http://git-wip-us.apache.org/repos/asf/geode/blob/f79beb1e/geode-core/src/main/java/org/apache/geode/internal/hll/HyperLogLogPlus.java ---------------------------------------------------------------------- diff --git a/geode-core/src/main/java/org/apache/geode/internal/hll/HyperLogLogPlus.java b/geode-core/src/main/java/org/apache/geode/internal/hll/HyperLogLogPlus.java new file mode 100644 index 0000000..03a00cc --- /dev/null +++ b/geode-core/src/main/java/org/apache/geode/internal/hll/HyperLogLogPlus.java @@ -0,0 +1,1864 @@ +/* + * Copyright (C) 2011 Clearspring Technologies, Inc. + * + * Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except + * in compliance with the License. You may obtain a copy of the License at + * + * http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software distributed under the License + * is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express + * or implied. See the License for the specific language governing permissions and limitations under + * the License. + */ +package org.apache.geode.internal.hll; + +import java.io.ByteArrayInputStream; +import java.io.ByteArrayOutputStream; +import java.io.DataInput; +import java.io.DataInputStream; +import java.io.DataOutput; +import java.io.DataOutputStream; +import java.io.Externalizable; +import java.io.IOException; +import java.io.ObjectInput; +import java.io.ObjectOutput; +import java.io.Serializable; +import java.util.ArrayList; +import java.util.Collections; +import java.util.Comparator; +import java.util.List; +import java.util.SortedMap; +import java.util.TreeMap; + + +/** + * Implementation of HyperLogLog++ described in + * <p/> + * <p> + * http://static.googleusercontent.com/external_content/untrusted_dlcp/research.google.com/en/us/pubs/archive/40671.pdf + * </p> + * <p/> + * Brief HyperLogLog++ Overview + * <p/> + * Uses 64 bit hashing instead of 32 Has two representation modes: sparse and normal + * <p/> + * 'normal' is approximately the same as regular hyperloglog (still uses 64 bits) + * <p/> + * 'sparse' handles lower cardinality values with a highly accurate but poorly scaling strategy and + * leverages data compression to compete with 'normal' for as long as possible (sparse has the + * advantage on accuracy per unit of memory at low cardinality but quickly falls behind). + */ +public class HyperLogLogPlus implements ICardinality, Serializable { + + private static final long serialVersionUID = 7504952025744337762L; + + private enum Format { + SPARSE, NORMAL + } + + /** + * used to mark codec version for serialization + */ + private static final int VERSION = 2; + + // threshold and bias data taken from google's bias correction data set: + // https://docs.google.com/document/d/1gyjfMHy43U9OWBXxfaeG-3MjGzejW1dlpyMwEYAAWEI/view?fullscreen# + static final double[] thresholdData = + {10, 20, 40, 80, 220, 400, 900, 1800, 3100, 6500, 15500, 20000, 50000, 120000, 350000}; + + static final double[][] rawEstimateData = { + // 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,}, + // precision 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,}, + // precision 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, 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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,}}; + + static final double[][] biasData = { + // 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, 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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,}, + // 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, 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,}, + // precision 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,}, + // precision 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,}, + // precision 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,}}; + + private Format format; + private RegisterSet registerSet; + private final int m; + private final int p; + + // Sparse versions of m and p + private int sm; + private int sp; + + private final double alphaMM; + + // How big the sparse set is allowed to get before we convert to 'normal' + private int sparseSetThreshold; + // How big the temp list is allowed to get before we batch merge it into the sparse set + private int sortThreshold; + + private int[] tmpSet; + private int tmpIndex = 0; + private int[] sparseSet; + + /** + * This constructor disables the sparse set. If the counter is likely to exceed the sparse set + * thresholds than using this constructor will help avoid the extra memory pressure created by + * maintaining the sparse set until that threshold is breached. + * + * @param p - the precision value for the normal set + */ + public HyperLogLogPlus(int p) { + this(p, 0); + } + + /** + * Basic constructor for creating a instance that supports sparse and normal representations. The + * values of <code>p</code> and <code>sp</code> define the precision of the Normal and Sparse set + * representations for the data structure. <code>p</code> must be a value between 4 and + * <code>sp</code> and <code>sp</code> must be less than 32. + * + * @param p - the precision value for the normal set + * @param sp - the precision value for the sparse set + */ + public HyperLogLogPlus(int p, int sp) { + this(p, sp, null, null); + } + + /** + * Constructor to support instances serialized with the legacy sparse encoding scheme. + * + * @param p - the precision value for the normal set + * @param sp - the precision value for the sparse set + * @param deltaByteSet - a list of varint byte arrays encoded using a delta encoding scheme + */ + public HyperLogLogPlus(int p, int sp, List<byte[]> deltaByteSet) { + this(p, sp); + sparseSet = new int[deltaByteSet.size()]; + int previousValue = 0; + for (int i = 0; i < deltaByteSet.size(); i++) { + int nextValue = Varint.readUnsignedVarInt(deltaByteSet.get(i)); + sparseSet[i] = nextValue + previousValue; + previousValue = sparseSet[i]; + } + } + + // for constructing a sparse mode hllp + private HyperLogLogPlus(int p, int sp, int[] sparseSet) { + this(p, sp, sparseSet, null); + } + + // for constructing a normal mode hllp + private HyperLogLogPlus(int p, int sp, RegisterSet registerSet) { + this(p, sp, null, registerSet); + } + + private HyperLogLogPlus(int p, int sp, int[] sparseSet, RegisterSet registerSet) { + if (p < 4 || (p > sp && sp != 0)) { + throw new IllegalArgumentException("p must be between 4 and sp (inclusive)"); + } + if (sp > 32) { + throw new IllegalArgumentException("sp values greater than 32 not supported"); + } + + this.p = p; + m = (int) Math.pow(2, p); + format = Format.NORMAL; + this.registerSet = registerSet; + if (registerSet == null) { + if (sp > 0) // Use sparse representation + { + format = Format.SPARSE; + this.sp = sp; + sm = (int) Math.pow(2, sp); + this.sparseSet = sparseSet; + sparseSetThreshold = (int) (m * 0.75); + sortThreshold = sparseSetThreshold / 4; + } else { + this.registerSet = new RegisterSet((int) Math.pow(2, p)); + } + } + + this.alphaMM = HyperLogLog.getAlphaMM(p, m); + } + + @Override + public boolean offerHashed(long hashedLong) { + switch (format) { + case NORMAL: + // find first p bits of x + final long idx = hashedLong >>> (64 - p); + // Ignore the first p bits (the idx), and then find the number of leading zeros + // Push a 1 to where the bit string would have ended if we didnt just push the idx out of + // the way + // A one is always added to runLength for estimation calculation purposes + final int runLength = + Long.numberOfLeadingZeros((hashedLong << this.p) | (1 << (this.p - 1))) + 1; + return registerSet.updateIfGreater((int) idx, runLength); + case SPARSE: + // Call the sparse encoding scheme which attempts to stuff as much helpful data into 32 bits + // as possible + int k = encodeHash(hashedLong, p, sp); + if (tmpSet == null) { + tmpSet = new int[sortThreshold + 1]; + } + // Put the encoded data into the temp set + tmpSet[tmpIndex++] = k; + if (sparseSet != null && sparseSet.length > sparseSetThreshold) { + mergeTempList(); + convertToNormal(); + } else if (tmpIndex > sortThreshold) { + mergeTempList(); + } + return true; + } + return false; + } + + @Override + public boolean offerHashed(int hashedInt) { + throw new UnsupportedOperationException(); + } + + /** + * Add data to estimator based on the mode it is in + * + * @param o stream element + * @return Will almost always return true for sparse mode because the additions are batched in + */ + @Override + public boolean offer(Object o) { + long x = MurmurHash.hash64(o); + return offer
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