// // Copyright (c) 2023-2026, Manticore Software LTD (https://manticoresearch.com) // All rights reserved // // This program is free software; you can redistribute it and/or modify // it under the terms of the GNU General Public License. You should have // received a copy of the GPL license along with this program; if you // did not, you can find it at http://www.gnu.org/ // #include "hyperloglog.h" double LinearCounting ( int iV, int iM ) { return -double(iM)*log ( double(iV)/iM ); } ///////////////////////////////////////////////////////////////////// RegistersNonPacked_c::RegistersNonPacked_c ( int iBitsPerBucket, int iBuckets ) : m_dValues ( iBuckets ) , m_uMaxValue ( m_dValues.GetLength()-1 ) { Reset(); } void RegistersNonPacked_c::Reset() { m_dValues.ZeroVec(); m_iUsed = 0; } ///////////////////////////////////////////////////////////////////// // See "Appendix to HyperLogLog in Practice: Algorithmic Engineering of a State of the Art Cardinality Estimation Algorithm" // https://docs.google.com/document/d/1gyjfMHy43U9OWBXxfaeG-3MjGzejW1dlpyMwEYAAWEI/view?fullscreen const std::vector> g_dRawEstimateData = { // precision 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, }, // precision 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, }, // precision 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, }, // precision 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, }, // precision 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, } }; const std::vector> g_dBiasData = { // precision 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, }, // precision 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, 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