hyperloglog-rs 0.1.56

A Rust implementation of HyperLogLog trying to be parsimonious with memory.
Documentation
// bias estimates for the corresponding raw estimate as determined by Google.
pub const BIAS_DATA: [&[f32]; 15] = [
    // 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, 0.9996, 0.7956, 0.5366, 0.5894,
        0.5738, 0.2698, 0.3682, 0.0544, 0.2342, 0.0108, -0.2034, -0.0702, -0.1296, -0.3642,
        -0.4806, -0.227, -0.3228, -0.3826, -0.5112, -0.6696, -0.7494, -0.5004, -0.6176, -0.6922,
        -0.6016, -0.4162, -0.3382, -0.7826, -0.6486, -0.9198, -0.8518, -0.9624, -0.6402, -1.1922,
        -1.0256, -1.086, -1.219, -0.8194, -0.9406, -1.1554, -1.2072, -1.1752, -1.1676, -1.1402,
        -1.3754, -1.2986, -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, 1.4386, 1.4916,
        1.1524, 1.1892, 0.8414, 0.8798, 0.8376, 0.4698, 0.7656, 0.331, 0.5914, 0.6012, 0.7016,
        0.5582, 0.3394, 0.3544, 0.4912, 0.308, 0.3552, -0.0254, 0.2052, -0.273, 0.1322, 0.3944,
        -0.2412, 0.242, 0.1914, 0.2538, -0.1224, -0.3708, 0.1932, -0.0848, 0.0868, -0.3272,
        -0.2856, 0.3114, -0.1284, -0.755, -0.2092, -0.2936, -0.364, -0.2536, -0.8212, -0.2536,
        -0.5104, -0.3834, -0.4918, -0.2202, -0.0972, -0.5574, -0.1146, -0.295, -0.5348, 0.3464,
        -0.6538, 0.0398, 0.0342, -0.9958, -0.5234, -0.489, -0.2748, -0.575, -0.4828, 0.0572,
        -0.3306, -0.6288, -0.1402, -0.5406, -0.446, -0.5994, -0.2626, 0.1634, -0.1006, -0.395,
        -1.0696, -0.8364, -0.7532, -0.4124, -0.7904, -0.2968, -0.2854, -0.193, -0.0772, -0.9628,
        -0.4148,
    ],
    // 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, 9.5174, 9.0576, 8.7476, 8.427, 8.1326,
        8.2372, 8.2788, 7.6776, 7.7926, 7.1952, 6.9564, 6.6454, 6.87, 6.5428, 6.2, 6.0294, 5.6278,
        5.6782, 5.792, 5.3516, 5.2832, 5.0394, 5.0748, 4.4912, 4.849, 4.696, 4.5404, 4.073, 4.3714,
        3.7216, 3.7328, 3.4208, 3.4184, 3.9424, 3.2772, 3.411, 3.1308, 2.769, 2.9258, 2.6828,
        2.7502, 2.706, 2.3886, 3.0186, 2.4518, 2.927, 2.4172, 2.4114, 2.033, 2.5124, 2.5564,
        2.6008, 2.4172, 1.8044, 1.997, 2.4548, 1.8948, 2.2346, 2.3086, 2.1548, 1.8842, 1.6508,
        0.6772, 1.7254, 1.4752, 1.7228, 1.6614, 1.1676, 1.793, 1.0006, 0.9052, 0.66, 1.5588,
        1.1636, 0.6882, 0.7126, 0.4502, 1.1978, 0.9756, 0.1654, 1.727, 1.1974, -0.2526, 1.1346,
        1.3048, 1.1948, 0.3134, 0.879, 1.1204, 0.853, 1.6792, 0.857, 0.4486, 1.2362, 0.9534,
        1.0286, 0.5632, 0.663, 0.723, 0.7566, 0.2566, -0.8376, 0.62, 0.8216, 0.2166, 0.2056,
        0.2202, 0.3726, 0.3344, 0.9284, 0.9728, 0.1924, 0.4872, -0.413, 0.807, 0.1206, 0.769,
        0.8708, 0.665, 0.1182, 0.4012, 0.6352, 0.1354, 0.1756, 1.1606, 0.3462, 0.5214, -0.5866,
        -1.1648, 0.9684, 0.837, 0.7796, 0.9858,
    ],
    // 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, 9.7472, 10.1456, 9.2928, 8.7504, 8.5528, 8.979, 8.2102, 8.1834, 7.3494, 7.325,
        7.6614, 6.903, 7.2544, 6.9042, 7.215, 6.2864, 6.0814, 6.6764, 6.301, 5.139, 5.658, 5.1732,
        4.5902, 4.9538, 5.0828, 4.922, 4.9902, 4.7328, 5.4538, 4.1136, 4.2234, 4.0878, 3.708,
        4.1556, 4.1852, 3.6372, 3.6822, 3.7796, 3.6078, 2.4916, 3.131, 2.5376, 3.1988, 3.211,
        2.4502, 3.5282, 2.912, 3.0448, 2.7432, 2.8524, 2.7988, 2.7858, 1.8868, 2.9886, 2.5064,
        1.9124, 2.6616, 2.4682, 1.582, 1.304, 2.2738, 2.6894, 1.329, 3.106, 1.6908, 2.1374, 2.5322,
        1.8848, 1.3324, 1.4512, 1.179, 2.4412, 1.6066, 2.167, 0.7794, 2.379, 2.067, 1.46, 2.9116,
        1.692, 0.9546, 2.493, 2.2722, 1.335, 2.449, 1.2014, 3.0738, 2.0974, 2.8564, 2.2996, 2.409,
        1.9704, 0.8098, 1.6528, 2.5998, 0.958, 2.068, 2.3278, 4.2016, 1.9632, 1.864, 1.43, 3.7794,
        1.272, 1.8644, 2.206, 3.219, 1.5154, 2.6102,
    ],
    // 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, 25.5496, 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, 12.4282,
        11.3324, 10.4794, 11.5038, 10.129, 9.528, 10.3204, 9.463, 9.7928, 9.123, 8.7418, 9.2192,
        7.5102, 7.6066, 7.0184, 7.2224, 7.4014, 6.7618, 7.1436, 5.6506, 5.6378, 5.766, 6.7514,
        5.5776, 3.7322, 5.8048, 5.6302, 4.9336, 3.4798, 4.3388, 3.9894, 3.8196, 3.3136, 3.2308,
        3.4588, 3.0816, 3.4076, 3.0064, 2.3878, 2.619, 1.998, 3.3482, 2.9506, 0.991, 2.1144, 2.203,
        2.8222, 2.7324, 2.7826, 3.7666, 2.2648, 2.3128, 2.4082, 2.7536, 3.3376, 2.7156, 1.7478,
        1.4292, 2.393, 2.2278, 2.3434, 0.8726, 3.884, 1.806, 1.9176, 1.1678, 1.5032, 2.525, 0.2264,
        2.315, 0.93, 1.252, 2.1496, 0.0408, 2.5448, 1.3296, 0.1974, 2.5262, 3.3328, -1.343, 0.4222,
        0.9172, 1.1292, 1.4606, 1.4578, 2.8728, 3.3336, -1.3408, 1.5768, 0.363, 1.4074, 0.6566,
        0.8014, -0.4546, 1.5192,
    ],
    // 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,
        89.781, 87.5716, 84.7048, 82.5322, 79.875, 78.3972, 75.3464, 73.7274, 71.2834, 70.1444,
        68.4264, 66.0166, 64.018, 62.0438, 60.34, 58.6856, 57.9836, 55.0312, 54.677, 52.3188,
        51.4846, 49.4424, 47.739, 46.1488, 44.9202, 43.406, 42.5342, 41.2834, 38.8954, 38.3286,
        36.2146, 36.6684, 35.9946, 33.123, 33.4338, 31.7378, 29.076, 28.9692, 27.4964, 27.0998,
        25.9864, 26.7754, 24.3208, 23.4838, 22.7388, 24.0758, 21.9098, 20.9728, 19.9228, 19.9292,
        16.617, 17.05, 18.2996, 15.6128, 15.7392, 14.5174, 13.6322, 12.2584, 13.3766, 11.423,
        13.1232, 9.5164, 10.5938, 9.5972, 8.1222, 9.7674, 7.5044, 7.57, 6.7044, 6.4142, 6.7102,
        5.6094, 4.6522, 6.841, 3.4072, 3.9786, 3.3276, 5.5216, 3.3186, 2.0694, 4.354, 1.575,
        0.2808, 2.1288, -0.2148, -0.0378, -0.6582, 0.6548, -0.0698, 0.8584, -2.527, -2.1752,
        -3.3554, -1.0402, -0.651, -2.1444, -1.9666, -3.9794, -0.6044, -3.0826, -3.3916, -5.2964,
        -5.3892, -5.0876, -4.699, -5.2372, -3.1578, -4.9788, -4.899, -7.4888, -5.948, -5.6806,
        -6.6718, -4.705, -7.2778, -4.658, -4.4362, -4.3214, -5.1886, -6.6688, -6.484, -5.126,
        -4.4032, -6.135, -5.8082, -4.1672, -4.1504, -7.456, -7.2408, -9.8318, -5.8042, -8.6562,
        -6.9994, -10.5474, -7.3414, -6.81, -6.2972, -6.232,
    ],
    // 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, 99.4832, 96.39, 93.7202, 90.1714, 87.2358, 85.9346, 82.891, 80.0264,
        78.3834, 75.1544, 73.8684, 70.9896, 69.4368, 64.8702, 65.0408, 61.6738, 59.5208, 57.0158,
        54.2302, 53.0962, 50.4986, 52.2588, 47.3914, 45.6244, 42.8378, 43.0072, 40.6516, 40.2454,
        35.2136, 36.4546, 33.785, 33.2294, 32.468, 30.867, 28.6508, 28.91, 27.5984, 26.162,
        24.5564, 23.2328, 21.9484, 21.5902, 21.3346, 17.7032, 20.6112, 19.5546, 15.7376, 17.072,
        16.9518, 15.326, 13.1818, 14.6926, 13.086, 13.2754, 10.8698, 11.248, 7.3768, 4.7234, 7.979,
        8.7504, 7.6812, 9.72, 7.7392, 5.6224, 7.4456, 6.6602, 5.9058, 4.002, 4.517, 4.6824, 3.8622,
        5.1364, 5.985, 2.4772, 2.62, 1.628, 4.65, 0.2256, 0.831, -0.3594, 1.276, -2.9256, -0.0304,
        2.3708, -2.0034, 0.8046, 0.302, 1.1248, -2.688, 0.0322, -1.181, -3.9402, -1.4794, -0.1884,
        -2.1072, -2.0416, -3.1288, -4.1616, -0.6128, -3.4872, -8.179, -5.3778, -4.0138, -5.5826,
        -5.7372, -7.668, -5.6952, -1.1248, -5.5852, -8.0456, -4.6484, -11.6468, -7.9752, -5.783,
        -7.6742, -10.6328, -9.8172,
    ],
    // precision 11
    &[
        1_476., 1_449.601, 1_423.58, 1_397.794, 1_372.304, 1_347.206, 1_321.84, 1_297.229,
        1_272.946, 1_248.993, 1_225.303, 1_201.425, 1_178.058, 1_155.609, 1_132.626, 1_110.557,
        1_088.527, 1_066.515, 1_045.187, 1_024.388, 1_003.37, 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,
        98.6018, 95.7618, 93.5822, 88.59, 86.9992, 82.88, 80.454, 74.6982, 74.3644, 73.2914,
        65.571, 66.9232, 65.1914, 62.5882, 61.5702, 55.7036, 56.1764, 52.7596, 53.0302, 49.061,
        48.4694, 44.933, 46.0474, 44.7166, 41.9416, 39.9208, 35.6328, 35.5276, 33.1934, 33.2372,
        33.3864, 33.9228, 30.2372, 29.1374, 25.2272, 24.2942, 19.8338, 18.9006, 23.0908, 21.8544,
        19.5176, 15.4148, 16.9314, 18.6738, 12.9878, 14.3688, 12.0448, 15.522, 12.53, 14.594,
        14.3132, 9.455, 12.9442, 3.9114, 13.1374, 5.4472, 9.8278, 7.8728, 3.6776, 5.4698, 5.551,
        5.6598, 3.8944, 3.1276, 5.6514, 6.3062, 3.908, 1.8706, 5.1702, 2.4668, 0.77, -3.7234,
        1.164, 8.0534, 0.1354, 2.1594, 0.767, 1.0594, 3.155, -0.2874, 2.3722, -2.8662, -1.632,
        -2.2298, -0.1552, -1.4604, -0.2622, -2.3446, -2.8078, -3.2218, -5.6016, -8.422, -9.4374,
        0.1618, -10.4756, -10.0824,
    ],
    // precision 12
    &[
        2_953., 2_900.478, 2_848.357, 2_796.367, 2_745.324, 2_694.96, 2_644.648, 2_595.539,
        2_546.147, 2_498.258, 2_450.838, 2_403.608, 2_357.451, 2_311.38, 2_266.41, 2_221.564,
        2_176.968, 2_134.193, 2_090.838, 2_048.855, 2_007.018, 1_966.174, 1_925.448, 1_885.129,
        1_846.478, 1_807.404, 1_768.872, 1_731.373, 1_693.43, 1_657.533, 1_621.949, 1_586.553,
        1_551.726, 1_517.618, 1_483.519, 1_450.453, 1_417.865, 1_385.716, 1_352.683, 1_322.671,
        1_291.831, 1_260.904, 1_231.476, 1_201.865, 1_173.672, 1_145.757, 1_119.207, 1_092.283,
        1_065.043, 1_038.626, 1_014.319, 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, 520.4554, 505.5832, 488.366, 476.4808, 459.7682, 450.0522, 434.3288, 423.9528,
        408.727, 399.0794, 387.2522, 373.988, 360.852, 351.6394, 339.642, 330.9024, 322.6616,
        311.6622, 301.3254, 291.7484, 279.9392, 276.7508, 263.2152, 254.8114, 245.5494, 242.3064,
        234.8734, 223.7872, 217.7156, 212.0196, 200.793, 195.9748, 189.0702, 182.4492, 177.2772,
        170.2336, 164.741, 158.6136, 155.311, 147.5964, 142.837, 137.3724, 132.0162, 130.0424,
        121.9804, 120.4518, 114.8968, 111.586, 105.9332, 101.705, 98.5142, 95.0488, 89.788, 91.475,
        83.7764, 80.9698, 72.8574, 73.1616, 67.5838, 62.6264, 63.2638, 66.0978, 52.0844, 58.9956,
        47.0912, 46.4956, 48.4384, 47.1082, 43.2392, 37.276, 40.0284, 35.1864, 35.8596, 32.0998,
        28.027, 23.6694, 33.8266, 26.3736, 27.2008, 21.3246, 26.4116, 23.4522, 19.5014, 19.8514,
        10.7492, 18.6424, 13.1266, 18.2436, 6.7186, 3.3946, 6.3376, 7.7672, 0.814, 3.8282, 0.8262,
        8.0744, -1.5908, 5.0178, 0.4554, -0.242, 0.1748, -9.0764, -4.2016, -3.7752, -4.7518,
        -5.3724, -8.9068, -6.1024, -5.7412, -9.9534, -3.8634, -13.7304, -16.271, -7.5136, -3.3068,
        -13.134, -10.0552, -6.7202, -8.5966, -10.9308, -1.8776, -4.8226, -13.7788, -21.647,
        -10.6736, -15.78,
    ],
    // precision 13
    &[
        5_907.505, 5_802.267, 5_697.347, 5_593.579, 5_491.262, 5_390.551, 5_290.338, 5_191.695,
        5_093.599, 4_997.355, 4_902.597, 4_808.308, 4_715.565, 4_624.109, 4_533.822, 4_444.434,
        4_356.38, 4_269.296, 4_183.378, 4_098.292, 4_014.79, 3_932.457, 3_850.604, 3_771.271,
        3_691.771, 3_615.099, 3_538.186, 3_463.475, 3_388.85, 3_315.679, 3_244.545, 3_173.752,
        3_103.311, 3_033.609, 2_966.564, 2_900.794, 2_833.726, 2_769.81, 2_707.32, 2_644.078,
        2_583.992, 2_523.466, 2_464.124, 2_406.073, 2_347.036, 2_292.101, 2_238.172, 2_182.751,
        2_128.488, 2_077.131, 2_025.037, 1_975.376, 1_928.933, 1_879.311, 1_831.001, 1_783.214,
        1_738.31, 1_694.514, 1_649.024, 1_606.847, 1_564.753, 1_525.317, 1_482.537, 1_443.967,
        1_406.507, 1_365.867, 1_329.219, 1_295.419, 1_257.972, 1_225.339, 1_193.297, 1_156.358,
        1_125.869, 1_091.187, 1_061.409, 1_029.419, 1_000.913, 972.3272, 944.0042, 915.7592,
        889.965, 862.8342, 840.4254, 812.5984, 785.9242, 763.051, 741.7938, 721.466, 699.0408,
        677.9972, 649.867, 634.9118, 609.8694, 591.9816, 570.2922, 557.1292, 538.3858, 521.8726,
        502.9514, 495.7764, 475.1714, 459.751, 439.9952, 426.709, 413.7016, 402.3868, 387.2626,
        372.0524, 357.051, 342.5098, 334.8492, 322.5294, 311.6138, 295.848, 289.273, 274.093,
        263.3296, 251.3896, 245.7392, 231.9614, 229.7952, 217.1552, 208.9588, 199.0166, 190.8392,
        180.6976, 176.2728, 166.977, 162.5252, 151.1964, 149.387, 133.9812, 130.0586, 130.164,
        122.0534, 110.7428, 108.1276, 106.2324, 100.3816, 98.7668, 86.644, 79.9768, 82.4722,
        68.7026, 70.1186, 71.9948, 58.9986, 59.0492, 56.9818, 47.5338, 42.9928, 51.1592, 37.274,
        42.722, 31.3734, 26.809, 25.8934, 26.5286, 29.5442, 19.3504, 26.076, 17.9528, 14.842,
        10.4684, 8.659, 9.8672, 4.3414, -0.9078, -3.3208, -0.9362, -11.9916, -8.87, -6.331,
        -11.3366, -15.9208, -9.3466, -15.5034, -19.2098, -15.3578, -28.2236, -30.6898, -19.3272,
        -25.6084, -24.4096, -13.6386, -33.4474, -32.695, -28.9064, -31.7484, -32.2936, -35.833,
        -47.6206, -39.0856, -33.1434, -46.1372, -37.5892, -46.8164, -47.3142, -60.2914, -37.7576,
    ],
    // precision 14
    &[
        11_816.48, 11_605., 11_395.38, 11_188.75, 10_984.18, 10_782.01, 10_582.01, 10_384.5,
        10_189.18, 9_996.274, 9_806.034, 9_617.98, 9_431.394, 9_248.778, 9_067.689, 8_889.682,
        8_712.913, 8_538.862, 8_368.494, 8_197.796, 8_031.892, 7_866.632, 7_703.733, 7_544.573,
        7_386.204, 7_230.666, 7_077.852, 6_926.789, 6_778.69, 6_631.963, 6_487.304, 6_346.749,
        6_206.441, 6_070.202, 5_935.258, 5_799.924, 5_671.032, 5_541.979, 5_414.611, 5_290.027,
        5_166.723, 5_047.691, 4_929.162, 4_815.141, 4_699.127, 4_588.561, 4_477.739, 4_369.401,
        4_264.273, 4_155.922, 4_055.581, 3_955.505, 3_856.962, 3_761.383, 3_666.97, 3_575.776,
        3_482.413, 3_395.019, 3_305.885, 3_221.415, 3_138.602, 3_056.296, 2_970.449, 2_896.153,
        2_816.801, 2_740.216, 2_670.497, 2_594.146, 2_527.111, 2_460.817, 2_387.511, 2_322.95,
        2_260.675, 2_194.269, 2_133.779, 2_074.767, 2_015.204, 1_959.423, 1_898.65, 1_850.006,
        1_792.849, 1_741.484, 1_687.978, 1_638.132, 1_589.327, 1_543.139, 1_496.827, 1_447.852,
        1_402.735, 1_361.961, 1_327.069, 1_285.411, 1_241.811, 1_201.673, 1_161.973, 1_130.261,
        1_094.204, 1_048.204, 1_020.644, 990.9014, 961.1998, 924.7698, 899.5264, 872.3464, 834.375,
        810.432, 780.6598, 756.0138, 733.4794, 707.924, 673.858, 652.2224, 636.5724, 615.7386,
        586.6964, 564.1472, 541.6796, 523.9436, 505.7146, 475.7296, 461.7796, 449.7508, 439.0208,
        412.7886, 400.2456, 383.1882, 362.0796, 357.5338, 334.319, 327.5534, 308.5594, 291.2702,
        279.352, 271.7914, 252.577, 247.4824, 236.1748, 218.7746, 220.1552, 208.7944, 201.2236,
        182.9956, 185.5268, 164.5474, 176.5962, 150.6896, 157.8004, 138.3788, 134.0212, 117.6144,
        108.194, 97.0696, 89.6042, 95.603, 84.781, 72.635, 77.3482, 59.4908, 55.5876, 50.7346,
        61.3916, 50.915, 39.0384, 58.9396, 29.6336, 28.2032, 26.0078, 17.0388, 9.22, 13.8388,
        8.0724, 14.155, 15.357, 3.4266, 6.2482, -2.9694, -8.7994, -5.9786, -14.4048, -3.4144,
        -13.0148, -11.6978, -25.7878, -22.3186, -24.4096, -31.9756, -18.9722, -22.8678, -30.8972,
        -32.3716, -22.3908, -43.672, -35.9038, -39.7492, -54.1642, -45.275, -42.299, -44.109,
        -64.3564, -49.9552, -42.6116,
    ],
    // precision 15
    &[
        23_634., 23_210.8, 22_792.47, 22_379.15, 21_969.79, 21_565.33, 21_165.35, 20_770.28,
        20_379.99, 19_994.71, 19_613.32, 19_236.8, 18_865.44, 18_498.82, 18_136.51, 17_778.87,
        17_426.23, 17_079.32, 16_734.78, 16_397.24, 16_063.33, 15_734.02, 15_409.73, 15_088.73,
        14_772.99, 14_464.14, 14_157.56, 13_855.6, 13_559.33, 13_264.91, 12_978.33, 12_692.08,
        12_413.88, 12_137.32, 11_870.23, 11_602.56, 11_340.31, 11_079.61, 10_829.59, 10_583.55,
        10_334.03, 10_095.51, 9_859.694, 9_625.282, 9_395.786, 9_174.059, 8_957.316, 8_738.064,
        8_524.155, 8_313.74, 8_116.917, 7_913.542, 7_718.478, 7_521.65, 7_335.56, 7_154.291,
        6_968.74, 6_786.4, 6_613.236, 6_437.406, 6_270.66, 6_107.796, 5_945.717, 5_787.678,
        5_635.578, 5_482.308, 5_337.978, 5_190.086, 5_045.916, 4_919.139, 4_771.817, 4_645.774,
        4_518.477, 4_385.545, 4_262.662, 4_142.747, 4_015.532, 3_897.928, 3_790.776, 3_685.138,
        3_573.627, 3_467.971, 3_368.611, 3_271.52, 3_170.385, 3_076.466, 2_982.384, 2_888.466,
        2_806.487, 2_711.956, 2_634.143, 2_551.32, 2_469.766, 2_396.611, 2_318.99, 2_243.866,
        2_171.925, 2_105.014, 2_028.854, 1_960.995, 1_901.41, 1_841.861, 1_777.547, 1_714.58,
        1_654.651, 1_596.311, 1_546.202, 1_492.33, 1_433.897, 1_383.846, 1_339.415, 1_293.552,
        1_245.869, 1_193.507, 1_162.28, 1_107.194, 1_069.181, 1_035.092, 999.679, 957.68, 925.3002,
        888.0994, 848.6386, 818.1564, 796.7484, 752.1392, 725.2712, 692.216, 671.6336, 647.9398,
        621.6706, 575.3988, 561.2266, 532.238, 521.7876, 483.0958, 467.0496, 465.2864, 415.5486,
        401.0474, 380.608, 377.3626, 347.2588, 338.3716, 310.097, 301.4092, 276.2808, 265.5868,
        258.9944, 223.916, 215.9254, 213.5038, 191.0454, 166.7182, 166.259, 162.9412, 148.8294,
        141.646, 123.5354, 122.3298, 89.4734, 80.1962, 77.5458, 59.1056, 83.351, 52.2906, 36.398,
        40.6558, 42.0004, 19.663, 19.7154, -8.3854, -0.6928, 0.8548, 3.2322, -3.8904, -5.2588,
        -24.9052, -22.6838, -26.4286, -34.997, -37.0216, -43.4304, -58.239, -68.8034, -56.9246,
        -57.8584, -77.3098, -73.2794, -81.0738, -87.453, -65.0254, -57.2964, -96.2746, -103.25,
        -96.0816, -91.5542, -102.465, -107.689, -101.458, -109.716,
    ],
    // precision 16
    &[
        47_270., 46_423.36, 45_585.71, 44_757.15, 43_938.84, 43_130.95, 42_330.03, 41_540.41,
        40_759.64, 39_988.21, 39_226.51, 38_473.21, 37_729.79, 36_997.27, 36_272.64, 35_558.67,
        34_853.03, 34_157.45, 33_470.52, 32_793.57, 32_127.02, 31_469.42, 30_817.61, 30_178.7,
        29_546.89, 28_922.85, 28_312.27, 27_707.09, 27_114.03, 26_526.69, 25_948.63, 25_383.78,
        24_823.6, 24_272.3, 23_732.26, 23_201.5, 22_674.28, 22_163.63, 21_656.51, 21_161.74,
        20_669.94, 20_189.44, 19_717.34, 19_256.37, 18_795.96, 18_352.2, 17_908.57, 17_474.39,
        17_052.92, 16_637.22, 16_228.46, 15_823.35, 15_428.7, 15_043.03, 14_667.63, 14_297.46,
        13_935.29, 13_578.54, 13_234.6, 12_882.16, 12_548.07, 12_219.23, 11_898.01, 11_587.26,
        11_279.91, 10_973.5, 10_678.52, 10_392.49, 10_105.26, 9_825.766, 9_562.544, 9_294.222,
        9_038.235, 8_784.848, 8_533.264, 8_301.778, 8_058.309, 7_822.946, 7_599.113, 7_366.908,
        7_161.217, 6_957.531, 6_736.212, 6_548.212, 6_343.068, 6_156.287, 5_975.154, 5_791.757,
        5_621.32, 5_451.66, 5_287.61, 5_118.095, 4_957.288, 4_798.425, 4_662.176, 4_512.059,
        4_364.685, 4_220.777, 4_082.673, 3_957.195, 3_842.158, 3_699.333, 3_583.012, 3_473.896,
        3_338.666, 3_233.556, 3_117.799, 3_008.111, 2_909.691, 2_814.865, 2_719.461, 2_624.742,
        2_532.47, 2_444.789, 2_370.187, 2_272.453, 2_196.193, 2_117.904, 2_023.297, 1_969.768,
        1_885.59, 1_833.282, 1_733.912, 1_682.549, 1_604.58, 1_556.112, 1_491.306, 1_421.72,
        1_371.229, 1_322.132, 1_264.789, 1_196.239, 1_143.847, 1_088.672, 1_073.604, 1_023.117,
        959.0364, 927.4332, 906.7928, 853.4336, 841.8738, 791.1054, 756.9, 704.3432, 672.4956,
        622.7904, 611.2548, 567.2832, 519.4066, 519.1884, 495.3128, 451.3508, 443.9734, 431.8822,
        392.027, 380.9242, 345.129, 298.9014, 287.772, 272.625, 247.253, 222.4906, 223.59,
        196.4076, 176.426, 134.7252, 132.4804, 110.4456, 86.794, 56.7038, 64.9154, 38.3726,
        37.1606, 46.171, 49.1716, 15.3362, 6.7164, -34.8186, -39.4476, 12.683, -12.3332, -50.6566,
        -59.9538, -65.1054, -70.7576, -106.325, -126.852, -110.228, -132.886, -113.897, -142.714,
        -151.145, -150.799, -177.756, -156.036, -182.735, -177.259, -198.664, -174.578, -193.846,
    ],
    // precision 17
    &[
        94_541., 92_848.81, 91_174.02, 89_517.56, 87_879.97, 86_262.76, 84_663.51, 83_083.74,
        81_521.79, 79_977.27, 78_455.95, 76_950.22, 75_465.43, 73_994.15, 72_546.71, 71_115.24,
        69_705.68, 68_314.94, 66_944.27, 65_591.26, 64_252.95, 62_938.02, 61_636.82, 60_355.59,
        59_092.79, 57_850.57, 56_624.52, 55_417.34, 54_231.14, 53_067.39, 51_903.53, 50_774.65,
        49_657.64, 48_561.05, 47_475.76, 46_410.16, 45_364.85, 44_327.05, 43_318.4, 42_325.62,
        41_348.46, 40_383.63, 39_436.77, 38_509.5, 37_594.04, 36_695.94, 35_818.69, 34_955.69,
        34_115.81, 33_293.95, 32_465.08, 31_657.67, 30_877.26, 30_093.78, 29_351.37, 28_594.14,
        27_872.12, 27_168.75, 26_477.08, 25_774.54, 25_106.54, 24_452.51, 23_815.51, 23_174.07,
        22_555.27, 21_960.21, 21_376.36, 20_785.19, 20_211.52, 19_657.07, 19_141.69, 18_579.74,
        18_081.4, 17_578.99, 17_073.44, 16_608.33, 16_119.91, 15_651.27, 15_194.58, 14_749.05,
        14_343.48, 13_925.64, 13_504.51, 13_099.39, 12_691.28, 12_328.02, 11_969.03, 11_596.51,
        11_245.64, 10_917.66, 10_580.98, 10_277.86, 9_926.581, 9_605.538, 9_300.43, 8_989.978,
        8_728.733, 8_448.324, 8_175.31, 7_898.987, 7_629.791, 7_413.762, 7_149.923, 6_921.127,
        6_677.154, 6_443.28, 6_278.234, 6_014.2, 5_791.203, 5_605.784, 5_438.488, 5_234.225,
        5_059.682, 4_887.434, 4_682.935, 4_496.311, 4_322.523, 4_191.425, 4_021.242, 3_900.648,
        3_762.843, 3_609.981, 3_502.296, 3_363.843, 3_206.548, 3_079.7, 2_971.423, 2_867.803,
        2_727.081, 2_630.749, 2_496.617, 2_440.902, 2_356.191, 2_235.582, 2_120.541, 2_012.255,
        1_933.356, 1_820.931, 1_761.548, 1_663.093, 1_578.846, 1_509.482, 1_427.334, 1_379.562,
        1_306.681, 1_212.634, 1_084.173, 1_124.165, 1_060.699, 1_007.489, 941.1945, 879.8805,
        836.0075, 782.802, 748.3855, 647.9915, 626.7305, 570.776, 484.0005, 513.9855, 418.9855,
        386.997, 370.0265, 355.497, 356.7315, 255.922, 259.094, 205.4345, 165.3745, 197.3475,
        95.7185, 67.6165, 54.697, 31.7395, -15.8785, 8.425, -26.3755, -118.425, -66.663, -42.9745,
        -107.365, -189.839, -162.612, -164.965, -189.08, -223.931, -235.33, -269.639, -249.088,
        -206.476, -283.045, -290.667, -304.562, -336.784, -380.387, -283.281, -364.533, -389.06,
        -364.454, -415.748, -417.155,
    ],
    // precision 18
    &[
        189_083., 185_696.9, 182_348.8, 179_036., 175_762.8, 172_526.4, 169_329.8, 166_166.1,
        163_043.3, 159_958.9, 156_907.9, 153_906.9, 150_924.2, 147_996.6, 145_093.5, 142_239.2,
        139_421.5, 136_632.3, 133_889.6, 131_174.2, 128_511.6, 125_868.6, 123_265.4, 120_721.1,
        118_181.8, 115_709.5, 113_252.4, 110_840.2, 108_465.1, 106_126.2, 103_823.5, 101_556.6,
        99_308., 97_124.51, 94_937.8, 92_833.73, 90_745.06, 88_677.63, 86_617.47, 84_650.44,
        82_697.83, 80_769.13, 78_879.63, 77_014.43, 75_215.63, 73_384.59, 71_652.48, 69_895.93,
        68_209.3, 66_553.67, 64_921.98, 63_310.32, 61_742.11, 60_205.02, 58_698.66, 57_190.66,
        55_760.86, 54_331.17, 52_908.17, 51_550.27, 50_225.25, 48_922.42, 47_614.53, 46_362.05,
        45_098.57, 43_926.08, 42_736.03, 41_593.47, 40_425.26, 39_316.24, 38_243.65, 37_170.62,
        36_114.61, 35_084.19, 34_117.23, 33_206.51, 32_231.51, 31_318.73, 30_403.4, 29_540.06,
        28_679.24, 27_825.86, 26_965.22, 26_179.15, 25_462.08, 24_645.95, 23_922.52, 23_198.14,
        22_529.13, 21_762.42, 21_134.78, 20_459.12, 19_840.82, 19_187.04, 18_636.37, 17_982.83,
        17_439.74, 16_874.55, 16_358.22, 15_835.68, 15_352.91, 14_823.68, 14_329.31, 13_816.9,
        13_342.87, 12_880.88, 12_491.65, 12_021.25, 11_625.39, 11_293.76, 10_813.7, 10_456.21,
        10_099.07, 9_755.39, 9_393.185, 9_047.579, 8_657.985, 8_395.859, 8_033., 7_736.959,
        7_430.597, 7_258.477, 6_924.582, 6_691.294, 6_357.925, 6_202.057, 5_921.197, 5_628.284,
        5_404.968, 5_226.711, 4_990.756, 4_799.774, 4_622.931, 4_472.478, 4_171.787, 3_957.463,
        3_868.952, 3_691.143, 3_474.631, 3_341.672, 3_109.14, 3_071.974, 2_796.404, 2_756.178,
        2_611.47, 2_471.93, 2_382.264, 2_209.224, 2_142.284, 2_013.961, 1_911.19, 1_818.271,
        1_668.479, 1_519.658, 1_469.676, 1_367.138, 1_248.529, 1_181.236, 1_022.719, 1_088.207,
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