766.1142, 6847.0818, 6927.9664, 7010.9096, 7091.0816, 7175.3962, 7260.3454, 7344.018,
		7426.4214, 7511.3106, 7596.0686, 7679.8094, 7765.818, 7852.4248, 7936.834, 8022.363,
		8109.5066, 8200.4554, 8288.5832, 8373.366, 8463.4808, 8549.7682, 8642.0522, 8728.3288,
		8820.9528, 8907.727, 9001.0794, 9091.2522, 9179.988, 9269.852, 9362.6394, 9453.642, 9546.9024,
		9640.6616, 9732.6622, 9824.3254, 9917.7484, 10007.9392, 10106.7508, 10196.2152, 10289.8114,
		10383.5494, 10482.3064, 10576.8734, 10668.7872, 10764.7156, 10862.0196, 10952.793, 11049.9748,
		11146.0702, 11241.4492, 11339.2772, 11434.2336, 11530.741, 11627.6136, 11726.311, 11821.5964,
		11918.837, 12015.3724, 12113.0162, 12213.0424, 12306.9804, 12408.4518, 12504.8968, 12604.586,
		12700.9332, 12798.705, 12898.5142, 12997.0488, 13094.788, 13198.475, 13292.7764, 13392.9698,
		13486.8574, 13590.1616, 13686.5838, 13783.6264, 13887.2638, 13992.0978, 14081.0844,
		14189.9956, 14280.0912, 14382.4956, 14486.4384, 14588.1082, 14686.2392, 14782.276, 14888.0284,
		14985.1864, 15088.8596, 15187.0998, 15285.027, 15383.6694, 15495.8266, 15591.3736, 15694.2008,
		15790.3246, 15898.4116, 15997.4522, 16095.5014, 16198.8514, 16291.7492, 16402.6424,
		16499.1266, 16606.2436, 16697.7186, 16796.3946, 16902.3376, 17005.7672, 17100.814, 17206.8282,
		17305.8262, 17416.0744, 17508.4092, 17617.0178, 17715.4554, 17816.758, 17920.1748, 18012.9236,
		18119.7984, 18223.2248, 18324.2482, 18426.6276, 18525.0932, 18629.8976, 18733.2588,
		18831.0466, 18940.1366, 19032.2696, 19131.729, 19243.4864, 19349.6932, 19442.866, 19547.9448,
		19653.2798, 19754.4034, 19854.0692, 19965.1224, 20065.1774, 20158.2212, 20253.353, 20366.3264,
		20463.22,
	},
	-- prec 13
	{
		5908.5052, 6007.2672, 6107.347, 6208.5794, 6311.2622, 6414.5514, 6519.3376, 6625.6952,
		6732.5988, 6841.3552, 6950.5972, 7061.3082, 7173.5646, 7287.109, 7401.8216, 7516.4344,
		7633.3802, 7751.2962, 7870.3784, 7990.292, 8110.79, 8233.4574, 8356.6036, 8482.2712,
		8607.7708, 8735.099, 8863.1858, 8993.4746, 9123.8496, 9255.6794, 9388.5448, 9522.7516,
		9657.3106, 9792.6094, 9930.5642, 10068.794, 10206.7256, 10347.81, 10490.3196, 10632.0778,
		10775.9916, 10920.4662, 11066.124, 11213.073, 11358.0362, 11508.1006, 11659.1716, 11808.7514,
		11959.4884, 12112.1314, 12265.037, 12420.3756, 12578.933, 12734.311, 12890.0006, 13047.2144,
		13207.3096, 13368.5144, 13528.024, 13689.847, 13852.7528, 14018.3168, 14180.5372, 14346.9668,
		14513.5074, 14677.867, 14846.2186, 15017.4186, 15184.9716, 15356.339, 15529.2972, 15697.3578,
		15871.8686, 16042.187, 16216.4094, 16389.4188, 16565.9126, 16742.3272, 16919.0042, 17094.7592,
		17273.965, 17451.8342, 17634.4254, 17810.5984, 17988.9242, 18171.051, 18354.7938, 18539.466,
		18721.0408, 18904.9972, 19081.867, 19271.9118, 19451.8694, 19637.9816, 19821.2922, 20013.1292,
		20199.3858, 20387.8726, 20572.9514, 20770.7764, 20955.1714, 21144.751, 21329.9952, 21520.709,
		21712.7016, 21906.3868, 22096.2626, 22286.0524, 22475.051, 22665.5098, 22862.8492, 23055.5294,
		23249.6138, 23437.848, 23636.273, 23826.093, 24020.3296, 24213.3896, 24411.7392, 24602.9614,
		24805.7952, 24998.1552, 25193.9588, 25389.0166, 25585.8392, 25780.6976, 25981.2728, 26175.977,
		26376.5252, 26570.1964, 26773.387, 26962.9812, 27163.0586, 27368.164, 27565.0534, 27758.7428,
		27961.1276, 28163.2324, 28362.3816, 28565.7668, 28758.644, 28956.9768, 29163.4722, 29354.7026,
		29561.1186, 29767.9948, 29959.9986, 30164.0492, 30366.9818, 30562.5338, 30762.9928,
		30976.1592, 31166.274, 31376.722, 31570.3734, 31770.809, 31974.8934, 32179.5286, 32387.5442,
		32582.3504, 32794.076, 32989.9528, 33191.842, 33392.4684, 33595.659, 33801.8672, 34000.3414,
		34200.0922, 34402.6792, 34610.0638, 34804.0084, 35011.13, 35218.669, 35418.6634, 35619.0792,
		35830.6534, 36028.4966, 36229.7902, 36438.6422, 36630.7764, 36833.3102, 37048.6728,
		37247.3916, 37453.5904, 37669.3614, 37854.5526, 38059.305, 38268.0936, 38470.2516, 38674.7064,
		38876.167, 39068.3794, 39281.9144, 39492.8566, 39684.8628, 39898.4108, 40093.1836, 40297.6858,
		40489.7086, 40717.2424,
	},
	-- prec 14
	{
		11817.475, 12015.0046, 12215.3792, 12417.7504, 12623.1814, 12830.0086, 13040.0072, 13252.503,
		13466.178, 13683.2738, 13902.0344, 14123.9798, 14347.394, 14573.7784, 14802.6894, 15033.6824,
		15266.9134, 15502.8624, 15741.4944, 15980.7956, 16223.8916, 16468.6316, 16715.733, 16965.5726,
		17217.204, 17470.666, 17727.8516, 17986.7886, 18247.6902, 18510.9632, 18775.304, 19044.7486,
		19314.4408, 19587.202, 19862.2576, 20135.924, 20417.0324, 20697.9788, 20979.6112, 21265.0274,
		21550.723, 21841.6906, 22132.162, 22428.1406, 22722.127, 23020.5606, 23319.7394, 23620.4014,
		23925.2728, 24226.9224, 24535.581, 24845.505, 25155.9618, 25470.3828, 25785.9702, 26103.7764,
		26420.4132, 26742.0186, 27062.8852, 27388.415, 27714.6024, 28042.296, 28365.4494, 28701.1526,
		29031.8008, 29364.2156, 29704.497, 30037.1458, 30380.111, 30723.8168, 31059.5114, 31404.9498,
		31751.6752, 32095.2686, 32444.7792, 32794.767, 33145.204, 33498.4226, 33847.6502, 34209.006,
		34560.849, 34919.4838, 35274.9778, 35635.1322, 35996.3266, 36359.1394, 36722.8266, 37082.8516,
		37447.7354, 37815.9606, 38191.0692, 38559.4106, 38924.8112, 39294.6726, 39663.973, 40042.261,
		40416.2036, 40779.2036, 41161.6436, 41540.9014, 41921.1998, 42294.7698, 42678.5264,
		43061.3464, 43432.375, 43818.432, 44198.6598, 44583.0138, 44970.4794, 45353.924, 45729.858,
		46118.2224, 46511.5724, 46900.7386, 47280.6964, 47668.1472, 48055.6796, 48446.9436,
		48838.7146, 49217.7296, 49613.7796, 50010.7508, 50410.0208, 50793.7886, 51190.2456,
		51583.1882, 51971.0796, 52376.5338, 52763.319, 53165.5534, 53556.5594, 53948.2702, 54346.352,
		54748.7914, 55138.577, 55543.4824, 55941.1748, 56333.7746, 56745.1552, 57142.7944, 57545.2236,
		57935.9956, 58348.5268, 58737.5474, 59158.5962, 59542.6896, 59958.8004, 60349.3788,
		60755.0212, 61147.6144, 61548.194, 61946.0696, 62348.6042, 62763.603, 63162.781, 63560.635,
		63974.3482, 64366.4908, 64771.5876, 65176.7346, 65597.3916, 65995.915, 66394.0384, 66822.9396,
		67203.6336, 67612.2032, 68019.0078, 68420.0388, 68821.22, 69235.8388, 69640.0724, 70055.155,
		70466.357, 70863.4266, 71276.2482, 71677.0306, 72080.2006, 72493.0214, 72893.5952, 73314.5856,
		73714.9852, 74125.3022, 74521.2122, 74933.6814, 75341.5904, 75743.0244, 76166.0278,
		76572.1322, 76973.1028, 77381.6284, 77800.6092, 78189.328, 78607.0962, 79012.2508, 79407.8358,
		79825.725, 80238.701, 80646.891, 81035.6436, 81460.0448, 81876.3884,
	},
	-- prec 15
	{
		23635.0036, 24030.8034, 24431.4744, 24837.1524, 25246.7928, 25661.326, 26081.3532, 26505.2806,
		26933.9892, 27367.7098, 27805.318, 28248.799, 28696.4382, 29148.8244, 29605.5138, 30066.8668,
		30534.2344, 31006.32, 31480.778, 31962.2418, 32447.3324, 32938.0232, 33432.731, 33930.728,
		34433.9896, 34944.1402, 35457.5588, 35974.5958, 36497.3296, 37021.9096, 37554.326, 38088.0826,
		38628.8816, 39171.3192, 39723.2326, 40274.5554, 40832.3142, 41390.613, 41959.5908, 42532.5466,
		43102.0344, 43683.5072, 44266.694, 44851.2822, 45440.7862, 46038.0586, 46640.3164, 47241.064,
		47846.155, 48454.7396, 49076.9168, 49692.542, 50317.4778, 50939.65, 51572.5596, 52210.2906,
		52843.7396, 53481.3996, 54127.236, 54770.406, 55422.6598, 56078.7958, 56736.7174, 57397.6784,
		58064.5784, 58730.308, 59404.9784, 60077.0864, 60751.9158, 61444.1386, 62115.817, 62808.7742,
		63501.4774, 64187.5454, 64883.6622, 65582.7468, 66274.5318, 66976.9276, 67688.7764, 68402.138,
		69109.6274, 69822.9706, 70543.6108, 71265.5202, 71983.3848, 72708.4656, 73433.384, 74158.4664,
		74896.4868, 75620.9564, 76362.1434, 77098.3204, 77835.7662, 78582.6114, 79323.9902,
		80067.8658, 80814.9246, 81567.0136, 82310.8536, 83061.9952, 83821.4096, 84580.8608, 85335.547,
		86092.5802, 86851.6506, 87612.311, 88381.2016, 89146.3296, 89907.8974, 90676.846, 91451.4152,
		92224.5518, 92995.8686, 93763.5066, 94551.2796, 95315.1944, 96096.1806, 96881.0918, 97665.679,
		98442.68, 99229.3002, 100011.0994, 100790.6386, 101580.1564, 102377.7484, 103152.1392,
		103944.2712, 104730.216, 105528.6336, 106324.9398, 107117.6706, 107890.3988, 108695.2266,
		109485.238, 110294.7876, 111075.0958, 111878.0496, 112695.2864, 113464.5486, 114270.0474,
		115068.608, 115884.3626, 116673.2588, 117483.3716, 118275.097, 119085.4092, 119879.2808,
		120687.5868, 121499.9944, 122284.916, 123095.9254, 123912.5038, 124709.0454, 125503.7182,
		126323.259, 127138.9412, 127943.8294, 128755.646, 129556.5354, 130375.3298, 131161.4734,
		131971.1962, 132787.5458, 133588.1056, 134431.351, 135220.2906, 136023.398, 136846.6558,
		137667.0004, 138463.663, 139283.7154, 140074.6146, 140901.3072, 141721.8548, 142543.2322,
		143356.1096, 144173.7412, 144973.0948, 145794.3162, 146609.5714, 147420.003, 148237.9784,
		149050.5696, 149854.761, 150663.1966, 151494.0754, 152313.1416, 153112.6902, 153935.7206,
		154746.9262, 155559.547, 156401.9746, 157228.7036, 158008.7254, 158820.75, 159646.9184,
		160470.4458, 161279.5348, 162093.3114, 162918.542, 163729.2842,
	},
	-- prec 16
	{
		47271, 48062.3584, 48862.7074, 49673.152, 50492.8416, 51322.9514, 52161.03, 53009.407,
		53867.6348, 54734.206, 55610.5144, 56496.2096, 57390.795, 58297.268, 59210.6448, 60134.665,
		61068.0248, 62010.4472, 62962.5204, 63923.5742, 64895.0194, 65876.4182, 66862.6136,
		67862.6968, 68868.8908, 69882.8544, 70911.271, 71944.0924, 72990.0326, 74040.692, 75100.6336,
		76174.7826, 77252.5998, 78340.2974, 79438.2572, 80545.4976, 81657.2796, 82784.6336, 83915.515,
		85059.7362, 86205.9368, 87364.4424, 88530.3358, 89707.3744, 90885.9638, 92080.197, 93275.5738,
		94479.391, 95695.918, 96919.2236, 98148.4602, 99382.3474, 100625.6974, 101878.0284,
		103141.6278, 104409.4588, 105686.2882, 106967.5402, 108261.6032, 109548.1578, 110852.0728,
		112162.231, 113479.0072, 114806.2626, 116137.9072, 117469.5048, 118813.5186, 120165.4876,
		121516.2556, 122875.766, 124250.5444, 125621.2222, 127003.2352, 128387.848, 129775.2644,
		131181.7776, 132577.3086, 133979.9458, 135394.1132, 136800.9078, 138233.217, 139668.5308,
		141085.212, 142535.2122, 143969.0684, 145420.2872, 146878.1542, 148332.7572, 149800.3202,
		151269.66, 152743.6104, 154213.0948, 155690.288, 157169.4246, 158672.1756, 160160.059,
		161650.6854, 163145.7772, 164645.6726, 166159.1952, 167682.1578, 169177.3328, 170700.0118,
		172228.8964, 173732.6664, 175265.5556, 176787.799, 178317.111, 179856.6914, 181400.865,
		182943.4612, 184486.742, 186033.4698, 187583.7886, 189148.1868, 190688.4526, 192250.1926,
		193810.9042, 195354.2972, 196938.7682, 198493.5898, 200079.2824, 201618.912, 203205.5492,
		204765.5798, 206356.1124, 207929.3064, 209498.7196, 211086.229, 212675.1324, 214256.7892,
		215826.2392, 217412.8474, 218995.6724, 220618.6038, 222207.1166, 223781.0364, 225387.4332,
		227005.7928, 228590.4336, 230217.8738, 231805.1054, 233408.9, 234995.3432, 236601.4956,
		238190.7904, 239817.2548, 241411.2832, 243002.4066, 244640.1884, 246255.3128, 247849.3508,
		249479.9734, 251106.8822, 252705.027, 254332.9242, 255935.129, 257526.9014, 259154.772,
		260777.625, 262390.253, 264004.4906, 265643.59, 267255.4076, 268873.426, 270470.7252,
		272106.4804, 273722.4456, 275337.794, 276945.7038, 278592.9154, 280204.3726, 281841.1606,
		283489.171, 285130.1716, 286735.3362, 288364.7164, 289961.1814, 291595.5524, 293285.683,
		294899.6668, 296499.3434, 298128.0462, 299761.8946, 301394.2424, 302997.6748, 304615.1478,
		306269.7724, 307886.114, 309543.1028, 311153.2862, 312782.8546, 314421.2008, 316033.2438,
		317692.9636, 319305.2648, 320948.7406, 322566.3364, 324228.4224, 325847.1542,
	},
	-- prec 17
	{
		94542, 96125.811, 97728.019, 99348.558, 100987.9705, 102646.7565, 104324.5125, 106021.7435,
		107736.7865, 109469.272, 111223.9465, 112995.219, 114787.432, 116593.152, 118422.71,
		120267.2345, 122134.6765, 124020.937, 125927.2705, 127851.255, 129788.9485, 131751.016,
		133726.8225, 135722.592, 137736.789, 139770.568, 141821.518, 143891.343, 145982.1415,
		148095.387, 150207.526, 152355.649, 154515.6415, 156696.05, 158887.7575, 161098.159,
		163329.852, 165569.053, 167837.4005, 170121.6165, 172420.4595, 174732.6265, 177062.77,
		179412.502, 181774.035, 184151.939, 186551.6895, 188965.691, 191402.8095, 193857.949,
		196305.0775, 198774.6715, 201271.2585, 203764.78, 206299.3695, 208818.1365, 211373.115,
		213946.7465, 216532.076, 219105.541, 221714.5375, 224337.5135, 226977.5125, 229613.0655,
		232270.2685, 234952.2065, 237645.3555, 240331.1925, 243034.517, 245756.0725, 248517.6865,
		251232.737, 254011.3955, 256785.995, 259556.44, 262368.335, 265156.911, 267965.266,
		270785.583, 273616.0495, 276487.4835, 279346.639, 282202.509, 285074.3885, 287942.2855,
		290856.018, 293774.0345, 296678.5145, 299603.6355, 302552.6575, 305492.9785, 308466.8605,
		311392.581, 314347.538, 317319.4295, 320285.9785, 323301.7325, 326298.3235, 329301.3105,
		332301.987, 335309.791, 338370.762, 341382.923, 344431.1265, 347464.1545, 350507.28,
		353619.2345, 356631.2005, 359685.203, 362776.7845, 365886.488, 368958.2255, 372060.6825,
		375165.4335, 378237.935, 381328.311, 384430.5225, 387576.425, 390683.242, 393839.648,
		396977.8425, 400101.9805, 403271.296, 406409.8425, 409529.5485, 412678.7, 415847.423,
		419020.8035, 422157.081, 425337.749, 428479.6165, 431700.902, 434893.1915, 438049.582,
		441210.5415, 444379.2545, 447577.356, 450741.931, 453959.548, 457137.0935, 460329.846,
		463537.4815, 466732.3345, 469960.5615, 473164.681, 476347.6345, 479496.173, 482813.1645,
		486025.6995, 489249.4885, 492460.1945, 495675.8805, 498908.0075, 502131.802, 505374.3855,
		508550.9915, 511806.7305, 515026.776, 518217.0005, 521523.9855, 524705.9855, 527950.997,
		531210.0265, 534472.497, 537750.7315, 540926.922, 544207.094, 547429.4345, 550666.3745,
		553975.3475, 557150.7185, 560399.6165, 563662.697, 566916.7395, 570146.1215, 573447.425,
		576689.6245, 579874.5745, 583202.337, 586503.0255, 589715.635, 592910.161, 596214.3885,
		599488.035, 602740.92, 605983.0685, 609248.67, 612491.3605, 615787.912, 619107.5245,
		622307.9555, 625577.333, 628840.4385, 632085.2155, 635317.6135, 638691.7195, 641887.467,
		645139.9405, 648441.546, 651666.252, 654941.845,
	},
	-- prec 18
	{
		189084, 192250.913, 195456.774, 198696.946, 201977.762, 205294.444, 208651.754, 212042.099,
		215472.269, 218941.91, 222443.912, 225996.845, 229568.199, 233193.568, 236844.457, 240543.233,
		244279.475, 248044.27, 251854.588, 255693.2, 259583.619, 263494.621, 267445.385, 271454.061,
		275468.769, 279549.456, 283646.446, 287788.198, 291966.099, 296181.164, 300431.469,
		304718.618, 309024.004, 313393.508, 317760.803, 322209.731, 326675.061, 331160.627, 335654.47,
		340241.442, 344841.833, 349467.132, 354130.629, 358819.432, 363574.626, 368296.587,
		373118.482, 377914.93, 382782.301, 387680.669, 392601.981, 397544.323, 402529.115, 407546.018,
		412593.658, 417638.657, 422762.865, 427886.169, 433017.167, 438213.273, 443441.254,
		448692.421, 453937.533, 459239.049, 464529.569, 469910.083, 475274.03, 480684.473, 486070.26,
		491515.237, 496995.651, 502476.617, 507973.609, 513497.19, 519083.233, 524726.509, 530305.505,
		535945.728, 541584.404, 547274.055, 552967.236, 558667.862, 564360.216, 570128.148, 575965.08,
		581701.952, 587532.523, 593361.144, 599246.128, 605033.418, 610958.779, 616837.117,
		622772.818, 628672.04, 634675.369, 640574.831, 646585.739, 652574.547, 658611.217, 664642.684,
		670713.914, 676737.681, 682797.313, 688837.897, 694917.874, 701009.882, 707173.648,
		713257.254, 719415.392, 725636.761, 731710.697, 737906.209, 744103.074, 750313.39, 756504.185,
		762712.579, 768876.985, 775167.859, 781359, 787615.959, 793863.597, 800245.477, 806464.582,
		812785.294, 819005.925, 825403.057, 831676.197, 837936.284, 844266.968, 850642.711,
		856959.756, 863322.774, 869699.931, 876102.478, 882355.787, 888694.463, 895159.952,
		901536.143, 907872.631, 914293.672, 920615.14, 927130.974, 933409.404, 939922.178, 946331.47,
		952745.93, 959209.264, 965590.224, 972077.284, 978501.961, 984953.19, 991413.271, 997817.479,
		1004222.658, 1010725.676, 1017177.138, 1023612.529, 1030098.236, 1036493.719, 1043112.207,
		1049537.036, 1056008.096, 1062476.184, 1068942.337, 1075524.95, 1081932.864, 1088426.025,
		1094776.005, 1101327.448, 1107901.673, 1114423.639, 1120884.602, 1127324.923, 1133794.24,
		1140328.886, 1146849.376, 1153346.682, 1159836.502, 1166478.703, 1172953.304, 1179391.502,
		1185950.982, 1192544.052, 1198913.41, 1205430.994, 1212015.525, 1218674.042, 1225121.683,
		1231551.101, 1238126.379, 1244673.795, 1251260.649, 1257697.86, 1264320.983, 1270736.319,
		1277274.694, 1283804.95, 1290211.514, 1296858.568, 1303455.691,
	}
})

--stylua: ignore
-- Empirically determined biases. These values have been determined in a simulation of HLL++ on
-- random input data and are used to correct the bias of the raw estimate.
local BIAS_DATA = table.freeze({
	-- precision 4
	{
		10, 9.717, 9.207, 8.7896, 8.2882, 7.8204, 7.3772, 6.9342, 6.5202, 6.161, 5.7722, 5.4636,
		5.0396, 4.6766, 4.3566, 4.0454, 3.7936, 3.4856, 3.2666, 2.9946, 2.766, 2.4692, 2.3638, 2.0764,
		1.7864, 1.7602, 1.4814, 1.433, 1.2926, 1.0664, 0.999600000000001, 0.7956, 0.5366,
		0.589399999999998, 0.573799999999999, 0.269799999999996, 0.368200000000002,
		0.0544000000000011, 0.234200000000001, 0.0108000000000033, -0.203400000000002,
		-0.0701999999999998, -0.129600000000003, -0.364199999999997, -0.480600000000003,
		-0.226999999999997, -0.322800000000001, -0.382599999999996, -0.511200000000002,
		-0.669600000000003, -0.749400000000001, -0.500399999999999, -0.617600000000003, -0.6922,
		-0.601599999999998, -0.416200000000003, -0.338200000000001, -0.782600000000002,
		-0.648600000000002, -0.919800000000002, -0.851799999999997, -0.962400000000002, -0.6402,
		-1.1922, -1.0256, -1.086, -1.21899999999999, -0.819400000000002, -0.940600000000003, -1.1554,
		-1.2072, -1.1752, -1.16759999999999, -1.14019999999999, -1.3754, -1.29859999999999, -1.607,
		-1.3292, -1.7606,
	},
	-- precision 5
	{
		22, 21.1194, 20.8208, 20.2318, 19.77, 19.2436, 18.7774, 18.2848, 17.8224, 17.3742, 16.9336,
		16.503, 16.0494, 15.6292, 15.2124, 14.798, 14.367, 13.9728, 13.5944, 13.217, 12.8438, 12.3696,
		12.0956, 11.7044, 11.324, 11.0668, 10.6698, 10.3644, 10.049, 9.6918, 9.4146, 9.082, 8.687,
		8.5398, 8.2462, 7.857, 7.6606, 7.4168, 7.1248, 6.9222, 6.6804, 6.447, 6.3454, 5.9594, 5.7636,
		5.5776, 5.331, 5.19, 4.9676, 4.7564, 4.5314, 4.4442, 4.3708, 3.9774, 3.9624, 3.8796, 3.755,
		3.472, 3.2076, 3.1024, 2.8908, 2.7338, 2.7728, 2.629, 2.413, 2.3266, 2.1524, 2.2642, 2.1806,
		2.0566, 1.9192, 1.7598, 1.3516, 1.5802, 1.43859999999999, 1.49160000000001, 1.1524, 1.1892,
		0.841399999999993, 0.879800000000003, 0.837599999999995, 0.469800000000006, 0.765600000000006,
		0.331000000000003, 0.591399999999993, 0.601200000000006, 0.701599999999999, 0.558199999999999,
		0.339399999999998, 0.354399999999998, 0.491200000000006, 0.308000000000007, 0.355199999999996,
		-0.0254000000000048, 0.205200000000005, -0.272999999999996, 0.132199999999997,
		0.394400000000005, -0.241200000000006, 0.242000000000004, 0.191400000000002,
		0.253799999999998, -0.122399999999999, -0.370800000000003, 0.193200000000004,
		-0.0848000000000013, 0.0867999999999967, -0.327200000000005, -0.285600000000002,
		0.311400000000006, -0.128399999999999, -0.754999999999995, -0.209199999999996,
		-0.293599999999998, -0.364000000000004, -0.253600000000006, -0.821200000000005,
		-0.253600000000006, -0.510400000000004, -0.383399999999995, -0.491799999999998,
		-0.220200000000006, -0.0972000000000008, -0.557400000000001, -0.114599999999996,
		-0.295000000000002, -0.534800000000004, 0.346399999999988, -0.65379999999999,
		0.0398000000000138, 0.0341999999999985, -0.995800000000003, -0.523400000000009,
		-0.489000000000004, -0.274799999999999, -0.574999999999989, -0.482799999999997,
		0.0571999999999946, -0.330600000000004, -0.628800000000012, -0.140199999999993,
		-0.540600000000012, -0.445999999999998, -0.599400000000003, -0.262599999999992,
		0.163399999999996, -0.100599999999986, -0.39500000000001, -1.06960000000001,
		-0.836399999999998, -0.753199999999993, -0.412399999999991, -0.790400000000005,
		-0.29679999999999, -0.28540000000001, -0.193000000000012, -0.0772000000000048,
		-0.962799999999987, -0.414800000000014,
	},
	-- precision 6
	{
		45, 44.1902, 43.271, 42.8358, 41.8142, 41.2854, 40.317, 39.354, 38.8924, 37.9436, 37.4596,
		36.5262, 35.6248, 35.1574, 34.2822, 33.837, 32.9636, 32.074, 31.7042, 30.7976, 30.4772,
		29.6564, 28.7942, 28.5004, 27.686, 27.291, 26.5672, 25.8556, 25.4982, 24.8204, 24.4252,
		23.7744, 23.0786, 22.8344, 22.0294, 21.8098, 21.0794, 20.5732, 20.1878, 19.5648, 19.2902,
		18.6784, 18.3352, 17.8946, 17.3712, 17.0852, 16.499, 16.2686, 15.6844, 15.2234, 14.9732,
		14.3356, 14.2286, 13.7262, 13.3284, 13.1048, 12.5962, 12.3562, 12.1272, 11.4184, 11.4974,
		11.0822, 10.856, 10.48, 10.2834, 10.0208, 9.637, 9.51739999999999, 9.05759999999999,
		8.74760000000001, 8.42700000000001, 8.1326, 8.2372, 8.2788, 7.6776, 7.79259999999999, 7.1952,
		6.9564, 6.6454, 6.87, 6.5428, 6.19999999999999, 6.02940000000001, 5.62780000000001, 5.6782,
		5.792, 5.35159999999999, 5.28319999999999, 5.0394, 5.07480000000001, 4.49119999999999,
		4.84899999999999, 4.696, 4.54040000000001, 4.07300000000001, 4.37139999999999, 3.7216,
		3.7328, 3.42080000000001, 3.41839999999999, 3.94239999999999, 3.27719999999999, 3.411,
		3.13079999999999, 2.76900000000001, 2.92580000000001, 2.68279999999999, 2.75020000000001,
		2.70599999999999, 2.3886, 3.01859999999999, 2.45179999999999, 2.92699999999999,
		2.41720000000001, 2.41139999999999, 2.03299999999999, 2.51240000000001, 2.5564,
		2.60079999999999, 2.41720000000001, 1.80439999999999, 1.99700000000001, 2.45480000000001,
		1.8948, 2.2346, 2.30860000000001, 2.15479999999999, 1.88419999999999, 1.6508,
		0.677199999999999, 1.72540000000001, 1.4752, 1.72280000000001, 1.66139999999999,
		1.16759999999999, 1.79300000000001, 1.00059999999999, 0.905200000000008, 0.659999999999997,
		1.55879999999999, 1.1636, 0.688199999999995, 0.712600000000009, 0.450199999999995, 1.1978,
		0.975599999999986, 0.165400000000005, 1.727, 1.19739999999999, -0.252600000000001,
		1.13460000000001, 1.3048, 1.19479999999999, 0.313400000000001, 0.878999999999991,
		1.12039999999999, 0.853000000000009, 1.67920000000001, 0.856999999999999, 0.448599999999999,
		1.2362, 0.953399999999988, 1.02859999999998, 0.563199999999995, 0.663000000000011,
		0.723000000000013, 0.756599999999992, 0.256599999999992, -0.837600000000009,
		0.620000000000005, 0.821599999999989, 0.216600000000028, 0.205600000000004, 0.220199999999977,
		0.372599999999977, 0.334400000000016, 0.928400000000011, 0.972800000000007, 0.192400000000021,
		0.487199999999973, -0.413000000000011, 0.807000000000016, 0.120600000000024,
		0.769000000000005, 0.870799999999974, 0.66500000000002, 0.118200000000002, 0.401200000000017,
		0.635199999999998, 0.135400000000004, 0.175599999999974, 1.16059999999999, 0.34620000000001,
		0.521400000000028, -0.586599999999976, -1.16480000000001, 0.968399999999974,
		0.836999999999989, 0.779600000000016, 0.985799999999983,
	},
	-- precision 7
	{
		91, 89.4934, 87.9758, 86.4574, 84.9718, 83.4954, 81.5302, 80.0756, 78.6374, 77.1782, 75.7888,
		73.9522, 72.592, 71.2532, 69.9086, 68.5938, 66.9474, 65.6796, 64.4394, 63.2176, 61.9768,
		60.4214, 59.2528, 58.0102, 56.8658, 55.7278, 54.3044, 53.1316, 52.093, 51.0032, 49.9092,
		48.6306, 47.5294, 46.5756, 45.6508, 44.662, 43.552, 42.3724, 41.617, 40.5754, 39.7872,
		38.8444, 37.7988, 36.8606, 36.2118, 35.3566, 34.4476, 33.5882, 32.6816, 32.0824, 31.0258,
		30.6048, 29.4436, 28.7274, 27.957, 27.147, 26.4364, 25.7592, 25.3386, 24.781, 23.8028,
		23.656, 22.6544, 21.996, 21.4718, 21.1544, 20.6098, 19.5956, 19.0616, 18.5758, 18.4878,
		17.5244, 17.2146, 16.724, 15.8722, 15.5198, 15.0414, 14.941, 14.9048, 13.87, 13.4304,
		13.028, 12.4708, 12.37, 12.0624, 11.4668, 11.5532, 11.4352, 11.2564, 10.2744, 10.2118,
		9.74720000000002, 10.1456, 9.2928, 8.75040000000001, 8.55279999999999, 8.97899999999998,
		8.21019999999999, 8.18340000000001, 7.3494, 7.32499999999999, 7.66140000000001,
		6.90300000000002, 7.25439999999998, 6.9042, 7.21499999999997, 6.28640000000001,
		6.08139999999997, 6.6764, 6.30099999999999, 5.13900000000001, 5.65800000000002,
		5.17320000000001, 4.59019999999998, 4.9538, 5.08280000000002, 4.92200000000003,
		4.99020000000002, 4.7328, 5.4538, 4.11360000000002, 4.22340000000003, 4.08780000000002,
		3.70800000000003, 4.15559999999999, 4.18520000000001, 3.63720000000001, 3.68220000000002,
		3.77960000000002, 3.6078, 2.49160000000001, 3.13099999999997, 2.5376, 3.19880000000001,
		3.21100000000001, 2.4502, 3.52820000000003, 2.91199999999998, 3.04480000000001, 2.7432,
		2.85239999999999, 2.79880000000003, 2.78579999999999, 1.88679999999999, 2.98860000000002,
		2.50639999999999, 1.91239999999999, 2.66160000000002, 2.46820000000002, 1.58199999999999,
		1.30399999999997, 2.27379999999999, 2.68939999999998, 1.32900000000001, 3.10599999999999,
		1.69080000000002, 2.13740000000001, 2.53219999999999, 1.88479999999998, 1.33240000000001,
		1.45119999999997, 1.17899999999997, 2.44119999999998, 1.60659999999996, 2.16700000000003,
		0.77940000000001, 2.37900000000002, 2.06700000000001, 1.46000000000004, 2.91160000000002,
		1.69200000000001, 0.954600000000028, 2.49300000000005, 2.2722, 1.33500000000004,
		2.44899999999996, 1.20140000000004, 3.07380000000001, 2.09739999999999, 2.85640000000001,
		2.29960000000005, 2.40899999999999, 1.97040000000004, 0.809799999999996, 1.65279999999996,
		2.59979999999996, 0.95799999999997, 2.06799999999998, 2.32780000000002, 4.20159999999998,
		1.96320000000003, 1.86400000000003, 1.42999999999995, 3.77940000000001, 1.27200000000005,
		1.86440000000005, 2.20600000000002, 3.21900000000005, 1.5154, 2.61019999999996,
	},
	-- precision 8
	{
		183.2152, 180.2454, 177.2096, 173.6652, 170.6312, 167.6822, 164.249, 161.3296, 158.0038,
		155.2074, 152.4612, 149.27, 146.5178, 143.4412, 140.8032, 138.1634, 135.1688, 132.6074,
		129.6946, 127.2664, 124.8228, 122.0432, 119.6824, 116.9464, 114.6268, 112.2626, 109.8376,
		107.4034, 104.8956, 102.8522, 100.7638, 98.3552, 96.3556, 93.7526, 91.9292, 89.8954, 87.8198,
		85.7668, 83.298, 81.6688, 79.9466, 77.9746, 76.1672, 74.3474, 72.3028, 70.8912, 69.114,
		67.4646, 65.9744, 64.4092, 62.6022, 60.843, 59.5684, 58.1652, 56.5426, 55.4152, 53.5388,
		52.3592, 51.1366, 49.486, 48.3918, 46.5076, 45.509, 44.3834, 43.3498, 42.0668, 40.7346,
		40.1228, 38.4528, 37.7, 36.644, 36.0518, 34.5774, 33.9068, 32.432, 32.1666, 30.434, 29.6644,
		28.4894, 27.6312, 26.3804, 26.292, 25.5496000000001, 25.0234, 24.8206, 22.6146, 22.4188,
		22.117, 20.6762, 20.6576, 19.7864, 19.509, 18.5334, 17.9204, 17.772, 16.2924, 16.8654,
		15.1836, 15.745, 15.1316, 15.0386, 14.0136, 13.6342, 12.6196, 12.1866, 12.4281999999999,
		11.3324, 10.4794000000001, 11.5038, 10.129, 9.52800000000002, 10.3203999999999,
		9.46299999999997, 9.79280000000006, 9.12300000000005, 8.74180000000001, 9.2192,
		7.51020000000005, 7.60659999999996, 7.01840000000004, 7.22239999999999, 7.40139999999997,
		6.76179999999999, 7.14359999999999, 5.65060000000005, 5.63779999999997, 5.76599999999996,
		6.75139999999999, 5.57759999999996, 3.73220000000003, 5.8048, 5.63019999999995,
		4.93359999999996, 3.47979999999995, 4.33879999999999, 3.98940000000005, 3.81960000000004,
		3.31359999999995, 3.23080000000004, 3.4588, 3.08159999999998, 3.4076, 3.00639999999999,
		2.38779999999997, 2.61900000000003, 1.99800000000005, 3.34820000000002, 2.95060000000001,
		0.990999999999985, 2.11440000000005, 2.20299999999997, 2.82219999999995, 2.73239999999998,
		2.7826, 3.76660000000004, 2.26480000000004, 2.31280000000004, 2.40819999999997,
		2.75360000000001, 3.33759999999995, 2.71559999999999, 1.7478000000001, 1.42920000000004,
		2.39300000000003, 2.22779999999989, 2.34339999999997, 0.87259999999992, 3.88400000000001,
		1.80600000000004, 1.91759999999999, 1.16779999999994, 1.50320000000011, 2.52500000000009,
		0.226400000000012, 2.31500000000005, 0.930000000000064, 1.25199999999995, 2.14959999999996,
		0.0407999999999902, 2.5447999999999, 1.32960000000003, 0.197400000000016, 2.52620000000002,
		3.33279999999991, -1.34300000000007, 0.422199999999975, 0.917200000000093, 1.12920000000008,
		1.46060000000011, 1.45779999999991, 2.8728000000001, 3.33359999999993, -1.34079999999994,
		1.57680000000005, 0.363000000000056, 1.40740000000005, 0.656600000000026, 0.801400000000058,
		-0.454600000000028, 1.51919999999996,
	},
	-- precision 9
	{
		368, 361.8294, 355.2452, 348.6698, 342.1464, 336.2024, 329.8782, 323.6598, 317.462, 311.2826,
		305.7102, 299.7416, 293.9366, 288.1046, 282.285, 277.0668, 271.306, 265.8448, 260.301,
		254.9886, 250.2422, 244.8138, 239.7074, 234.7428, 229.8402, 225.1664, 220.3534, 215.594,
		210.6886, 205.7876, 201.65, 197.228, 192.8036, 188.1666, 184.0818, 180.0824, 176.2574,
		172.302, 168.1644, 164.0056, 160.3802, 156.7192, 152.5234, 149.2084, 145.831, 142.485,
		139.1112, 135.4764, 131.76, 129.3368, 126.5538, 122.5058, 119.2646, 116.5902, 113.3818,
		110.8998, 107.9532, 105.2062, 102.2798, 99.4728, 96.9582, 94.3292, 92.171, 89.7809999999999,
		87.5716, 84.7048, 82.5322, 79.875, 78.3972, 75.3464, 73.7274, 71.2834, 70.1444,
		68.4263999999999, 66.0166, 64.018, 62.0437999999999, 60.3399999999999, 58.6856, 57.9836,
		55.0311999999999, 54.6769999999999, 52.3188, 51.4846, 49.4423999999999, 47.739,
		46.1487999999999, 44.9202, 43.4059999999999, 42.5342000000001, 41.2834, 38.8954000000001,
		38.3286000000001, 36.2146, 36.6684, 35.9946, 33.123, 33.4338, 31.7378000000001, 29.076,
		28.9692, 27.4964, 27.0998, 25.9864, 26.7754, 24.3208, 23.4838, 22.7388000000001,
		24.0758000000001, 21.9097999999999, 20.9728, 19.9228000000001, 19.9292, 16.617, 17.05,
		18.2996000000001, 15.6128000000001, 15.7392, 14.5174, 13.6322, 12.2583999999999,
		13.3766000000001, 11.423, 13.1232, 9.51639999999998, 10.5938000000001, 9.59719999999993,
		8.12220000000002, 9.76739999999995, 7.50440000000003, 7.56999999999994, 6.70440000000008,
		6.41419999999994, 6.71019999999999, 5.60940000000005, 4.65219999999999, 6.84099999999989,
		3.4072000000001, 3.97859999999991, 3.32760000000007, 5.52160000000003, 3.31860000000006,
		2.06940000000009, 4.35400000000004, 1.57500000000005, 0.280799999999999, 2.12879999999996,
		-0.214799999999968, -0.0378000000000611, -0.658200000000079, 0.654800000000023,
		-0.0697999999999865, 0.858400000000074, -2.52700000000004, -2.1751999999999,
		-3.35539999999992, -1.04019999999991, -0.651000000000067, -2.14439999999991,
		-1.96659999999997, -3.97939999999994, -0.604400000000169, -3.08260000000018,
		-3.39159999999993, -5.29640000000018, -5.38920000000007, -5.08759999999984, -4.69900000000007,
		-5.23720000000003, -3.15779999999995, -4.97879999999986, -4.89899999999989, -7.48880000000008,
		-5.94799999999987, -5.68060000000014, -6.67180000000008, -4.70499999999993, -7.27779999999984,
		-4.6579999999999, -4.4362000000001, -4.32139999999981, -5.18859999999995, -6.66879999999992,
		-6.48399999999992, -5.1260000000002, -4.4032000000002, -6.13500000000022, -5.80819999999994,
		-4.16719999999987, -4.15039999999999, -7.45600000000013, -7.24080000000004, -9.83179999999993,
		-5.80420000000004, -8.6561999999999, -6.99940000000015, -10.5473999999999, -7.34139999999979,
		-6.80999999999995, -6.29719999999998, -6.23199999999997,
	},
	-- prec 10
	{
		737.1256, 724.4234, 711.1064, 698.4732, 685.4636, 673.0644, 660.488, 647.9654, 636.0832,
		623.7864, 612.1992, 600.2176, 588.5228, 577.1716, 565.7752, 554.899, 543.6126, 532.6492,
		521.9474, 511.5214, 501.1064, 490.6364, 480.2468, 470.4588, 460.3832, 451.0584, 440.8606,
		431.3868, 422.5062, 413.1862, 404.463, 395.339, 386.1936, 378.1292, 369.1854, 361.2908,
		353.3324, 344.8518, 337.5204, 329.4854, 321.9318, 314.552, 306.4658, 299.4256, 292.849,
		286.152, 278.8956, 271.8792, 265.118, 258.62, 252.5132, 245.9322, 239.7726, 233.6086,
		227.5332, 222.5918, 216.4294, 210.7662, 205.4106, 199.7338, 194.9012, 188.4486, 183.1556,
		178.6338, 173.7312, 169.6264, 163.9526, 159.8742, 155.8326, 151.1966, 147.5594, 143.07,
		140.037, 134.1804, 131.071, 127.4884, 124.0848, 120.2944, 117.333, 112.9626, 110.2902,
		107.0814, 103.0334, 99.4832000000001, 96.3899999999999, 93.7202000000002, 90.1714000000002,
		87.2357999999999, 85.9346, 82.8910000000001, 80.0264000000002, 78.3834000000002,
		75.1543999999999, 73.8683999999998, 70.9895999999999, 69.4367999999999, 64.8701999999998,
		65.0408000000002, 61.6738, 59.5207999999998, 57.0158000000001, 54.2302, 53.0962,
		50.4985999999999, 52.2588000000001, 47.3914, 45.6244000000002, 42.8377999999998, 43.0072,
		40.6516000000001, 40.2453999999998, 35.2136, 36.4546, 33.7849999999999, 33.2294000000002,
		32.4679999999998, 30.8670000000002, 28.6507999999999, 28.9099999999999, 27.5983999999999,
		26.1619999999998, 24.5563999999999, 23.2328000000002, 21.9484000000002, 21.5902000000001,
		21.3346000000001, 17.7031999999999, 20.6111999999998, 19.5545999999999, 15.7375999999999,
		17.0720000000001, 16.9517999999998, 15.326, 13.1817999999998, 14.6925999999999,
		13.0859999999998, 13.2754, 10.8697999999999, 11.248, 7.3768, 4.72339999999986,
		7.97899999999981, 8.7503999999999, 7.68119999999999, 9.7199999999998, 7.73919999999998,
		5.6224000000002, 7.44560000000001, 6.6601999999998, 5.9058, 4.00199999999995,
		4.51699999999983, 4.68240000000014, 3.86220000000003, 5.13639999999987, 5.98500000000013,
		2.47719999999981, 2.61999999999989, 1.62800000000016, 4.65000000000009, 0.225599999999758,
		0.831000000000131, -0.359400000000278, 1.27599999999984, -2.92559999999958,
		-0.0303999999996449, 2.37079999999969, -2.0033999999996, 0.804600000000391, 0.30199999999968,
		1.1247999999996, -2.6880000000001, 0.0321999999996478, -1.18099999999959, -3.9402,
		-1.47940000000017, -0.188400000000001, -2.10720000000038, -2.04159999999956,
		-3.12880000000041, -4.16160000000036, -0.612799999999879, -3.48719999999958,
		-8.17900000000009, -5.37780000000021, -4.01379999999972, -5.58259999999973, -5.73719999999958,
		-7.66799999999967, -5.69520000000011, -1.1247999999996, -5.58520000000044, -8.04560000000038,
		-4.64840000000004, -11.6468000000004, -7.97519999999986, -5.78300000000036, -7.67420000000038,
		-10.6328000000003, -9.81720000000041,
	},
	-- prec 11
	{
		1476, 1449.6014, 1423.5802, 1397.7942, 1372.3042, 1347.2062, 1321.8402, 1297.2292, 1272.9462,
		1248.9926, 1225.3026, 1201.4252, 1178.0578, 1155.6092, 1132.626, 1110.5568, 1088.527,
		1066.5154, 1045.1874, 1024.3878, 1003.37, 982.1972, 962.5728, 942.1012, 922.9668, 903.292,
		884.0772, 864.8578, 846.6562, 828.041, 809.714, 792.3112, 775.1806, 757.9854, 740.656,
		724.346, 707.5154, 691.8378, 675.7448, 659.6722, 645.5722, 630.1462, 614.4124, 600.8728,
		585.898, 572.408, 558.4926, 544.4938, 531.6776, 517.282, 505.7704, 493.1012, 480.7388,
		467.6876, 456.1872, 445.5048, 433.0214, 420.806, 411.409, 400.4144, 389.4294, 379.2286,
		369.651, 360.6156, 350.337, 342.083, 332.1538, 322.5094, 315.01, 305.6686, 298.1678, 287.8116,
		280.9978, 271.9204, 265.3286, 257.5706, 249.6014, 242.544, 235.5976, 229.583, 220.9438,
		214.672, 208.2786, 201.8628, 195.1834, 191.505, 186.1816, 178.5188, 172.2294, 167.8908,
		161.0194, 158.052, 151.4588, 148.1596, 143.4344, 138.5238, 133.13, 127.6374, 124.8162,
		118.7894, 117.3984, 114.6078, 109.0858, 105.1036, 103.6258, 98.6018000000004,
		95.7618000000002, 93.5821999999998, 88.5900000000001, 86.9992000000002, 82.8800000000001,
		80.4539999999997, 74.6981999999998, 74.3644000000004, 73.2914000000001, 65.5709999999999,
		66.9232000000002, 65.1913999999997, 62.5882000000001, 61.5702000000001, 55.7035999999998,
		56.1764000000003, 52.7596000000003, 53.0302000000001, 49.0609999999997, 48.4694, 44.933,
		46.0474000000004, 44.7165999999997, 41.9416000000001, 39.9207999999999, 35.6328000000003,
		35.5276000000003, 33.1934000000001, 33.2371999999996, 33.3864000000003, 33.9228000000003,
		30.2371999999996, 29.1373999999996, 25.2272000000003, 24.2942000000003, 19.8338000000003,
		18.9005999999999, 23.0907999999999, 21.8544000000002, 19.5176000000001, 15.4147999999996,
		16.9314000000004, 18.6737999999996, 12.9877999999999, 14.3688000000002, 12.0447999999997,
		15.5219999999999, 12.5299999999997, 14.5940000000001, 14.3131999999996, 9.45499999999993,
		12.9441999999999, 3.91139999999996, 13.1373999999996, 5.44720000000052, 9.82779999999912,
		7.87279999999919, 3.67760000000089, 5.46980000000076, 5.55099999999948, 5.65979999999945,
		3.89439999999922, 3.1275999999998, 5.65140000000065, 6.3062000000009, 3.90799999999945,
		1.87060000000019, 5.17020000000048, 2.46680000000015, 0.770000000000437, -3.72340000000077,
		1.16400000000067, 8.05340000000069, 0.135399999999208, 2.15940000000046, 0.766999999999825,
		1.0594000000001, 3.15500000000065, -0.287399999999252, 2.37219999999979, -2.86620000000039,
		-1.63199999999961, -2.22979999999916, -0.15519999999924, -1.46039999999994,
		-0.262199999999211, -2.34460000000036, -2.8078000000005, -3.22179999999935, -5.60159999999996,
		-8.42200000000048, -9.43740000000071, 0.161799999999857, -10.4755999999998, -10.0823999999993,
	},
	-- prec 12
	{
		2953, 2900.4782, 2848.3568, 2796.3666, 2745.324, 2694.9598, 2644.648, 2595.539, 2546.1474,
		2498.2576, 2450.8376, 2403.6076, 2357.451, 2311.38, 2266.4104, 2221.5638, 2176.9676, 2134.193,
		2090.838, 2048.8548, 2007.018, 1966.1742, 1925.4482, 1885.1294, 1846.4776, 1807.4044,
		1768.8724, 1731.3732, 1693.4304, 1657.5326, 1621.949, 1586.5532, 1551.7256, 1517.6182,
		1483.5186, 1450.4528, 1417.865, 1385.7164, 1352.6828, 1322.6708, 1291.8312, 1260.9036,
		1231.476, 1201.8652, 1173.6718, 1145.757, 1119.2072, 1092.2828, 1065.0434, 1038.6264,
		1014.3192, 988.5746, 965.0816, 940.1176, 917.9796, 894.5576, 871.1858, 849.9144, 827.1142,
		805.0818, 783.9664, 763.9096, 742.0816, 724.3962, 706.3454, 688.018, 667.4214, 650.3106,
		633.0686, 613.8094, 597.818, 581.4248, 563.834, 547.363, 531.5066, 520.455400000001,
		505.583199999999, 488.366, 476.480799999999, 459.7682, 450.0522, 434.328799999999,
		423.952799999999, 408.727000000001, 399.079400000001, 387.252200000001, 373.987999999999,
		360.852000000001, 351.6394, 339.642, 330.902400000001, 322.661599999999, 311.662200000001,
		301.3254, 291.7484, 279.939200000001, 276.7508, 263.215200000001, 254.811400000001, 245.5494,
		242.306399999999, 234.8734, 223.787200000001, 217.7156, 212.0196, 200.793, 195.9748, 189.0702,
		182.449199999999, 177.2772, 170.2336, 164.741, 158.613600000001, 155.311, 147.5964, 142.837,
		137.3724, 132.0162, 130.0424, 121.9804, 120.451800000001, 114.8968, 111.585999999999,
		105.933199999999, 101.705, 98.5141999999996, 95.0488000000005, 89.7880000000005,
		91.4750000000004, 83.7764000000006, 80.9698000000008, 72.8574000000008, 73.1615999999995,
		67.5838000000003, 62.6263999999992, 63.2638000000006, 66.0977999999996, 52.0843999999997,
		58.9956000000002, 47.0912000000008, 46.4956000000002, 48.4383999999991, 47.1082000000006,
		43.2392, 37.2759999999998, 40.0283999999992, 35.1864000000005, 35.8595999999998, 32.0998,
		28.027, 23.6694000000007, 33.8266000000003, 26.3736000000008, 27.2008000000005,
		21.3245999999999, 26.4115999999995, 23.4521999999997, 19.5013999999992, 19.8513999999996,
		10.7492000000002, 18.6424000000006, 13.1265999999996, 18.2436000000016, 6.71860000000015,
		3.39459999999963, 6.33759999999893, 7.76719999999841, 0.813999999998487, 3.82819999999992,
		0.826199999999517, 8.07440000000133, -1.59080000000176, 5.01780000000144, 0.455399999998917,
		-0.24199999999837, 0.174800000000687, -9.07640000000174, -4.20160000000033, -3.77520000000004,
		-4.75179999999818, -5.3724000000002, -8.90680000000066, -6.10239999999976, -5.74120000000039,
		-9.95339999999851, -3.86339999999836, -13.7304000000004, -16.2710000000006, -7.51359999999841,
		-3.30679999999847, -13.1339999999982, -10.0551999999989, -6.72019999999975, -8.59660000000076,
		-10.9307999999983, -1.8775999999998, -4.82259999999951, -13.7788, -21.6470000000008,
		-10.6735999999983, -15.7799999999988,
	},
	-- prec 13
	{
		5907.5052, 5802.2672, 5697.347, 5593.5794, 5491.2622, 5390.5514, 5290.3376, 5191.6952,
		5093.5988, 4997.3552, 4902.5972, 4808.3082, 4715.5646, 4624.109, 4533.8216, 4444.4344,
		4356.3802, 4269.2962, 4183.3784, 4098.292, 4014.79, 3932.4574, 3850.6036, 3771.2712,
		3691.7708, 3615.099, 3538.1858, 3463.4746, 3388.8496, 3315.6794, 3244.5448, 3173.7516,
		3103.3106, 3033.6094, 2966.5642, 2900.794, 2833.7256, 2769.81, 2707.3196, 2644.0778,
		2583.9916, 2523.4662, 2464.124, 2406.073, 2347.0362, 2292.1006, 2238.1716, 2182.7514,
		2128.4884, 2077.1314, 2025.037, 1975.3756, 1928.933, 1879.311, 1831.0006, 1783.2144,
		1738.3096, 1694.5144, 1649.024, 1606.847, 1564.7528, 1525.3168, 1482.5372, 1443.9668,
		1406.5074, 1365.867, 1329.2186, 1295.4186, 1257.9716, 1225.339, 1193.2972, 1156.3578,
		1125.8686, 1091.187, 1061.4094, 1029.4188, 1000.9126, 972.3272, 944.004199999999, 915.7592,
		889.965, 862.834200000001, 840.4254, 812.598399999999, 785.924200000001, 763.050999999999,
		741.793799999999, 721.466, 699.040799999999, 677.997200000002, 649.866999999998,
		634.911800000002, 609.8694, 591.981599999999, 570.2922, 557.129199999999, 538.3858,
		521.872599999999, 502.951400000002, 495.776399999999, 475.171399999999, 459.751,
		439.995200000001, 426.708999999999, 413.7016, 402.3868, 387.262599999998, 372.0524,
		357.050999999999, 342.5098, 334.849200000001, 322.529399999999, 311.613799999999,
		295.848000000002, 289.273000000001, 274.093000000001, 263.329600000001, 251.389599999999,
		245.7392, 231.9614, 229.7952, 217.155200000001, 208.9588, 199.016599999999, 190.839199999999,
		180.6976, 176.272799999999, 166.976999999999, 162.5252, 151.196400000001, 149.386999999999,
		133.981199999998, 130.0586, 130.164000000001, 122.053400000001, 110.7428, 108.1276,
		106.232400000001, 100.381600000001, 98.7668000000012, 86.6440000000002, 79.9768000000004,
		82.4722000000002, 68.7026000000005, 70.1186000000016, 71.9948000000004, 58.998599999999,
		59.0492000000013, 56.9818000000014, 47.5338000000011, 42.9928, 51.1591999999982,
		37.2740000000013, 42.7220000000016, 31.3734000000004, 26.8090000000011, 25.8934000000008,
		26.5286000000015, 29.5442000000003, 19.3503999999994, 26.0760000000009, 17.9527999999991,
		14.8419999999969, 10.4683999999979, 8.65899999999965, 9.86720000000059, 4.34139999999752,
		-0.907800000000861, -3.32080000000133, -0.936199999996461, -11.9916000000012,
		-8.87000000000262, -6.33099999999831, -11.3366000000024, -15.9207999999999, -9.34659999999712,
		-15.5034000000014, -19.2097999999969, -15.357799999998, -28.2235999999975, -30.6898000000001,
		-19.3271999999997, -25.6083999999973, -24.409599999999, -13.6385999999984, -33.4473999999973,
		-32.6949999999997, -28.9063999999998, -31.7483999999968, -32.2935999999972, -35.8329999999987,
		-47.620600000002, -39.0855999999985, -33.1434000000008, -46.1371999999974, -37.5892000000022,
		-46.8164000000033, -47.3142000000007, -60.2914000000019, -37.7575999999972,
	},
	-- prec 14
	{
		11816.475, 11605.0046, 11395.3792, 11188.7504, 10984.1814, 10782.0086, 10582.0072, 10384.503,
		10189.178, 9996.2738, 9806.0344, 9617.9798, 9431.394, 9248.7784, 9067.6894, 8889.6824,
		8712.9134, 8538.8624, 8368.4944, 8197.7956, 8031.8916, 7866.6316, 7703.733, 7544.5726,
		7386.204, 7230.666, 7077.8516, 6926.7886, 6778.6902, 6631.9632, 6487.304, 6346.7486,
		6206.4408, 6070.202, 5935.2576, 5799.924, 5671.0324, 5541.9788, 5414.6112, 5290.0274,
		5166.723, 5047.6906, 4929.162, 4815.1406, 4699.127, 4588.5606, 4477.7394, 4369.4014,
		4264.2728, 4155.9224, 4055.581, 3955.505, 3856.9618, 3761.3828, 3666.9702, 3575.7764,
		3482.4132, 3395.0186, 3305.8852, 3221.415, 3138.6024, 3056.296, 2970.4494, 2896.1526,
		2816.8008, 2740.2156, 2670.497, 2594.1458, 2527.111, 2460.8168, 2387.5114, 2322.9498,
		2260.6752, 2194.2686, 2133.7792, 2074.767, 2015.204, 1959.4226, 1898.6502, 1850.006, 1792.849,
		1741.4838, 1687.9778, 1638.1322, 1589.3266, 1543.1394, 1496.8266, 1447.8516, 1402.7354,
		1361.9606, 1327.0692, 1285.4106, 1241.8112, 1201.6726, 1161.973, 1130.261, 1094.2036,
		1048.2036, 1020.6436, 990.901400000002, 961.199800000002, 924.769800000002, 899.526400000002,
		872.346400000002, 834.375, 810.432000000001, 780.659800000001, 756.013800000001,
		733.479399999997, 707.923999999999, 673.858, 652.222399999999, 636.572399999997,
		615.738599999997, 586.696400000001, 564.147199999999, 541.679600000003, 523.943599999999,
		505.714599999999, 475.729599999999, 461.779600000002, 449.750800000002, 439.020799999998,
		412.7886, 400.245600000002, 383.188199999997, 362.079599999997, 357.533799999997,
		334.319000000003, 327.553399999997, 308.559399999998, 291.270199999999, 279.351999999999,
		271.791400000002, 252.576999999997, 247.482400000001, 236.174800000001, 218.774599999997,
		220.155200000001, 208.794399999999, 201.223599999998, 182.995600000002, 185.5268,
		164.547400000003, 176.5962, 150.689599999998, 157.8004, 138.378799999999, 134.021200000003,
		117.614399999999, 108.194000000003, 97.0696000000025, 89.6042000000016, 95.6030000000028,
		84.7810000000027, 72.635000000002, 77.3482000000004, 59.4907999999996, 55.5875999999989,
		50.7346000000034, 61.3916000000027, 50.9149999999936, 39.0384000000049, 58.9395999999979,
		29.633600000001, 28.2032000000036, 26.0078000000067, 17.0387999999948, 9.22000000000116,
		13.8387999999977, 8.07240000000456, 14.1549999999988, 15.3570000000036, 3.42660000000615,
		6.24820000000182, -2.96940000000177, -8.79940000000352, -5.97860000000219, -14.4048000000039,
		-3.4143999999942, -13.0148000000045, -11.6977999999945, -25.7878000000055, -22.3185999999987,
		-24.409599999999, -31.9756000000052, -18.9722000000038, -22.8678000000073, -30.8972000000067,
		-32.3715999999986, -22.3907999999938, -43.6720000000059, -35.9038, -39.7492000000057,
		-54.1641999999993, -45.2749999999942, -42.2989999999991, -44.1089999999967, -64.3564000000042,
		-49.9551999999967, -42.6116000000038,
	},
	-- prec 15
	{
		23634.0036, 23210.8034, 22792.4744, 22379.1524, 21969.7928, 21565.326, 21165.3532, 20770.2806,
		20379.9892, 19994.7098, 19613.318, 19236.799, 18865.4382, 18498.8244, 18136.5138, 17778.8668,
		17426.2344, 17079.32, 16734.778, 16397.2418, 16063.3324, 15734.0232, 15409.731, 15088.728,
		14772.9896, 14464.1402, 14157.5588, 13855.5958, 13559.3296, 13264.9096, 12978.326, 12692.0826,
		12413.8816, 12137.3192, 11870.2326, 11602.5554, 11340.3142, 11079.613, 10829.5908, 10583.5466,
		10334.0344, 10095.5072, 9859.694, 9625.2822, 9395.7862, 9174.0586, 8957.3164, 8738.064,
		8524.155, 8313.7396, 8116.9168, 7913.542, 7718.4778, 7521.65, 7335.5596, 7154.2906, 6968.7396,
		6786.3996, 6613.236, 6437.406, 6270.6598, 6107.7958, 5945.7174, 5787.6784, 5635.5784,
		5482.308, 5337.9784, 5190.0864, 5045.9158, 4919.1386, 4771.817, 4645.7742, 4518.4774,
		4385.5454, 4262.6622, 4142.74679999999, 4015.5318, 3897.9276, 3790.7764, 3685.13800000001,
		3573.6274, 3467.9706, 3368.61079999999, 3271.5202, 3170.3848, 3076.4656, 2982.38400000001,
		2888.4664, 2806.4868, 2711.9564, 2634.1434, 2551.3204, 2469.7662, 2396.61139999999, 2318.9902,
		2243.8658, 2171.9246, 2105.01360000001, 2028.8536, 1960.9952, 1901.4096, 1841.86079999999,
		1777.54700000001, 1714.5802, 1654.65059999999, 1596.311, 1546.2016, 1492.3296, 1433.8974,
		1383.84600000001, 1339.4152, 1293.5518, 1245.8686, 1193.50659999999, 1162.27959999999,
		1107.19439999999, 1069.18060000001, 1035.09179999999, 999.679000000004, 957.679999999993,
		925.300199999998, 888.099400000006, 848.638600000006, 818.156400000007, 796.748399999997,
		752.139200000005, 725.271200000003, 692.216, 671.633600000001, 647.939799999993,
		621.670599999998, 575.398799999995, 561.226599999995, 532.237999999998, 521.787599999996,
		483.095799999996, 467.049599999998, 465.286399999997, 415.548599999995, 401.047399999996,
		380.607999999993, 377.362599999993, 347.258799999996, 338.371599999999, 310.096999999994,
		301.409199999995, 276.280799999993, 265.586800000005, 258.994399999996, 223.915999999997,
		215.925399999993, 213.503800000006, 191.045400000003, 166.718200000003, 166.259000000005,
		162.941200000001, 148.829400000002, 141.645999999993, 123.535399999993, 122.329800000007,
		89.473399999988, 80.1962000000058, 77.5457999999926, 59.1056000000099, 83.3509999999951,
		52.2906000000075, 36.3979999999865, 40.6558000000077, 42.0003999999899, 19.6630000000005,
		19.7153999999864, -8.38539999999921, -0.692799999989802, 0.854800000000978, 3.23219999999856,
		-3.89040000000386, -5.25880000001052, -24.9052000000083, -22.6837999999989, -26.4286000000138,
		-34.997000000003, -37.0216000000073, -43.430400000012, -58.2390000000014, -68.8034000000043,
		-56.9245999999985, -57.8583999999973, -77.3097999999882, -73.2793999999994, -81.0738000000129,
		-87.4530000000086, -65.0254000000132, -57.296399999992, -96.2746000000043, -103.25,
		-96.081600000005, -91.5542000000132, -102.465200000006, -107.688599999994, -101.458000000013,
		-109.715800000005,
	},
	-- prec 16
	{
		47270, 46423.3584, 45585.7074, 44757.152, 43938.8416, 43130.9514, 42330.03, 41540.407,
		40759.6348, 39988.206, 39226.5144, 38473.2096, 37729.795, 36997.268, 36272.6448, 35558.665,
		34853.0248, 34157.4472, 33470.5204, 32793.5742, 32127.0194, 31469.4182, 30817.6136,
		30178.6968, 29546.8908, 28922.8544, 28312.271, 27707.0924, 27114.0326, 26526.692, 25948.6336,
		25383.7826, 24823.5998, 24272.2974, 23732.2572, 23201.4976, 22674.2796, 22163.6336, 21656.515,
		21161.7362, 20669.9368, 20189.4424, 19717.3358, 19256.3744, 18795.9638, 18352.197, 17908.5738,
		17474.391, 17052.918, 16637.2236, 16228.4602, 15823.3474, 15428.6974, 15043.0284, 14667.6278,
		14297.4588, 13935.2882, 13578.5402, 13234.6032, 12882.1578, 12548.0728, 12219.231, 11898.0072,
		11587.2626, 11279.9072, 10973.5048, 10678.5186, 10392.4876, 10105.2556, 9825.766, 9562.5444,
		9294.2222, 9038.2352, 8784.848, 8533.2644, 8301.7776, 8058.30859999999, 7822.94579999999,
		7599.11319999999, 7366.90779999999, 7161.217, 6957.53080000001, 6736.212, 6548.21220000001,
		6343.06839999999, 6156.28719999999, 5975.15419999999, 5791.75719999999, 5621.32019999999,
		5451.66, 5287.61040000001, 5118.09479999999, 4957.288, 4798.4246, 4662.17559999999,
		4512.05900000001, 4364.68539999999, 4220.77720000001, 4082.67259999999, 3957.19519999999,
		3842.15779999999, 3699.3328, 3583.01180000001, 3473.8964, 3338.66639999999, 3233.55559999999,
		3117.799, 3008.111, 2909.69140000001, 2814.86499999999, 2719.46119999999, 2624.742,
		2532.46979999999, 2444.7886, 2370.1868, 2272.45259999999, 2196.19260000001, 2117.90419999999,
		2023.2972, 1969.76819999999, 1885.58979999999, 1833.2824, 1733.91200000001, 1682.54920000001,
		1604.57980000001, 1556.11240000001, 1491.3064, 1421.71960000001, 1371.22899999999, 1322.1324,
		1264.7892, 1196.23920000001, 1143.8474, 1088.67240000001, 1073.60380000001, 1023.11660000001,
		959.036400000012, 927.433199999999, 906.792799999996, 853.433599999989, 841.873800000001,
		791.1054, 756.899999999994, 704.343200000003, 672.495599999995, 622.790399999998,
		611.254799999995, 567.283200000005, 519.406599999988, 519.188400000014, 495.312800000014,
		451.350799999986, 443.973399999988, 431.882199999993, 392.027000000002, 380.924200000009,
		345.128999999986, 298.901400000002, 287.771999999997, 272.625, 247.253000000026,
		222.490600000019, 223.590000000026, 196.407599999977, 176.425999999978, 134.725199999986,
		132.4804, 110.445599999977, 86.7939999999944, 56.7038000000175, 64.915399999998,
		38.3726000000024, 37.1606000000029, 46.170999999973, 49.1716000000015, 15.3362000000197,
		6.71639999997569, -34.8185999999987, -39.4476000000141, 12.6830000000191, -12.3331999999937,
		-50.6565999999875, -59.9538000000175, -65.1054000000004, -70.7576000000117, -106.325200000021,
		-126.852200000023, -110.227599999984, -132.885999999999, -113.897200000007, -142.713800000027,
		-151.145399999979, -150.799200000009, -177.756200000003, -156.036399999983, -182.735199999996,
		-177.259399999981, -198.663600000029, -174.577600000019, -193.84580000001,
	},
	-- prec 17
	{
		94541, 92848.811, 91174.019, 89517.558, 87879.9705, 86262.7565, 84663.5125, 83083.7435,
		81521.7865, 79977.272, 78455.9465, 76950.219, 75465.432, 73994.152, 72546.71, 71115.2345,
		69705.6765, 68314.937, 66944.2705, 65591.255, 64252.9485, 62938.016, 61636.8225, 60355.592,
		59092.789, 57850.568, 56624.518, 55417.343, 54231.1415, 53067.387, 51903.526, 50774.649,
		49657.6415, 48561.05, 47475.7575, 46410.159, 45364.852, 44327.053, 43318.4005, 42325.6165,
		41348.4595, 40383.6265, 39436.77, 38509.502, 37594.035, 36695.939, 35818.6895, 34955.691,
		34115.8095, 33293.949, 32465.0775, 31657.6715, 30877.2585, 30093.78, 29351.3695, 28594.1365,
		27872.115, 27168.7465, 26477.076, 25774.541, 25106.5375, 24452.5135, 23815.5125, 23174.0655,
		22555.2685, 21960.2065, 21376.3555, 20785.1925, 20211.517, 19657.0725, 19141.6865, 18579.737,
		18081.3955, 17578.995, 17073.44, 16608.335, 16119.911, 15651.266, 15194.583, 14749.0495,
		14343.4835, 13925.639, 13504.509, 13099.3885, 12691.2855, 12328.018, 11969.0345, 11596.5145,
		11245.6355, 10917.6575, 10580.9785, 10277.8605, 9926.58100000001, 9605.538, 9300.42950000003,
		8989.97850000003, 8728.73249999998, 8448.3235, 8175.31050000002, 7898.98700000002,
		7629.79100000003, 7413.76199999999, 7149.92300000001, 6921.12650000001, 6677.1545,
		6443.28000000003, 6278.23450000002, 6014.20049999998, 5791.20299999998, 5605.78450000001,
		5438.48800000001, 5234.2255, 5059.6825, 4887.43349999998, 4682.935, 4496.31099999999,
		4322.52250000002, 4191.42499999999, 4021.24200000003, 3900.64799999999, 3762.84250000003,
		3609.98050000001, 3502.29599999997, 3363.84250000003, 3206.54849999998, 3079.70000000001,
		2971.42300000001, 2867.80349999998, 2727.08100000001, 2630.74900000001, 2496.6165, 2440.902,
		2356.19150000002, 2235.58199999999, 2120.54149999999, 2012.25449999998, 1933.35600000003,
		1820.93099999998, 1761.54800000001, 1663.09350000002, 1578.84600000002, 1509.48149999999,
		1427.3345, 1379.56150000001, 1306.68099999998, 1212.63449999999, 1084.17300000001,
		1124.16450000001, 1060.69949999999, 1007.48849999998, 941.194499999983, 879.880500000028,
		836.007500000007, 782.802000000025, 748.385499999975, 647.991500000004, 626.730500000005,
		570.776000000013, 484.000500000024, 513.98550000001, 418.985499999952, 386.996999999974,
		370.026500000036, 355.496999999974, 356.731499999994, 255.92200000002, 259.094000000041,
		205.434499999974, 165.374500000034, 197.347500000033, 95.718499999959, 67.6165000000037,
		54.6970000000438, 31.7395000000251, -15.8784999999916, 8.42500000004657, -26.3754999999655,
		-118.425500000012, -66.6629999999423, -42.9745000000112, -107.364999999991, -189.839000000036,
		-162.611499999999, -164.964999999967, -189.079999999958, -223.931499999948, -235.329999999958,
		-269.639500000048, -249.087999999989, -206.475499999942, -283.04449999996, -290.667000000016,
		-304.561499999953, -336.784499999951, -380.386500000022, -283.280499999993, -364.533000000054,
		-389.059499999974, -364.454000000027, -415.748000000021, -417.155000000028,
	},
	-- prec 18
	{
		189083, 185696.913, 182348.774, 179035.946, 175762.762, 172526.444, 169329.754, 166166.099,
		163043.269, 159958.91, 156907.912, 153906.845, 150924.199, 147996.568, 145093.457, 142239.233,
		139421.475, 136632.27, 133889.588, 131174.2, 128511.619, 125868.621, 123265.385, 120721.061,
		118181.769, 115709.456, 113252.446, 110840.198, 108465.099, 106126.164, 103823.469,
		101556.618, 99308.004, 97124.508, 94937.803, 92833.731, 90745.061, 88677.627, 86617.47,
		84650.442, 82697.833, 80769.132, 78879.629, 77014.432, 75215.626, 73384.587, 71652.482,
		69895.93, 68209.301, 66553.669, 64921.981, 63310.323, 61742.115, 60205.018, 58698.658,
		57190.657, 55760.865, 54331.169, 52908.167, 51550.273, 50225.254, 48922.421, 47614.533,
		46362.049, 45098.569, 43926.083, 42736.03, 41593.473, 40425.26, 39316.237, 38243.651,
		37170.617, 36114.609, 35084.19, 34117.233, 33206.509, 32231.505, 31318.728, 30403.404,
		29540.0550000001, 28679.236, 27825.862, 26965.216, 26179.148, 25462.08, 24645.952, 23922.523,
		23198.144, 22529.128, 21762.4179999999, 21134.779, 20459.117, 19840.818, 19187.04,
		18636.3689999999, 17982.831, 17439.7389999999, 16874.547, 16358.2169999999, 15835.684,
		15352.914, 14823.681, 14329.313, 13816.897, 13342.874, 12880.882, 12491.648, 12021.254,
		11625.392, 11293.7610000001, 10813.697, 10456.209, 10099.074, 9755.39000000001,
		9393.18500000006, 9047.57900000003, 8657.98499999999, 8395.85900000005, 8033,
		7736.95900000003, 7430.59699999995, 7258.47699999996, 6924.58200000005, 6691.29399999999,
		6357.92500000005, 6202.05700000003, 5921.19700000004, 5628.28399999999, 5404.96799999999,
		5226.71100000001, 4990.75600000005, 4799.77399999998, 4622.93099999998, 4472.478,
		4171.78700000001, 3957.46299999999, 3868.95200000005, 3691.14300000004, 3474.63100000005,
		3341.67200000002, 3109.14000000001, 3071.97400000005, 2796.40399999998, 2756.17799999996,
		2611.46999999997, 2471.93000000005, 2382.26399999997, 2209.22400000005, 2142.28399999999,
		2013.96100000001, 1911.18999999994, 1818.27099999995, 1668.47900000005, 1519.65800000005,
		1469.67599999998, 1367.13800000004, 1248.52899999998, 1181.23600000003, 1022.71900000004,
		1088.20700000005, 959.03600000008, 876.095999999903, 791.183999999892, 703.337000000058,
		731.949999999953, 586.86400000006, 526.024999999907, 323.004999999888, 320.448000000091,
		340.672999999952, 309.638999999966, 216.601999999955, 102.922999999952, 19.2399999999907,
		-0.114000000059605, -32.6240000000689, -89.3179999999702, -153.497999999905,
		-64.2970000000205, -143.695999999996, -259.497999999905, -253.017999999924, -213.948000000091,
		-397.590000000084, -434.006000000052, -403.475000000093, -297.958000000101, -404.317000000039,
		-528.898999999976, -506.621000000043, -513.205000000075, -479.351000000024, -596.139999999898,
		-527.016999999993, -664.681000000099, -680.306000000099, -704.050000000047, -850.486000000034,
		-757.43200000003, -713.308999999892,
	}
})

local MINIMUM_PRECISION = 4
local MAXIMUM_PRECISION = 18

local SPARSE_PRECISION = 25
local DENSE_THRESHOLD_RATIO = 0.25

local COUNTING_THRESHOLD = table.freeze({
	10, -- precision 4
	20, -- precision 5
	40, -- precision 6
	80, -- precision 7
	220, -- precision 8
	400, -- precision 9
	900, -- precision 10
	1800, -- precision 11
	3100, -- precision 12
	6500, -- precision 13
	11500, -- precision 14
	20000, -- precision 15
	50000, -- precision 16
	120000, -- precision 17
	350000, -- precision 18
})

local function linearCountingThreshold(p: number)
	if MINIMUM_PRECISION <= p and p <= MAXIMUM_PRECISION then
		return COUNTING_THRESHOLD[p - MINIMUM_PRECISION + 1]
	end
	return 5 * 2 ^ p / 2
end

local function getVarIntSize(value: number): number
	if value < 128 then
		return 1
	elseif value < 16384 then
		return 2
	elseif value < 2097152 then
		return 3
	elseif value < 268435456 then
		return 4
	end
	return 5
end

local function readVarInt(b: buffer, offset: number): (number, number)
	local b0 = buffer.readu8(b, offset)
	if b0 < 128 then
		return b0, offset + 1
	end

	local b1 = buffer.readu8(b, offset + 1)
	if b1 < 128 then
		return (b0 - 128) + (b1 * 128), offset + 2
	end

	local b2 = buffer.readu8(b, offset + 2)
	if b2 < 128 then
		return (b0 - 128) + (b1 - 128) * 128 + (b2 * 16384), offset + 3
	end

	local b3 = buffer.readu8(b, offset + 3)
	if b3 < 128 then
		return (b0 - 128) + (b1 - 128) * 128 + (b2 - 128) * 16384 + (b3 * 2097152), offset + 4
	end

	local b4 = buffer.readu8(b, offset + 4)
	return (b0 - 128) + (b1 - 128) * 128 + (b2 - 128) * 16384 + (b3 - 128) * 2097152 + (b4 * 268435456), offset + 5
end

local function writeVarInt(b: buffer, offset: number, value: number): number
	if value < 128 then
		buffer.writeu8(b, offset, value)
		return offset + 1
	elseif value < 16384 then
		buffer.writeu16(b, offset, (value % 128 + 128) + (value // 128) * 256)
		return offset + 2
	elseif value < 2097152 then
		buffer.writeu16(b, offset, (value % 128 + 128) + ((value // 128) % 128 + 128) * 256)
		buffer.writeu8(b, offset + 2, value // 16384)
		return offset + 3
	elseif value < 268435456 then
		buffer.writeu32(
			b,
			offset,
			(value % 128 + 128)
				+ ((value // 128) % 128 + 128) * 256
				+ ((value // 16384) % 128 + 128) * 65536
				+ (value // 2097152) * 16777216
		)
		return offset + 4
	else
		buffer.writeu32(
			b,
			offset,
			(value % 128 + 128)
				+ ((value // 128) % 128 + 128) * 256
				+ ((value // 16384) % 128 + 128) * 65536
				+ (value // 2097152) * 16777216
		)
		buffer.writeu8(b, offset + 4, value // 268435456)
		return offset + 5
	end
end

local function getAlpha(m: number): number
	if m == 16 then
		return 0.673101517
	elseif m == 32 then
		return 0.697121585
	elseif m == 64 then
		return 0.709209798
	else
		return 0.7213 / (1 + 1.079 / m)
	end
end

local function getDenseBuffer(hll: HyperLogLog): buffer
	local band = bit32.band
	local countlz = bit32.countlz
	local lshift = bit32.lshift
	local rshift = bit32.rshift
	local readu8 = buffer.readu8
	local writeu8 = buffer.writeu8

	local b = buffer.create(1 + hll.m)
	writeu8(b, 0, hll.p + (if hll.is_sparse then 128 else 0))

	local diff = hll.dense_diff
	local mask = hll.dense_mask
	local shift = hll.dense_shift

	for index_sparse, rho_sparse in hll.sparse_registers :: any do
		local index_dense = rshift(index_sparse, diff)
		local residual = band(index_sparse, mask)

		local rho_dense
		if residual == 0 then
			rho_dense = rho_sparse + diff
		else
			rho_dense = countlz(lshift(residual, shift)) + 1
		end

		local ptr = index_dense + 1
		if rho_dense > readu8(b, ptr) then
			writeu8(b, ptr, rho_dense)
		end
	end

	return b
end

local function toDense(hll: HyperLogLog)
	if not hll.is_sparse then
		return
	end

	hll.buffer = getDenseBuffer(hll)
	table.clear(hll.sparse_registers :: any)

	hll.is_sparse = false
	hll.sparse_registers = nil
	hll.sparse_count = 0
end

local HyperLogLog = {}
HyperLogLog.__index = HyperLogLog

export type HLL = {
	p: number,
	m: number,
	alpha: number,
	buffer: buffer?,
	is_sparse: boolean,
	sparse_registers: { [number]: number }?,
	sparse_count: number,
	shift_p: number,
	witness_mask: number,
	p_prime: number,
	m_prime: number,
	shift_p_prime: number,
	witness_mask_prime: number,
	dense_diff: number,
	dense_mask: number,
	dense_shift: number,
}
export type HyperLogLog = typeof(setmetatable({} :: HLL, HyperLogLog))

local function newRaw(precision: number?): HLL
	local p = math.clamp(precision or 14, 4, 18)
	local m = 2 ^ p
	local p_prime = SPARSE_PRECISION
	local m_prime = 2 ^ p_prime
	local diff = p_prime - p

	return {
		p = p,
		m = m,
		alpha = getAlpha(m) * m ^ 2,
		buffer = nil,
		is_sparse = true,
		sparse_registers = {},
		sparse_count = 0,
		shift_p = 32 - p,
		witness_mask = bit32.lshift(1, 32 - p) - 1,
		p_prime = p_prime,
		m_prime = m_prime,
		shift_p_prime = 32 - p_prime,
		witness_mask_prime = bit32.lshift(1, 32 - p_prime) - 1,
		dense_diff = diff,
		dense_mask = bit32.lshift(1, diff) - 1,
		dense_shift = 32 - diff,
	}
end

--- Creates a new HyperLogLog counter.
--- @param precision (p) -- An integer between 4 and 18. Defaults to 14.
--- @return HyperLogLog Object
function HyperLogLog.new(precision: number?): HyperLogLog
	return setmetatable(newRaw(precision), HyperLogLog)
end

local temp = buffer.create(8)

--- Adds an item to the HLL counter.
function HyperLogLog.add(self: HyperLogLog, item: buffer | number)
	if type(item) == "number" then
		buffer.writef64(temp, 0, item)
		item = temp
	end

	local hash = EncodingService:ComputeBufferHash(item :: buffer, Enum.HashAlgorithm.Blake3)
	local hi, lo = buffer.readu32(hash, 0), buffer.readu32(hash, 4)

	if self.is_sparse then
		local index = bit32.rshift(hi, self.shift_p_prime)
		local witness_hi = bit32.band(hi, self.witness_mask_prime)

		local rho
		if witness_hi > 0 then
			rho = bit32.countlz(witness_hi) - self.p_prime + 1
		else
			rho = self.shift_p_prime + bit32.countlz(lo) + 1
		end

		local regs = self.sparse_registers :: { [number]: number }
		local old_rho = regs[index] or 0
		if rho > old_rho then
			regs[index] = rho
			if old_rho == 0 then
				self.sparse_count += 1
				if self.sparse_count > (self.m * DENSE_THRESHOLD_RATIO) then
					toDense(self)
				end
			end
		end
	else
		local index = bit32.rshift(hi, self.shift_p) + 1
		local witness_hi = bit32.band(hi, self.witness_mask)

		local rho
		if witness_hi > 0 then
			rho = bit32.countlz(witness_hi) - self.p + 1
		else
			rho = self.shift_p + bit32.countlz(lo) + 1
		end

		if rho > buffer.readu8(self.buffer :: buffer, index) then
			buffer.writeu8(self.buffer :: buffer, index, rho)
		end
	end
end

--- Estimates the current unique count (cardinality).
function HyperLogLog.estimate(self: HyperLogLog): number
	if self.is_sparse then
		local nZeros = self.m_prime - self.sparse_count
		if nZeros > 0 then
			return math.round(self.m_prime * math.log(self.m_prime / nZeros))
		else
			toDense(self)
		end
	end

	local m = self.m
	local sum = 0
	local nZeros = 0

	local b = self.buffer :: buffer
	local lookup = POW_2_NEG
	local extract = bit32.extract
	local readu32 = buffer.readu32

	for i = 1, m, 4 do
		local chunk = readu32(b, i)

		local v1 = extract(chunk, 0, 8)
		if v1 == 0 then
			nZeros += 1
		end
		sum += lookup[v1 + 1]

		local v2 = extract(chunk, 8, 8)
		if v2 == 0 then
			nZeros += 1
		end
		sum += lookup[v2 + 1]

		local v3 = extract(chunk, 16, 8)
		if v3 == 0 then
			nZeros += 1
		end
		sum += lookup[v3 + 1]

		local v4 = extract(chunk, 24, 8)
		if v4 == 0 then
			nZeros += 1
		end
		sum += lookup[v4 + 1]
	end

	if nZeros > 0 then
		local h = m * math.log(m / nZeros)
		if h <= linearCountingThreshold(self.p) then
			return math.round(h)
		end
	end

	local estimate = self.alpha / sum

	if estimate <= 5 * m then
		local i = self.p - MINIMUM_PRECISION + 1
		local means = MEAN_DATA[i]
		local biases = BIAS_DATA[i]

		if means then
			local low = 1
			local high = #means

			while low <= high do
				local mid = math.floor((low + high) / 2)
				local v: number = means[mid]
				if v == estimate then
					return mid + 1
				elseif v < estimate then
					low = mid + 1
				else
					high = mid - 1
				end
			end

			if low == 1 then
				estimate -= biases[1]
			elseif low > #means then
				estimate -= biases[#means]
			else
				local x1, x2 = means[low - 1], means[low]
				local y1, y2 = biases[low - 1], biases[low]
				estimate -= y1 + (y2 - y1) * ((estimate - x1) / (x2 - x1))
			end
		end
	end

	return math.round(estimate)
end

--- Merges another HLL counter into this one.
function HyperLogLog.merge(self: HyperLogLog, other: HyperLogLog)
	if self.p ~= other.p then
		error("Cannot merge HyperLogLog objects with different precision")
	end

	if self.is_sparse and other.is_sparse then
		local regs = self.sparse_registers :: { [number]: number }
		local other_regs = other.sparse_registers :: { [number]: number }

		for idx, rho_other in other_regs do
			local rho_self = regs[idx] or 0
			if rho_other > rho_self then
				regs[idx] = rho_other
				if rho_self == 0 then
					self.sparse_count += 1
				end
			end
		end

		if self.sparse_count > (self.m * DENSE_THRESHOLD_RATIO) then
			toDense(self)
		end
		return
	end

	if self.is_sparse then
		toDense(self)
	end

	local readu8 = buffer.readu8
	local writeu8 = buffer.writeu8

	if other.is_sparse then
		local b = self.buffer :: buffer
		local p_prime = other.p_prime
		local p = other.p
		local diff = p_prime - p
		local rshift = bit32.rshift

		for idx_sparse, rho_sparse in other.sparse_registers :: { [number]: number } do
			local idx_dense = rshift(idx_sparse, diff) + 1
			local rho_dense = rho_sparse + diff
			if rho_dense > readu8(b, idx_dense) then
				writeu8(b, idx_dense, rho_dense)
			end
		end
		return
	end

	local b1 = self.buffer :: buffer
	local b2 = other.buffer :: buffer
	for i = 1, self.m do
		local rho = readu8(b2, i)
		if rho > readu8(b1, i) then
			writeu8(b1, i, rho)
		end
	end
end

--- Returns a serialized buffer.
function HyperLogLog.serialize(self: HyperLogLog): buffer
	if self.is_sparse then
		local bor = bit32.bor
		local lshift = bit32.lshift
		local values = table.create(self.sparse_count)
		local count = 0
		for idx, rho in self.sparse_registers :: { [number]: number } do
			count += 1
			values[count] = bor(lshift(idx, 6), rho)
		end

		table.sort(values)

		local totalSize = 5
		local prev = 0
		for _, val in values do
			local delta = val - prev
			totalSize += getVarIntSize(delta)
			prev = val
		end

		local b = buffer.create(totalSize)
		buffer.writeu8(b, 0, bor(self.p, 128))
		buffer.writeu32(b, 1, count)

		local offset = 5
		prev = 0
		for _, val in values do
			local delta = val - prev
			offset = writeVarInt(b, offset, delta)
			prev = val
		end

		return b
	else
		local b = buffer.create(buffer.len(self.buffer :: buffer))
		buffer.copy(b, 0, self.buffer :: buffer)
		buffer.writeu8(b, 0, self.p) -- Ensure clean header
		return b
	end
end

--- Reloads an HLL counter from a serialized buffer.
--- @param data: buffer
--- @return HyperLogLog Object
function HyperLogLog.deserialize(data: buffer): HyperLogLog?
	if type(data) ~= "buffer" then
		warn(`Expected type "buffer", got "{type(data)}"`)
		return nil
	end

	local ok, header = pcall(buffer.readu8, data, 0)
	if not ok then
		warn("Failed to deserialize HyperLogLog: buffer is corrupted or too small")
		return nil
	end

	local is_sparse = header >= 128
	local p = header % 128

	if is_sparse then
		if buffer.len(data) < 5 then
			return nil
		end

		local count = buffer.readu32(data, 1)
		local hll = newRaw(p)
		local regs = hll.sparse_registers :: { [number]: number }

		local offset = 5
		local value = 0

		local readVarInt = readVarInt
		local band = bit32.band
		local rshift = bit32.rshift

		local len = buffer.len(data)

		for _ = 1, count do
			if offset >= len then
				warn("Malformed sparse buffer: unexpected end of data")
				return nil
			end

			local delta, new_offset = readVarInt(data, offset)
			offset = new_offset
			value += delta

			regs[rshift(value, 6)] = band(value, 63)
		end

		hll.sparse_count = count
		return setmetatable(hll, HyperLogLog)
	else -- dense
		local m = 2 ^ p
		if buffer.len(data) ~= 1 + m then
			warn(`Expected buffer length of {1 + m}, got {buffer.len(data)}`)
			return nil
		end

		local hll = newRaw(p)
		hll.buffer = data
		hll.is_sparse = false
		hll.sparse_registers = nil

		return setmetatable(hll, HyperLogLog)
	end
end

return HyperLogLog