/*
 * Licensed to Elasticsearch under one or more contributor
 * license agreements. See the NOTICE file distributed with
 * this work for additional information regarding copyright
 * ownership. Elasticsearch licenses this file to you 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.elasticsearch.search.aggregations.metrics;

import org.apache.lucene.util.BytesRef;
import org.apache.lucene.util.LongBitSet;
import org.apache.lucene.util.packed.PackedInts;
import org.elasticsearch.common.io.stream.StreamInput;
import org.elasticsearch.common.io.stream.StreamOutput;
import org.elasticsearch.common.lease.Releasable;
import org.elasticsearch.common.lease.Releasables;
import org.elasticsearch.common.util.BigArrays;
import org.elasticsearch.common.util.ByteArray;
import org.elasticsearch.common.util.ByteUtils;
import org.elasticsearch.common.util.IntArray;

import java.io.IOException;
import java.nio.ByteBuffer;
import java.nio.ByteOrder;
import java.util.HashMap;
import java.util.HashSet;
import java.util.Map;
import java.util.Objects;
import java.util.Set;

/**
 * Hyperloglog++ counter, implemented based on pseudo code from
 * http://static.googleusercontent.com/media/research.google.com/fr//pubs/archive/40671.pdf and its appendix
 * https://docs.google.com/document/d/1gyjfMHy43U9OWBXxfaeG-3MjGzejW1dlpyMwEYAAWEI/view?fullscreen
 *
 * This implementation is different from the original implementation in that it uses a hash table instead of a sorted list for linear
 * counting. Although this requires more space and makes hyperloglog (which is less accurate) used sooner, this is also considerably faster.
 *
 * Trying to understand what this class does without having read the paper is considered adventurous.
 */
public final class HyperLogLogPlusPlus implements Releasable {

    public static final int MIN_PRECISION = 4;
    public static final int DEFAULT_PRECISION = 14;
    public static final int MAX_PRECISION = 18;
    private static final boolean LINEAR_COUNTING = false;
    private static final boolean HYPERLOGLOG = true;
    private static final float MAX_LOAD_FACTOR = 0.75f;
    private static final int P2 = 25;
    private static final int BIAS_K = 6;

    /**
     * Compute the required precision so that <code>count</code> distinct entries would be counted with linear counting.
     */
    public static int precisionFromThreshold(long count) {
        final long hashTableEntries = (long) Math.ceil(count / MAX_LOAD_FACTOR);
        int precision = PackedInts.bitsRequired(hashTableEntries * Integer.BYTES);
        precision = Math.max(precision, MIN_PRECISION);
        precision = Math.min(precision, MAX_PRECISION);
        return precision;
    }

    /**
     * Return the expected per-bucket memory usage for the given precision.
     */
    public static long memoryUsage(int precision) {
        return 1L << precision;
    }

    // these static tables come from the appendix of the paper
    private static final double[][] RAW_ESTIMATE_DATA = {
            // 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,
                    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, },
            // precision 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, },
            // precision 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, },
            // 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, } };

    private static final double[][] BIAS_DATA = {
            // 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, },
            // precision 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, },
            // precision 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, },
            // precision 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, },
            // precision 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, },
            // 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 static final long[] THRESHOLDS = new long[] { 10, 20, 40, 80, 220, 400, 900, 1800, 3100, 6500, 11500, 20000, 50000, 120000,
            350000 };

    private final BigArrays bigArrays;
    private final OpenBitSet algorithm;
    private ByteArray runLens;
    private final Hashset hashSet;
    private final int p, m;
    private final double alphaMM;

    public HyperLogLogPlusPlus(int precision, BigArrays bigArrays, long initialBucketCount) {
        if (precision < 4) {
            throw new IllegalArgumentException("precision must be >= 4");
        }
        if (precision > 18) {
            throw new IllegalArgumentException("precision must be <= 18");
        }
        p = precision;
        m = 1 << p;
        this.bigArrays = bigArrays;
        algorithm = new OpenBitSet();
        runLens = bigArrays.newByteArray(initialBucketCount << p);
        hashSet = new Hashset(initialBucketCount);
        final double alpha;
        switch (p) {
        case 4:
            alpha = 0.673;
            break;
        case 5:
            alpha = 0.697;
            break;
        default:
            alpha = 0.7213 / (1 + 1.079 / m);
            break;
        }
        alphaMM = alpha * m * m;
    }

    public int precision() {
        return p;
    }

    public long maxBucket() {
        return runLens.size() >>> p;
    }

    private void ensureCapacity(long numBuckets) {
        runLens = bigArrays.grow(runLens, numBuckets << p);
    }

    public void merge(long thisBucket, HyperLogLogPlusPlus other, long otherBucket) {
        if (p != other.p) {
            throw new IllegalArgumentException();
        }
        ensureCapacity(thisBucket + 1);
        if (other.algorithm.get(otherBucket) == LINEAR_COUNTING) {
            final IntArray values = other.hashSet.values(otherBucket);
            try {
                for (long i = 0; i < values.size(); ++i) {
                    final int encoded = values.get(i);
                    if (algorithm.get(thisBucket) == LINEAR_COUNTING) {
                        collectLcEncoded(thisBucket, encoded);
                    } else {
                        collectHllEncoded(thisBucket, encoded);
                    }
                }
            } finally {
                Releasables.close(values);
            }
        } else {
            if (algorithm.get(thisBucket) != HYPERLOGLOG) {
                upgradeToHll(thisBucket);
            }
            final long thisStart = thisBucket << p;
            final long otherStart = otherBucket << p;
            for (int i = 0; i < m; ++i) {
                runLens.set(thisStart + i, (byte) Math.max(runLens.get(thisStart + i), other.runLens.get(otherStart + i)));
            }
        }
    }

    public void collect(long bucket, long hash) {
        ensureCapacity(bucket + 1);
        if (algorithm.get(bucket) == LINEAR_COUNTING) {
            collectLc(bucket, hash);
        } else {
            collectHll(bucket, hash);
        }
    }

    private void collectLc(long bucket, long hash) {
        final int k = encodeHash(hash, p);
        collectLcEncoded(bucket, k);
    }

    private void collectLcEncoded(long bucket, int encoded) {
        final int newSize = hashSet.add(bucket, encoded);
        if (newSize > hashSet.threshold) {
            upgradeToHll(bucket);
        }
    }

    private void collectHll(long bucket, long hash) {
        final long index = index(hash, p);
        final int runLen = runLen(hash, p);
        collectHll(bucket, index, runLen);
    }

    private void collectHllEncoded(long bucket, int encoded) {
        final int runLen = decodeRunLen(encoded, p);
        final int index = decodeIndex(encoded, p);
        collectHll(bucket, index, runLen);
    }

    private void collectHll(long bucket, long index, int runLen) {
        final long bucketIndex = (bucket << p) + index;
        runLens.set(bucketIndex, (byte) Math.max(runLen, runLens.get(bucketIndex)));
    }

    public long cardinality(long bucket) {
        if (algorithm.get(bucket) == LINEAR_COUNTING) {
            return cardinalityLc(bucket);
        } else {
            return cardinalityHll(bucket);
        }
    }

    private long cardinalityLc(long bucket) {
        final long m = 1 << P2;
        final long v = m - hashSet.size(bucket);
        return linearCounting(m, v);
    }

    private long cardinalityHll(long bucket) {
        double inverseSum = 0;
        int zeros = 0;
        for (long i = bucket << p, end = i + m; i < end; ++i) {
            final int runLen = runLens.get(i);
            inverseSum += 1. / (1L << runLen);
            if (runLen == 0) {
                ++zeros;
            }
        }
        double e1 = alphaMM / inverseSum;
        double e2 = e1 <= 5 * m ? e1 - estimateBias(e1) : e1;
        long h;
        if (zeros != 0) {
            h = linearCounting(m, zeros);
        } else {
            h = Math.round(e2);
        }
        if (h <= threshold()) {
            return h;
        } else {
            return Math.round(e2);
        }
    }

    void upgradeToHll(long bucket) {
        ensureCapacity(bucket + 1);
        final IntArray values = hashSet.values(bucket);
        try {
            runLens.fill(bucket << p, (bucket << p) + m, (byte) 0);
            for (long i = 0; i < values.size(); ++i) {
                final int encoded = values.get(i);
                collectHllEncoded(bucket, encoded);
            }
            algorithm.set(bucket);
        } finally {
            Releasables.close(values);
        }
    }

    static long linearCounting(long m, long v) {
        return Math.round(m * Math.log((double) m / v));
    }

    static long mask(int bits) {
        return (1L << bits) - 1;
    }

    /**
     * Encode the hash on 32 bits. The encoded hash cannot be equal to <code>0</code>.
     */
    static int encodeHash(long hash, int p) {
        final long e = hash >>> (64 - P2);
        final long encoded;
        if ((e & mask(P2 - p)) == 0) {
            final int runLen = 1 + Math.min(Long.numberOfLeadingZeros(hash << P2), 64 - P2);
            encoded = (e << 7) | (runLen << 1) | 1;
        } else {
            encoded = e << 1;
        }
        assert PackedInts.bitsRequired(encoded) <= 32;
        assert encoded != 0;
        return (int) encoded;
    }

    static int decodeRunLen(int encoded, int p) {
        if ((encoded & 1) == 1) {
            return (((encoded >>> 1) & 0x3F) + (P2 - p));
        } else {
            final int bits = encoded << (31 + p - P2);
            assert bits != 0;
            return 1 + Integer.numberOfLeadingZeros(bits);
        }
    }

    static int decodeIndex(int encoded, int p) {
        long index;
        if ((encoded & 1) == 1) {
            index = encoded >>> 7;
        } else {
            index = encoded >>> 1;
        }
        return (int) (index >>> (P2 - p));
    }

    static long index(long hash, int p) {
        return hash >>> (64 - p);
    }

    static int runLen(long hash, int p) {
        return 1 + Math.min(Long.numberOfLeadingZeros(hash << p), 64 - p);
    }

    private double estimateBias(double e) {
        final double[] rawEstimateData = rawEstimateData();
        final double[] biasData = biasData();

        final double[] weights = new double[BIAS_K];
        int index = biasData.length - BIAS_K;
        for (int i = 0; i < rawEstimateData.length; ++i) {
            final double w = 1.0 / Math.abs(rawEstimateData[i] - e);
            final int j = i % weights.length;
            if (Double.isInfinite(w)) {
                return biasData[i];
            } else if (weights[j] >= w) {
                index = i - BIAS_K;
                break;
            }
            weights[j] = w;
        }

        double weightSum = 0.0;
        double biasSum = 0.0;
        for (int i = 0, j = index; i < BIAS_K; ++i, ++j) {
            final double w = weights[i];
            final double b = biasData[j];
            biasSum += w * b;
            weightSum += w;
        }
        return biasSum / weightSum;
    }

    private double[] biasData() {
        return BIAS_DATA[p - 4];
    }

    private double[] rawEstimateData() {
        return RAW_ESTIMATE_DATA[p - 4];
    }

    private long threshold() {
        return THRESHOLDS[p - 4];
    }

    @Override
    public void close() {
        Releasables.close(runLens, hashSet.sizes);
    }

    private Object getComparableData(long bucket) {
        if (algorithm.get(bucket) == LINEAR_COUNTING) {
            Set<Integer> values = new HashSet<>();
            try (IntArray hashSetValues = hashSet.values(bucket)) {
                for (long i = 0; i < hashSetValues.size(); i++) {
                    values.add(hashSetValues.get(i));
                }
            }
            return values;
        } else {
            Map<Byte, Integer> values = new HashMap<>();
            for (long i = 0; i < runLens.size(); i++) {
                byte runLength = runLens.get((bucket << p) + i);
                Integer numOccurances = values.get(runLength);
                if (numOccurances == null) {
                    values.put(runLength, 1);
                } else {
                    values.put(runLength, numOccurances + 1);
                }
            }
            return values;
        }
    }

    public int hashCode(long bucket) {
        return Objects.hash(p, algorithm.get(bucket), getComparableData(bucket));
    }

    public boolean equals(long bucket, HyperLogLogPlusPlus other) {
        return Objects.equals(p, other.p)
                && Objects.equals(algorithm.get(bucket), other.algorithm.get(bucket))
                && Objects.equals(getComparableData(bucket), other.getComparableData(bucket));
    }

    /**
     * We are actually using HyperLogLog's runLens array but interpreting it as a hash set for linear counting.
     */
    private class Hashset {

        private final int capacity;
        private final int threshold;
        private final int mask;
        private IntArray sizes;
        private final BytesRef readSpare;
        private final ByteBuffer writeSpare;

        Hashset(long initialBucketCount) {
            capacity = m / 4; // because ints take 4 bytes
            threshold = (int) (capacity * MAX_LOAD_FACTOR);
            mask = capacity - 1;
            sizes = bigArrays.newIntArray(initialBucketCount);
            readSpare = new BytesRef();
            writeSpare = ByteBuffer.allocate(4).order(ByteOrder.LITTLE_ENDIAN);
        }

        private long index(long bucket, int index) {
            return (bucket << p) + (index << 2);
        }

        private int get(long bucket, int index) {
            runLens.get(index(bucket, index), 4, readSpare);
            return ByteUtils.readIntLE(readSpare.bytes, readSpare.offset);
        }

        private void set(long bucket, int index, int value) {
            writeSpare.putInt(0, value);
            runLens.set(index(bucket, index), writeSpare.array(), 0, 4);
        }

        private int recomputedSize(long bucket) {
            int size = 0;
            for (int i = 0; i <= mask; ++i) {
                final int v = get(bucket, i);
                if (v != 0) {
                    ++size;
                }
            }
            return size;
        }

        public int size(long bucket) {
            if (bucket >= sizes.size()) {
                return 0;
            }
            final int size = sizes.get(bucket);
            assert size == recomputedSize(bucket);
            return size;
        }

        /**
         * Add <code>k</code> to the hash table associated with <code>bucket</code>. Return {@code -1} if the value was already in the set
         * or the new set size if it was added.
         */
        public int add(long bucket, int k) {
            sizes = bigArrays.grow(sizes, bucket + 1);
            assert k != 0;
            for (int i = (k & mask);; i = (i + 1) & mask) {
                final int v = get(bucket, i);
                if (v == 0) {
                    // means unused, take it!
                    set(bucket, i, k);
                    return sizes.increment(bucket, 1);
                } else if (v == k) {
                    // k is already in the set
                    return -1;
                }
            }
        }

        public IntArray values(final long bucket) {
            final int size = size(bucket);
            final IntArray values = bigArrays.newIntArray(size);
            if (size == 0) {
                return values;
            }
            int i = 0;
            for (int j = 0; j < capacity; ++j) {
                final int k = get(bucket, j);
                if (k != 0) {
                    values.set(i++, k);
                }
            }
            assert i == values.size();
            return values;
        }

    }

    public void writeTo(long bucket, StreamOutput out) throws IOException {
        out.writeVInt(p);
        if (algorithm.get(bucket) == LINEAR_COUNTING) {
            out.writeBoolean(LINEAR_COUNTING);
            try (IntArray hashes = hashSet.values(bucket)) {
                out.writeVLong(hashes.size());
                for (long i = 0; i < hashes.size(); ++i) {
                    out.writeInt(hashes.get(i));
                }
            }
        } else {
            out.writeBoolean(HYPERLOGLOG);
            for (long i = bucket << p, end = i + m; i < end; ++i) {
                out.writeByte(runLens.get(i));
            }
        }
    }

    public static HyperLogLogPlusPlus readFrom(StreamInput in, BigArrays bigArrays) throws IOException {
        final int precision = in.readVInt();
        HyperLogLogPlusPlus counts = new HyperLogLogPlusPlus(precision, bigArrays, 1);
        final boolean algorithm = in.readBoolean();
        if (algorithm == LINEAR_COUNTING) {
            counts.algorithm.clear(0);
            final long size = in.readVLong();
            for (long i = 0; i < size; ++i) {
                final int encoded = in.readInt();
                counts.hashSet.add(0, encoded);
            }
        } else {
            counts.algorithm.set(0);
            for (int i = 0; i < counts.m; ++i) {
                counts.runLens.set(i, in.readByte());
            }
        }
        return counts;
    }

    /** looks and smells like the old openbitset. */
    static class OpenBitSet {
        LongBitSet impl = new LongBitSet(64);

        boolean get(long bit) {
            if (bit < impl.length()) {
                return impl.get(bit);
            } else {
                return false;
            }
        }

        void ensureCapacity(long bit) {
            impl = LongBitSet.ensureCapacity(impl, bit);
        }

        void set(long bit) {
            ensureCapacity(bit);
            impl.set(bit);
        }

        void clear(long bit) {
            ensureCapacity(bit);
            impl.clear(bit);
        }
    }

}
